Finite Group Databasebeta

← C2×#23778178 #35202108

Subgroups — C2×#23778178 #35202108

Order 20224.

11138 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099400C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D79C211yesmaximal, characteristic, complemented
3#23778178C2132yesmaximal, direct product factor
4C2×#19099372C213yesmaximal, complemented
5C2×#19099371C211yesmaximal, characteristic, complemented
6C2×#19099369C213yesmaximal, complemented
7C2×#19099368C211yesmaximal, characteristic, complemented
8C2×#19099367C213yesmaximal, complemented
9C2×#19099366C211yesmaximal, characteristic, complemented
10C2×#19099365C213yesmaximal, complemented
11C2×#19099362C213yesmaximal, complemented
12C2×#19099360C213yesmaximal, complemented
13C22×#14579188C213yesmaximal, complemented
14C2×AGL(1,ℤ/8)×D79C213yesmaximal, complemented
15C2×#19099328C211yesmaximal, characteristic, complemented
16C2×#577×C79C211yesmaximal, characteristic, complemented
17#19099400—28no—
18#19099400C22116yescomplemented
19C2×#14579209—21no—
20C2×#14579209C2213yescomplemented
21C2×#14579207—23no—
22C2×#14579207—21no—
23C2×#14579207C2213yescomplemented
24C2×#14579207C2213yescomplemented
25C2×#14579207C2211yescharacteristic, complemented
26C2×#14579207C2211yescharacteristic, complemented
27C2×#14579206—23no—
28C2×#14579206C2213yescomplemented
29H(5,𝔽2)×D79—28no—
30H(5,𝔽2)×D79C22116yescomplemented
31C22×#11929625—21no—
32C22×#11929625C2213yescomplemented
33C2×#41×D79—23no—
34C2×#41×D79—21no—
35C2×#41×D79C2211yescharacteristic
36C2×#41×D79C2213yescomplemented
37C2×#41×D79C2213yescomplemented
38C22×D4×D79—23no—
39C22×D4×D79C2213yescomplemented
40#19099372C22148yescomplemented
41#19099371C22116yescomplemented
42#19099369C22148yescomplemented
43#19099368C22116yescomplemented
44#19099367C22148yescomplemented
45#19099366C22116yescomplemented
46#19099365C22148yescomplemented
47#19099362C22148yescomplemented
48#19099360C22148yescomplemented
49C2×#14579193C2213yescomplemented
50C2×#14579193C2213yescomplemented
51C2×#14579192C2213yescomplemented
52C2×#14579190C2211yescharacteristic, complemented
53C2×#14579190C2213yescomplemented
54C2×#14579189C2213yescomplemented
55C2×#14579189C2213yescomplemented
56C2×#14579188C2216yescomplemented
57C2×#14579188C2213yescomplemented
58C2×#14579188C2213yescomplemented
59C2×#14579188C2216yescomplemented
60C2×#14579188C2216yescomplemented
61C2×#14579188C22148yescomplemented
62C2×#14579187C2213yescomplemented
63C2×#14579186C2213yescomplemented
64C2×#14579186C2213yescomplemented
65C2×#14579185C2213yescomplemented
66C2×#14579185C2213yescomplemented
67AGL(1,ℤ/8)×D79C22148yescomplemented
68C2×#14579184C2216yescomplemented
69C2×#14579183C2213yescomplemented
70C2×#14579182C2216yescomplemented
71C2×#14579181C2213yescomplemented
72C2×#14579181C2213yescomplemented
73C22×#11929611C2213yescomplemented
74C2×SD16×D79C2216yescomplemented
75C22×D632C2213yescomplemented
76C22×#11929609C2213yescomplemented
77C2×D8×D79C2216yescomplemented
78#19099328C22116yescomplemented
79C2×#14579169C2213yescomplemented
80C2×#14579168C2211yescharacteristic, complemented
81C2×#14579167C2213yescomplemented
82C22×#11929607C2213yescomplemented
83C2×M16×D79C2213yescomplemented
84C2×2−1+4×C79C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C79C2211yescharacteristic, complemented
86#577×C79C22116yescomplemented
87C2×#137×C79C2213yescomplemented
88C2×AGL(1,ℤ/8)×C79C2213yescomplemented
89C2×#135×C79C2213yescomplemented
90C22×SD16×C79C2213yescomplemented
91C2×#131×C79C2211yescharacteristic, complemented
92C24×D79—23no—
93#14579209—212no—
94#14579209—216no—
95#14579209C23124yescomplemented
96#14579207—24no—
97#14579207—24no—
98#14579207—216no—
99#14579207—212no—
100#14579207—212no—
101#14579207—248no—
102#14579207C2318yescomplemented
103#14579207C2318yescomplemented
104#14579207C23124yescomplemented
105#14579207C23124yescomplemented
106#14579206—212no—
107#14579206—248no—
108#14579206C23124yescomplemented
109C2×#11929625—21no—
110C2×#11929625—21no—
111C2×#11929625—216no—
112C2×#11929625—23no—
113C2×#11929625—23no—
114C2×#11929625—212no—
115C2×#11929625—23no—
116C2×#11929625D411yescharacteristic
117C2×#11929625C2313yes—
118C2×#11929625C2313yes—
119C2×#11929625C2316yescomplemented
120C2×#11929625C23124yescomplemented
121C2×#11929624—23no—
122C2×#11929624—23no—
123C2×#11929624—26no—
124C2×#11929624—23no—
125C2×#11929624—23no—
126C2×#11929624C2313yes—
127C2×#11929624C2313yes—
128C2×#11929624C2313yescomplemented
129C2×#11929623—23no—
130C2×#11929623—23no—
131C2×#11929623—23no—
132C2×#11929623D413yes—
133C2×#11929623C2313yes—
134C2×#11929623C2311yescharacteristic
135#41×D79—248no—
136#41×D79—216no—
137#41×D79—212no—
138#41×D79—212no—
139#41×D79D418yes—
140#41×D79C2318yes—
141#41×D79C23124yescomplemented
142#41×D79C23124yescomplemented
143C2×Q8×D79—23no—
144C2×Q8×D79D411yescharacteristic
145C2×Q8×D79C2311yescharacteristic
146C2×Q8×D79C2313yescomplemented
147C22×D316—23no—
148C22×D316—23no—
149C22×D316—23no—
150C22×D316C2313yes—
151C22×D316C2313yescomplemented
152C22×C22⋊D79—26no—
153C22×C22⋊D79—23no—
154C2×D4×D79—23no—
155C2×D4×D79—23no—
156C2×D4×D79—23no—
157C2×D4×D79—23no—
158C2×D4×D79—23no—
159C2×D4×D79—26no—
160C2×D4×D79—26no—
161C2×D4×D79—248no—
162C2×D4×D79—212no—
163C2×D4×D79—23no—
164C2×D4×D79—23no—
165C2×D4×D79D413yes—
166C2×D4×D79C2316yes—
167C2×D4×D79C2313yes—
168C2×D4×D79C23124yescomplemented
169C2×D4×D79C2313yescomplemented
170C22×C4×D79—23no—
171C22×C4×D79—23no—
172C22×C4×D79—23no—
173C22×C4×D79C2313yes—
174#14579193C23124yescomplemented
175#14579193C23124yescomplemented
176#14579192C23124yescomplemented
177#14579190C2318yescomplemented
178#14579190C23124yescomplemented
179#14579189C23124yescomplemented
180#14579189C23124yescomplemented
181#14579188C23148yescomplemented
182#14579188C23124yescomplemented
183#14579188C23148yescomplemented
184#14579188C23148yescomplemented
185#14579188C23124yescomplemented
186#14579187C23124yescomplemented
187#14579186C23124yescomplemented
188#14579186C23124yescomplemented
189#14579185C23124yescomplemented
190#14579185C23124yescomplemented
191#14579184C23148yescomplemented
192#14579183C23124yescomplemented
193#14579182C23148yescomplemented
194#14579181C23124yescomplemented
195#14579181C23124yescomplemented
196C2×Dic316C2311yescharacteristic, complemented
197C2×#11929614C2311yescharacteristic, complemented
198C2×#11929614C2313yescomplemented
199C2×#11929613C2313yescomplemented
200C2×#11929613C2313yescomplemented
201C2×#11929612C2313yescomplemented
202C2×#11929612C2311yescharacteristic, complemented
203C2×#11929611C2316yescomplemented
204C2×#11929611C2313yescomplemented
205C2×#11929611C2313yescomplemented
206C2×#11929611C23124yescomplemented
207SD16×D79C23148yescomplemented
208C2×D632C2316yescomplemented
209C2×D632C2313yescomplemented
210C2×D632C23124yescomplemented
211C2×#11929609C2313yescomplemented
212C2×#11929609C2316yescomplemented
213C2×#11929609C2313yescomplemented
214C2×#11929609C23124yescomplemented
215D8×D79C23148yescomplemented
216#14579169C23124yescomplemented
217#14579168C2318yescomplemented
218#14579167C23124yescomplemented
219C2×#11929608C2313yescomplemented
220C2×#11929607C2313yes—
221C2×#11929607C2311yescharacteristic
222C2×#11929607C2313yescomplemented
223C2×#11929607C2313yescomplemented
224C2×#11929607C23124yescomplemented
225M16×D79C23124yescomplemented
226C22×C79⋊C8C2313yescomplemented
227C2×C8×D79C2316yescomplemented
2282−1+4×C79—24no—
2292−1+4×C79C2318yescomplemented
230H(5,𝔽2)×C79—24no—
231H(5,𝔽2)×C79C2318yescomplemented
232C2×#41×C79—21no—
233C2×#41×C79—23no—
234C2×#41×C79C2313yes—
235C2×#41×C79C2311yescharacteristic
236C2×#41×C79C2313yescomplemented
237C22×Q8×C79—21no—
238C22×Q8×C79C2313yescomplemented
239C22×D4×C79—23no—
240C22×D4×C79C2313yes—
241#137×C79C23124yescomplemented
242AGL(1,ℤ/8)×C79C23124yescomplemented
243#135×C79C23124yescomplemented
244C2×Q16×C79C2313yescomplemented
245C2×SD16×C79C2313yescomplemented
246C2×SD16×C79C2316yescomplemented
247C2×SD16×C79C2311yescharacteristic, complemented
248C2×SD16×C79C23124yescomplemented
249C2×D8×C79C2313yescomplemented
250#131×C79C2318yescomplemented
251C2×M16×C79C2313yescomplemented
252C22×C8×C79C2313yescomplemented
253C23×D79—23no—
254C23×D79—23no—
255C23×D79—23no—
256C23×D79—224no—
257C23×D79—26no—
258C23×D79—23no—
259C23×D79—812no—
260C23×D79C2×D413yes—
261#11929625—224no—
262#11929625—26no—
263#11929625—224no—
264#11929625—26no—
265#11929625—212no—
266#11929625—224no—
267#11929625—28no—
268#11929625—28no—
269#11929625C2×D418yes—
270#11929625C24112yes—
271#11929625C24112yes—
272#11929625C24124yescomplemented
273#11929624—224no—
274#11929624—224no—
275#11929624—224no—
276#11929624—224no—
277#11929624—26no—
278#11929624—26no—
279#11929624—248no—
280#11929624C2×D4112yes—
281#11929624C24112yes—
282#11929624C24112yes—
283#11929624C24112yescomplemented
284#11929623—224no—
285#11929623—224no—
286#11929623—22no—
287#11929623—26no—
288#11929623—224no—
289#11929623C2×D4124yes—
290#11929623C2414yes—
291#11929623C24112yes—
292C2×Dic158—23no—
293C2×Dic158—21no—
294C2×Dic158C2×D413yes—
295C2×Dic158C2411yescharacteristic
296C2×Dic158C2411yescharacteristic
297Q8×D79—22no—
298Q8×D79—26no—
299Q8×D79—224no—
300Q8×D79C2×D418yes—
301Q8×D79C2414yes—
302Q8×D79C24112yescomplemented
303C2×D316—224no—
304C2×D316—224no—
305C2×D316—23no—
306C2×D316—26no—
307C2×D316—23no—
308C2×D316—224no—
309C2×D316—23no—
310C2×D316—23no—
311C2×D316—26no—
312C2×D316—26no—
313C2×D316C2×D413yes—
314C2×D316C2413yes—
315C2×D316C2413yes—
316C2×D316C24112yes—
317C2×D316C24112yescomplemented
318C2×C22⋊D79—23no—
319C2×C22⋊D79—23no—
320C2×C22⋊D79—26no—
321C2×C22⋊D79—224no—
322C2×C22⋊D79—23no—
323C2×C22⋊D79—23no—
324C2×C22⋊D79—21no—
325C2×C22⋊D79—23no—
326C2×C22⋊D79—248no—
327C2×C22⋊D79C2×D416yes—
328D4×D79—224no—
329D4×D79—26no—
330D4×D79—26no—
331D4×D79—224no—
332D4×D79—212no—
333D4×D79—224no—
334D4×D79—224no—
335D4×D79—224no—
336D4×D79—224no—
337D4×D79—224no—
338D4×D79—248no—
339D4×D79—248no—
340D4×D79C2×D4124yes—
341D4×D79C24112yes—
342D4×D79C24124yes—
343D4×D79C24112yescomplemented
344C22×Dic79—21no—
345C22×Dic79—23no—
346C22×Dic79C2×D413yes—
347C2×C4×D79—26no—
348C2×C4×D79—224no—
349C2×C4×D79—23no—
350C2×C4×D79—23no—
351C2×C4×D79—224no—
352C2×C4×D79—224no—
353C2×C4×D79—21no—
354C2×C4×D79—23no—
355C2×C4×D79—23no—
356C2×C4×D79—23no—
357C2×C4×D79C2×D413yes—
358C2×C4×D79C2×D4112yes—
359C2×C4×D79C2×D413yes—
360C2×C4×D79C2411yescharacteristic
361C2×C4×D79C2413yes—
362C2×C4×D79C24112yes—
363Dic316C2414yescomplemented
364#11929614C2414yescomplemented
365#11929614C24112yescomplemented
366#11929613C24112yescomplemented
367#11929613C24112yescomplemented
368#11929612C24112yescomplemented
369#11929612C2414yescomplemented
370#11929611C24124yescomplemented
371#11929611C24112yescomplemented
372#11929611C24112yescomplemented
373D632C24124yescomplemented
374D632C24112yescomplemented
375#11929609C24112yescomplemented
376#11929609C24124yescomplemented
377#11929609C24112yescomplemented
378#11929608C24112yescomplemented
379#11929607C24112yes—
380#11929607C2414yes—
381#11929607C24112yescomplemented
382#11929607C24112yescomplemented
383C2×C79⋊C8C2413yes—
384C2×C79⋊C8C2411yescharacteristic
385C2×C79⋊C8C24112yescomplemented
386C8×D79C24124yescomplemented
387C24×C79—23no—
388#41×C79—28no—
389#41×C79—224no—
390#41×C79—26no—
391#41×C79—26no—
392#41×C79C2×D414yes—
393#41×C79C24112yes—
394#41×C79C2414yes—
395#41×C79C24112yescomplemented
396C2×Q8×C79—28no—
397C2×Q8×C79—23no—
398C2×Q8×C79—26no—
399C2×Q8×C79C2×D411yescharacteristic
400C2×Q8×C79C2411yescharacteristic
401C2×Q8×C79C2413yes—
402C2×Q8×C79C24112yescomplemented
403C2×D4×C79—23no—
404C2×D4×C79—23no—
405C2×D4×C79—224no—
406C2×D4×C79—23no—
407C2×D4×C79—26no—
408C2×D4×C79C2×D413yes—
409C2×D4×C79C2411yescharacteristic
410C2×D4×C79C2413yes—
411C2×D4×C79C24112yes—
412C22×C4×C79—23no—
413C22×C4×C79—23no—
414C22×C4×C79—23no—
415C22×C4×C79C2413yes—
416Q16×C79C24112yescomplemented
417SD16×C79C24112yescomplemented
418SD16×C79C24124yescomplemented
419SD16×C79C2414yescomplemented
420D8×C79C24112yescomplemented
421M16×C79C24112yescomplemented
422C2×C8×C79C2411yescharacteristic
423C2×C8×C79C2413yes—
424C2×C8×C79C24112yescomplemented
425C23×C79—21no—
426C23×C79—23no—
427C23×C79—212no—
428C23×C79—86no—
429C23×C79C22×D413yes—
430C22×D79—23no—
431C22×D79—23no—
432C22×D79—212no—
433C22×D79—212no—
434C22×D79—212no—
435C22×D79—212no—
436C22×D79—224no—
437C22×D79—46no—
438C22×D79—412no—
439C22×D79—86no—
440C22×D79—812no—
441C22×D79—848no—
442C22×D79—86no—
443C22×D79—86no—
444C22×D79C22×D411yescharacteristic
445C22×D79C22×D413yes—
446C22×D79C22×D4112yes—
447Q8×C79—23no—
448Q8×C79—212no—
449Q8×C79—21no—
450Q8×C79C22×D414yes—
451Q8×C79C2512yes—
452Q8×C79C2516yes—
453D4×C79—212no—
454D4×C79—212no—
455D4×C79—212no—
456D4×C79—23no—
457D4×C79—21no—
458D4×C79C22×D4112yes—
459D4×C79C2516yes—
460D4×C79C2512yes—
461C2×C4×C79—21no—
462C2×C4×C79—23no—
463C2×C4×C79—212no—
464C2×C4×C79—212no—
465C2×C4×C79—212no—
466C2×C4×C79C22×D413yes—
467C2×C4×C79C22×D416yes—
468C2×C4×C79C2511yescharacteristic
469C2×C4×C79C2516yes—
470C22⋊D79—212no—
471C22⋊D79—212no—
472C22⋊D79—212no—
473C22⋊D79—24no—
474C22⋊D79—224no—
475C22⋊D79—212no—
476C22⋊D79—212no—
477C22⋊D79C22×D4124yes—
478C2×Dic79—21no—
479C2×Dic79—21no—
480C2×Dic79—24no—
481C2×Dic79—212no—
482C2×Dic79C22×D411yescharacteristic
483C2×Dic79C22×D413yes—
484C2×Dic79C22×D4112yes—
485D316—212no—
486D316—212no—
487D316—224no—
488D316—212no—
489D316—23no—
490D316—23no—
491D316—212no—
492D316C22×D4112yes—
493D316C2516yes—
494D316C2516yes—
495C4×D79—24no—
496C4×D79—212no—
497C4×D79—212no—
498C4×D79—212no—
499C4×D79—212no—
500C4×D79—212no—
501C4×D79—224no—
502C4×D79C22×D4112yes—
503C4×D79C22×D4112yes—
504C4×D79C22×D412yes—
505C4×D79C22×D416yes—
506C4×D79C2516yes—
507C4×D79C2512yes—
508Dic158—21no—
509Dic158—21no—
510Dic158—212no—
511Dic158—24no—
512Dic158C22×D4112yes—
513Dic158C2512yes—
514Dic158C2512yes—
515C8×C79C2516yes—
516C8×C79C2512yes—
517C79⋊C8C2516yes—
518C79⋊C8C2512yes—
519C22×C79—26no—
520C22×C79—22no—
521C22×C79—26no—
522C22×C79—46no—
523C22×C79—42no—
524C22×C79—812no—
525C22×C79C23×D416yes—
526C22×C79C23×D411yescharacteristic
527C2×D79—22no—
528C2×D79—26no—
529C2×D79—26no—
530C2×D79—26no—
531C2×D79—412no—
532C2×D79—424no—
533C2×D79—46no—
534C2×D79—46no—
535C2×D79—812no—
536C2×D79—824no—
537C2×D79—812no—
538C2×D79—812no—
539C2×D79C23×D416yes—
540C2×D79C23×D412yes—
541C4×C79—22no—
542C4×C79—26no—
543C4×C79C23×D416yes—
544C4×C79C23×D411yescharacteristic
545C4×C79C2611yescharacteristic
546Dic79—22no—
547Dic79—22no—
548Dic79C23×D416yes—
549Dic79C23×D412yes—
550C2×#3585—791nomaximal, Sylow
551C2×C79—26no—
552C2×C79—46no—
553C2×C79—42no—
554C2×C79#358512yescomplemented
555C2×C79C24×D411yescharacteristic
556D79—22no—
557D79—26no—
558D79—46no—
559D79—46no—
560C2×#585—791no—
561C22×H(5,𝔽2)—791no—
562#3585—7932no—
563C2×#577—791no—
564C2×#577—793no—
565C2×#577—793no—
566C2×#577D7911yescharacteristic, complemented
567C2×#576—791no—
568C2×#576—793no—
569C2×#576—793no—
570C2×#576—791no—
571C2×#575—793no—
572C2×#575—793no—
573C22×AGL(1,ℤ/8)—793no—
574C22×AGL(1,ℤ/8)—793no—
575C2×#568—791no—
576C79C2×#358511yescharacteristic, complemented, Sylow
577#585—7916no—
578#585—1588no—
579C2×2−1+4—793no—
580C2×2−1+4—1581no—
581C2×2−1+4C2×D7911yescharacteristic, complemented
582C2×H(5,𝔽2)—7916no—
583C2×H(5,𝔽2)—793no—
584C2×H(5,𝔽2)—791no—
585C2×H(5,𝔽2)—791no—
586C2×H(5,𝔽2)—793no—
587C2×H(5,𝔽2)—793no—
588C2×H(5,𝔽2)—1583no—
589C2×H(5,𝔽2)—1583no—
590C2×H(5,𝔽2)—1581no—
591C2×H(5,𝔽2)—1588no—
592C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
593C22×#41—791no—
594C22×#41—793no—
595C22×#41—793no—
596C22×#41—793no—
597C22×#41—1581no—
598C22×#41—1581no—
599C22×#41—1583no—
600C23×D4—793no—
601C23×D4—1583no—
602#577—7916no—
603#577—7948no—
604#577—7948no—
605#577C2×D79116yescomplemented
606#576—7916no—
607#576—7948no—
608#576—7948no—
609#576—7916no—
610#575—7948no—
611#575—7948no—
612C2×#137—793no—
613C2×#137—793no—
614C2×#137—793no—
615C2×#137—791no—
616C2×#137—793no—
617C2×#137C2×D7913yescomplemented
618C2×AGL(1,ℤ/8)—793no—
619C2×AGL(1,ℤ/8)—793no—
620C2×AGL(1,ℤ/8)—793no—
621C2×AGL(1,ℤ/8)—7948no—
622C2×AGL(1,ℤ/8)—7948no—
623C2×AGL(1,ℤ/8)—796no—
624C2×AGL(1,ℤ/8)—793no—
625C2×AGL(1,ℤ/8)—796no—
626C2×AGL(1,ℤ/8)—796no—
627C2×AGL(1,ℤ/8)—793no—
628C2×AGL(1,ℤ/8)—793no—
629C2×AGL(1,ℤ/8)—793no—
630C2×AGL(1,ℤ/8)—793no—
631C2×AGL(1,ℤ/8)—793no—
632C2×AGL(1,ℤ/8)C2×D7913yescomplemented
633C2×#135—793no—
634C2×#135—793no—
635C2×#135—796no—
636C2×#135—796no—
637C2×#135—793no—
638C2×#135C2×D7913yescomplemented
639C22×SD16—793no—
640C22×SD16—796no—
641C22×SD16C2×D7913yescomplemented
642C22×D8—793no—
643C22×D8—796no—
644C22×D8—793no—
645#568—7916no—
646C2×#131—791no—
647C2×#131—793no—
648C2×#131—793no—
649C2×#131C2×D7911yescharacteristic, complemented
650C22×M16—793no—
651C22×M16—793no—
652C25—1583no—
6532−1+4—24no—
6542−1+4—7924no—
6552−1+4—15816no—
6562−1+4—15812no—
6572−1+4C22×D7918yescomplemented
658H(5,𝔽2)—24no—
659H(5,𝔽2)—798no—
660H(5,𝔽2)—7924no—
661H(5,𝔽2)—798no—
662H(5,𝔽2)—7924no—
663H(5,𝔽2)—7924no—
664H(5,𝔽2)—15848no—
665H(5,𝔽2)—15812no—
666H(5,𝔽2)—15848no—
667H(5,𝔽2)—15816no—
668H(5,𝔽2)—15812no—
669H(5,𝔽2)—15812no—
670H(5,𝔽2)—1584no—
671H(5,𝔽2)—1584no—
672H(5,𝔽2)C22×D7918yescomplemented
673C2×#41—21no—
674C2×#41—23no—
675C2×#41—798no—
676C2×#41—798no—
677C2×#41—791no—
678C2×#41—793no—
679C2×#41—793no—
680C2×#41—7924no—
681C2×#41—7924no—
682C2×#41—793no—
683C2×#41—793no—
684C2×#41—796no—
685C2×#41—7924no—
686C2×#41—793no—
687C2×#41—791no—
688C2×#41—793no—
689C2×#41—793no—
690C2×#41—1583no—
691C2×#41—1583no—
692C2×#41—1586no—
693C2×#41—1583no—
694C2×#41—1583no—
695C2×#41—1583no—
696C2×#41—1583no—
697C2×#41—1583no—
698C2×#41—1583no—
699C2×#41—15812no—
700C2×#41—15812no—
701C2×#41—15812no—
702C2×#41—1583no—
703C2×#41—1583no—
704C2×#41—15816no—
705C2×#41—15816no—
706C2×#41—15848no—
707C2×#41—1581no—
708C2×#41—1581no—
709C2×#41C22×D7913yes—
710C2×#41C22×D7911yescharacteristic
711C2×#41C22×D7913yescomplemented
712C22×Q8—21no—
713C22×Q8—791no—
714C22×Q8—791no—
715C22×Q8—793no—
716C22×Q8—1583no—
717C22×Q8C22×D7913yescomplemented
718C22×D4—23no—
719C22×D4—793no—
720C22×D4—793no—
721C22×D4—796no—
722C22×D4—793no—
723C22×D4—7924no—
724C22×D4—793no—
725C22×D4—793no—
726C22×D4—1583no—
727C22×D4—1583no—
728C22×D4—1583no—
729C22×D4—1583no—
730C22×D4—1583no—
731C22×D4—15812no—
732C22×D4—1583no—
733C22×D4—1586no—
734C22×D4—15848no—
735C22×D4—1583no—
736C22×D4—1586no—
737C22×D4—1583no—
738C22×D4—1583no—
739C22×D4—1586no—
740C22×D4—1583no—
741C22×D4—1583no—
742C22×D4C22×D7913yes—
743C23×C4—793no—
744C23×C4—1583no—
745C23×C4—1583no—
746C23×C4—1583no—
747#137—7924no—
748#137—7924no—
749#137—7924no—
750#137—798no—
751#137—7924no—
752#137C22×D79124yescomplemented
753AGL(1,ℤ/8)—7924no—
754AGL(1,ℤ/8)—7924no—
755AGL(1,ℤ/8)—7924no—
756AGL(1,ℤ/8)—7948no—
757AGL(1,ℤ/8)—7924no—
758AGL(1,ℤ/8)—7948no—
759AGL(1,ℤ/8)—7948no—
760AGL(1,ℤ/8)—7924no—
761AGL(1,ℤ/8)—7924no—
762AGL(1,ℤ/8)—7924no—
763AGL(1,ℤ/8)—7924no—
764AGL(1,ℤ/8)—7924no—
765AGL(1,ℤ/8)C22×D79124yescomplemented
766#135—7924no—
767#135—7924no—
768#135—7948no—
769#135—7948no—
770#135—7924no—
771#135C22×D79124yescomplemented
772C2×Q16—791no—
773C2×Q16—793no—
774C2×Q16—791no—
775C2×Q16C22×D7913yescomplemented
776C2×SD16—793no—
777C2×SD16—796no—
778C2×SD16—793no—
779C2×SD16—7924no—
780C2×SD16—793no—
781C2×SD16—791no—
782C2×SD16—7948no—
783C2×SD16—793no—
784C2×SD16—793no—
785C2×SD16C22×D7916yescomplemented
786C2×SD16C22×D7913yescomplemented
787C2×SD16C22×D7911yescharacteristic, complemented
788C2×SD16C22×D79124yescomplemented
789C2×D8—793no—
790C2×D8—796no—
791C2×D8—793no—
792C2×D8—7924no—
793C2×D8—7948no—
794C2×D8—796no—
795C2×D8—793no—
796C2×D8—7924no—
797C2×D8C22×D7913yescomplemented
798#131—798no—
799#131—7924no—
800#131—7924no—
801#131C22×D7918yescomplemented
802C2×M16—793no—
803C2×M16—7924no—
804C2×M16—793no—
805C2×M16—791no—
806C2×M16—793no—
807C2×M16—793no—
808C2×M16—7924no—
809C2×M16C22×D7913yescomplemented
810C22×C8—793no—
811C22×C8—796no—
812C22×C8C22×D7913yescomplemented
813C24—23no—
814C24—793no—
815C24—63212no—
816C24—1583no—
817C24—1583no—
818C24—1586no—
819C24—15824no—
820C24—1583no—
821C24—1583no—
822#41—28no—
823#41—224no—
824#41—26no—
825#41—26no—
826#41—798no—
827#41—7924no—
828#41—7912no—
829#41—7912no—
830#41—7912no—
831#41—7912no—
832#41—7924no—
833#41—7912no—
834#41—794no—
835#41—7912no—
836#41—7912no—
837#41—15824no—
838#41—15824no—
839#41—15848no—
840#41—15824no—
841#41—15824no—
842#41—15824no—
843#41—1582no—
844#41—15824no—
845#41—1586no—
846#41—1586no—
847#41—15824no—
848#41—1586no—
849#41—15824no—
850#41—15812no—
851#41—15824no—
852#41—15824no—
853#41—1588no—
854#41—1588no—
855#41—1586no—
856#41—1586no—
857#41D4×D7914yes—
858#41C23×D79112yes—
859#41C23×D7914yes—
860#41C23×D79112yescomplemented
861C2×Q8—28no—
862C2×Q8—23no—
863C2×Q8—26no—
864C2×Q8—798no—
865C2×Q8—793no—
866C2×Q8—794no—
867C2×Q8—7912no—
868C2×Q8—791no—
869C2×Q8—791no—
870C2×Q8—1583no—
871C2×Q8—1581no—
872C2×Q8—1582no—
873C2×Q8—1586no—
874C2×Q8—15824no—
875C2×Q8D4×D7911yescharacteristic
876C2×Q8C23×D7913yes—
877C2×Q8C23×D7911yescharacteristic
878C2×Q8C23×D79112yescomplemented
879C2×D4—23no—
880C2×D4—23no—
881C2×D4—224no—
882C2×D4—23no—
883C2×D4—26no—
884C2×D4—796no—
885C2×D4—7924no—
886C2×D4—7924no—
887C2×D4—7912no—
888C2×D4—7912no—
889C2×D4—793no—
890C2×D4—793no—
891C2×D4—7912no—
892C2×D4—7912no—
893C2×D4—793no—
894C2×D4—15824no—
895C2×D4—15824no—
896C2×D4—1583no—
897C2×D4—1583no—
898C2×D4—1586no—
899C2×D4—15824no—
900C2×D4—1586no—
901C2×D4—15824no—
902C2×D4—15824no—
903C2×D4—15812no—
904C2×D4—1586no—
905C2×D4—1583no—
906C2×D4—1586no—
907C2×D4—1583no—
908C2×D4—15824no—
909C2×D4—15848no—
910C2×D4—15824no—
911C2×D4—15848no—
912C2×D4—15824no—
913C2×D4—15824no—
914C2×D4—15848no—
915C2×D4—1583no—
916C2×D4—1581no—
917C2×D4—1583no—
918C2×D4—1583no—
919C2×D4—15824no—
920C2×D4—15824no—
921C2×D4—1583no—
922C2×D4—1583no—
923C2×D4—1586no—
924C2×D4—1586no—
925C2×D4D4×D7913yes—
926C2×D4C23×D7911yescharacteristic
927C2×D4C23×D7913yes—
928C2×D4C23×D79112yes—
929C22×C4—23no—
930C22×C4—23no—
931C22×C4—23no—
932C22×C4—793no—
933C22×C4—793no—
934C22×C4—791no—
935C22×C4—7912no—
936C22×C4—793no—
937C22×C4—793no—
938C22×C4—7912no—
939C22×C4—1583no—
940C22×C4—1583no—
941C22×C4—15824no—
942C22×C4—1586no—
943C22×C4—15824no—
944C22×C4—15824no—
945C22×C4—1581no—
946C22×C4—1583no—
947C22×C4—1581no—
948C22×C4—1583no—
949C22×C4—1583no—
950C22×C4—1583no—
951C22×C4C23×D7913yes—
952Q16—794no—
953Q16—7912no—
954Q16—794no—
955Q16C23×D79112yescomplemented
956SD16—7924no—
957SD16—7912no—
958SD16—7912no—
959SD16—7912no—
960SD16—794no—
961SD16—7912no—
962SD16—7912no—
963SD16C23×D79124yescomplemented
964SD16C23×D79112yescomplemented
965SD16C23×D7914yescomplemented
966D8—7924no—
967D8—7912no—
968D8—7912no—
969D8—7924no—
970D8—7912no—
971D8C23×D79112yescomplemented
972M16—7912no—
973M16—7912no—
974M16—794no—
975M16—7912no—
976M16—7912no—
977M16C23×D79112yescomplemented
978C2×C8—793no—
979C2×C8—791no—
980C2×C8—7912no—
981C2×C8—7924no—
982C2×C8C23×D7913yes—
983C2×C8C23×D7911yescharacteristic
984C2×C8C23×D79112yescomplemented
985C23—21no—
986C23—23no—
987C23—212no—
988C23—86no—
989C23—3166no—
990C23—31612no—
991C23—7912no—
992C23—791no—
993C23—793no—
994C23—6326no—
995C23—6326no—
996C23—63212no—
997C23—6326no—
998C23—63248no—
999C23—15812no—
1000C23—15812no—
1001C23—15824no—
1002C23—1583no—
1003C23—1583no—
1004C23—15812no—
1005C23—15812no—
1006C23C2×D4×D7913yes—
1007Q8—23no—
1008Q8—212no—
1009Q8—21no—
1010Q8—7912no—
1011Q8—792no—
1012Q8—792no—
1013Q8—15812no—
1014Q8—1584no—
1015Q8—1581no—
1016Q8—1581no—
1017Q8C2×D4×D7914yes—
1018Q8C24×D7916yes—
1019Q8C24×D7912yes—
1020D4—212no—
1021D4—212no—
1022D4—212no—
1023D4—23no—
1024D4—21no—
1025D4—7924no—
1026D4—796no—
1027D4—796no—
1028D4—7912no—
1029D4—15812no—
1030D4—15812no—
1031D4—15824no—
1032D4—15812no—
1033D4—15824no—
1034D4—15812no—
1035D4—15812no—
1036D4—1584no—
1037D4—15812no—
1038D4—15812no—
1039D4—15812no—
1040D4—1583no—
1041D4—15812no—
1042D4—1583no—
1043D4C2×D4×D79112yes—
1044D4C24×D7912yes—
1045D4C24×D7916yes—
1046C2×C4—212no—
1047C2×C4—21no—
1048C2×C4—23no—
1049C2×C4—212no—
1050C2×C4—212no—
1051C2×C4—7912no—
1052C2×C4—791no—
1053C2×C4—793no—
1054C2×C4—796no—
1055C2×C4—792no—
1056C2×C4—792no—
1057C2×C4—7912no—
1058C2×C4—7912no—
1059C2×C4—796no—
1060C2×C4—15812no—
1061C2×C4—15812no—
1062C2×C4—15824no—
1063C2×C4—1584no—
1064C2×C4—15812no—
1065C2×C4—1584no—
1066C2×C4—15812no—
1067C2×C4—1581no—
1068C2×C4—1581no—
1069C2×C4—15812no—
1070C2×C4—15812no—
1071C2×C4C2×D4×D7916yes—
1072C2×C4C2×D4×D7913yes—
1073C2×C4C24×D7916yes—
1074C2×C4C24×D7911yescharacteristic
1075C8—792no—
1076C8—796no—
1077C8C24×D7916yes—
1078C8C24×D7912yes—
1079C22—26no—
1080C22—22no—
1081C22—26no—
1082C22—46no—
1083C22—42no—
1084C22—812no—
1085C22—31612no—
1086C22—31624no—
1087C22—3166no—
1088C22—3166no—
1089C22—792no—
1090C22—796no—
1091C22—63212no—
1092C22—63212no—
1093C22—63224no—
1094C22—63212no—
1095C22—1586no—
1096C22—1586no—
1097C22—1582no—
1098C22—1586no—
1099C22C22×D4×D7916yes—
1100C22C22×D4×D7911yescharacteristic
1101C4—22no—
1102C4—26no—
1103C4—792no—
1104C4—796no—
1105C4—1582no—
1106C4—1582no—
1107C4C22×D4×D7916yes—
1108C4C22×D4×D7911yescharacteristic
1109C4C25×D7911yescharacteristic
1110C2—26no—
1111C2—46no—
1112C2—42no—
1113C2—3166no—
1114C2—3166no—
1115C2—1582no—
1116C2—1586no—
1117C2#2377817812yesdirect product factor
1118C2C23×D4×D7911yescharacteristic
subgroupG/H
centerC22C22×D4×D79
commutator, cosocleC4×C79C26
FrattiniC4C25×D79
FittingC2×#577×C79C2
socleC22×C79C23×D4
hypercenterC2×#577D79
hypocenterC79C2×#3585
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19099400C2semidirect
2. C2×H(5,𝔽2)×D79C2semidirect
3. #23778178C2direct (N × H)
4. C2×#19099372C2semidirect
5. C2×#19099371C2semidirect
6. C2×#19099369C2semidirect
7. C2×#19099368C2semidirect
8. C2×#19099367C2semidirect
9. C2×#19099366C2semidirect
10. C2×#19099365C2semidirect
11. C2×#19099362C2semidirect
12. C2×#19099360C2semidirect
13. C22×#14579188C2semidirect
14. C2×AGL(1,ℤ/8)×D79C2semidirect
15. C2×#19099328C2semidirect
16. C2×#577×C79C2semidirect
18. #19099400C22semidirect
20. C2×#14579209C22semidirect
23. C2×#14579207C22semidirect
24. C2×#14579207C22semidirect
25. C2×#14579207C22semidirect
26. C2×#14579207C22semidirect
28. C2×#14579206C22semidirect
30. H(5,𝔽2)×D79C22semidirect
32. C22×#11929625C22semidirect
36. C2×#41×D79C22semidirect
37. C2×#41×D79C22semidirect
39. C22×D4×D79C22semidirect
40. #19099372C22semidirect
41. #19099371C22semidirect
42. #19099369C22semidirect
43. #19099368C22semidirect
44. #19099367C22semidirect
45. #19099366C22semidirect
46. #19099365C22semidirect
47. #19099362C22semidirect
48. #19099360C22semidirect
49. C2×#14579193C22semidirect
50. C2×#14579193C22semidirect
51. C2×#14579192C22semidirect
52. C2×#14579190C22semidirect
53. C2×#14579190C22semidirect
54. C2×#14579189C22semidirect
55. C2×#14579189C22semidirect
56. C2×#14579188C22semidirect
57. C2×#14579188C22semidirect
58. C2×#14579188C22semidirect
59. C2×#14579188C22semidirect
60. C2×#14579188C22semidirect
61. C2×#14579188C22semidirect
62. C2×#14579187C22semidirect
63. C2×#14579186C22semidirect
64. C2×#14579186C22semidirect
65. C2×#14579185C22semidirect
66. C2×#14579185C22semidirect
67. AGL(1,ℤ/8)×D79C22semidirect
68. C2×#14579184C22semidirect
69. C2×#14579183C22semidirect
70. C2×#14579182C22semidirect
71. C2×#14579181C22semidirect
72. C2×#14579181C22semidirect
73. C22×#11929611C22semidirect
74. C2×SD16×D79C22semidirect
75. C22×D632C22semidirect
76. C22×#11929609C22semidirect
77. C2×D8×D79C22semidirect
78. #19099328C22semidirect
79. C2×#14579169C22semidirect
80. C2×#14579168C22semidirect
81. C2×#14579167C22semidirect
82. C22×#11929607C22semidirect
83. C2×M16×D79C22semidirect
84. C2×2−1+4×C79C22semidirect
85. C2×H(5,𝔽2)×C79C22semidirect
86. #577×C79C22semidirect
87. C2×#137×C79C22semidirect
88. C2×AGL(1,ℤ/8)×C79C22semidirect
89. C2×#135×C79C22semidirect
90. C22×SD16×C79C22semidirect
91. C2×#131×C79C22semidirect
95. #14579209C23semidirect
102. #14579207C23semidirect
103. #14579207C23semidirect
104. #14579207C23semidirect
105. #14579207C23semidirect
108. #14579206C23semidirect
119. C2×#11929625C23semidirect
120. C2×#11929625C23semidirect
128. C2×#11929624C23semidirect
141. #41×D79C23semidirect
142. #41×D79C23semidirect
146. C2×Q8×D79C23semidirect
151. C22×D316C23semidirect
168. C2×D4×D79C23semidirect
169. C2×D4×D79C23semidirect
174. #14579193C23semidirect
175. #14579193C23semidirect
176. #14579192C23semidirect
177. #14579190C23semidirect
178. #14579190C23semidirect
179. #14579189C23semidirect
180. #14579189C23semidirect
181. #14579188C23semidirect
182. #14579188C23semidirect
183. #14579188C23semidirect
184. #14579188C23semidirect
185. #14579188C23semidirect
186. #14579187C23semidirect
187. #14579186C23semidirect
188. #14579186C23semidirect
189. #14579185C23semidirect
190. #14579185C23semidirect
191. #14579184C23semidirect
192. #14579183C23semidirect
193. #14579182C23semidirect
194. #14579181C23semidirect
195. #14579181C23semidirect
196. C2×Dic316C23semidirect
197. C2×#11929614C23semidirect
198. C2×#11929614C23semidirect
199. C2×#11929613C23semidirect
200. C2×#11929613C23semidirect
201. C2×#11929612C23semidirect
202. C2×#11929612C23semidirect
203. C2×#11929611C23semidirect
204. C2×#11929611C23semidirect
205. C2×#11929611C23semidirect
206. C2×#11929611C23semidirect
207. SD16×D79C23semidirect
208. C2×D632C23semidirect
209. C2×D632C23semidirect
210. C2×D632C23semidirect
211. C2×#11929609C23semidirect
212. C2×#11929609C23semidirect
213. C2×#11929609C23semidirect
214. C2×#11929609C23semidirect
215. D8×D79C23semidirect
216. #14579169C23semidirect
217. #14579168C23semidirect
218. #14579167C23semidirect
219. C2×#11929608C23semidirect
222. C2×#11929607C23semidirect
223. C2×#11929607C23semidirect
224. C2×#11929607C23semidirect
225. M16×D79C23semidirect
226. C22×C79⋊C8C23semidirect
227. C2×C8×D79C23semidirect
229. 2−1+4×C79C23semidirect
231. H(5,𝔽2)×C79C23semidirect
236. C2×#41×C79C23semidirect
238. C22×Q8×C79C23semidirect
241. #137×C79C23semidirect
242. AGL(1,ℤ/8)×C79C23semidirect
243. #135×C79C23semidirect
244. C2×Q16×C79C23semidirect
245. C2×SD16×C79C23semidirect
246. C2×SD16×C79C23semidirect
247. C2×SD16×C79C23semidirect
248. C2×SD16×C79C23semidirect
249. C2×D8×C79C23semidirect
250. #131×C79C23semidirect
251. C2×M16×C79C23semidirect
252. C22×C8×C79C23semidirect
272. #11929625C24semidirect
283. #11929624C24semidirect
302. Q8×D79C24semidirect
317. C2×D316C24semidirect
343. D4×D79C24semidirect
363. Dic316C24semidirect
364. #11929614C24semidirect
365. #11929614C24semidirect
366. #11929613C24semidirect
367. #11929613C24semidirect
368. #11929612C24semidirect
369. #11929612C24semidirect
370. #11929611C24semidirect
371. #11929611C24semidirect
372. #11929611C24semidirect
373. D632C24semidirect
374. D632C24semidirect
375. #11929609C24semidirect
376. #11929609C24semidirect
377. #11929609C24semidirect
378. #11929608C24semidirect
381. #11929607C24semidirect
382. #11929607C24semidirect
385. C2×C79⋊C8C24semidirect
386. C8×D79C24semidirect
395. #41×C79C24semidirect
402. C2×Q8×C79C24semidirect
416. Q16×C79C24semidirect
417. SD16×C79C24semidirect
418. SD16×C79C24semidirect
419. SD16×C79C24semidirect
420. D8×C79C24semidirect
421. M16×C79C24semidirect
424. C2×C8×C79C24semidirect
554. C2×C79#3585semidirect
566. C2×#577D79semidirect
576. C79C2×#3585semidirect
581. C2×2−1+4C2×D79semidirect
592. C2×H(5,𝔽2)C2×D79semidirect
605. #577C2×D79semidirect
617. C2×#137C2×D79semidirect
632. C2×AGL(1,ℤ/8)C2×D79semidirect
638. C2×#135C2×D79semidirect
641. C22×SD16C2×D79semidirect
649. C2×#131C2×D79semidirect
657. 2−1+4C22×D79semidirect
672. H(5,𝔽2)C22×D79semidirect
711. C2×#41C22×D79semidirect
717. C22×Q8C22×D79semidirect
752. #137C22×D79semidirect
765. AGL(1,ℤ/8)C22×D79semidirect
771. #135C22×D79semidirect
775. C2×Q16C22×D79semidirect
785. C2×SD16C22×D79semidirect
786. C2×SD16C22×D79semidirect
787. C2×SD16C22×D79semidirect
788. C2×SD16C22×D79semidirect
797. C2×D8C22×D79semidirect
801. #131C22×D79semidirect
809. C2×M16C22×D79semidirect
812. C22×C8C22×D79semidirect
860. #41C23×D79semidirect
878. C2×Q8C23×D79semidirect
955. Q16C23×D79semidirect
963. SD16C23×D79semidirect
964. SD16C23×D79semidirect
965. SD16C23×D79semidirect
971. D8C23×D79semidirect
977. M16C23×D79semidirect
984. C2×C8C23×D79semidirect
1117. C2#23778178direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#190994002
C2×H(5,𝔽2)×D792
#237781782
C2×#190993722
C2×#190993712
C2×#190993692
C2×#190993682
C2×#190993672
C2×#190993662
C2×#190993652
C2×#190993622
C2×#190993602
C22×#145791882
C2×AGL(1,ℤ/8)×D792
C2×#190993282
C2×#577×C792
C2×#358579