Finite Group Databasebeta

← C2×#23778172 #35202101

Subgroups — C2×#23778172 #35202101

Order 20224.

10858 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099400C211yesmaximal, characteristic, complemented
2C2×#19099398C211yesmaximal, characteristic, complemented
3#23778172C2132yesmaximal, direct product factor
4C2×#19099379C213yesmaximal, complemented
5C2×#19099378C211yesmaximal, characteristic, complemented
6C2×#19099375C211yesmaximal, characteristic, complemented
7C2×#19099370C213yesmaximal, complemented
8C2×#19099369C213yesmaximal, complemented
9C2×#19099367C213yesmaximal, complemented
10C2×#19099366C211yesmaximal, characteristic, complemented
11C2×#19099362C213yesmaximal, complemented
12C2×#19099359C213yesmaximal, complemented
13C22×#14579182C213yesmaximal, complemented
14C2×#135×D79C213yesmaximal, complemented
15C2×#131×D79C211yesmaximal, characteristic, complemented
16C2×#577×C79C211yesmaximal, characteristic, complemented
17#19099400—28no—
18#19099400C22116yescomplemented
19#19099398—28no—
20#19099398C22116yescomplemented
21C2×#14579209—21no—
22C2×#14579209C2213yescomplemented
23C2×#14579208—21no—
24C2×#14579208C2211yescharacteristic, complemented
25C2×#14579208C2213yescomplemented
26C2×#14579207—23no—
27C2×#14579207C2213yescomplemented
28C2×#14579207C2211yescharacteristic, complemented
29C2×#14579206—23no—
30C2×#14579206C2213yescomplemented
31C22×#11929625—21no—
32C22×#11929625C2213yescomplemented
33C22×#11929623—23no—
34C22×#11929623C2213yescomplemented
35C2×#41×D79—21no—
36C2×#41×D79—23no—
37C2×#41×D79C2211yescharacteristic
38C2×#41×D79C2213yescomplemented
39C2×#41×D79C2213yescomplemented
40#19099379C22148yescomplemented
41#19099378C22116yescomplemented
42#19099375C22116yescomplemented
43#19099370C22148yescomplemented
44#19099369C22148yescomplemented
45#19099367C22148yescomplemented
46#19099366C22116yescomplemented
47#19099362C22148yescomplemented
48#19099359C22148yescomplemented
49C2×#14579194C2213yescomplemented
50C2×#14579193C2216yescomplemented
51C2×#14579192C2213yescomplemented
52C2×#14579191C2213yescomplemented
53C2×#14579190C2216yescomplemented
54C2×#14579189C2213yescomplemented
55C2×#14579188C2216yescomplemented
56C2×#14579187C2213yescomplemented
57C2×#14579186C2213yescomplemented
58C2×#14579185C2216yescomplemented
59C2×#14579184C2213yescomplemented
60C2×#14579183C2213yescomplemented
61C2×#14579182C2211yescharacteristic, complemented
62C2×#14579182C2213yescomplemented
63C2×#14579182C2216yescomplemented
64C2×#14579182C2216yescomplemented
65C2×#14579182C2216yescomplemented
66C2×#14579182C22148yescomplemented
67C2×#14579181C2213yescomplemented
68C2×#14579181C2213yescomplemented
69C2×#14579180C2213yescomplemented
70#135×D79C22148yescomplemented
71C22×#11929614C2213yescomplemented
72C2×Q16×D79C2213yescomplemented
73C22×#11929613C2213yescomplemented
74C2×SD16×D79C2213yescomplemented
75C2×SD16×D79C2213yescomplemented
76C22×#11929609C2213yescomplemented
77C2×D8×D79C2213yescomplemented
78C2×#14579169C2213yescomplemented
79C2×#14579168C2211yescharacteristic, complemented
80C2×#14579167C2213yescomplemented
81#131×D79C22116yescomplemented
82C2×M16×D79C2213yescomplemented
83C22×C8×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
92#14579209—212no—
93#14579209—216no—
94#14579209C23124yescomplemented
95#14579208—24no—
96#14579208—212no—
97#14579208—216no—
98#14579208C2318yescomplemented
99#14579208C23124yescomplemented
100#14579207—24no—
101#14579207—212no—
102#14579207—248no—
103#14579207C2318yescomplemented
104#14579207C23124yescomplemented
105#14579206—212no—
106#14579206—248no—
107#14579206C23124yescomplemented
108C2×#11929625—21no—
109C2×#11929625—216no—
110C2×#11929625—23no—
111C2×#11929625—23no—
112C2×#11929625—212no—
113C2×#11929625—23no—
114C2×#11929625D411yescharacteristic
115C2×#11929625C2316yes—
116C2×#11929625C2313yes—
117C2×#11929625C2311yescharacteristic
118C2×#11929625C23124yescomplemented
119C2×#11929624—23no—
120C2×#11929624—23no—
121C2×#11929624—26no—
122C2×#11929624—23no—
123C2×#11929624—23no—
124C2×#11929624C2313yes—
125C2×#11929624C2313yes—
126C2×#11929624C2313yes—
127C2×#11929623—23no—
128C2×#11929623—248no—
129C2×#11929623—23no—
130C2×#11929623—26no—
131C2×#11929623—23no—
132C2×#11929623—23no—
133C2×#11929623—23no—
134C2×#11929623—212no—
135C2×#11929623—23no—
136C2×#11929623D413yes—
137C2×#11929623C2316yes—
138C2×#11929623C2311yescharacteristic
139C2×#11929623C2313yes—
140C2×#11929623C23124yescomplemented
141#41×D79—216no—
142#41×D79—248no—
143#41×D79—212no—
144#41×D79—212no—
145#41×D79D418yes—
146#41×D79C2318yes—
147#41×D79C23124yescomplemented
148#41×D79C23124yescomplemented
149C22×Dic158—23no—
150C22×Dic158C2313yes—
151C2×Q8×D79—21no—
152C2×Q8×D79—23no—
153C2×Q8×D79D411yescharacteristic
154C2×Q8×D79C2313yes—
155C2×Q8×D79C2313yes—
156C22×D316—23no—
157C22×D316—23no—
158C22×D316C2313yes—
159C22×C22⋊D79—23no—
160C22×C22⋊D79—26no—
161C2×D4×D79—23no—
162C2×D4×D79—23no—
163C2×D4×D79—23no—
164C2×D4×D79—23no—
165C2×D4×D79—26no—
166C2×D4×D79D413yes—
167C2×D4×D79C2313yes—
168C2×D4×D79C2313yes—
169C23×Dic79—23no—
170C22×C4×D79—23no—
171C22×C4×D79—23no—
172C22×C4×D79—23no—
173C22×C4×D79C2313yes—
174#14579194C23124yescomplemented
175#14579193C23148yescomplemented
176#14579192C23124yescomplemented
177#14579191C23124yescomplemented
178#14579190C23148yescomplemented
179#14579189C23124yescomplemented
180#14579188C23148yescomplemented
181#14579187C23124yescomplemented
182#14579186C23124yescomplemented
183#14579185C23148yescomplemented
184#14579184C23124yescomplemented
185#14579183C23124yescomplemented
186#14579182C2318yescomplemented
187#14579182C23124yescomplemented
188#14579182C23148yescomplemented
189#14579182C23148yescomplemented
190#14579182C23148yescomplemented
191#14579181C23124yescomplemented
192#14579181C23124yescomplemented
193#14579180C23124yescomplemented
194C2×Dic316C2313yes—
195C2×#11929614C2311yescharacteristic
196C2×#11929614C2313yes—
197C2×#11929614C2316yes—
198C2×#11929614C23124yescomplemented
199Q16×D79C23124yescomplemented
200C2×#11929613C2311yescharacteristic
201C2×#11929613C2313yes—
202C2×#11929613C2316yes—
203C2×#11929613C23124yescomplemented
204C2×#11929612C2313yes—
205C2×#11929612C2313yes—
206C2×#11929611C2313yes—
207C2×#11929611C2313yes—
208SD16×D79C23124yescomplemented
209SD16×D79C23124yescomplemented
210C2×D632C2313yes—
211C2×#11929609C2311yescharacteristic
212C2×#11929609C2313yes—
213C2×#11929609C2316yes—
214C2×#11929609C23124yescomplemented
215D8×D79C23124yescomplemented
216#14579169C23124yescomplemented
217#14579168C2318yescomplemented
218#14579167C23124yescomplemented
219C2×#11929608C2313yes—
220C2×#11929607C2316yes—
221M16×D79C23124yescomplemented
222C22×C79⋊C8C2313yes—
223C2×C8×D79C2311yescharacteristic
224C2×C8×D79C2313yes—
225C2×C8×D79C2313yes—
226C2×C8×D79C2313yes—
227C2×C8×D79C23124yescomplemented
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×C79C2313yes—
236C2×#41×C79C2311yescharacteristic
237C22×Q8×C79—21no—
238C22×Q8×C79C2313yes—
239C22×D4×C79—23no—
240C22×D4×C79C2313yes—
241#137×C79C23124yescomplemented
242AGL(1,ℤ/8)×C79C23124yescomplemented
243#135×C79C23124yescomplemented
244C2×Q16×C79C2313yes—
245C2×SD16×C79C2313yes—
246C2×SD16×C79C2316yes—
247C2×SD16×C79C2311yescharacteristic
248C2×SD16×C79C23124yescomplemented
249C2×D8×C79C2313yes—
250#131×C79C2318yescomplemented
251C2×M16×C79C2313yes—
252C22×C8×C79C2313yes—
253C23×D79—23no—
254C23×D79—23no—
255C23×D79—23no—
256C23×D79C2×D413yes—
257#11929625—224no—
258#11929625—22no—
259#11929625—26no—
260#11929625—224no—
261#11929625—212no—
262#11929625—224no—
263#11929625—28no—
264#11929625C2×D418yes—
265#11929625C2414yes—
266#11929625C24112yes—
267#11929625C24124yes—
268#11929624—224no—
269#11929624—224no—
270#11929624—224no—
271#11929624—224no—
272#11929624—26no—
273#11929624—26no—
274#11929624—248no—
275#11929624C2×D4112yes—
276#11929624C24112yes—
277#11929624C24112yes—
278#11929624C24112yes—
279#11929623—224no—
280#11929623—224no—
281#11929623—22no—
282#11929623—26no—
283#11929623—224no—
284#11929623—212no—
285#11929623—224no—
286#11929623—224no—
287#11929623—224no—
288#11929623—248no—
289#11929623C2×D4124yes—
290#11929623C2414yes—
291#11929623C24112yes—
292#11929623C24124yes—
293C2×Dic158—23no—
294C2×Dic158—23no—
295C2×Dic158—224no—
296C2×Dic158—23no—
297C2×Dic158—26no—
298C2×Dic158C2×D413yes—
299C2×Dic158C2411yescharacteristic
300C2×Dic158C2413yes—
301C2×Dic158C24112yes—
302Q8×D79—26no—
303Q8×D79—26no—
304Q8×D79—224no—
305Q8×D79—28no—
306Q8×D79C2×D418yes—
307Q8×D79C24112yes—
308Q8×D79C24112yes—
309C2×D316—224no—
310C2×D316—21no—
311C2×D316—26no—
312C2×D316—23no—
313C2×D316—224no—
314C2×D316—23no—
315C2×D316—26no—
316C2×D316C2×D413yes—
317C2×D316C2411yescharacteristic
318C2×D316C2413yes—
319C2×D316C24112yes—
320C2×C22⋊D79—23no—
321C2×C22⋊D79—23no—
322C2×C22⋊D79—23no—
323C2×C22⋊D79—23no—
324C2×C22⋊D79—26no—
325C2×C22⋊D79—23no—
326C2×C22⋊D79—224no—
327C2×C22⋊D79—21no—
328C2×C22⋊D79—248no—
329C2×C22⋊D79C2×D416yes—
330D4×D79—224no—
331D4×D79—26no—
332D4×D79—26no—
333D4×D79—224no—
334D4×D79—224no—
335D4×D79—224no—
336D4×D79—248no—
337D4×D79C2×D4124yes—
338D4×D79C24112yes—
339D4×D79C24112yes—
340C22×Dic79—26no—
341C22×Dic79—224no—
342C22×Dic79—21no—
343C22×Dic79—23no—
344C22×Dic79—23no—
345C22×Dic79C2×D413yes—
346C2×C4×D79—26no—
347C2×C4×D79—224no—
348C2×C4×D79—21no—
349C2×C4×D79—23no—
350C2×C4×D79—224no—
351C2×C4×D79—224no—
352C2×C4×D79—23no—
353C2×C4×D79—23no—
354C2×C4×D79—23no—
355C2×C4×D79—23no—
356C2×C4×D79C2×D413yes—
357C2×C4×D79C2×D4112yes—
358C2×C4×D79C2×D413yes—
359C2×C4×D79C2413yes—
360C2×C4×D79C24112yes—
361C2×C4×D79C2411yescharacteristic
362Dic316C24112yes—
363#11929614C2414yes—
364#11929614C24112yes—
365#11929614C24124yes—
366#11929613C2414yes—
367#11929613C24112yes—
368#11929613C24124yes—
369#11929612C24112yes—
370#11929612C24112yes—
371#11929611C24112yes—
372#11929611C24112yes—
373D632C24112yes—
374#11929609C2414yes—
375#11929609C24112yes—
376#11929609C24124yes—
377#11929608C24112yes—
378#11929607C24124yes—
379C2×C79⋊C8C2411yescharacteristic
380C2×C79⋊C8C2413yes—
381C2×C79⋊C8C24112yes—
382C8×D79C2414yes—
383C8×D79C24112yes—
384C8×D79C24112yes—
385C8×D79C24112yes—
386C24×C79—23no—
387#41×C79—28no—
388#41×C79—224no—
389#41×C79—26no—
390#41×C79—26no—
391#41×C79C2×D414yes—
392#41×C79C24112yes—
393#41×C79C24112yes—
394#41×C79C2414yes—
395C2×Q8×C79—28no—
396C2×Q8×C79—23no—
397C2×Q8×C79—26no—
398C2×Q8×C79C2×D411yescharacteristic
399C2×Q8×C79C2411yescharacteristic
400C2×Q8×C79C2413yes—
401C2×Q8×C79C24112yes—
402C2×D4×C79—23no—
403C2×D4×C79—23no—
404C2×D4×C79—224no—
405C2×D4×C79—23no—
406C2×D4×C79—26no—
407C2×D4×C79C2×D413yes—
408C2×D4×C79C2413yes—
409C2×D4×C79C2411yescharacteristic
410C2×D4×C79C24112yes—
411C22×C4×C79—23no—
412C22×C4×C79—23no—
413C22×C4×C79—23no—
414C22×C4×C79C2413yes—
415Q16×C79C24112yes—
416SD16×C79C24112yes—
417SD16×C79C24124yes—
418SD16×C79C2414yes—
419D8×C79C24112yes—
420M16×C79C24112yes—
421C2×C8×C79C2411yescharacteristic
422C2×C8×C79C2413yes—
423C2×C8×C79C24112yes—
424C23×C79—23no—
425C23×C79—21no—
426C23×C79—212no—
427C23×C79—86no—
428C23×C79C22×D413yes—
429C22×D79—21no—
430C22×D79—23no—
431C22×D79—212no—
432C22×D79—212no—
433C22×D79—212no—
434C22×D79—46no—
435C22×D79—86no—
436C22×D79—86no—
437C22×D79—86no—
438C22×D79C22×D413yes—
439C22×D79C22×D411yescharacteristic
440C22×D79C22×D4112yes—
441Q8×C79—21no—
442Q8×C79—212no—
443Q8×C79—23no—
444Q8×C79C22×D414yes—
445Q8×C79C2512yes—
446Q8×C79C2516yes—
447D4×C79—212no—
448D4×C79—212no—
449D4×C79—21no—
450D4×C79—212no—
451D4×C79—23no—
452D4×C79C22×D4112yes—
453D4×C79C2516yes—
454D4×C79C2512yes—
455C2×C4×C79—23no—
456C2×C4×C79—21no—
457C2×C4×C79—212no—
458C2×C4×C79—212no—
459C2×C4×C79—212no—
460C2×C4×C79C22×D413yes—
461C2×C4×C79C22×D416yes—
462C2×C4×C79C2511yescharacteristic
463C2×C4×C79C2516yes—
464C22⋊D79—212no—
465C22⋊D79—212no—
466C22⋊D79—24no—
467C22⋊D79—212no—
468C22⋊D79—224no—
469C22⋊D79—212no—
470C22⋊D79—212no—
471C22⋊D79C22×D4124yes—
472C2×Dic79—21no—
473C2×Dic79—23no—
474C2×Dic79—212no—
475C2×Dic79—24no—
476C2×Dic79—212no—
477C2×Dic79—224no—
478C2×Dic79C22×D411yescharacteristic
479C2×Dic79C22×D413yes—
480C2×Dic79C22×D4112yes—
481D316—24no—
482D316—212no—
483D316—224no—
484D316—21no—
485D316—212no—
486D316—23no—
487D316C22×D4112yes—
488D316C2516yes—
489D316C2512yes—
490C4×D79—212no—
491C4×D79—212no—
492C4×D79—212no—
493C4×D79—212no—
494C4×D79—24no—
495C4×D79—212no—
496C4×D79—224no—
497C4×D79C22×D4112yes—
498C4×D79C22×D412yes—
499C4×D79C22×D416yes—
500C4×D79C22×D4112yes—
501C4×D79C2512yes—
502C4×D79C2516yes—
503Dic158—21no—
504Dic158—212no—
505Dic158—23no—
506Dic158—212no—
507Dic158—212no—
508Dic158C22×D4112yes—
509Dic158C2512yes—
510Dic158C2516yes—
511C8×C79C2512yes—
512C8×C79C2516yes—
513C79⋊C8C2512yes—
514C79⋊C8C2516yes—
515C22×C79—26no—
516C22×C79—22no—
517C22×C79—26no—
518C22×C79—42no—
519C22×C79—46no—
520C22×C79—812no—
521C22×C79C23×D416yes—
522C22×C79C23×D411yescharacteristic
523C2×D79—22no—
524C2×D79—26no—
525C2×D79—22no—
526C2×D79—26no—
527C2×D79—412no—
528C2×D79—42no—
529C2×D79—46no—
530C2×D79—812no—
531C2×D79—812no—
532C2×D79—812no—
533C2×D79C23×D412yes—
534C2×D79C23×D416yes—
535C4×C79—22no—
536C4×C79—26no—
537C4×C79C23×D416yes—
538C4×C79C23×D411yescharacteristic
539C4×C79C2611yescharacteristic
540Dic79—22no—
541Dic79—26no—
542Dic79C23×D416yes—
543Dic79C23×D412yes—
544C2×#3584—791nomaximal, Sylow
545C2×C79—26no—
546C2×C79—42no—
547C2×C79—46no—
548C2×C79#358412yescomplemented
549C2×C79C24×D411yescharacteristic
550D79—22no—
551D79—26no—
552D79—42no—
553D79—46no—
554C2×#585—791no—
555C2×#585—791no—
556#3584—7932no—
557C2×#578—791no—
558C2×#578—793no—
559C2×#577—793no—
560C2×#577—793no—
561C2×#577—791no—
562C2×#577D7911yescharacteristic, complemented
563C2×#576—791no—
564C2×#576—793no—
565C2×#575—793no—
566C2×#575—793no—
567C22×#135—793no—
568C22×#135—793no—
569C22×#131—791no—
570C79C2×#358411yescharacteristic, complemented, Sylow
571#585—7916no—
572#585—7916no—
573#585—1588no—
574#585—1588no—
575C2×2−1+4—793no—
576C2×2−1+4—791no—
577C2×2−1+4—793no—
578C2×2−1+4—1581no—
579C2×2−1+4—1581no—
580C2×2−1+4C2×D7911yescharacteristic, complemented
581C2×H(5,𝔽2)—793no—
582C2×H(5,𝔽2)—791no—
583C2×H(5,𝔽2)—793no—
584C2×H(5,𝔽2)—1583no—
585C2×H(5,𝔽2)—1583no—
586C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
587C22×#41—791no—
588C22×#41—793no—
589C22×#41—793no—
590C22×#41—793no—
591C22×#41—793no—
592C22×#41—1583no—
593C22×#41—1581no—
594C22×#41—1581no—
595C22×#41—1583no—
596#578—7916no—
597#578—7948no—
598#577—7948no—
599#577—7948no—
600#577—7916no—
601#577C2×D79116yescomplemented
602#576—7916no—
603#576—7948no—
604#575—7948no—
605#575—7948no—
606C2×#137—793no—
607C2×#137—793no—
608C2×#137—796no—
609C2×#137—796no—
610C2×#137—793no—
611C2×#137C2×D7913yescomplemented
612C2×AGL(1,ℤ/8)—793no—
613C2×AGL(1,ℤ/8)—793no—
614C2×AGL(1,ℤ/8)—796no—
615C2×AGL(1,ℤ/8)—796no—
616C2×AGL(1,ℤ/8)—793no—
617C2×AGL(1,ℤ/8)C2×D7913yescomplemented
618C2×#135—793no—
619C2×#135—793no—
620C2×#135—7948no—
621C2×#135—793no—
622C2×#135—791no—
623C2×#135—793no—
624C2×#135—796no—
625C2×#135—796no—
626C2×#135—796no—
627C2×#135—7948no—
628C2×#135—793no—
629C2×#135—793no—
630C2×#135C2×D7913yescomplemented
631C22×Q16—793no—
632C22×Q16—793no—
633C22×SD16—793no—
634C22×SD16—793no—
635C22×SD16—793no—
636C22×SD16C2×D7913yescomplemented
637C22×D8—793no—
638C22×D8—793no—
639C2×#131—791no—
640C2×#131—7916no—
641C2×#131—793no—
642C2×#131—793no—
643C2×#131C2×D7911yescharacteristic, complemented
644C22×M16—793no—
645C23×C8—793no—
6462−1+4—24no—
6472−1+4—7924no—
6482−1+4—798no—
6492−1+4—7924no—
6502−1+4—15816no—
6512−1+4—15812no—
6522−1+4—15816no—
6532−1+4—15812no—
6542−1+4—1584no—
6552−1+4C22×D7918yescomplemented
656H(5,𝔽2)—24no—
657H(5,𝔽2)—7924no—
658H(5,𝔽2)—798no—
659H(5,𝔽2)—7924no—
660H(5,𝔽2)—15848no—
661H(5,𝔽2)—15812no—
662H(5,𝔽2)—15848no—
663H(5,𝔽2)—15812no—
664H(5,𝔽2)—1584no—
665H(5,𝔽2)C22×D7918yescomplemented
666C2×#41—21no—
667C2×#41—23no—
668C2×#41—798no—
669C2×#41—798no—
670C2×#41—791no—
671C2×#41—793no—
672C2×#41—793no—
673C2×#41—7924no—
674C2×#41—7924no—
675C2×#41—791no—
676C2×#41—793no—
677C2×#41—796no—
678C2×#41—7924no—
679C2×#41—793no—
680C2×#41—791no—
681C2×#41—796no—
682C2×#41—7924no—
683C2×#41—793no—
684C2×#41—793no—
685C2×#41—1583no—
686C2×#41—1583no—
687C2×#41—1586no—
688C2×#41—1583no—
689C2×#41—1583no—
690C2×#41—1583no—
691C2×#41—1583no—
692C2×#41—1583no—
693C2×#41—1583no—
694C2×#41—15812no—
695C2×#41—1583no—
696C2×#41—1583no—
697C2×#41—15812no—
698C2×#41—15812no—
699C2×#41—15812no—
700C2×#41—1586no—
701C2×#41—1583no—
702C2×#41—15848no—
703C2×#41—1583no—
704C2×#41—15816no—
705C2×#41—15816no—
706C2×#41—15848no—
707C2×#41—1581no—
708C2×#41—1583no—
709C2×#41C22×D7913yes—
710C2×#41C22×D7913yes—
711C2×#41C22×D7911yescharacteristic
712C22×Q8—21no—
713C22×Q8—791no—
714C22×Q8—793no—
715C22×Q8—793no—
716C22×Q8—793no—
717C22×Q8—1583no—
718C22×Q8—1583no—
719C22×Q8—1581no—
720C22×Q8C22×D7913yes—
721C22×D4—23no—
722C22×D4—793no—
723C22×D4—793no—
724C22×D4—793no—
725C22×D4—793no—
726C22×D4—1583no—
727C22×D4—1583no—
728C22×D4—1586no—
729C22×D4—1583no—
730C22×D4—1583no—
731C22×D4—1583no—
732C22×D4—1586no—
733C22×D4—1583no—
734C22×D4—1583no—
735C22×D4C22×D7913yes—
736C23×C4—793no—
737C23×C4—1583no—
738C23×C4—1583no—
739C23×C4—1583no—
740C23×C4—1583no—
741#137—7924no—
742#137—7924no—
743#137—7948no—
744#137—7948no—
745#137—7924no—
746#137C22×D79124yescomplemented
747AGL(1,ℤ/8)—7924no—
748AGL(1,ℤ/8)—7924no—
749AGL(1,ℤ/8)—7948no—
750AGL(1,ℤ/8)—7948no—
751AGL(1,ℤ/8)—7924no—
752AGL(1,ℤ/8)C22×D79124yescomplemented
753#135—7924no—
754#135—7924no—
755#135—7924no—
756#135—798no—
757#135—7924no—
758#135—7948no—
759#135—7948no—
760#135—7948no—
761#135—7924no—
762#135—7924no—
763#135C22×D79124yescomplemented
764C2×Q16—791no—
765C2×Q16—793no—
766C2×Q16—796no—
767C2×Q16—7924no—
768C2×Q16—7924no—
769C2×Q16—793no—
770C2×Q16C22×D7913yes—
771C2×SD16—793no—
772C2×SD16—793no—
773C2×SD16—793no—
774C2×SD16—793no—
775C2×SD16—7924no—
776C2×SD16—7924no—
777C2×SD16—791no—
778C2×SD16—793no—
779C2×SD16—796no—
780C2×SD16—7924no—
781C2×SD16C22×D7911yescharacteristic
782C2×SD16C22×D7913yes—
783C2×SD16C22×D7916yes—
784C2×SD16C22×D79124yescomplemented
785C2×D8—793no—
786C2×D8—791no—
787C2×D8—796no—
788C2×D8—7924no—
789C2×D8—7924no—
790C2×D8—793no—
791C2×D8C22×D7913yes—
792#131—798no—
793#131—7924no—
794#131—7924no—
795#131C22×D7918yescomplemented
796C2×M16—793no—
797C2×M16—7924no—
798C2×M16—796no—
799C2×M16C22×D7913yes—
800C22×C8—793no—
801C22×C8—791no—
802C22×C8—793no—
803C22×C8—793no—
804C22×C8—793no—
805C22×C8—7924no—
806C22×C8C22×D7913yes—
807C24—23no—
808C24—793no—
809C24—1583no—
810C24—1583no—
811C24—1583no—
812#41—28no—
813#41—224no—
814#41—26no—
815#41—26no—
816#41—798no—
817#41—7924no—
818#41—7912no—
819#41—7912no—
820#41—794no—
821#41—7912no—
822#41—7924no—
823#41—7912no—
824#41—794no—
825#41—7924no—
826#41—7912no—
827#41—7912no—
828#41—15824no—
829#41—15824no—
830#41—15848no—
831#41—15824no—
832#41—15824no—
833#41—15824no—
834#41—15824no—
835#41—1586no—
836#41—1582no—
837#41—15824no—
838#41—15824no—
839#41—15812no—
840#41—1586no—
841#41—1582no—
842#41—15824no—
843#41—15824no—
844#41—15812no—
845#41—15848no—
846#41—15824no—
847#41—15824no—
848#41—1588no—
849#41—15824no—
850#41—1586no—
851#41—1586no—
852#41D4×D7914yes—
853#41C23×D79112yes—
854#41C23×D79112yes—
855#41C23×D7914yes—
856C2×Q8—28no—
857C2×Q8—23no—
858C2×Q8—26no—
859C2×Q8—798no—
860C2×Q8—793no—
861C2×Q8—7912no—
862C2×Q8—7912no—
863C2×Q8—791no—
864C2×Q8—793no—
865C2×Q8—7912no—
866C2×Q8—1583no—
867C2×Q8—1583no—
868C2×Q8—15824no—
869C2×Q8—1586no—
870C2×Q8—1586no—
871C2×Q8—15824no—
872C2×Q8—1588no—
873C2×Q8—1583no—
874C2×Q8—1586no—
875C2×Q8D4×D7911yescharacteristic
876C2×Q8C23×D7911yescharacteristic
877C2×Q8C23×D7913yes—
878C2×Q8C23×D79112yes—
879C2×D4—23no—
880C2×D4—23no—
881C2×D4—224no—
882C2×D4—23no—
883C2×D4—26no—
884C2×D4—796no—
885C2×D4—7924no—
886C2×D4—7912no—
887C2×D4—7912no—
888C2×D4—791no—
889C2×D4—793no—
890C2×D4—7912no—
891C2×D4—793no—
892C2×D4—15824no—
893C2×D4—1581no—
894C2×D4—1583no—
895C2×D4—1586no—
896C2×D4—15824no—
897C2×D4—1586no—
898C2×D4—1586no—
899C2×D4—1583no—
900C2×D4—1583no—
901C2×D4—15848no—
902C2×D4—15824no—
903C2×D4—15824no—
904C2×D4—15824no—
905C2×D4—15848no—
906C2×D4—1581no—
907C2×D4—1583no—
908C2×D4—1586no—
909C2×D4—15824no—
910C2×D4—1583no—
911C2×D4—1583no—
912C2×D4—15824no—
913C2×D4—1583no—
914C2×D4—1586no—
915C2×D4D4×D7913yes—
916C2×D4C23×D7913yes—
917C2×D4C23×D79112yes—
918C2×D4C23×D7911yescharacteristic
919C22×C4—23no—
920C22×C4—23no—
921C22×C4—23no—
922C22×C4—793no—
923C22×C4—791no—
924C22×C4—793no—
925C22×C4—7912no—
926C22×C4—793no—
927C22×C4—793no—
928C22×C4—7912no—
929C22×C4—1581no—
930C22×C4—1583no—
931C22×C4—1586no—
932C22×C4—15824no—
933C22×C4—15824no—
934C22×C4—15824no—
935C22×C4—1583no—
936C22×C4—1583no—
937C22×C4—1581no—
938C22×C4—1583no—
939C22×C4—1586no—
940C22×C4—15824no—
941C22×C4—1583no—
942C22×C4—1583no—
943C22×C4—1583no—
944C22×C4C23×D7913yes—
945Q16—794no—
946Q16—7912no—
947Q16—7924no—
948Q16—7912no—
949Q16C23×D79112yes—
950SD16—7912no—
951SD16—7912no—
952SD16—7912no—
953SD16—7912no—
954SD16—794no—
955SD16—7912no—
956SD16—7924no—
957SD16C23×D7914yes—
958SD16C23×D79112yes—
959SD16C23×D79124yes—
960D8—7912no—
961D8—794no—
962D8—7924no—
963D8—7912no—
964D8C23×D79112yes—
965M16—7912no—
966M16—7924no—
967M16C23×D79112yes—
968C2×C8—791no—
969C2×C8—793no—
970C2×C8—7912no—
971C2×C8—794no—
972C2×C8—7912no—
973C2×C8—7912no—
974C2×C8—7912no—
975C2×C8C23×D7911yescharacteristic
976C2×C8C23×D7913yes—
977C2×C8C23×D79112yes—
978C23—21no—
979C23—23no—
980C23—212no—
981C23—86no—
982C23—3166no—
983C23—7912no—
984C23—791no—
985C23—793no—
986C23—6326no—
987C23—6326no—
988C23—6326no—
989C23—15812no—
990C23—15812no—
991C23—1581no—
992C23—1583no—
993C23—15812no—
994C23C2×D4×D7913yes—
995Q8—212no—
996Q8—23no—
997Q8—21no—
998Q8—7912no—
999Q8—792no—
1000Q8—796no—
1001Q8—15812no—
1002Q8—15812no—
1003Q8—15812no—
1004Q8—1581no—
1005Q8—1583no—
1006Q8C2×D4×D7914yes—
1007Q8C24×D7912yes—
1008Q8C24×D7916yes—
1009D4—212no—
1010D4—212no—
1011D4—212no—
1012D4—23no—
1013D4—21no—
1014D4—7924no—
1015D4—796no—
1016D4—792no—
1017D4—7912no—
1018D4—1584no—
1019D4—15812no—
1020D4—15824no—
1021D4—15812no—
1022D4—15812no—
1023D4—1584no—
1024D4—15812no—
1025D4—15824no—
1026D4—15812no—
1027D4—15812no—
1028D4—15812no—
1029D4—1581no—
1030D4—1583no—
1031D4C2×D4×D79112yes—
1032D4C24×D7916yes—
1033D4C24×D7912yes—
1034C2×C4—212no—
1035C2×C4—21no—
1036C2×C4—23no—
1037C2×C4—212no—
1038C2×C4—212no—
1039C2×C4—7912no—
1040C2×C4—791no—
1041C2×C4—793no—
1042C2×C4—792no—
1043C2×C4—796no—
1044C2×C4—792no—
1045C2×C4—7912no—
1046C2×C4—7912no—
1047C2×C4—796no—
1048C2×C4—1584no—
1049C2×C4—15812no—
1050C2×C4—15824no—
1051C2×C4—15812no—
1052C2×C4—15812no—
1053C2×C4—1584no—
1054C2×C4—15812no—
1055C2×C4—15824no—
1056C2×C4—15812no—
1057C2×C4—1581no—
1058C2×C4—1583no—
1059C2×C4—15812no—
1060C2×C4—15812no—
1061C2×C4C2×D4×D7916yes—
1062C2×C4C2×D4×D7913yes—
1063C2×C4C24×D7916yes—
1064C2×C4C24×D7911yescharacteristic
1065C8—792no—
1066C8—796no—
1067C8C24×D7912yes—
1068C8C24×D7916yes—
1069C22—26no—
1070C22—22no—
1071C22—26no—
1072C22—46no—
1073C22—42no—
1074C22—812no—
1075C22—31612no—
1076C22—3166no—
1077C22—3162no—
1078C22—792no—
1079C22—796no—
1080C22—63212no—
1081C22—63212no—
1082C22—63212no—
1083C22—1586no—
1084C22—1582no—
1085C22—1582no—
1086C22—1586no—
1087C22C22×D4×D7916yes—
1088C22C22×D4×D7911yescharacteristic
1089C4—22no—
1090C4—26no—
1091C4—792no—
1092C4—796no—
1093C4—1582no—
1094C4—1586no—
1095C4C22×D4×D7916yes—
1096C4C22×D4×D7911yescharacteristic
1097C4C25×D7911yescharacteristic
1098C2—26no—
1099C2—46no—
1100C2—42no—
1101C2—3166no—
1102C2—3162no—
1103C2—1582no—
1104C2—1586no—
1105C2#2377817212yesdirect product factor
1106C2C23×D4×D7911yescharacteristic
subgroupG/H
centerC22C22×D4×D79
commutator, cosocleC4×C79C26
FrattiniC4C25×D79
FittingC2×#577×C79C2
socleC22×C79C23×D4
hypercenterC2×#577D79
hypocenterC79C2×#3584
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×#19099398C2semidirect
3. #23778172C2direct (N × H)
4. C2×#19099379C2semidirect
5. C2×#19099378C2semidirect
6. C2×#19099375C2semidirect
7. C2×#19099370C2semidirect
8. C2×#19099369C2semidirect
9. C2×#19099367C2semidirect
10. C2×#19099366C2semidirect
11. C2×#19099362C2semidirect
12. C2×#19099359C2semidirect
13. C22×#14579182C2semidirect
14. C2×#135×D79C2semidirect
15. C2×#131×D79C2semidirect
16. C2×#577×C79C2semidirect
18. #19099400C22semidirect
20. #19099398C22semidirect
22. C2×#14579209C22semidirect
24. C2×#14579208C22semidirect
25. C2×#14579208C22semidirect
27. C2×#14579207C22semidirect
28. C2×#14579207C22semidirect
30. C2×#14579206C22semidirect
32. C22×#11929625C22semidirect
34. C22×#11929623C22semidirect
38. C2×#41×D79C22semidirect
39. C2×#41×D79C22semidirect
40. #19099379C22semidirect
41. #19099378C22semidirect
42. #19099375C22semidirect
43. #19099370C22semidirect
44. #19099369C22semidirect
45. #19099367C22semidirect
46. #19099366C22semidirect
47. #19099362C22semidirect
48. #19099359C22semidirect
49. C2×#14579194C22semidirect
50. C2×#14579193C22semidirect
51. C2×#14579192C22semidirect
52. C2×#14579191C22semidirect
53. C2×#14579190C22semidirect
54. C2×#14579189C22semidirect
55. C2×#14579188C22semidirect
56. C2×#14579187C22semidirect
57. C2×#14579186C22semidirect
58. C2×#14579185C22semidirect
59. C2×#14579184C22semidirect
60. C2×#14579183C22semidirect
61. C2×#14579182C22semidirect
62. C2×#14579182C22semidirect
63. C2×#14579182C22semidirect
64. C2×#14579182C22semidirect
65. C2×#14579182C22semidirect
66. C2×#14579182C22semidirect
67. C2×#14579181C22semidirect
68. C2×#14579181C22semidirect
69. C2×#14579180C22semidirect
70. #135×D79C22semidirect
71. C22×#11929614C22semidirect
72. C2×Q16×D79C22semidirect
73. C22×#11929613C22semidirect
74. C2×SD16×D79C22semidirect
75. C2×SD16×D79C22semidirect
76. C22×#11929609C22semidirect
77. C2×D8×D79C22semidirect
78. C2×#14579169C22semidirect
79. C2×#14579168C22semidirect
80. C2×#14579167C22semidirect
81. #131×D79C22semidirect
82. C2×M16×D79C22semidirect
83. C22×C8×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
94. #14579209C23semidirect
98. #14579208C23semidirect
99. #14579208C23semidirect
103. #14579207C23semidirect
104. #14579207C23semidirect
107. #14579206C23semidirect
118. C2×#11929625C23semidirect
140. C2×#11929623C23semidirect
147. #41×D79C23semidirect
148. #41×D79C23semidirect
174. #14579194C23semidirect
175. #14579193C23semidirect
176. #14579192C23semidirect
177. #14579191C23semidirect
178. #14579190C23semidirect
179. #14579189C23semidirect
180. #14579188C23semidirect
181. #14579187C23semidirect
182. #14579186C23semidirect
183. #14579185C23semidirect
184. #14579184C23semidirect
185. #14579183C23semidirect
186. #14579182C23semidirect
187. #14579182C23semidirect
188. #14579182C23semidirect
189. #14579182C23semidirect
190. #14579182C23semidirect
191. #14579181C23semidirect
192. #14579181C23semidirect
193. #14579180C23semidirect
198. C2×#11929614C23semidirect
199. Q16×D79C23semidirect
203. C2×#11929613C23semidirect
208. SD16×D79C23semidirect
209. SD16×D79C23semidirect
214. C2×#11929609C23semidirect
215. D8×D79C23semidirect
216. #14579169C23semidirect
217. #14579168C23semidirect
218. #14579167C23semidirect
221. M16×D79C23semidirect
227. C2×C8×D79C23semidirect
229. 2−1+4×C79C23semidirect
231. H(5,𝔽2)×C79C23semidirect
241. #137×C79C23semidirect
242. AGL(1,ℤ/8)×C79C23semidirect
243. #135×C79C23semidirect
248. C2×SD16×C79C23semidirect
250. #131×C79C23semidirect
548. C2×C79#3584semidirect
562. C2×#577D79semidirect
570. C79C2×#3584semidirect
580. C2×2−1+4C2×D79semidirect
586. C2×H(5,𝔽2)C2×D79semidirect
601. #577C2×D79semidirect
611. C2×#137C2×D79semidirect
617. C2×AGL(1,ℤ/8)C2×D79semidirect
630. C2×#135C2×D79semidirect
636. C22×SD16C2×D79semidirect
643. C2×#131C2×D79semidirect
655. 2−1+4C22×D79semidirect
665. H(5,𝔽2)C22×D79semidirect
746. #137C22×D79semidirect
752. AGL(1,ℤ/8)C22×D79semidirect
763. #135C22×D79semidirect
784. C2×SD16C22×D79semidirect
795. #131C22×D79semidirect
1105. C2#23778172direct (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×#190993982
#237781722
C2×#190993792
C2×#190993782
C2×#190993752
C2×#190993702
C2×#190993692
C2×#190993672
C2×#190993662
C2×#190993622
C2×#190993592
C22×#145791822
C2×#135×D792
C2×#131×D792
C2×#577×C792
C2×#358479