Finite Group Databasebeta

← C2×#23774071 #35158140

Subgroups — C2×#23774071 #35158140

Order 20224.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099186C211yesmaximal, characteristic
2C2×#19099173C211yesmaximal, characteristic, complemented
3#23774071C2116yesmaximal, direct product factor
4C2×#19098971C211yesmaximal, characteristic, complemented
5C2×#19098956C211yesmaximal, characteristic, complemented
6C2×#19098919C211yesmaximal, characteristic, complemented
7C2×#19098912C211yesmaximal, characteristic, complemented
8C2×#19098819C211yesmaximal, characteristic, complemented
9C2×#19098811C211yesmaximal, characteristic
10C2×#19098792C211yesmaximal, characteristic
11C2×#19098670C211yesmaximal, characteristic, complemented
12C2×#19098662C211yesmaximal, characteristic, complemented
13C2×#19098655C211yesmaximal, characteristic, complemented
14C2×#19098648C211yesmaximal, characteristic, complemented
15C2×#19098518C211yesmaximal, characteristic, complemented
16C2×#467×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929613C2211yescharacteristic
19C22×#11929611C2211yescharacteristic
20C22×#11929608C2211yescharacteristic
21#19099186—24no—
22#19099186C2218yes—
23#19099173—24no—
24#19099173C2218yescomplemented
25C2×#14579160C2211yescharacteristic
26C2×#14579159C2211yescharacteristic
27C2×#14579156—21no—
28C2×#14579154—21no—
29C2×#14579154—21no—
30C2×#14579152—21no—
31C2×#14579152C2211yescharacteristic
32C2×#14579151—21no—
33C2×#14579150C2211yescharacteristic
34C2×#14579147—21no—
35C2×#14579143—21no—
36C2×#14579141—21no—
37C2×#14579140C2211yescharacteristic
38C2×#14579135C2211yescharacteristic
39C2×Q8×Dic79C2211yescharacteristic
40C2×Q8×Dic79C2211yescharacteristic
41C2×#14579126C2211yescharacteristic
42C2×#14579123C2211yescharacteristic
43C2×#14579120C2211yescharacteristic
44#19098971C2218yescomplemented
45#19098956C2218yescomplemented
46#19098919C2218yescomplemented
47#19098912C2218yescomplemented
48#19098819C2218yescomplemented
49#19098811C2218yes—
50#19098792C2218yes—
51#19098670C2218yescomplemented
52#19098662C2218yescomplemented
53#19098655C2218yescomplemented
54#19098648C2218yescomplemented
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579086C2211yescharacteristic
59C2×#14579085C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579083C2211yescharacteristic
63C2×#14579081C2211yescharacteristic
64#19098518C2218yescomplemented
65C2×#14579071C2211yescharacteristic
66C2×#14579071C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#467×C79C2218yescomplemented
74C2×#107×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C4×D79—21no—
82C2×#11929614—24no—
83C2×#11929614C2314yes—
84C2×#11929613—24no—
85C2×#11929613C2314yes—
86C2×#11929611—24no—
87C2×#11929611C2314yes—
88C2×#11929608—24no—
89C2×#11929608C2314yes—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92#14579160—22no—
93#14579160C2314yes—
94#14579159—22no—
95#14579159C2314yes—
96#14579156—28no—
97#14579154—28no—
98#14579154—28no—
99#14579152—28no—
100#14579152—22no—
101#14579152C2314yes—
102#14579151—28no—
103#14579150—22no—
104#14579150C2314yes—
105#14579147—28no—
106#14579143—28no—
107#14579141—28no—
108#14579140—22no—
109#14579140C2314yes—
110#14579135—22no—
111#14579135C2314yes—
112Q8×Dic79—22no—
113Q8×Dic79—22no—
114Q8×Dic79C2314yes—
115Q8×Dic79C2314yes—
116#14579126—22no—
117#14579126C2314yes—
118#14579123—22no—
119#14579123C2314yes—
120#14579120D414yes—
121#14579120C2314yes—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79D411yescharacteristic
126C2×C4⋊Dic79D411yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79D411yescharacteristic
137C2×C22⋊Dic79D411yescharacteristic
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79C2311yescharacteristic
146C2×C4×Dic79C2311yescharacteristic
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150#14579086C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579084C2314yes—
154#14579083C2314yes—
155#14579081C2314yes—
156#14579071C2314yes—
157#14579071C2314yes—
158C8×Dic79C2314yes—
159C8×Dic79C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×Q8×C79C2311yescharacteristic
162C23×C4×C79C2311yescharacteristic
163C2×Q16×C79—24no—
164C2×Q16×C79C2314yes—
165C22×C8×C79—24no—
166C22×C8×C79C2314yes—
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C22⋊Q8×C79—22no—
170C22⋊Q8×C79—22no—
171C22⋊Q8×C79C2314yes—
172C22⋊Q8×C79C2314yes—
173C2×C4⋊C4×C79—21no—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179#107×C79C2314yes—
180#103×C79C2314yes—
181#103×C79C2314yes—
182C23×D79—21no—
183C2×Dic158—24no—
184C2×Dic158—21no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—82no—
188C2×Dic158C2412yes—
189C2×D316—21no—
190C2×D316—22no—
191C2×D316—22no—
192C2×D316C2412yes—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—82no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C2×C4×D79—24no—
203C2×C4×D79—82no—
204#11929614—28no—
205#11929613—28no—
206#11929611—28no—
207#11929608—28no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8#4114yes—
210C2×C79⋊C8C2412yes—
211C2×C79⋊C8C2412yes—
212C4⋊Dic79—24no—
213C4⋊Dic79—24no—
214C4⋊Dic79—24no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79C2×D414yes—
218C4⋊Dic79C2×D414yes—
219C4⋊Dic79C2412yes—
220C4⋊Dic79C2412yes—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227C22⋊Dic79—24no—
228C22⋊Dic79C2×D414yes—
229C22⋊Dic79C2×D414yes—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79C2×D412yes—
238C4×Dic79C2×D412yes—
239C4×Dic79C2412yes—
240C4×Dic79C2412yes—
241C24×C79C2×D411yescharacteristic
242C2×Q8×C79—21no—
243C2×Q8×C79—21no—
244C2×Q8×C79—22no—
245C2×Q8×C79—22no—
246C2×Q8×C79—22no—
247C2×Q8×C79—22no—
248C2×Q8×C79C2412yes—
249C2×Q8×C79C2412yes—
250C22×C4×C79—22no—
251C22×C4×C79—22no—
252C22×C4×C79—21no—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2411yescharacteristic
260Q16×C79—28no—
261C2×C8×C79—28no—
262C2×C8×C79—22no—
263C2×C8×C79#4114yes—
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C4⋊C4×C79—24no—
267C4⋊C4×C79—24no—
268C4⋊C4×C79—21no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79C2412yes—
271C4⋊C4×C79C2412yes—
272C22⋊C4×C79—24no—
273C22⋊C4×C79—24no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79C22×D412yes—
278C23×C79C22×D411yescharacteristic
279C22×D79—22no—
280C22×D79—42no—
281C22×D79—42no—
282C22×D79—42no—
283Q8×C79—22no—
284Q8×C79—22no—
285Q8×C79—22no—
286Q8×C79—22no—
287Q8×C79—42no—
288Q8×C79—42no—
289C2×C4×C79—22no—
290C2×C4×C79—24no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—42no—
298C2×C4×C79—42no—
299C2×C4×C79—42no—
300C2×C4×C79—42no—
301C2×C4×C79C22×D412yes—
302C2×C4×C79C22×D411yescharacteristic
303C2×C4×C79C2×#4112yes—
304C2×C4×C79C2×#4112yes—
305C2×C4×C79C2511yescharacteristic
306C22⋊D79—84no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79C22×D412yes—
318C2×Dic79C22×D412yes—
319C2×Dic79C22×D412yes—
320C2×Dic79C22×D412yes—
321D316—22no—
322D316—22no—
323D316—42no—
324C4×D79—84no—
325Dic158—22no—
326Dic158—22no—
327Dic158—42no—
328Dic158—84no—
329C8×C79—22no—
330C8×C79C2×#4114yes—
331C79⋊C8—22no—
332C79⋊C8C2×#4114yes—
333C22×C79—22no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—44no—
337C22×C79#53212yes—
338C22×C79#57712yes—
339C22×C79#57812yes—
340C22×C79C23×D411yescharacteristic
341C2×D79—42no—
342C2×D79—42no—
343C2×D79—42no—
344C2×D79—84no—
345C4×C79—22no—
346C4×C79—42no—
347C4×C79—42no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79#53212yes—
351C4×C79C22×#4111yescharacteristic
352C4×C79C22×#4111yescharacteristic
353Dic79—22no—
354Dic79—22no—
355Dic79—22no—
356Dic79—22no—
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360C2×#3178—791nomaximal, Sylow
361C2×C79—42no—
362C2×C79#317814yescomplemented
363C2×C79C2×#53211yescharacteristic
364C2×C79C2×#57711yescharacteristic
365C2×C79C2×#57811yescharacteristic
366D79—82no—
367C2×#542—791no—
368C2×#541—791no—
369#3178—7916no—
370C2×#501—791no—
371C2×#497—791no—
372C2×#488—791no—
373C2×#487—791no—
374C2×#470—791no—
375C2×#468—791no—
376C2×#467D7911yescharacteristic, complemented
377C2×#465—791no—
378C2×#441—791no—
379C2×#440—791no—
380C2×C4×Q16—791no—
381C2×C4×SD16—791no—
382C2×#405—791no—
383C79C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—791no—
385C22×Q16C2×D7911yescharacteristic
386C22×SD16—791no—
387C22×SD16—791no—
388C22×M16—791no—
389C23×C8C2×D7911yescharacteristic
390#542—798no—
391#542—1584no—
392#541—798no—
393#541—1584no—
394C2×C4⋊Q8—791no—
395C2×C4⋊Q8—791no—
396C2×#126—1581no—
397C2×#126—1581no—
398C2×#126—1581no—
399C2×#125—791no—
400C2×#125—1581no—
401C2×#125—1581no—
402C2×#124—791no—
403C2×#124—1581no—
404C2×#123—1581no—
405C2×C22⋊Q8—791no—
406C2×C22⋊Q8—1581no—
407C2×C22⋊Q8C2×D7911yescharacteristic
408C2×C22⋊Q8C2×D7911yescharacteristic
409C2×#121—791no—
410C2×C4×Q8—791no—
411C2×C4×Q8—791no—
412C2×C4×Q8—791no—
413C2×C4×D4—791no—
414C2×#117—791no—
415#501—798no—
416#497—798no—
417#488—798no—
418#487—798no—
419#470—798no—
420#468—798no—
421#467C2×D7918yescomplemented
422#465—798no—
423#441—798no—
424#440—798no—
425C4×Q16—798no—
426C4×SD16—798no—
427C2×#107—791no—
428C2×#107C2×D7911yescharacteristic
429C2×#106—791no—
430C2×#106—791no—
431C2×#103—791no—
432C2×#103—791no—
433C2×#103—791no—
434C2×#103—791no—
435C2×#103C2×D7911yescharacteristic
436C2×#103C2×D7911yescharacteristic
437C2×#102—791no—
438C2×#102—791no—
439#405—798no—
440C2×#97—791no—
441C2×#97—791no—
442C2×C4×C8—791no—
443C2×C4×C8—791no—
444C22×Q8—791no—
445C22×Q8—1581no—
446C22×Q8C22×D7911yescharacteristic
447C22×Q8C22×D7911yescharacteristic
448C22×D4—791no—
449C22×D4—1581no—
450C23×C4—1581no—
451C23×C4C22×D7911yescharacteristic
452C2×Q16—24no—
453C2×Q16—794no—
454C2×Q16—1584no—
455C2×Q16C22×D7914yes—
456C2×SD16—794no—
457C2×SD16—794no—
458C2×SD16—1584no—
459C2×SD16—1584no—
460C2×M16—794no—
461C2×M16—1584no—
462C22×C8—24no—
463C22×C8—791no—
464C22×C8—791no—
465C22×C8C22×D7911yescharacteristic
466C22×C8C22×D7914yes—
467C22×C8C22×D7911yescharacteristic
468C4⋊Q8—794no—
469C4⋊Q8—794no—
470C4⋊Q8—1582no—
471C4⋊Q8—1582no—
472#126—1588no—
473#126—1588no—
474#126—1588no—
475#125—794no—
476#125—1582no—
477#125—1588no—
478#125—1588no—
479#124—794no—
480#124—1582no—
481#124—1588no—
482#123—1588no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—794no—
486C22⋊Q8—1588no—
487C22⋊Q8—1582no—
488C22⋊Q8C22×D7914yes—
489C22⋊Q8C22×D7914yes—
490#121—794no—
491#121—1582no—
492C4×Q8—794no—
493C4×Q8—794no—
494C4×Q8—794no—
495C4×Q8—1582no—
496C4×Q8—1582no—
497C4×Q8—1582no—
498C4×D4—794no—
499C4×D4—1582no—
500#117—794no—
501#117—794no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4C22×D7911yescharacteristic
518C2×C4⋊C4C22×D7911yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—791no—
522C2×C22⋊C4—791no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—791no—
529C2×C42—791no—
530C2×C42—1581no—
531C2×C42—1581no—
532C2×C42—1581no—
533#107—794no—
534#107C22×D7914yes—
535#106—794no—
536#106—794no—
537#103—794no—
538#103—794no—
539#103—794no—
540#103—794no—
541#103C22×D7914yes—
542#103C22×D7914yes—
543#102—794no—
544#102—794no—
545#97—794no—
546#97—794no—
547C4×C8—794no—
548C4×C8—794no—
549C24—1581no—
550C24D4×D7911yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—792no—
558C2×Q8—6322no—
559C2×Q8—1584no—
560C2×Q8—1582no—
561C2×Q8—1582no—
562C2×Q8—1581no—
563C2×Q8C23×D7912yes—
564C2×Q8C23×D7912yes—
565C2×D4—792no—
566C2×D4—6322no—
567C2×D4—1584no—
568C2×D4—1582no—
569C2×D4—1582no—
570C2×D4—1581no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—791no—
578C22×C4—791no—
579C22×C4—791no—
580C22×C4—791no—
581C22×C4—6322no—
582C22×C4—1584no—
583C22×C4—1581no—
584C22×C4—1581no—
585C22×C4—1581no—
586C22×C4D4×D7912yes—
587C22×C4D4×D7911yescharacteristic
588C22×C4C23×D7912yes—
589C22×C4C23×D7911yescharacteristic
590Q16—28no—
591Q16—1588no—
592SD16—1588no—
593SD16—1588no—
594M16—1588no—
595C2×C8—22no—
596C2×C8—28no—
597C2×C8—794no—
598C2×C8—792no—
599C2×C8—792no—
600C2×C8—1582no—
601C2×C8#1192962314yes—
602C2×C8C23×D7912yes—
603C2×C8C23×D7912yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—794no—
609C4⋊C4—794no—
610C4⋊C4—792no—
611C4⋊C4—792no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1584no—
617C4⋊C4—1584no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4—1581no—
622C4⋊C4—1581no—
623C4⋊C4C23×D7912yes—
624C4⋊C4C23×D7912yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—794no—
628C22⋊C4—794no—
629C22⋊C4—1584no—
630C22⋊C4—1584no—
631C22⋊C4—1584no—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C42—792no—
635C42—792no—
636C42—792no—
637C42—792no—
638C42—1584no—
639C42—1584no—
640C42—1584no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—3162no—
645C23—3162no—
646C23—3162no—
647C23—1582no—
648C23C2×D4×D7912yes—
649C23C2×D4×D7911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—3162no—
657Q8—6324no—
658Q8—1582no—
659Q8—1582no—
660D4—3162no—
661D4—6324no—
662D4—1582no—
663D4—1582no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—3162no—
677C2×C4—3162no—
678C2×C4—3162no—
679C2×C4—792no—
680C2×C4—792no—
681C2×C4—792no—
682C2×C4—792no—
683C2×C4—6324no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4C2×D4×D7912yes—
692C2×C4C2×D4×D7911yescharacteristic
693C2×C4#41×D7912yes—
694C2×C4C2×#1192962312yes—
695C2×C4C24×D7911yescharacteristic
696C8—22no—
697C8—794no—
698C8—1582no—
699C8C2×#1192962314yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3162no—
705C22—3162no—
706C22—3162no—
707C22—6324no—
708C22#1909910812yes—
709C22#1909937012yes—
710C22#1909937612yes—
711C22C22×D4×D7911yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—3162no—
718C4—3162no—
719C4—3162no—
720C4—1582no—
721C4—1582no—
722C4—1582no—
723C4—1582no—
724C4#1909910812yes—
725C4C2×#41×D7911yescharacteristic
726C4C22×#1192962311yescharacteristic
727C2—42no—
728C2—6322no—
729C2#2377407114yesdirect product factor
730C2C2×#1909910811yescharacteristic
731C2C2×#1909937011yescharacteristic
732C2C2×#1909937611yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#467×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenterC2×#467D79
hypocenterC79C2×#3178
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
2. C2×#19099173C2semidirect
3. #23774071C2direct (N × H)
4. C2×#19098971C2semidirect
5. C2×#19098956C2semidirect
6. C2×#19098919C2semidirect
7. C2×#19098912C2semidirect
8. C2×#19098819C2semidirect
11. C2×#19098670C2semidirect
12. C2×#19098662C2semidirect
13. C2×#19098655C2semidirect
14. C2×#19098648C2semidirect
15. C2×#19098518C2semidirect
16. C2×#467×C79C2semidirect
24. #19099173C22semidirect
44. #19098971C22semidirect
45. #19098956C22semidirect
46. #19098919C22semidirect
47. #19098912C22semidirect
48. #19098819C22semidirect
51. #19098670C22semidirect
52. #19098662C22semidirect
53. #19098655C22semidirect
54. #19098648C22semidirect
64. #19098518C22semidirect
73. #467×C79C22semidirect
362. C2×C79#3178semidirect
376. C2×#467D79semidirect
383. C79C2×#3178semidirect
421. #467C2×D79semidirect
729. C2#23774071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991862
C2×#190991732
#237740712
C2×#190989712
C2×#190989562
C2×#190989192
C2×#190989122
C2×#190988192
C2×#190988112
C2×#190987922
C2×#190986702
C2×#190986622
C2×#190986552
C2×#190986482
C2×#190985182
C2×#467×C792
C2×#317879