Finite Group Databasebeta

← C2×#23775920 #35166885

Subgroups — C2×#23775920 #35166885

Order 20224.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099278C211yesmaximal, characteristic
2C2×#19099254C211yesmaximal, characteristic, complemented
3#23775920C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098880C211yesmaximal, characteristic, complemented
6C2×#19098903C211yesmaximal, characteristic, complemented
7C2×#19098902C211yesmaximal, characteristic, complemented
8C2×#19098885C211yesmaximal, characteristic, complemented
9C2×#19098848C211yesmaximal, characteristic, complemented
10C2×#19098863C211yesmaximal, characteristic, complemented
11C2×#19098806C211yesmaximal, characteristic, complemented
12C2×#19098789C211yesmaximal, characteristic, complemented
13C2×#19098636C211yesmaximal, characteristic, complemented
14C2×#19098604C211yesmaximal, characteristic, complemented
15C2×#19098600C211yesmaximal, characteristic, complemented
16C2×#440×C79C211yesmaximal, characteristic, complemented
17C22×#11929607C2211yescharacteristic
18C22×C8×D79C2211yescharacteristic
19#19099278—24no—
20#19099278C2218yes—
21#19099254—24no—
22#19099254C2218yescomplemented
23C2×#14579161C2211yescharacteristic
24C2×#14579155—21no—
25C2×#14579153C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579147—21no—
28C2×#14579147—21no—
29C2×#14579146—21no—
30C2×#14579137C2211yescharacteristic
31C2×#14579137C2211yescharacteristic
32C2×#14579135—21no—
33C2×#14579132C2211yescharacteristic
34C2×#14579132C2211yescharacteristic
35C2×C4×D316C2211yescharacteristic
36C2×#14579120—21no—
37C2×#14579119C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C2×#14579119C2211yescharacteristic
40C2×#14579118—21no—
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098972C2218yescomplemented
43#19098903C2218yescomplemented
44#19098902C2218yescomplemented
45#19098885C2218yescomplemented
46#19098880C2218yescomplemented
47#19098863C2218yescomplemented
48#19098848C2218yescomplemented
49#19098806C2218yescomplemented
50#19098789C2218yescomplemented
51#19098636C2218yescomplemented
52#19098604C2218yescomplemented
53#19098600C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579095C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×#14579092C2211yescharacteristic
62C2×C4⋊(C79⋊C8)C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579082C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#440×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×D316D411yescharacteristic
79C22×C22⋊D79—21no—
80C22×C22⋊D79—21no—
81C22×C4×D79—21no—
82C22×C4×D79C2311yescharacteristic
83C22×C4×D79C2311yescharacteristic
84C2×#11929607—24no—
85C2×#11929607C2314yes—
86C22×C79⋊C8C2311yescharacteristic
87C22×C79⋊C8C2311yescharacteristic
88C2×C8×D79—24no—
89C2×C8×D79C2314yes—
90#14579161—22no—
91#14579161C2314yes—
92#14579155—28no—
93#14579153—22no—
94#14579153C2314yes—
95#14579151—28no—
96#14579147—28no—
97#14579147—28no—
98#14579146—28no—
99#14579137—22no—
100#14579137—22no—
101#14579137C2314yes—
102#14579137C2314yes—
103#14579135—28no—
104#14579132—22no—
105#14579132—22no—
106#14579132C2314yes—
107#14579132C2314yes—
108C4×D316D414yes—
109C4×D316C2314yes—
110#14579120—28no—
111#14579119—22no—
112#14579119—22no—
113#14579119—22no—
114#14579119C2314yes—
115#14579119C2314yes—
116#14579119C2314yes—
117#14579118—28no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79D411yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C4⋊C4×D79—22no—
130C4⋊C4×D79C2314yes—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4D411yescharacteristic
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143#14579095C2314yes—
144#14579095C2314yes—
145#14579094C2314yes—
146#14579093C2314yes—
147#14579093C2314yes—
148#14579092C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151C4⋊(C79⋊C8)C2314yes—
152#14579085C2314yes—
153#14579085C2314yes—
154#14579082C2314yes—
155#14579082C2314yes—
156(C2×D79)⋊C8C2314yes—
157(C2×D79)⋊C8C2314yes—
158C22×Q8×C79C2311yescharacteristic
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C2×SD16×C79—24no—
162C2×SD16×C79C2314yes—
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C4×Q8×C79—22no—
166C4×Q8×C79C2314yes—
167C4×D4×C79—22no—
168C4×D4×C79C2314yes—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#107×C79C2314yes—
176#103×C79C2314yes—
177#102×C79C2314yes—
178#97×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C23×D79C2×D411yescharacteristic
181C2×Dic158—24no—
182C2×Dic158—82no—
183C2×D316—42no—
184C2×D316C2×D414yes—
185C2×C22⋊D79—24no—
186C2×C22⋊D79—24no—
187C2×C22⋊D79—82no—
188C2×C22⋊D79—82no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79C2×D411yescharacteristic
194C22×Dic79C2×D411yescharacteristic
195C2×C4×D79—24no—
196C2×C4×D79—22no—
197C2×C4×D79—22no—
198C2×C4×D79—22no—
199C2×C4×D79—22no—
200C2×C4×D79—44no—
201C2×C4×D79C2×D412yes—
202C2×C4×D79C2×D412yes—
203C2×C4×D79C2412yes—
204C2×C4×D79C2412yes—
205#11929607—28no—
206C2×C79⋊C8—22no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8C2412yes—
209C2×C79⋊C8C2412yes—
210C8×D79—28no—
211C4⋊Dic79—21no—
212C4⋊Dic79—24no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216C4⋊Dic79C2×D414yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220C4⋊Dic79C2412yes—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4C2×D414yes—
234(C2×D79)⋊C4C2×D414yes—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79—24no—
238C24×C79—21no—
239C2×Q8×C79—21no—
240C2×Q8×C79—22no—
241C2×Q8×C79—22no—
242C2×Q8×C79C2412yes—
243C2×D4×C79—21no—
244C2×D4×C79—22no—
245C2×D4×C79—22no—
246C2×D4×C79C2412yes—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—24no—
251C22×C4×C79—44no—
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2411yescharacteristic
255SD16×C79—28no—
256C2×C8×C79—22no—
257C2×C8×C79#4114yes—
258C2×C8×C79C2412yes—
259C2×C8×C79C2412yes—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C22⋊C4×C79—24no—
266C42×C79—24no—
267C42×C79C2×D412yes—
268C42×C79C2412yes—
269C23×C79—22no—
270C23×C79—42no—
271C23×C79—42no—
272C23×C79—42no—
273C23×C79C22×D411yescharacteristic
274C22×D79—22no—
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—22no—
280C22×D79C22×D412yes—
281C22×D79C22×D412yes—
282Q8×C79—22no—
283Q8×C79—22no—
284Q8×C79—42no—
285D4×C79—22no—
286D4×C79—22no—
287D4×C79—42no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—48no—
294C2×C4×C79—42no—
295C2×C4×C79—42no—
296C2×C4×C79—42no—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D411yescharacteristic
300C2×C4×C79C2×#4112yes—
301C2×C4×C792−1+412yes—
302C2×C4×C79C2511yescharacteristic
303C22⋊D79—84no—
304C22⋊D79—84no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—42no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79—42no—
315C2×Dic79C22×D412yes—
316C2×Dic79C22×D412yes—
317D316—44no—
318C4×D79—24no—
319C4×D79—24no—
320C4×D79—22no—
321C4×D79—22no—
322C4×D79—22no—
323C4×D79—22no—
324C4×D79—48no—
325Dic158—84no—
326C8×C79—22no—
327C8×C79C2×#4114yes—
328C79⋊C8—22no—
329C79⋊C8—22no—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79—42no—
333C22×C79—84no—
334C22×C79#54712yes—
335C22×C79#57512yes—
336C22×C79#57712yes—
337C22×C79C23×D411yescharacteristic
338C2×D79—22no—
339C2×D79—22no—
340C2×D79—22no—
341C2×D79—22no—
342C2×D79—22no—
343C2×D79—22no—
344C2×D79—44no—
345C2×D79—44no—
346C4×C79—22no—
347C4×C79—22no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79—42no—
351C4×C79#54712yes—
352C4×C79C22×#4111yescharacteristic
353C4×C79C2×2−1+411yescharacteristic
354Dic79—22no—
355Dic79—22no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360C2×#3348—791nomaximal, Sylow
361C2×C79—82no—
362C2×C79#334814yescomplemented
363C2×C79C2×#54711yescharacteristic
364C2×C79C2×#57511yescharacteristic
365C2×C79C2×#57711yescharacteristic
366D79—42no—
367D79—42no—
368C2×#555—791no—
369C2×#552—791no—
370#3348—7916no—
371C2×#501—791no—
372C2×#481—791no—
373C2×#485—791no—
374C2×#485—791no—
375C2×#482—791no—
376C2×#475—791no—
377C2×#478—791no—
378C2×#468—791no—
379C2×#465—791no—
380C2×#440D7911yescharacteristic, complemented
381C2×#435—791no—
382C2×#428—791no—
383C2×#427—791no—
384C79C2×#334811yescharacteristic, complemented, Sylow
385C22×SD16C2×D7911yescharacteristic
386C22×M16—791no—
387C23×C8—791no—
388#555—798no—
389#555—1584no—
390#552—798no—
391#552—1584no—
392C2×C4⋊Q8—791no—
393C2×#126—1581no—
394C2×#125—791no—
395C2×#125—1581no—
396C2×#124—1581no—
397C2×#124—1581no—
398C2×#123—1581no—
399C2×C22⋊Q8—791no—
400C2×C22⋊Q8—791no—
401C2×#121—791no—
402C2×#121—791no—
403C2×#121—1581no—
404C2×C4×Q8C2×D7911yescharacteristic
405C2×C4×D4—791no—
406C2×C4×D4C2×D7911yescharacteristic
407C2×#117—791no—
408C2×#117—791no—
409C2×#117—791no—
410C2×#117—1581no—
411C2×#117—1581no—
412C22×C4⋊C4—791no—
413#501—798no—
414#485—798no—
415#485—798no—
416#482—798no—
417#481—798no—
418#478—798no—
419#475—798no—
420#468—798no—
421#465—798no—
422#440C2×D7918yescomplemented
423#435—798no—
424#428—798no—
425#427—798no—
426C2×#107—791no—
427C2×#107—791no—
428C2×#107—791no—
429C2×#107C2×D7911yescharacteristic
430C2×#106—791no—
431C2×#106—791no—
432C2×#106—791no—
433C2×#106—791no—
434C2×#106—791no—
435C2×C4⋊C8—791no—
436C2×#103—791no—
437C2×#103—791no—
438C2×#103C2×D7911yescharacteristic
439C2×#102—791no—
440C2×#102—791no—
441C2×#102C2×D7911yescharacteristic
442C2×C22⋊C8—791no—
443C2×C22⋊C8—791no—
444C2×#97C2×D7911yescharacteristic
445C22×Q8—1581no—
446C22×Q8C22×D7911yescharacteristic
447C22×D4—791no—
448C22×D4—1581no—
449C22×D4—1581no—
450C22×D4C22×D7911yescharacteristic
451C23×C4—21no—
452C23×C4—791no—
453C23×C4—791no—
454C23×C4—1581no—
455C2×SD16—24no—
456C2×SD16C22×D7914yes—
457C2×M16—794no—
458C2×M16—1584no—
459C22×C8—791no—
460C22×C8—791no—
461C22×C8—794no—
462C22×C8—1584no—
463C22×C8C22×D7911yescharacteristic
464C22×C8C22×D7911yescharacteristic
465C4⋊Q8—794no—
466C4⋊Q8—1582no—
467#126—1588no—
468#125—794no—
469#125—1588no—
470#125—1582no—
471#124—1588no—
472#124—1588no—
473#123—1588no—
474C22⋊Q8—794no—
475C22⋊Q8—794no—
476C22⋊Q8—1582no—
477C22⋊Q8—1582no—
478#121—794no—
479#121—794no—
480#121—1588no—
481#121—1582no—
482#121—1582no—
483C4×Q8—22no—
484C4×Q8C22×D7914yes—
485C4×D4—22no—
486C4×D4—794no—
487C4×D4—794no—
488C4×D4C22×D7914yes—
489#117—794no—
490#117—794no—
491#117—794no—
492#117—1588no—
493#117—1582no—
494#117—1582no—
495#117—1582no—
496#117—1588no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—791no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—791no—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—794no—
504C2×C4⋊C4—1582no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4C22×D7911yescharacteristic
512C2×C4⋊C4C22×D7911yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—791no—
515C2×C22⋊C4—791no—
516C2×C22⋊C4—1581no—
517C2×C22⋊C4—1581no—
518C2×C22⋊C4—1581no—
519C2×C22⋊C4—1581no—
520C2×C22⋊C4—1581no—
521C2×C22⋊C4—1581no—
522C2×C22⋊C4—1581no—
523C2×C42—21no—
524C2×C42—1581no—
525C2×C42—1581no—
526C2×C42—1581no—
527C2×C42C22×D7911yescharacteristic
528#107—794no—
529#107—794no—
530#107—794no—
531#107C22×D7914yes—
532#106—794no—
533#106—794no—
534#106—794no—
535#106—794no—
536#106—794no—
537C4⋊C8—794no—
538#103—794no—
539#103—794no—
540#103C22×D7914yes—
541#102—794no—
542#102—794no—
543#102C22×D7914yes—
544C22⋊C8—794no—
545C22⋊C8—794no—
546#97C22×D7914yes—
547C24—21no—
548C24—791no—
549C24—791no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—6322no—
554C2×Q8—1584no—
555C2×Q8C23×D7912yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—3162no—
560C2×D4—794no—
561C2×D4—6322no—
562C2×D4—6322no—
563C2×D4—1584no—
564C2×D4—1584no—
565C2×D4C23×D7912yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—44no—
571C22×C4—3164no—
572C22×C4—791no—
573C22×C4—791no—
574C22×C4—792no—
575C22×C4—792no—
576C22×C4—792no—
577C22×C4—792no—
578C22×C4—1584no—
579C22×C4—1581no—
580C22×C4—1581no—
581C22×C4—1581no—
582C22×C4—1581no—
583C22×C4—1582no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4D4×D7911yescharacteristic
588C22×C4D4×D7911yescharacteristic
589C22×C4C23×D7911yescharacteristic
590SD16—28no—
591M16—1588no—
592C2×C8—22no—
593C2×C8—792no—
594C2×C8—792no—
595C2×C8—1582no—
596C2×C8—1582no—
597C2×C8—1588no—
598C2×C8#1192962414yes—
599C2×C8C23×D7912yes—
600C2×C8C23×D7912yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—794no—
605C4⋊C4—792no—
606C4⋊C4—792no—
607C4⋊C4—792no—
608C4⋊C4—792no—
609C4⋊C4—1584no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1581no—
615C4⋊C4—1581no—
616C4⋊C4—1581no—
617C4⋊C4—1581no—
618C4⋊C4—1584no—
619C4⋊C4C23×D7912yes—
620C4⋊C4C23×D7912yes—
621C22⋊C4—24no—
622C22⋊C4—794no—
623C22⋊C4—794no—
624C22⋊C4—1584no—
625C22⋊C4—1584no—
626C22⋊C4—1584no—
627C22⋊C4—1584no—
628C22⋊C4—1584no—
629C22⋊C4—1584no—
630C22⋊C4—1584no—
631C42—24no—
632C42—1584no—
633C42—1584no—
634C42—1584no—
635C42D4×D7912yes—
636C42C23×D7912yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—792no—
642C23—792no—
643C23—1582no—
644C23—1582no—
645C23—1582no—
646C23—1582no—
647C23—1582no—
648C23—1582no—
649C23C2×D4×D7911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—6324no—
654D4—22no—
655D4—22no—
656D4—42no—
657D4—3164no—
658D4—6324no—
659D4—6324no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—48no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—3168no—
670C2×C4—3162no—
671C2×C4—3162no—
672C2×C4—3162no—
673C2×C4—3162no—
674C2×C4—792no—
675C2×C4—792no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1584no—
685C2×C4—1584no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4C2×D4×D7912yes—
689C2×C4C2×D4×D7912yes—
690C2×C4C2×D4×D7911yescharacteristic
691C2×C4C2×#1192962412yes—
692C2×C4#1457920812yes—
693C2×C4C24×D7911yescharacteristic
694C8—22no—
695C8—1582no—
696C8—1582no—
697C8C2×#1192962414yes—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—3164no—
703C22—3164no—
704C22—1582no—
705C22—1582no—
706C22—1582no—
707C22—1582no—
708C22—1582no—
709C22—1582no—
710C22#1909921812yes—
711C22#1909935912yes—
712C22#1909937212yes—
713C22C22×D4×D7911yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—3162no—
720C4—3162no—
721C4—3162no—
722C4—3162no—
723C4—1582no—
724C4—1582no—
725C4#1909921812yes—
726C4C22×#1192962411yescharacteristic
727C4C2×#1457920811yescharacteristic
728C2—82no—
729C2—3162no—
730C2—3162no—
731C2#2377592014yesdirect product factor
732C2C2×#1909921811yescharacteristic
733C2C2×#1909935911yescharacteristic
734C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#440×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099278C2
hypercenterC2×#440D79
hypocenterC79C2×#3348
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#19099254C2semidirect
3. #23775920C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098880C2semidirect
6. C2×#19098903C2semidirect
7. C2×#19098902C2semidirect
8. C2×#19098885C2semidirect
9. C2×#19098848C2semidirect
10. C2×#19098863C2semidirect
11. C2×#19098806C2semidirect
12. C2×#19098789C2semidirect
13. C2×#19098636C2semidirect
14. C2×#19098604C2semidirect
15. C2×#19098600C2semidirect
16. C2×#440×C79C2semidirect
22. #19099254C22semidirect
42. #19098972C22semidirect
43. #19098903C22semidirect
44. #19098902C22semidirect
45. #19098885C22semidirect
46. #19098880C22semidirect
47. #19098863C22semidirect
48. #19098848C22semidirect
49. #19098806C22semidirect
50. #19098789C22semidirect
51. #19098636C22semidirect
52. #19098604C22semidirect
53. #19098600C22semidirect
72. #440×C79C22semidirect
362. C2×C79#3348semidirect
380. C2×#440D79semidirect
384. C79C2×#3348semidirect
422. #440C2×D79semidirect
731. C2#23775920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992782
C2×#190992542
#237759202
C2×#190989722
C2×#190988802
C2×#190989032
C2×#190989022
C2×#190988852
C2×#190988482
C2×#190988632
C2×#190988062
C2×#190987892
C2×#190986362
C2×#190986042
C2×#190986002
C2×#440×C792
C2×#334879