Finite Group Databasebeta

← C2×#23775619 #35165085

Subgroups — C2×#23775619 #35165085

Order 20224.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099248C211yesmaximal, characteristic, complemented
2C2×#19099210C211yesmaximal, characteristic
3#23775619C2116yesmaximal, direct product factor
4C2×#19098916C211yesmaximal, characteristic, complemented
5C2×#19098907C211yesmaximal, characteristic, complemented
6C2×#19098862C211yesmaximal, characteristic, complemented
7C2×#19098822C211yesmaximal, characteristic, complemented
8C2×#19098807C211yesmaximal, characteristic, complemented
9C2×#19098784C211yesmaximal, characteristic, complemented
10C2×#19098727C211yesmaximal, characteristic, complemented
11C2×#19098715C211yesmaximal, characteristic, complemented
12C2×#19098650C211yesmaximal, characteristic, complemented
13C2×#19098638C211yesmaximal, characteristic, complemented
14C2×#19098562C211yesmaximal, characteristic, complemented
15C2×#19098566C211yesmaximal, characteristic, complemented
16C2×#481×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×D4×D79C2211yescharacteristic
19C22×Dic316C2211yescharacteristic, complemented
20C22×#11929613C2211yescharacteristic
21C22×#11929612C2211yescharacteristic
22C22×#11929608C2211yescharacteristic, complemented
23C22×#11929607C2211yescharacteristic
24#19099248—24no—
25#19099248C2218yescomplemented
26#19099210—24no—
27#19099210C2218yes—
28C2×#14579156—21no—
29C2×#14579152C2211yescharacteristic, complemented
30C2×#14579151—21no—
31C2×#14579148C2211yescharacteristic
32C2×#14579144—21no—
33C2×#14579143—21no—
34C2×#14579141C2211yescharacteristic
35C2×#14579141C2211yescharacteristic
36C2×#14579140C2211yescharacteristic, complemented
37C2×#14579132—21no—
38C2×#14579129—21no—
39C2×#14579126C2211yescharacteristic, complemented
40C2×#14579123C2211yescharacteristic
41C2×C4×C22⋊D79C2211yescharacteristic
42C2×#14579120—21no—
43C2×#14579119C2211yescharacteristic
44C2×C22⋊C4×D79—21no—
45#19098916C2218yescomplemented
46#19098907C2218yescomplemented
47#19098862C2218yescomplemented
48#19098822C2218yescomplemented
49#19098807C2218yescomplemented
50#19098784C2218yescomplemented
51#19098727C2218yescomplemented
52#19098715C2218yescomplemented
53#19098650C2218yescomplemented
54#19098638C2218yescomplemented
55C2×#14579094C2211yescharacteristic, complemented
56C2×Dic79⋊C8C2211yescharacteristic, complemented
57#19098566C2218yescomplemented
58#19098562C2218yescomplemented
59C2×#14579086C2211yescharacteristic, complemented
60C2×#14579084C2211yescharacteristic, complemented
61C2×#14579084C2211yescharacteristic, complemented
62C2×#14579084C2211yescharacteristic, complemented
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic, complemented
69C2×#121×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic, complemented
71#481×C79C2218yescomplemented
72C2×#106×C79C2211yescharacteristic, complemented
73C2×#106×C79C2211yescharacteristic, complemented
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic, complemented
77C24×D79—21no—
78C2×#11929624—22no—
79C2×#11929624—24no—
80C2×#11929624—42no—
81C2×#11929624C2314yes—
82C22×Dic158C2311yescharacteristic
83C22×Dic158C2311yescharacteristic
84C22×D316C2311yescharacteristic
85C22×C22⋊D79—21no—
86C22×C22⋊D79—21no—
87C22×C22⋊D79D411yescharacteristic
88C2×D4×D79—24no—
89C2×D4×D79—22no—
90C2×D4×D79—42no—
91C2×D4×D79C2314yes—
92C22×C4×D79—21no—
93C22×C4×D79—21no—
94C22×C4×D79C2311yescharacteristic
95C2×Dic316—42no—
96C2×Dic316C2314yescomplemented
97C2×#11929613—24no—
98C2×#11929613C2314yes—
99C2×#11929612—42no—
100C2×#11929612C2314yes—
101C2×#11929608—42no—
102C2×#11929608C2314yescomplemented
103C2×#11929607—42no—
104C2×#11929607C2314yes—
105C22×C79⋊C8C2311yescharacteristic
106C22×C79⋊C8C2311yescharacteristic
107#14579156—28no—
108#14579152—22no—
109#14579152C2314yescomplemented
110#14579151—28no—
111#14579148—22no—
112#14579148C2314yes—
113#14579144—28no—
114#14579143—28no—
115#14579141—22no—
116#14579141—22no—
117#14579141C2314yes—
118#14579141C2314yes—
119#14579140—22no—
120#14579140C2314yescomplemented
121#14579132—28no—
122#14579129—28no—
123#14579126—22no—
124#14579126C2314yescomplemented
125#14579123—22no—
126#14579123C2314yes—
127C4×C22⋊D79D414yes—
128C4×C22⋊D79C2314yes—
129#14579120—28no—
130#14579119—22no—
131#14579119C2314yes—
132C2×C4⋊Dic79—21no—
133C2×C4⋊Dic79—21no—
134C2×C4⋊Dic79—21no—
135C2×C4⋊Dic79C2311yescharacteristic
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4D411yescharacteristic
140C2×C22⋊Dic79—21no—
141C2×C22⋊Dic79—21no—
142C2×C22⋊Dic79—21no—
143C2×C22⋊Dic79D411yescharacteristic
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4—21no—
148C2×(C2×D79)⋊C4D411yescharacteristic
149C22⋊C4×D79—28no—
150C2×C4×Dic79—21no—
151C2×C4×Dic79—21no—
152C2×C4×Dic79C2311yescharacteristic
153#14579094C2314yescomplemented
154Dic79⋊C8C2314yescomplemented
155#14579086C2314yescomplemented
156#14579084C2314yescomplemented
157#14579084C2314yescomplemented
158#14579084C2314yescomplemented
159#14579083C2314yes—
160#14579082C2314yes—
161#14579081C2314yes—
162#14579081C2314yes—
163(C2×D79)⋊C8C2314yes—
164C8×Dic79C2314yescomplemented
165C22×D4×C79—21no—
166C22×D4×C79C2311yescharacteristic
167C23×C4×C79—21no—
168C23×C4×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C22×C8×C79C2311yescharacteristic
171#121×C79—22no—
172#121×C79C2314yes—
173C2×C4⋊C4×C79—22no—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C4⋊C4×C79C2314yescomplemented
179C2×C22⋊C4×C79—21no—
180#106×C79C2314yescomplemented
181#106×C79C2314yescomplemented
182#102×C79C2314yes—
183#102×C79C2314yes—
184C22⋊C8×C79C2314yescomplemented
185C23×D79—21no—
186C23×D79—24no—
187C23×D79—44no—
188C23×D79—44no—
189C23×D79—82no—
190C23×D79C2×D411yescharacteristic
191#11929624—28no—
192#11929624—44no—
193#11929624—48no—
194C2×Dic158—21no—
195C2×Dic158—21no—
196C2×Dic158—22no—
197C2×Dic158—22no—
198C2×Dic158—22no—
199C2×Dic158—22no—
200C2×Dic158C2412yes—
201C2×Dic158C2412yes—
202C2×D316—21no—
203C2×D316—22no—
204C2×D316#4114yes—
205C2×D316C2412yes—
206C2×C22⋊D79—24no—
207C2×C22⋊D79—24no—
208C2×C22⋊D79—42no—
209C2×C22⋊D79—44no—
210C2×C22⋊D79—44no—
211C2×C22⋊D79C2×D414yes—
212D4×D79—28no—
213D4×D79—44no—
214D4×D79—48no—
215C22×Dic79—21no—
216C22×Dic79—21no—
217C22×Dic79—21no—
218C22×Dic79C2×D411yescharacteristic
219C22×Dic79C2×D411yescharacteristic
220C22×Dic79C2×D411yescharacteristic
221C2×C4×D79—24no—
222C2×C4×D79—24no—
223C2×C4×D79—22no—
224C2×C4×D79—22no—
225C2×C4×D79—44no—
226C2×C4×D79—82no—
227C2×C4×D79C2×D412yes—
228C2×C4×D79C2412yes—
229Dic316—44no—
230#11929613—28no—
231#11929612—44no—
232#11929608—44no—
233#11929607—44no—
234C2×C79⋊C8—22no—
235C2×C79⋊C8—22no—
236C2×C79⋊C8C2412yes—
237C2×C79⋊C8C2412yes—
238C4⋊Dic79—24no—
239C4⋊Dic79—24no—
240C4⋊Dic79—24no—
241C4⋊Dic79—21no—
242C4⋊Dic79C2412yes—
243Dic79⋊C4—24no—
244Dic79⋊C4—24no—
245Dic79⋊C4—24no—
246Dic79⋊C4C2×D414yes—
247C22⋊Dic79—24no—
248C22⋊Dic79—24no—
249C22⋊Dic79—24no—
250C22⋊Dic79C2×D414yes—
251(C2×D79)⋊C4—24no—
252(C2×D79)⋊C4—24no—
253(C2×D79)⋊C4—24no—
254(C2×D79)⋊C4—24no—
255(C2×D79)⋊C4C2×D414yes—
256C4×Dic79—24no—
257C4×Dic79—24no—
258C4×Dic79C2×D412yes—
259C4×Dic79C2412yes—
260C24×C79—21no—
261C24×C79C2×D411yescharacteristic
262C2×D4×C79—24no—
263C2×D4×C79—21no—
264C2×D4×C79—22no—
265C2×D4×C79—22no—
266C2×D4×C79—82no—
267C2×D4×C79C2412yes—
268C22×C4×C79—22no—
269C22×C4×C79—22no—
270C22×C4×C79—21no—
271C22×C4×C79—21no—
272C22×C4×C79—21no—
273C22×C4×C79—24no—
274C22×C4×C79—44no—
275C22×C4×C79C2×D412yes—
276C22×C4×C79C2×D411yescharacteristic
277C22×C4×C79C2412yes—
278C22×C4×C79C2411yescharacteristic
279C2×C8×C79—22no—
280C2×C8×C79—22no—
281C2×C8×C79C2412yes—
282C2×C8×C79C2412yes—
283C4⋊C4×C79—21no—
284C4⋊C4×C79—21no—
285C4⋊C4×C79—24no—
286C4⋊C4×C79—21no—
287C4⋊C4×C79C2412yes—
288C4⋊C4×C79C2412yes—
289C4⋊C4×C79C2412yes—
290C22⋊C4×C79—24no—
291C23×C79—22no—
292C23×C79—22no—
293C23×C79—22no—
294C23×C79—22no—
295C23×C79—42no—
296C23×C79—42no—
297C23×C79—42no—
298C23×C79C22×D412yes—
299C23×C79C22×D411yescharacteristic
300C22×D79—22no—
301C22×D79—24no—
302C22×D79—22no—
303C22×D79—22no—
304C22×D79—22no—
305C22×D79—48no—
306C22×D79—48no—
307C22×D79—42no—
308C22×D79—42no—
309C22×D79—84no—
310C22×D79—816no—
311C22×D79C22×D412yes—
312D4×C79—22no—
313D4×C79—22no—
314D4×C79—42no—
315D4×C79—84no—
316C2×C4×C79—22no—
317C2×C4×C79—24no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—48no—
324C2×C4×C79—42no—
325C2×C4×C79—42no—
326C2×C4×C79—42no—
327C2×C4×C79C22×D412yes—
328C2×C4×C79C22×D411yescharacteristic
329C2×C4×C79C2×#4112yes—
330C2×C4×C79H(5,𝔽2)12yes—
331C2×C4×C79C2511yescharacteristic
332C22⋊D79—44no—
333C22⋊D79—48no—
334C22⋊D79—48no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—22no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—42no—
342C2×Dic79—42no—
343C2×Dic79—42no—
344C2×Dic79C22×D412yes—
345C2×Dic79C22×D412yes—
346C2×Dic79C22×D412yes—
347D316—24no—
348D316—22no—
349D316C2×#4114yes—
350C4×D79—24no—
351C4×D79—22no—
352C4×D79—22no—
353C4×D79—48no—
354C4×D79—84no—
355Dic158—22no—
356Dic158—22no—
357Dic158—22no—
358Dic158—22no—
359Dic158—42no—
360Dic158—42no—
361C8×C79—22no—
362C8×C79—22no—
363C79⋊C8—22no—
364C79⋊C8—22no—
365C22×C79—22no—
366C22×C79—22no—
367C22×C79—22no—
368C22×C79—44no—
369C22×C79—42no—
370C22×C79—42no—
371C22×C79—42no—
372C22×C79—84no—
373C22×C79#54612yes—
374C22×C79#57512yes—
375C22×C79#57712yes—
376C22×C79C23×D411yescharacteristic
377C2×D79—24no—
378C2×D79—22no—
379C2×D79—22no—
380C2×D79—22no—
381C2×D79—44no—
382C2×D79—48no—
383C2×D79—42no—
384C2×D79—42no—
385C2×D79—816no—
386C4×C79—22no—
387C4×C79—42no—
388C4×C79—42no—
389C4×C79—42no—
390C4×C79#54612yes—
391C4×C79C22×#4111yescharacteristic
392C4×C79C2×H(5,𝔽2)11yescharacteristic
393Dic79—22no—
394Dic79—22no—
395Dic79—22no—
396Dic79—42no—
397Dic79—42no—
398Dic79—42no—
399C2×#3323—791nomaximal, Sylow
400C2×C79—42no—
401C2×C79—82no—
402C2×C79#332314yescomplemented
403C2×C79C2×#54611yescharacteristic
404C2×C79C2×#57511yescharacteristic
405C2×C79C2×#57711yescharacteristic
406D79—42no—
407D79—44no—
408C2×#552—791no—
409C2×#546—791no—
410#3323—7916no—
411C2×#488—791no—
412C2×#481D7911yescharacteristic, complemented
413C2×#485—791no—
414C2×#478—791no—
415C2×#470—791no—
416C2×#468—791no—
417C2×#464—791no—
418C2×#452—791no—
419C2×#450—791no—
420C2×C4×SD16—791no—
421C2×#436—791no—
422C2×#417—791no—
423C2×#418—791no—
424C79C2×#332311yescharacteristic, complemented, Sylow
425C22×#41—791no—
426C23×D4—791no—
427C22×Q16—791no—
428C22×SD16—791no—
429C22×SD16—791no—
430C22×M16—791no—
431C22×M16—791no—
432#552—798no—
433#552—1584no—
434#546—798no—
435#546—1584no—
436C2×#126—1581no—
437C2×#125—791no—
438C2×#125—1581no—
439C2×#124—791no—
440C2×#123—1581no—
441C2×#123—1581no—
442C2×C22⋊Q8—791no—
443C2×C22⋊Q8—791no—
444C2×C22⋊Q8—791no—
445C2×#121—1581no—
446C2×#121C2×D7911yescharacteristic
447C2×#120—1581no—
448C2×C4×Q8—791no—
449C2×C4×D4—791no—
450C2×C4×D4—791no—
451C2×#117—791no—
452C2×#117—1581no—
453C22×C4⋊C4C2×D7911yescharacteristic, complemented
454C22×C22⋊C4—1581no—
455#488—798no—
456#485—798no—
457#481C2×D7918yescomplemented
458#478—798no—
459#470—798no—
460#468—798no—
461#464—798no—
462#452—798no—
463#450—798no—
464C4×SD16—798no—
465#436—798no—
466C2×#107—791no—
467C2×#106C2×D7911yescharacteristic, complemented
468C2×#106C2×D7911yescharacteristic, complemented
469C2×C4⋊C8—791no—
470#418—798no—
471#417—798no—
472C2×#103—791no—
473C2×#103—791no—
474C2×#103—791no—
475C2×#103—791no—
476C2×#102—791no—
477C2×#102—791no—
478C2×#102—791no—
479C2×#102—791no—
480C2×#102C2×D7911yescharacteristic
481C2×#102C2×D7911yescharacteristic
482C2×C22⋊C8—791no—
483C2×C22⋊C8C2×D7911yescharacteristic, complemented
484C2×C4×C8—791no—
485C25—1581no—
486C2×#41—3162no—
487C2×#41—794no—
488C2×#41—1584no—
489C2×#41—1582no—
490C22×Q8—791no—
491C22×Q8—791no—
492C22×D4—21no—
493C22×D4—3162no—
494C22×D4—791no—
495C22×D4—794no—
496C22×D4—791no—
497C22×D4—1582no—
498C22×D4—1581no—
499C22×D4—1584no—
500C22×D4—1581no—
501C22×D4C22×D7911yescharacteristic
502C23×C4—21no—
503C23×C4—791no—
504C23×C4—1581no—
505C23×C4—1581no—
506C23×C4C22×D7911yescharacteristic
507C2×Q16—3162no—
508C2×Q16—794no—
509C2×SD16—3162no—
510C2×SD16—794no—
511C2×SD16—794no—
512C2×SD16—1584no—
513C2×M16—3162no—
514C2×M16—3162no—
515C2×M16—794no—
516C2×M16—794no—
517C22×C8—791no—
518C22×C8—791no—
519C22×C8C22×D7911yescharacteristic
520C22×C8C22×D7911yescharacteristic
521#126—1588no—
522#125—794no—
523#125—1582no—
524#125—1588no—
525#124—794no—
526#124—1582no—
527#123—1588no—
528#123—1588no—
529C22⋊Q8—794no—
530C22⋊Q8—794no—
531C22⋊Q8—794no—
532C22⋊Q8—1582no—
533C22⋊Q8—1582no—
534C22⋊Q8—1582no—
535#121—22no—
536#121—1588no—
537#121C22×D7914yes—
538#120—1588no—
539C4×Q8—794no—
540C4×Q8—1582no—
541C4×D4—794no—
542C4×D4—794no—
543C4×D4—794no—
544C4×D4—1582no—
545#117—794no—
546#117—1588no—
547#117—1582no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—791no—
551C2×C4⋊C4—791no—
552C2×C4⋊C4—1581no—
553C2×C4⋊C4—1581no—
554C2×C4⋊C4—1581no—
555C2×C4⋊C4—1581no—
556C2×C4⋊C4—1581no—
557C2×C4⋊C4—1581no—
558C2×C4⋊C4C22×D7911yescharacteristic
559C2×C4⋊C4C22×D7911yescharacteristic
560C2×C4⋊C4C22×D7911yescharacteristic
561C2×C4⋊C4C22×D7914yescomplemented
562C2×C22⋊C4—21no—
563C2×C22⋊C4—791no—
564C2×C22⋊C4—791no—
565C2×C22⋊C4—1588no—
566C2×C22⋊C4—1581no—
567C2×C22⋊C4—1581no—
568C2×C22⋊C4—1581no—
569C2×C22⋊C4—1581no—
570C2×C22⋊C4—1581no—
571C2×C22⋊C4—1581no—
572C2×C22⋊C4—1581no—
573C2×C42—791no—
574C2×C42—1581no—
575C2×C42—1581no—
576#107—794no—
577#106C22×D7914yescomplemented
578#106C22×D7914yescomplemented
579C4⋊C8—794no—
580#103—794no—
581#103—794no—
582#103—794no—
583#103—794no—
584#102—794no—
585#102—794no—
586#102—794no—
587#102—794no—
588#102C22×D7914yes—
589#102C22×D7914yes—
590C22⋊C8—794no—
591C22⋊C8C22×D7914yescomplemented
592C4×C8—794no—
593C24—21no—
594C24—3164no—
595C24—3164no—
596C24—791no—
597C24—6322no—
598C24—1584no—
599C24—1581no—
600C24D4×D7911yescharacteristic
601#41—3168no—
602#41—3164no—
603#41—1588no—
604C2×Q8—792no—
605C2×Q8—792no—
606C2×Q8—1582no—
607C2×Q8—1582no—
608C2×Q8—1582no—
609C2×Q8—1582no—
610C2×Q8—1581no—
611C2×Q8—1581no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—82no—
617C2×D4—3164no—
618C2×D4—3164no—
619C2×D4—3168no—
620C2×D4—3162no—
621C2×D4—3164no—
622C2×D4—794no—
623C2×D4—794no—
624C2×D4—792no—
625C2×D4—1584no—
626C2×D4—1588no—
627C2×D4—1584no—
628C2×D4—1582no—
629C2×D4—1581no—
630C2×D4C23×D7912yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—44no—
638C22×C4—3164no—
639C22×C4—791no—
640C22×C4—791no—
641C22×C4—791no—
642C22×C4—792no—
643C22×C4—792no—
644C22×C4—6322no—
645C22×C4—1584no—
646C22×C4—1581no—
647C22×C4—1581no—
648C22×C4—1581no—
649C22×C4—1584no—
650C22×C4—1582no—
651C22×C4—1582no—
652C22×C4D4×D7912yes—
653C22×C4D4×D7911yescharacteristic
654C22×C4C23×D7912yes—
655C22×C4C23×D7911yescharacteristic
656Q16—3164no—
657SD16—3164no—
658SD16—1588no—
659M16—3164no—
660M16—3164no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—792no—
664C2×C8—792no—
665C2×C8—1582no—
666C2×C8—1582no—
667C2×C8C23×D7912yes—
668C2×C8C23×D7912yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—794no—
674C4⋊C4—792no—
675C4⋊C4—1584no—
676C4⋊C4—1584no—
677C4⋊C4—1584no—
678C4⋊C4—1584no—
679C4⋊C4—1584no—
680C4⋊C4—1584no—
681C4⋊C4—1581no—
682C4⋊C4C23×D7912yes—
683C4⋊C4C23×D7912yes—
684C4⋊C4C23×D7912yes—
685C22⋊C4—24no—
686C22⋊C4—794no—
687C22⋊C4—794no—
688C22⋊C4—1584no—
689C22⋊C4—1584no—
690C22⋊C4—1584no—
691C22⋊C4—1584no—
692C22⋊C4—1584no—
693C22⋊C4—1584no—
694C22⋊C4—1584no—
695C42—792no—
696C42—792no—
697C42—1584no—
698C42—1584no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—3168no—
707C23—3168no—
708C23—3162no—
709C23—3162no—
710C23—792no—
711C23—6324no—
712C23—63216no—
713C23—1584no—
714C23—1582no—
715C23—1582no—
716C23—1582no—
717C23—1582no—
718C23C2×D4×D7912yes—
719C23C2×D4×D7911yescharacteristic
720Q8—3162no—
721Q8—3162no—
722Q8—1582no—
723Q8—1582no—
724Q8—1582no—
725Q8—1582no—
726D4—22no—
727D4—22no—
728D4—42no—
729D4—84no—
730D4—3168no—
731D4—3164no—
732D4—3168no—
733D4—794no—
734D4—1582no—
735D4—1584no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—3168no—
748C2×C4—3162no—
749C2×C4—3162no—
750C2×C4—3162no—
751C2×C4—792no—
752C2×C4—792no—
753C2×C4—792no—
754C2×C4—6324no—
755C2×C4—1582no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1582no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4—1584no—
763C2×C4—1582no—
764C2×C4C2×D4×D7912yes—
765C2×C4C2×D4×D7911yescharacteristic
766C2×C4#41×D7912yes—
767C2×C4#1457920712yes—
768C2×C4C24×D7911yescharacteristic
769C8—22no—
770C8—22no—
771C8—1582no—
772C8—1582no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—3162no—
782C22—3162no—
783C22—3168no—
784C22—3164no—
785C22—63216no—
786C22—1584no—
787C22—1582no—
788C22—1582no—
789C22—1582no—
790C22#1909920512yes—
791C22#1909935912yes—
792C22#1909936912yes—
793C22C22×D4×D7911yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—3162no—
799C4—3162no—
800C4—3162no—
801C4—1582no—
802C4—1582no—
803C4—1582no—
804C4#1909920512yes—
805C4C2×#41×D7911yescharacteristic
806C4C2×#1457920711yescharacteristic
807C2—42no—
808C2—82no—
809C2—3164no—
810C2—3162no—
811C2#2377561914yesdirect product factor
812C2C2×#1909920511yescharacteristic
813C2C2×#1909935911yescharacteristic
814C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#481×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099210C2
hypercenterC2×#481D79
hypocenterC79C2×#3323
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#19099248C2semidirect
3. #23775619C2direct (N × H)
4. C2×#19098916C2semidirect
5. C2×#19098907C2semidirect
6. C2×#19098862C2semidirect
7. C2×#19098822C2semidirect
8. C2×#19098807C2semidirect
9. C2×#19098784C2semidirect
10. C2×#19098727C2semidirect
11. C2×#19098715C2semidirect
12. C2×#19098650C2semidirect
13. C2×#19098638C2semidirect
14. C2×#19098562C2semidirect
15. C2×#19098566C2semidirect
16. C2×#481×C79C2semidirect
19. C22×Dic316C22semidirect
22. C22×#11929608C22semidirect
25. #19099248C22semidirect
29. C2×#14579152C22semidirect
36. C2×#14579140C22semidirect
39. C2×#14579126C22semidirect
45. #19098916C22semidirect
46. #19098907C22semidirect
47. #19098862C22semidirect
48. #19098822C22semidirect
49. #19098807C22semidirect
50. #19098784C22semidirect
51. #19098727C22semidirect
52. #19098715C22semidirect
53. #19098650C22semidirect
54. #19098638C22semidirect
55. C2×#14579094C22semidirect
56. C2×Dic79⋊C8C22semidirect
57. #19098566C22semidirect
58. #19098562C22semidirect
59. C2×#14579086C22semidirect
60. C2×#14579084C22semidirect
61. C2×#14579084C22semidirect
62. C2×#14579084C22semidirect
68. C2×C8×Dic79C22semidirect
70. C22×C4⋊C4×C79C22semidirect
71. #481×C79C22semidirect
72. C2×#106×C79C22semidirect
73. C2×#106×C79C22semidirect
76. C2×C22⋊C8×C79C22semidirect
96. C2×Dic316C23semidirect
102. C2×#11929608C23semidirect
109. #14579152C23semidirect
120. #14579140C23semidirect
124. #14579126C23semidirect
153. #14579094C23semidirect
154. Dic79⋊C8C23semidirect
155. #14579086C23semidirect
156. #14579084C23semidirect
157. #14579084C23semidirect
158. #14579084C23semidirect
164. C8×Dic79C23semidirect
178. C2×C4⋊C4×C79C23semidirect
180. #106×C79C23semidirect
181. #106×C79C23semidirect
184. C22⋊C8×C79C23semidirect
402. C2×C79#3323semidirect
412. C2×#481D79semidirect
424. C79C2×#3323semidirect
453. C22×C4⋊C4C2×D79semidirect
457. #481C2×D79semidirect
467. C2×#106C2×D79semidirect
468. C2×#106C2×D79semidirect
483. C2×C22⋊C8C2×D79semidirect
561. C2×C4⋊C4C22×D79semidirect
577. #106C22×D79semidirect
578. #106C22×D79semidirect
591. C22⋊C8C22×D79semidirect
811. C2#23775619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992482
C2×#190992102
#237756192
C2×#190989162
C2×#190989072
C2×#190988622
C2×#190988222
C2×#190988072
C2×#190987842
C2×#190987272
C2×#190987152
C2×#190986502
C2×#190986382
C2×#190985622
C2×#190985662
C2×#481×C792
C2×#332379