Finite Group Databasebeta

← C2×#23773630 #35156549

Subgroups — C2×#23773630 #35156549

Order 20224.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099186C211yesmaximal, characteristic
2C2×#19099041C211yesmaximal, characteristic, complemented
3#23773630C2116yesmaximal, direct product factor
4C2×#19098901C211yesmaximal, characteristic, complemented
5C2×#19098888C211yesmaximal, characteristic
6C2×#19098856C211yesmaximal, characteristic, complemented
7C2×#19098846C211yesmaximal, characteristic, complemented
8C2×#19098787C211yesmaximal, characteristic, complemented
9C2×#19098787C211yesmaximal, characteristic, complemented
10C2×#19098702C211yesmaximal, characteristic
11C2×#19098670C211yesmaximal, characteristic, complemented
12C2×#19098666C211yesmaximal, characteristic, complemented
13C2×Q16×Dic79C211yesmaximal, characteristic, complemented
14C2×#19098648C211yesmaximal, characteristic, complemented
15C2×#19098621C211yesmaximal, characteristic, complemented
16C2×#451×C79C211yesmaximal, characteristic, complemented
17C22×#11929611C2211yescharacteristic
18C22×#11929611C2211yescharacteristic
19#19099186—24no—
20#19099186C2218yes—
21C2×#14579160C2211yescharacteristic
22C2×#14579156—21no—
23C2×#14579150C2211yescharacteristic
24C2×#14579147—21no—
25C2×#14579143—21no—
26C2×#14579141—21no—
27C2×#14579135C2211yescharacteristic
28#19099041—24no—
29#19099041C2218yescomplemented
30C2×Q8×Dic79—21no—
31C2×Q8×Dic79—21no—
32C2×Q8×Dic79C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×Q8×Dic79C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×Q8×Dic79C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×#14579120—21no—
39C2×#14579120—21no—
40C2×#14579120C2211yescharacteristic
41C2×#14579120C2211yescharacteristic
42#19098901C2218yescomplemented
43#19098888C2218yes—
44#19098856C2218yescomplemented
45#19098846C2218yescomplemented
46#19098787C2218yescomplemented
47#19098787C2218yescomplemented
48#19098702C2218yes—
49#19098670C2218yescomplemented
50#19098666C2218yescomplemented
51Q16×Dic79C2218yescomplemented
52#19098648C2218yescomplemented
53#19098621C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C23×Q8×C79C2211yescharacteristic
70C22×Q16×C79C2211yescharacteristic
71C22×Q16×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#451×C79C2218yescomplemented
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×D316C2311yescharacteristic
79C22×C22⋊D79—21no—
80C22×C4×D79—21no—
81C2×#11929611—24no—
82C2×#11929611—24no—
83C2×#11929611C2314yes—
84C2×#11929611C2314yes—
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87#14579160—22no—
88#14579160C2314yes—
89#14579156—28no—
90#14579150—22no—
91#14579150C2314yes—
92#14579147—28no—
93#14579143—28no—
94#14579141—28no—
95#14579135—22no—
96#14579135C2314yes—
97Q8×Dic79—28no—
98Q8×Dic79—28no—
99Q8×Dic79—22no—
100Q8×Dic79—22no—
101Q8×Dic79—22no—
102Q8×Dic79—22no—
103Q8×Dic79—22no—
104Q8×Dic79C2314yes—
105Q8×Dic79C2314yes—
106Q8×Dic79C2314yes—
107Q8×Dic79C2314yes—
108Q8×Dic79C2314yes—
109#14579123—22no—
110#14579123C2314yes—
111#14579120—22no—
112#14579120—28no—
113#14579120—28no—
114#14579120D414yes—
115#14579120C2314yes—
116#14579120C2314yes—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79D411yescharacteristic
123C2×C4⋊Dic79D411yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×Dic79⋊C4—21no—
128C2×C22⋊Dic79—21no—
129C2×C22⋊Dic79D411yescharacteristic
130C2×C22⋊Dic79D411yescharacteristic
131C2×(C2×D79)⋊C4—21no—
132C2×(C2×D79)⋊C4—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×C4×Dic79—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143#14579095C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147Dic79⋊C8C2314yes—
148Dic79⋊C8C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579083C2314yes—
154#14579083C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79—24no—
159C22×Q8×C79—24no—
160C22×Q8×C79—21no—
161C22×Q8×C79—22no—
162C22×Q8×C79C2314yes—
163C22×Q8×C79C2311yescharacteristic
164C22×Q8×C79C2311yescharacteristic
165C22×Q8×C79C2311yescharacteristic
166C23×C4×C79—21no—
167C23×C4×C79C2311yescharacteristic
168C2×Q16×C79—24no—
169C2×Q16×C79—24no—
170C2×Q16×C79C2314yes—
171C2×Q16×C79C2314yes—
172C22×C8×C79C2311yescharacteristic
173C22×C8×C79C2311yescharacteristic
174C22⋊Q8×C79—22no—
175C22⋊Q8×C79C2314yes—
176C2×C4⋊C4×C79—21no—
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C22⋊C4×C79—21no—
179#103×C79C2314yes—
180#103×C79C2314yes—
181C22⋊C8×C79C2314yes—
182C23×D79—21no—
183C2×Dic158—24no—
184C2×Dic158—82no—
185C2×D316—21no—
186C2×D316—22no—
187C2×D316—22no—
188C2×D316C2412yes—
189C2×C22⋊D79—24no—
190C2×C22⋊D79—82no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79C2×D411yescharacteristic
195C22×Dic79C2×D411yescharacteristic
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C2×C4×D79—24no—
199C2×C4×D79—82no—
200#11929611—28no—
201#11929611—28no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8—22no—
204C2×C79⋊C8C2412yes—
205C2×C79⋊C8C2412yes—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—24no—
210C4⋊Dic79—24no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79C2×D414yes—
215C4⋊Dic79C2×D414yes—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219Dic79⋊C4—24no—
220C22⋊Dic79—24no—
221C22⋊Dic79C2×D414yes—
222C22⋊Dic79C2×D414yes—
223(C2×D79)⋊C4—24no—
224(C2×D79)⋊C4—24no—
225(C2×D79)⋊C4—24no—
226(C2×D79)⋊C4—24no—
227C4×Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C4×Dic79—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79C2×D412yes—
234C4×Dic79C2×D412yes—
235C4×Dic79C2412yes—
236C4×Dic79C2412yes—
237C24×C79C2×D411yescharacteristic
238C2×Q8×C79—216no—
239C2×Q8×C79—28no—
240C2×Q8×C79—28no—
241C2×Q8×C79—28no—
242C2×Q8×C79—24no—
243C2×Q8×C79—21no—
244C2×Q8×C79—21no—
245C2×Q8×C79—21no—
246C2×Q8×C79—22no—
247C2×Q8×C79—22no—
248C2×Q8×C79—22no—
249C2×Q8×C79—22no—
250C2×Q8×C79#4114yes—
251C2×Q8×C79#4114yes—
252C2×Q8×C79C2412yes—
253C2×Q8×C79C2412yes—
254C2×Q8×C79C2412yes—
255C22×C4×C79—28no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—24no—
259C22×C4×C79—22no—
260C22×C4×C79—22no—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79C2×D412yes—
265C22×C4×C79C2412yes—
266C22×C4×C79C2411yescharacteristic
267Q16×C79—28no—
268Q16×C79—28no—
269C2×C8×C79—22no—
270C2×C8×C79—22no—
271C2×C8×C79C2412yes—
272C2×C8×C79C2412yes—
273C4⋊C4×C79—24no—
274C4⋊C4×C79—21no—
275C4⋊C4×C79C2412yes—
276C22⋊C4×C79—24no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—22no—
280C23×C79C22×D412yes—
281C23×C79C22×D411yescharacteristic
282C22×D79—22no—
283C22×D79—42no—
284C22×D79—42no—
285C22×D79—42no—
286Q8×C79—216no—
287Q8×C79—24no—
288Q8×C79—24no—
289Q8×C79—22no—
290Q8×C79—22no—
291Q8×C79—22no—
292Q8×C79—22no—
293Q8×C79—42no—
294Q8×C79C2×#4114yes—
295Q8×C79C2×#4114yes—
296C2×C4×C79—216no—
297C2×C4×C79—24no—
298C2×C4×C79—24no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—24no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—42no—
308C2×C4×C79—42no—
309C2×C4×C79C22×D412yes—
310C2×C4×C79C22×D411yescharacteristic
311C2×C4×C79C2×#4112yes—
312C2×C4×C79C2×#4112yes—
313C2×C4×C79C2511yescharacteristic
314C22⋊D79—84no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—42no—
323C2×Dic79—42no—
324C2×Dic79—42no—
325C2×Dic79C22×D412yes—
326C2×Dic79C22×D412yes—
327C2×Dic79C22×D412yes—
328C2×Dic79C22×D412yes—
329D316—22no—
330D316—22no—
331D316—42no—
332C4×D79—84no—
333Dic158—84no—
334C8×C79—22no—
335C8×C79—22no—
336C79⋊C8—22no—
337C79⋊C8—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—44no—
342C22×C79#52512yes—
343C22×C79#57712yes—
344C22×C79#57812yes—
345C22×C79C23×D411yescharacteristic
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—84no—
350C4×C79—24no—
351C4×C79—24no—
352C4×C79—22no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79#52512yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C22×#4111yescharacteristic
358Dic79—22no—
359Dic79—22no—
360Dic79—22no—
361Dic79—22no—
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365C2×#3121—791nomaximal, Sylow
366C2×C79—42no—
367C2×C79#312114yescomplemented
368C2×C79C2×#52511yescharacteristic
369C2×C79C2×#57711yescharacteristic
370C2×C79C2×#57811yescharacteristic
371D79—82no—
372C2×#542—791no—
373C2×#519—791no—
374#3121—7916no—
375C2×#485—791no—
376C2×#482—791no—
377C2×#477—791no—
378C2×#475—791no—
379C2×#464—791no—
380C2×#464—791no—
381C2×#451D7911yescharacteristic, complemented
382C2×#448—791no—
383C2×#441—791no—
384C2×#440—791no—
385C2×C4×Q16—791no—
386C2×C4×SD16—791no—
387C2×#433—791no—
388C79C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8C2×D7911yescharacteristic
390C22×Q16C2×D7911yescharacteristic
391C22×Q16C2×D7911yescharacteristic
392C22×SD16—791no—
393C22×SD16—791no—
394#542—798no—
395#542—1584no—
396C2×C4⋊Q8—791no—
397C2×#126—1581no—
398C2×#124—791no—
399C2×#124—1581no—
400C2×#123—1581no—
401C2×C22⋊Q8—1581no—
402C2×C22⋊Q8C2×D7911yescharacteristic
403C2×#121—791no—
404#519—798no—
405#519—1584no—
406C2×C4×Q8—791no—
407C2×C4×Q8—791no—
408C2×C4×Q8—791no—
409C2×C4×Q8—791no—
410C2×C4×Q8—791no—
411C2×C4×Q8—1581no—
412C2×C4×Q8—1581no—
413C2×C4×D4—791no—
414C2×#117—791no—
415C2×#117—791no—
416C2×#117—1581no—
417C2×#117—1581no—
418#485—798no—
419#482—798no—
420#477—798no—
421#475—798no—
422#464—798no—
423#464—798no—
424#451C2×D7918yescomplemented
425#448—798no—
426#441—798no—
427#440—798no—
428C4×Q16—798no—
429C4×SD16—798no—
430#433—798no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#106—791no—
434C2×#106—791no—
435C2×C4⋊C8—791no—
436C2×C4⋊C8—791no—
437C2×#103—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103—791no—
441C2×#103C2×D7911yescharacteristic
442C2×#103C2×D7911yescharacteristic
443C2×#102—791no—
444C2×#102—791no—
445C2×C22⋊C8—791no—
446C2×C22⋊C8C2×D7911yescharacteristic
447C2×#97—791no—
448C2×C4×C8—791no—
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—1581no—
454C22×Q8C22×D7911yescharacteristic
455C22×Q8C22×D7914yes—
456C22×Q8C22×D7911yescharacteristic
457C22×Q8C22×D7911yescharacteristic
458C22×D4—791no—
459C22×D4—1581no—
460C23×C4—21no—
461C23×C4—1581no—
462C23×C4C22×D7911yescharacteristic
463C2×Q16—24no—
464C2×Q16—24no—
465C2×Q16C22×D7914yes—
466C2×Q16C22×D7914yes—
467C2×SD16—794no—
468C2×SD16—794no—
469C2×SD16—1584no—
470C2×SD16—1584no—
471C22×C8—791no—
472C22×C8—791no—
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—794no—
476C4⋊Q8—1582no—
477#126—1588no—
478#124—794no—
479#124—1582no—
480#124—1588no—
481#123—1588no—
482C22⋊Q8—22no—
483C22⋊Q8—1588no—
484C22⋊Q8C22×D7914yes—
485#121—794no—
486#121—1582no—
487C4×Q8—794no—
488C4×Q8—794no—
489C4×Q8—794no—
490C4×Q8—794no—
491C4×Q8—794no—
492C4×Q8—1582no—
493C4×Q8—1582no—
494C4×Q8—1582no—
495C4×Q8—1582no—
496C4×Q8—1582no—
497C4×Q8—1588no—
498C4×Q8—1588no—
499C4×D4—794no—
500C4×D4—1582no—
501#117—794no—
502#117—794no—
503#117—794no—
504#117—1588no—
505#117—1588no—
506#117—1582no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4C22×D7911yescharacteristic
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—
533C2×C42—1581no—
534C2×C42—1581no—
535C2×C42—1581no—
536#107—794no—
537#107—794no—
538#106—794no—
539#106—794no—
540C4⋊C8—794no—
541C4⋊C8—794no—
542#103—794no—
543#103—794no—
544#103—794no—
545#103—794no—
546#103C22×D7914yes—
547#103C22×D7914yes—
548#102—794no—
549#102—794no—
550C22⋊C8—794no—
551C22⋊C8C22×D7914yes—
552#97—794no—
553C4×C8—794no—
554C24—1581no—
555C24D4×D7911yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—6322no—
569C2×Q8—1584no—
570C2×Q8#1192962314yes—
571C2×Q8#1192962314yes—
572C2×Q8C23×D7912yes—
573C2×Q8C23×D7912yes—
574C2×Q8C23×D7912yes—
575C2×D4—792no—
576C2×D4—6322no—
577C2×D4—1584no—
578C2×D4—1582no—
579C2×D4—1582no—
580C2×D4—1581no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—791no—
590C22×C4—791no—
591C22×C4—791no—
592C22×C4—791no—
593C22×C4—6322no—
594C22×C4—1584no—
595C22×C4—1581no—
596C22×C4—1581no—
597C22×C4—1581no—
598C22×C4D4×D7912yes—
599C22×C4D4×D7911yescharacteristic
600C22×C4C23×D7912yes—
601C22×C4C23×D7911yescharacteristic
602Q16—28no—
603Q16—28no—
604SD16—1588no—
605SD16—1588no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—792no—
609C2×C8—792no—
610C2×C8—1582no—
611C2×C8—1582no—
612C2×C8C23×D7912yes—
613C2×C8C23×D7912yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—794no—
617C4⋊C4—794no—
618C4⋊C4—792no—
619C4⋊C4—792no—
620C4⋊C4—792no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1581no—
628C4⋊C4—1581no—
629C4⋊C4—1581no—
630C4⋊C4C23×D7912yes—
631C22⋊C4—24no—
632C22⋊C4—794no—
633C22⋊C4—794no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C42—792no—
640C42—792no—
641C42—792no—
642C42—792no—
643C42—1584no—
644C42—1584no—
645C42—1584no—
646C42—1584no—
647C42—1584no—
648C42—1584no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—3162no—
653C23—3162no—
654C23—3162no—
655C23—1582no—
656C23C2×D4×D7912yes—
657C23C2×D4×D7911yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8—22no—
665Q8—42no—
666Q8—6324no—
667Q8C2×#1192962314yes—
668Q8C2×#1192962314yes—
669D4—3162no—
670D4—6324no—
671D4—1582no—
672D4—1582no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—3162no—
687C2×C4—3162no—
688C2×C4—3162no—
689C2×C4—792no—
690C2×C4—792no—
691C2×C4—792no—
692C2×C4—792no—
693C2×C4—6324no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4C2×D4×D7912yes—
702C2×C4C2×D4×D7911yescharacteristic
703C2×C4C2×#1192962312yes—
704C2×C4C2×#1192962312yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1582no—
709C8—1582no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—3162no—
715C22—3162no—
716C22—3162no—
717C22—6324no—
718C22#1909906912yes—
719C22#1909937212yes—
720C22#1909937612yes—
721C22C22×D4×D7911yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—1582no—
731C4—1582no—
732C4—1582no—
733C4—1582no—
734C4#1909906912yes—
735C4C22×#1192962311yescharacteristic
736C4C22×#1192962311yescharacteristic
737C2—42no—
738C2—6322no—
739C2#2377363014yesdirect product factor
740C2C2×#1909906911yescharacteristic
741C2C2×#1909937211yescharacteristic
742C2C2×#1909937611yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#451×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenterC2×#451D79
hypocenterC79C2×#3121
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#19099041C2semidirect
3. #23773630C2direct (N × H)
4. C2×#19098901C2semidirect
6. C2×#19098856C2semidirect
7. C2×#19098846C2semidirect
8. C2×#19098787C2semidirect
9. C2×#19098787C2semidirect
11. C2×#19098670C2semidirect
12. C2×#19098666C2semidirect
13. C2×Q16×Dic79C2semidirect
14. C2×#19098648C2semidirect
15. C2×#19098621C2semidirect
16. C2×#451×C79C2semidirect
29. #19099041C22semidirect
42. #19098901C22semidirect
44. #19098856C22semidirect
45. #19098846C22semidirect
46. #19098787C22semidirect
47. #19098787C22semidirect
49. #19098670C22semidirect
50. #19098666C22semidirect
51. Q16×Dic79C22semidirect
52. #19098648C22semidirect
53. #19098621C22semidirect
73. #451×C79C22semidirect
367. C2×C79#3121semidirect
381. C2×#451D79semidirect
388. C79C2×#3121semidirect
424. #451C2×D79semidirect
739. C2#23773630direct (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×#190990412
#237736302
C2×#190989012
C2×#190988882
C2×#190988562
C2×#190988462
C2×#190987872
C2×#190987022
C2×#190986702
C2×#190986662
C2×Q16×Dic792
C2×#190986482
C2×#190986212
C2×#451×C792
C2×#312179