Finite Group Databasebeta

← C2×#23777068 #35196581

Subgroups — C2×#23777068 #35196581

Order 20224.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579207C211yesmaximal, characteristic, complemented
2C22×#41×D79C211yesmaximal, characteristic, complemented
3#23777068C2132yesmaximal, direct product factor
4C2×#19099232C211yesmaximal, characteristic, complemented
5C2×#19099225C211yesmaximal, characteristic, complemented
6C2×#19099220C211yesmaximal, characteristic, complemented
7C2×#19099210C213yesmaximal, complemented
8C2×#19099209C213yesmaximal, complemented
9C2×#19099198C213yesmaximal, complemented
10C2×#19099197C213yesmaximal, complemented
11C2×#19099142C213yesmaximal, complemented
12C2×#19099126C213yesmaximal, complemented
13C2×#19099072C213yesmaximal, complemented
14C2×#121×D79C213yesmaximal, complemented
15C2×#19099045C211yesmaximal, characteristic, complemented
16C2×#550×C79C211yesmaximal, characteristic, complemented
17C2×#14579207—216no—
18C2×#14579207C22116yescomplemented
19C22×#11929625C2211yescharacteristic
20C22×#11929625C2211yescharacteristic, complemented
21C22×#11929624C2213yescomplemented
22C22×#11929624C2213yescomplemented
23C22×#11929623C2213yescomplemented
24C2×#41×D79—216no—
25C2×#41×D79C22116yescomplemented
26C22×Q8×D79C2211yescharacteristic, complemented
27C23×D316C2213yescomplemented
28C22×D4×D79C2213yescomplemented
29C22×D4×D79C2213yescomplemented
30C22×D4×D79C2213yescomplemented
31C22×D4×D79C2216yescomplemented
32C23×C4×D79C2213yescomplemented
33#19099232C22116yescomplemented
34#19099225C22116yescomplemented
35#19099220C22116yescomplemented
36#19099210C22148yescomplemented
37#19099209C22148yescomplemented
38#19099198C22148yescomplemented
39#19099197C22148yescomplemented
40#19099142C22148yescomplemented
41#19099126C22148yescomplemented
42C2×#14579157C2213yescomplemented
43C2×#14579149C2213yescomplemented
44C2×#14579148C2213yescomplemented
45#19099072C22148yescomplemented
46C2×#14579146C2213yescomplemented
47C2×#14579143C2213yescomplemented
48C2×#14579141C2213yescomplemented
49C2×#14579140C2213yescomplemented
50C2×#14579139C2211yescharacteristic, complemented
51C2×#14579138C2213yescomplemented
52C2×#14579136C2213yescomplemented
53C2×#14579135C2213yescomplemented
54C2×#14579134C2216yescomplemented
55C2×#14579134C2213yescomplemented
56C2×#14579133C2216yescomplemented
57C2×#14579133C2213yescomplemented
58C2×#14579132C2216yescomplemented
59C2×#14579132C2213yescomplemented
60C2×#14579132C2213yescomplemented
61#121×D79C22148yescomplemented
62C2×#14579131C2213yescomplemented
63C2×#14579129C2216yescomplemented
64C2×#14579129C2213yescomplemented
65C2×#14579129C2216yescomplemented
66#19099045C22116yescomplemented
67C2×Q8×Dic79C2211yescharacteristic, complemented
68C2×C4×D316C2213yescomplemented
69C2×C4×D316C2213yescomplemented
70C2×#14579123C2213yescomplemented
71C2×C4×C22⋊D79C2213yescomplemented
72C2×C4×C22⋊D79C2213yescomplemented
73C2×#14579118C2213yescomplemented
74C2×C4⋊C4×D79C2213yescomplemented
75C2×C22⋊C4×D79C2216yescomplemented
76C22×#41×C79C2211yescharacteristic, complemented
77C22×#41×C79C2211yescharacteristic, complemented
78#550×C79C22116yescomplemented
79C2×#127×C79C2213yescomplemented
80C2×#121×C79C2213yescomplemented
81C2×#121×C79C2213yescomplemented
82C2×C4×Q8×C79C2211yescharacteristic, complemented
83C2×C4×D4×C79C2213yescomplemented
84C24×D79C2313yes—
85C24×D79C2316yes—
86#14579207—2128no—
87C2×#11929625—28no—
88C2×#11929625D4116yescomplemented
89C2×#11929625C2318yes—
90C2×#11929625C2318yescomplemented
91C2×#11929624—224no—
92C2×#11929624—224no—
93C2×#11929624C23124yescomplemented
94C2×#11929624C23124yescomplemented
95C2×#11929623—224no—
96C2×#11929623C23124yescomplemented
97#41×D79—2128no—
98C22×Dic158C2311yescharacteristic
99C22×Dic158C2313yes—
100C2×Q8×D79—28no—
101C2×Q8×D79C2318yescomplemented
102C22×D316—224no—
103C22×D316C2313yes—
104C22×D316C2313yes—
105C22×D316C2313yes—
106C22×D316C2313yes—
107C22×D316C23124yescomplemented
108C22×C22⋊D79C2313yes—
109C22×C22⋊D79C2316yes—
110C22×C22⋊D79C2313yes—
111C22×C22⋊D79C2313yes—
112C22×C22⋊D79C2313yes—
113C22×C22⋊D79C2316yes—
114C2×D4×D79—224no—
115C2×D4×D79—224no—
116C2×D4×D79—224no—
117C2×D4×D79—424no—
118C2×D4×D79C23124yescomplemented
119C2×D4×D79C23124yescomplemented
120C2×D4×D79C23124yescomplemented
121C2×D4×D79C23148yescomplemented
122C23×Dic79C2313yes—
123C22×C4×D79—224no—
124C22×C4×D79C2313yes—
125C22×C4×D79C2313yes—
126C22×C4×D79C2313yes—
127C22×C4×D79C2311yescharacteristic
128C22×C4×D79C2316yes—
129C22×C4×D79C2313yes—
130C22×C4×D79C23124yescomplemented
131#14579157C23124yescomplemented
132#14579149C23124yescomplemented
133#14579148C23124yescomplemented
134#14579146C23124yescomplemented
135#14579143C23124yescomplemented
136#14579141C23124yescomplemented
137#14579140C23124yescomplemented
138#14579139C2318yescomplemented
139#14579138C23124yescomplemented
140#14579136C23124yescomplemented
141#14579135C23124yescomplemented
142#14579134C23148yescomplemented
143#14579134C23124yescomplemented
144#14579133C23148yescomplemented
145#14579133C23124yescomplemented
146#14579132C23148yescomplemented
147#14579132C23124yescomplemented
148#14579132C23124yescomplemented
149#14579131C23124yescomplemented
150#14579129C23148yescomplemented
151#14579129C23124yescomplemented
152#14579129C23148yescomplemented
153Q8×Dic79C2318yescomplemented
154C4×D316C23124yescomplemented
155C4×D316C23124yescomplemented
156#14579123C23124yescomplemented
157C4×C22⋊D79C23124yescomplemented
158C4×C22⋊D79C23124yescomplemented
159#14579118C23124yescomplemented
160C2×C4⋊Dic79C2313yes—
161C2×C4⋊Dic79C2313yes—
162C2×Dic79⋊C4C2313yes—
163C2×Dic79⋊C4C2311yescharacteristic
164C2×Dic79⋊C4C2311yescharacteristic
165C2×Dic79⋊C4C2313yes—
166C4⋊C4×D79C23124yescomplemented
167C2×C22⋊Dic79C2316yes—
168C2×C22⋊Dic79C2313yes—
169C2×C22⋊Dic79C2313yes—
170C2×(C2×D79)⋊C4C2313yes—
171C2×(C2×D79)⋊C4C2316yes—
172C2×(C2×D79)⋊C4C2313yes—
173C2×(C2×D79)⋊C4C2313yes—
174C2×(C2×D79)⋊C4C2311yescharacteristic
175C2×(C2×D79)⋊C4C2311yescharacteristic
176C2×(C2×D79)⋊C4C2313yes—
177C22⋊C4×D79C23148yescomplemented
178C2×C4×Dic79C2313yes—
179C2×#41×C79—28no—
180C2×#41×C79—28no—
181C2×#41×C79C2318yescomplemented
182C2×#41×C79C2318yescomplemented
183C22×Q8×C79C2311yescharacteristic
184C22×D4×C79C2313yes—
185C22×D4×C79C2313yes—
186C22×D4×C79C2313yes—
187C22×D4×C79C2316yes—
188C23×C4×C79C2313yes—
189C23×C4×C79C2313yes—
190#127×C79C23124yescomplemented
191#121×C79C23124yescomplemented
192#121×C79C23124yescomplemented
193C4×Q8×C79C2318yescomplemented
194C4×D4×C79C23124yescomplemented
195C2×C4⋊C4×C79C2311yescharacteristic
196C2×C4⋊C4×C79C2313yes—
197C2×C22⋊C4×C79C2313yes—
198C2×C22⋊C4×C79C2313yes—
199C2×C42×C79C2313yes—
200C23×D79—212no—
201C23×D79—212no—
202C23×D79—224no—
203C23×D79—46no—
204C23×D79—412no—
205C23×D79—412no—
206C23×D79C2413yes—
207C23×D79C24112yes—
208C23×D79C2413yes—
209C23×D79C2411yescharacteristic
210C23×D79C24124yes—
211#11929625—232no—
212#11929625C2×D4164yescomplemented
213#11929624—296no—
214#11929624—296no—
215#11929623—296no—
216C2×Dic158—24no—
217C2×Dic158—212no—
218C2×Dic158C24112yes—
219C2×Dic158C2414yes—
220Q8×D79—232no—
221C2×D316—296no—
222C2×D316—212no—
223C2×D316—212no—
224C2×D316—212no—
225C2×D316C2×D4124yescomplemented
226C2×D316C24112yes—
227C2×D316C24112yes—
228C2×D316C24112yes—
229C2×D316C24112yes—
230C2×C22⋊D79—212no—
231C2×C22⋊D79—224no—
232C2×C22⋊D79—212no—
233C2×C22⋊D79—212no—
234C2×C22⋊D79—412no—
235C2×C22⋊D79—46no—
236C2×C22⋊D79C24124yes—
237C2×C22⋊D79C24112yes—
238C2×C22⋊D79C24112yes—
239C2×C22⋊D79C24112yes—
240C2×C22⋊D79C24112yes—
241C2×C22⋊D79C24124yes—
242D4×D79—296no—
243D4×D79—296no—
244D4×D79—296no—
245D4×D79—496no—
246C22×Dic79—212no—
247C22×Dic79C2413yes—
248C22×Dic79C2411yescharacteristic
249C22×Dic79C24112yes—
250C22×Dic79C2411yescharacteristic
251C22×Dic79C2413yes—
252C22×Dic79C2411yescharacteristic
253C2×C4×D79—24no—
254C2×C4×D79—296no—
255C2×C4×D79—212no—
256C2×C4×D79—212no—
257C2×C4×D79—212no—
258C2×C4×D79—412no—
259C2×C4×D79C2×D4124yescomplemented
260C2×C4×D79C24112yes—
261C2×C4×D79C24112yes—
262C2×C4×D79C24112yes—
263C2×C4×D79C2414yes—
264C2×C4×D79C24124yes—
265C2×C4×D79C24112yes—
266C4⋊Dic79C24112yes—
267C4⋊Dic79C24112yes—
268Dic79⋊C4C24112yes—
269Dic79⋊C4C2414yes—
270Dic79⋊C4C2414yes—
271Dic79⋊C4C24112yes—
272C22⋊Dic79C24124yes—
273C22⋊Dic79C24112yes—
274C22⋊Dic79C24112yes—
275(C2×D79)⋊C4C24112yes—
276(C2×D79)⋊C4C24124yes—
277(C2×D79)⋊C4C24112yes—
278(C2×D79)⋊C4C24112yes—
279(C2×D79)⋊C4C2414yes—
280(C2×D79)⋊C4C2414yes—
281(C2×D79)⋊C4C24112yes—
282C4×Dic79C24112yes—
283C24×C79C2413yes—
284C24×C79C2413yes—
285#41×C79—232no—
286#41×C79—232no—
287C2×Q8×C79C2×D418yescomplemented
288C2×Q8×C79C2414yes—
289C2×D4×C79—212no—
290C2×D4×C79—212no—
291C2×D4×C79—46no—
292C2×D4×C79—412no—
293C2×D4×C79C24112yes—
294C2×D4×C79C24112yes—
295C2×D4×C79C24112yes—
296C2×D4×C79C24124yes—
297C22×C4×C79—212no—
298C22×C4×C79—212no—
299C22×C4×C79C2411yescharacteristic
300C22×C4×C79C24112yes—
301C22×C4×C79C24112yes—
302C22×C4×C79C2411yescharacteristic
303C22×C4×C79C2413yes—
304C22×C4×C79C2411yescharacteristic
305C22×C4×C79C2413yes—
306C4⋊C4×C79C2414yes—
307C4⋊C4×C79C24112yes—
308C22⋊C4×C79C24112yes—
309C22⋊C4×C79C24112yes—
310C42×C79C24112yes—
311C23×C79—26no—
312C23×C79—26no—
313C23×C79—26no—
314C23×C79—26no—
315C23×C79—26no—
316C23×C79—26no—
317C23×C79C2516yes—
318C23×C79C2516yes—
319C23×C79C2511yescharacteristic
320C22×D79—22no—
321C22×D79—26no—
322C22×D79—22no—
323C22×D79—26no—
324C22×D79—26no—
325C22×D79—26no—
326C22×D79—26no—
327C22×D79—224no—
328C22×D79—224no—
329C22×D79—248no—
330C22×D79—412no—
331C22×D79—448no—
332C22×D79—424no—
333C22×D79—424no—
334C22×D79—848no—
335C22×D79C22×D4112yes—
336C22×D79H(5,𝔽2)14yescomplemented
337C22×D79C2516yes—
338C22×D79C2516yes—
339C22×D79C2512yes—
340Q8×C79C22×D4116yescomplemented
341D4×C79—224no—
342D4×C79—224no—
343D4×C79—424no—
344D4×C79—412no—
345C2×C4×C79—22no—
346C2×C4×C79—22no—
347C2×C4×C79—26no—
348C2×C4×C79—22no—
349C2×C4×C79—224no—
350C2×C4×C79—224no—
351C2×C4×C79C22×D4112yes—
352C2×C4×C79C2512yes—
353C2×C4×C79C2516yes—
354C2×C4×C79C2512yes—
355C2×C4×C79C2512yes—
356C2×C4×C79C2516yes—
357C22⋊D79—224no—
358C22⋊D79—248no—
359C22⋊D79—224no—
360C22⋊D79—224no—
361C22⋊D79—424no—
362C22⋊D79—412no—
363C2×Dic79—22no—
364C2×Dic79—26no—
365C2×Dic79—26no—
366C2×Dic79—22no—
367C2×Dic79—224no—
368C2×Dic79C22×D414yes—
369C2×Dic79C2512yes—
370C2×Dic79C2516yes—
371C2×Dic79C2516yes—
372C2×Dic79C2512yes—
373C2×Dic79C2512yes—
374D316—224no—
375D316—224no—
376D316—224no—
377D316C22×D4148yescomplemented
378C4×D79—224no—
379C4×D79—224no—
380C4×D79—224no—
381C4×D79—28no—
382C4×D79—424no—
383C4×D79C22×D4148yescomplemented
384Dic158—224no—
385Dic158—28no—
386C22×C79—26no—
387C22×C79—26no—
388C22×C79—26no—
389C22×C79—26no—
390C22×C79—26no—
391C22×C79—26no—
392C22×C79—412no—
393C22×C79—412no—
394C22×C79C23×D412yes—
395C22×C79C2×H(5,𝔽2)12yes—
396C22×C79#58512yes—
397C22×C79C2611yescharacteristic
398C2×D79—22no—
399C2×D79—26no—
400C2×D79—22no—
401C2×D79—26no—
402C2×D79—28no—
403C2×D79—224no—
404C2×D79—26no—
405C2×D79—26no—
406C2×D79—26no—
407C2×D79—448no—
408C2×D79—412no—
409C2×D79—848no—
410C2×D79C23×D4112yes—
411C2×D79C2×H(5,𝔽2)14yescomplemented
412C4×C79—22no—
413C4×C79—22no—
414C4×C79—26no—
415C4×C79—22no—
416C4×C79C23×D4112yes—
417Dic79—22no—
418Dic79—26no—
419Dic79—26no—
420Dic79—22no—
421Dic79C23×D414yes—
422C2×#3488—791nomaximal, Sylow
423C2×C79—46no—
424C2×C79—46no—
425C2×C79#348814yescomplemented
426C2×C79C24×D411yescharacteristic
427C2×C79C22×H(5,𝔽2)11yescharacteristic
428C2×C79C2×#58511yescharacteristic
429D79—24no—
430D79—212no—
431D79—46no—
432C22×H(5,𝔽2)—791no—
433C23×#41—791no—
434#3488—7932no—
435C2×#550—791no—
436C2×#550D7911yescharacteristic, complemented
437C2×#548—791no—
438C2×#548—791no—
439C2×#546—793no—
440C2×#546—793no—
441C2×D42—793no—
442C2×D42—793no—
443C2×#537—793no—
444C2×#535—793no—
445C2×#525—793no—
446C22×#121—793no—
447C2×#520—791no—
448C79C2×#348811yescharacteristic, complemented, Sylow
449C2×H(5,𝔽2)—7916no—
450C2×H(5,𝔽2)—15816no—
451C22×#41—7916no—
452C22×#41—791no—
453C22×#41—791no—
454C22×#41—793no—
455C22×#41—793no—
456C22×#41—793no—
457C22×#41—15816no—
458C22×#41C2×D7911yescharacteristic, complemented
459C22×#41C2×D7911yescharacteristic, complemented
460C23×Q8—791no—
461C23×D4—796no—
462C23×D4—793no—
463C23×D4—793no—
464C23×D4—793no—
465C23×D4—793no—
466C24×C4—793no—
467#550—7916no—
468#550C2×D79116yescomplemented
469#548—7916no—
470#548—7916no—
471#546—7948no—
472#546—7948no—
473D42—7948no—
474D42—7948no—
475#537—7948no—
476#535—7948no—
477C2×#127—793no—
478C2×#127C2×D7913yescomplemented
479C2×#124—793no—
480C2×#124—793no—
481#525—7948no—
482C2×#123—793no—
483C2×#123—793no—
484C2×C22⋊Q8—793no—
485C2×C22⋊Q8—791no—
486C2×C22⋊Q8—793no—
487C2×C22⋊Q8—793no—
488C2×#121—796no—
489C2×#121—793no—
490C2×#121—793no—
491C2×#121—796no—
492C2×#121—793no—
493C2×#121—793no—
494C2×#121—7948no—
495C2×#121—793no—
496C2×#121—793no—
497C2×#121—796no—
498C2×#121C2×D7913yescomplemented
499C2×#121C2×D7913yescomplemented
500C2×#120—793no—
501C2×#120—796no—
502C2×#120—796no—
503C2×#120—793no—
504#520—7916no—
505C2×C4×Q8—791no—
506C2×C4×Q8C2×D7911yescharacteristic, complemented
507C2×C4×D4—793no—
508C2×C4×D4—793no—
509C2×C4×D4—793no—
510C2×C4×D4—793no—
511C2×C4×D4—793no—
512C2×C4×D4C2×D7913yescomplemented
513C2×#117—793no—
514C22×C4⋊C4—793no—
515C22×C22⋊C4—796no—
516C25—796no—
517C25—793no—
518H(5,𝔽2)—158128no—
519C2×#41—28no—
520C2×#41—28no—
521C2×#41—7916no—
522C2×#41—798no—
523C2×#41—798no—
524C2×#41—7924no—
525C2×#41—7924no—
526C2×#41—7924no—
527C2×#41—15824no—
528C2×#41—15824no—
529C2×#41—15824no—
530C2×#41—158128no—
531C2×#41—1588no—
532C2×#41C22×D7918yescomplemented
533C2×#41C22×D7918yescomplemented
534C22×Q8—798no—
535C22×Q8—791no—
536C22×Q8—793no—
537C22×Q8—1588no—
538C22×Q8C22×D7911yescharacteristic
539C22×D4—31624no—
540C22×D4—793no—
541C22×D4—796no—
542C22×D4—7948no—
543C22×D4—793no—
544C22×D4—796no—
545C22×D4—793no—
546C22×D4—793no—
547C22×D4—7924no—
548C22×D4—7924no—
549C22×D4—7924no—
550C22×D4—793no—
551C22×D4—793no—
552C22×D4—793no—
553C22×D4—793no—
554C22×D4—7924no—
555C22×D4—15824no—
556C22×D4—15824no—
557C22×D4—15824no—
558C22×D4—15824no—
559C22×D4C22×D7913yes—
560C22×D4C22×D7913yes—
561C22×D4C22×D7913yes—
562C22×D4C22×D7916yes—
563C23×C4—796no—
564C23×C4—793no—
565C23×C4—793no—
566C23×C4—793no—
567C23×C4—793no—
568C23×C4—793no—
569C23×C4—791no—
570C23×C4—7924no—
571C23×C4—15824no—
572C23×C4C22×D7913yes—
573C23×C4C22×D7913yes—
574#127—7924no—
575#127C22×D79124yescomplemented
576#124—7924no—
577#124—7924no—
578#123—7924no—
579#123—7924no—
580C22⋊Q8—7924no—
581C22⋊Q8—798no—
582C22⋊Q8—7924no—
583C22⋊Q8—7924no—
584#121—7948no—
585#121—7924no—
586#121—7924no—
587#121—7948no—
588#121—7924no—
589#121—7924no—
590#121—7924no—
591#121—7924no—
592#121—7948no—
593#121C22×D79124yescomplemented
594#121C22×D79124yescomplemented
595#120—7924no—
596#120—7948no—
597#120—7948no—
598#120—7924no—
599C4×Q8—798no—
600C4×Q8C22×D7918yescomplemented
601C4×D4—7924no—
602C4×D4—7924no—
603C4×D4—7924no—
604C4×D4—7924no—
605C4×D4—7924no—
606C4×D4C22×D79124yescomplemented
607#117—7924no—
608C2×C4⋊C4—793no—
609C2×C4⋊C4—793no—
610C2×C4⋊C4—791no—
611C2×C4⋊C4—791no—
612C2×C4⋊C4—793no—
613C2×C4⋊C4—793no—
614C2×C4⋊C4—7924no—
615C2×C4⋊C4C22×D7913yes—
616C2×C4⋊C4C22×D7911yescharacteristic
617C2×C22⋊C4—796no—
618C2×C22⋊C4—793no—
619C2×C22⋊C4—793no—
620C2×C22⋊C4—793no—
621C2×C22⋊C4—796no—
622C2×C22⋊C4—793no—
623C2×C22⋊C4—793no—
624C2×C22⋊C4—791no—
625C2×C22⋊C4—791no—
626C2×C22⋊C4—793no—
627C2×C22⋊C4—7948no—
628C2×C22⋊C4C22×D7913yes—
629C2×C22⋊C4C22×D7913yes—
630C2×C42—793no—
631C2×C42C22×D7913yes—
632C24—3166no—
633C24—31612no—
634C24—31612no—
635C24—7924no—
636C24—7912no—
637C24—791no—
638C24—793no—
639C24—793no—
640C24—15812no—
641C24—15812no—
642C24—15824no—
643C24C23×D7913yes—
644C24C23×D7913yes—
645#41—232no—
646#41—232no—
647#41—7964no—
648#41—15896no—
649#41—15896no—
650#41—15896no—
651#41—15832no—
652C2×Q8—794no—
653C2×Q8—7912no—
654C2×Q8—1584no—
655C2×Q8—15832no—
656C2×Q8—15812no—
657C2×Q8D4×D7918yescomplemented
658C2×Q8C23×D7914yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—412no—
662C2×D4—46no—
663C2×D4—31696no—
664C2×D4—31612no—
665C2×D4—3166no—
666C2×D4—7912no—
667C2×D4—7924no—
668C2×D4—7912no—
669C2×D4—7924no—
670C2×D4—7912no—
671C2×D4—7912no—
672C2×D4—7912no—
673C2×D4—7912no—
674C2×D4—7912no—
675C2×D4—7912no—
676C2×D4—7924no—
677C2×D4—15896no—
678C2×D4—15812no—
679C2×D4—15812no—
680C2×D4—15896no—
681C2×D4—15812no—
682C2×D4—15896no—
683C2×D4—15896no—
684C2×D4—15812no—
685C2×D4—15812no—
686C2×D4—15824no—
687C2×D4—15812no—
688C2×D4C23×D79112yes—
689C2×D4C23×D79112yes—
690C2×D4C23×D79112yes—
691C2×D4C23×D79124yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—31612no—
695C22×C4—7924no—
696C22×C4—791no—
697C22×C4—7912no—
698C22×C4—7924no—
699C22×C4—7912no—
700C22×C4—791no—
701C22×C4—793no—
702C22×C4—793no—
703C22×C4—791no—
704C22×C4—7912no—
705C22×C4—7912no—
706C22×C4—7912no—
707C22×C4—794no—
708C22×C4—1584no—
709C22×C4—15896no—
710C22×C4—15812no—
711C22×C4—15812no—
712C22×C4—15812no—
713C22×C4—15812no—
714C22×C4C23×D79112yes—
715C22×C4C23×D79112yes—
716C22×C4C23×D7911yescharacteristic
717C22×C4C23×D7913yes—
718C22×C4C23×D7911yescharacteristic
719C22×C4C23×D7911yescharacteristic
720C22×C4C23×D7913yes—
721C4⋊C4—7912no—
722C4⋊C4—794no—
723C4⋊C4—794no—
724C4⋊C4—7912no—
725C4⋊C4—7912no—
726C4⋊C4—7912no—
727C4⋊C4C23×D79112yes—
728C4⋊C4C23×D7914yes—
729C22⋊C4—7924no—
730C22⋊C4—7912no—
731C22⋊C4—7912no—
732C22⋊C4—7912no—
733C22⋊C4—7924no—
734C22⋊C4—7912no—
735C22⋊C4—7912no—
736C22⋊C4—794no—
737C22⋊C4—794no—
738C22⋊C4—7912no—
739C22⋊C4C23×D79112yes—
740C22⋊C4C23×D79112yes—
741C42—7912no—
742C42C23×D79112yes—
743C23—26no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26no—
749C23—31612no—
750C23—31624no—
751C23—31624no—
752C23—31648no—
753C23—794no—
754C23—796no—
755C23—792no—
756C23—7912no—
757C23—796no—
758C23—63248no—
759C23—15824no—
760C23—15824no—
761C23—15848no—
762C23—1586no—
763C23—1586no—
764C23—1586no—
765C23—1586no—
766C23—1582no—
767C23—1586no—
768C23—1582no—
769C23C24×D7916yes—
770C23C24×D7916yes—
771C23C24×D7911yescharacteristic
772Q8—1588no—
773Q8—15824no—
774Q8C2×D4×D79116yescomplemented
775D4—224no—
776D4—224no—
777D4—424no—
778D4—412no—
779D4—31624no—
780D4—31612no—
781D4—7948no—
782D4—15824no—
783D4—15824no—
784D4—15824no—
785D4—15824no—
786D4—15824no—
787D4—15848no—
788D4—15824no—
789C2×C4—26no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—31624no—
796C2×C4—792no—
797C2×C4—794no—
798C2×C4—7948no—
799C2×C4—792no—
800C2×C4—796no—
801C2×C4—796no—
802C2×C4—792no—
803C2×C4—1588no—
804C2×C4—15824no—
805C2×C4—15824no—
806C2×C4—1586no—
807C2×C4—1582no—
808C2×C4—1582no—
809C2×C4—1586no—
810C2×C4—15824no—
811C2×C4—15824no—
812C2×C4C2×D4×D79112yes—
813C2×C4C24×D7912yes—
814C2×C4C24×D7916yes—
815C2×C4C24×D7912yes—
816C2×C4C24×D7912yes—
817C2×C4C24×D7916yes—
818C22—26no—
819C22—26no—
820C22—26no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—412no—
826C22—31648no—
827C22—31612no—
828C22—7912no—
829C22—794no—
830C22—63248no—
831C22—1586no—
832C22—1586no—
833C22—1586no—
834C22—1588no—
835C22—15824no—
836C22—1582no—
837C22—1586no—
838C22—1582no—
839C22—1586no—
840C22C22×D4×D7912yes—
841C22H(5,𝔽2)×D7912yes—
842C22#1909939912yes—
843C22C25×D7911yescharacteristic
844C4—22no—
845C4—22no—
846C4—26no—
847C4—22no—
848C4—794no—
849C4—1582no—
850C4—1586no—
851C4—1586no—
852C4—1582no—
853C4C22×D4×D79112yes—
854C2—46no—
855C2—46no—
856C2—3166no—
857C2—1584no—
858C2—15812no—
859C2#2377706814yesdirect product factor
860C2C23×D4×D7911yescharacteristic
861C2C2×H(5,𝔽2)×D7911yescharacteristic
862C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#550×C79C2
socleC23×C79C25
hypercenterC2×#550D79
hypocenterC79C2×#3488
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#14579207C2semidirect
2. C22×#41×D79C2semidirect
3. #23777068C2direct (N × H)
4. C2×#19099232C2semidirect
5. C2×#19099225C2semidirect
6. C2×#19099220C2semidirect
7. C2×#19099210C2semidirect
8. C2×#19099209C2semidirect
9. C2×#19099198C2semidirect
10. C2×#19099197C2semidirect
11. C2×#19099142C2semidirect
12. C2×#19099126C2semidirect
13. C2×#19099072C2semidirect
14. C2×#121×D79C2semidirect
15. C2×#19099045C2semidirect
16. C2×#550×C79C2semidirect
18. C2×#14579207C22semidirect
20. C22×#11929625C22semidirect
21. C22×#11929624C22semidirect
22. C22×#11929624C22semidirect
23. C22×#11929623C22semidirect
25. C2×#41×D79C22semidirect
26. C22×Q8×D79C22semidirect
27. C23×D316C22semidirect
28. C22×D4×D79C22semidirect
29. C22×D4×D79C22semidirect
30. C22×D4×D79C22semidirect
31. C22×D4×D79C22semidirect
32. C23×C4×D79C22semidirect
33. #19099232C22semidirect
34. #19099225C22semidirect
35. #19099220C22semidirect
36. #19099210C22semidirect
37. #19099209C22semidirect
38. #19099198C22semidirect
39. #19099197C22semidirect
40. #19099142C22semidirect
41. #19099126C22semidirect
42. C2×#14579157C22semidirect
43. C2×#14579149C22semidirect
44. C2×#14579148C22semidirect
45. #19099072C22semidirect
46. C2×#14579146C22semidirect
47. C2×#14579143C22semidirect
48. C2×#14579141C22semidirect
49. C2×#14579140C22semidirect
50. C2×#14579139C22semidirect
51. C2×#14579138C22semidirect
52. C2×#14579136C22semidirect
53. C2×#14579135C22semidirect
54. C2×#14579134C22semidirect
55. C2×#14579134C22semidirect
56. C2×#14579133C22semidirect
57. C2×#14579133C22semidirect
58. C2×#14579132C22semidirect
59. C2×#14579132C22semidirect
60. C2×#14579132C22semidirect
61. #121×D79C22semidirect
62. C2×#14579131C22semidirect
63. C2×#14579129C22semidirect
64. C2×#14579129C22semidirect
65. C2×#14579129C22semidirect
66. #19099045C22semidirect
67. C2×Q8×Dic79C22semidirect
68. C2×C4×D316C22semidirect
69. C2×C4×D316C22semidirect
70. C2×#14579123C22semidirect
71. C2×C4×C22⋊D79C22semidirect
72. C2×C4×C22⋊D79C22semidirect
73. C2×#14579118C22semidirect
74. C2×C4⋊C4×D79C22semidirect
75. C2×C22⋊C4×D79C22semidirect
76. C22×#41×C79C22semidirect
77. C22×#41×C79C22semidirect
78. #550×C79C22semidirect
79. C2×#127×C79C22semidirect
80. C2×#121×C79C22semidirect
81. C2×#121×C79C22semidirect
82. C2×C4×Q8×C79C22semidirect
83. C2×C4×D4×C79C22semidirect
88. C2×#11929625D4semidirect
90. C2×#11929625C23semidirect
93. C2×#11929624C23semidirect
94. C2×#11929624C23semidirect
96. C2×#11929623C23semidirect
101. C2×Q8×D79C23semidirect
107. C22×D316C23semidirect
118. C2×D4×D79C23semidirect
119. C2×D4×D79C23semidirect
120. C2×D4×D79C23semidirect
121. C2×D4×D79C23semidirect
130. C22×C4×D79C23semidirect
131. #14579157C23semidirect
132. #14579149C23semidirect
133. #14579148C23semidirect
134. #14579146C23semidirect
135. #14579143C23semidirect
136. #14579141C23semidirect
137. #14579140C23semidirect
138. #14579139C23semidirect
139. #14579138C23semidirect
140. #14579136C23semidirect
141. #14579135C23semidirect
142. #14579134C23semidirect
143. #14579134C23semidirect
144. #14579133C23semidirect
145. #14579133C23semidirect
146. #14579132C23semidirect
147. #14579132C23semidirect
148. #14579132C23semidirect
149. #14579131C23semidirect
150. #14579129C23semidirect
151. #14579129C23semidirect
152. #14579129C23semidirect
153. Q8×Dic79C23semidirect
154. C4×D316C23semidirect
155. C4×D316C23semidirect
156. #14579123C23semidirect
157. C4×C22⋊D79C23semidirect
158. C4×C22⋊D79C23semidirect
159. #14579118C23semidirect
166. C4⋊C4×D79C23semidirect
177. C22⋊C4×D79C23semidirect
181. C2×#41×C79C23semidirect
182. C2×#41×C79C23semidirect
190. #127×C79C23semidirect
191. #121×C79C23semidirect
192. #121×C79C23semidirect
193. C4×Q8×C79C23semidirect
194. C4×D4×C79C23semidirect
212. #11929625C2×D4semidirect
225. C2×D316C2×D4semidirect
259. C2×C4×D79C2×D4semidirect
287. C2×Q8×C79C2×D4semidirect
336. C22×D79H(5,𝔽2)semidirect
340. Q8×C79C22×D4semidirect
377. D316C22×D4semidirect
383. C4×D79C22×D4semidirect
411. C2×D79C2×H(5,𝔽2)semidirect
425. C2×C79#3488semidirect
436. C2×#550D79semidirect
448. C79C2×#3488semidirect
458. C22×#41C2×D79semidirect
459. C22×#41C2×D79semidirect
468. #550C2×D79semidirect
478. C2×#127C2×D79semidirect
498. C2×#121C2×D79semidirect
499. C2×#121C2×D79semidirect
506. C2×C4×Q8C2×D79semidirect
512. C2×C4×D4C2×D79semidirect
532. C2×#41C22×D79semidirect
533. C2×#41C22×D79semidirect
575. #127C22×D79semidirect
593. #121C22×D79semidirect
594. #121C22×D79semidirect
600. C4×Q8C22×D79semidirect
606. C4×D4C22×D79semidirect
657. C2×Q8D4×D79semidirect
774. Q8C2×D4×D79semidirect
859. C2#23777068direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792072
C22×#41×D792
#237770682
C2×#190992322
C2×#190992252
C2×#190992202
C2×#190992102
C2×#190992092
C2×#190991982
C2×#190991972
C2×#190991422
C2×#190991262
C2×#190990722
C2×#121×D792
C2×#190990452
C2×#550×C792
C2×#348879