Finite Group Databasebeta

← C2×#23773616 #35156534

Subgroups — C2×#23773616 #35156534

Order 20224.

2070 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×#19099175C211yesmaximal, characteristic, complemented
2C2×#19099043C211yesmaximal, characteristic
3#23773616C2116yesmaximal, direct product factor
4C2×#19098899C211yesmaximal, characteristic, complemented
5C2×#19098894C211yesmaximal, characteristic, complemented
6C2×#19098871C211yesmaximal, characteristic, complemented
7C2×#19098864C211yesmaximal, characteristic, complemented
8C2×#19098774C211yesmaximal, characteristic, complemented
9C2×#19098769C211yesmaximal, characteristic, complemented
10C2×#19098727C211yesmaximal, characteristic
11C2×#19098727C211yesmaximal, characteristic
12C2×#19098671C211yesmaximal, characteristic, complemented
13C2×#19098665C211yesmaximal, characteristic, complemented
14C2×C4×Dic316C211yesmaximal, characteristic, complemented
15C2×C4×#11929613C211yesmaximal, characteristic, complemented
16C2×#433×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×Dic316C2211yescharacteristic
20C22×#11929613C2211yescharacteristic
21C22×#11929613C2211yescharacteristic
22#19099175—24no—
23#19099175C2218yescomplemented
24C2×#14579161C2211yescharacteristic
25C2×#14579154—21no—
26C2×#14579154—21no—
27C2×#14579153C2211yescharacteristic
28C2×#14579151—21no—
29C2×#14579151—21no—
30C2×#14579140C2211yescharacteristic
31C2×#14579140C2211yescharacteristic
32#19099043—24no—
33#19099043C2218yes—
34C2×C4×Dic158C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×Dic158C2211yescharacteristic
37C2×C4×Dic158C2211yescharacteristic
38C2×C4×D316C2211yescharacteristic
39C2×C4×D316C2211yescharacteristic
40C2×(C22⋊D79)⋊C4—21no—
41C2×(C22⋊D79)⋊C4—21no—
42C2×#14579119—21no—
43C22×C4⋊Dic79C2211yescharacteristic
44C2×C4⋊C4×D79—21no—
45#19098899C2218yescomplemented
46#19098894C2218yescomplemented
47#19098871C2218yescomplemented
48#19098864C2218yescomplemented
49#19098774C2218yescomplemented
50#19098769C2218yescomplemented
51#19098727C2218yes—
52#19098727C2218yes—
53#19098671C2218yescomplemented
54#19098665C2218yescomplemented
55C4×Dic316C2218yescomplemented
56C4×#11929613C2218yescomplemented
57C2×#14579095C2211yescharacteristic
58C2×#14579095C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579093C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579086C2211yescharacteristic
66C2×#14579086C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579083C2211yescharacteristic
69C2×#117×C79C2211yescharacteristic
70#433×C79C2218yescomplemented
71C2×C4⋊C8×C79C2211yescharacteristic
72C2×C4⋊C8×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×#97×C79C2211yescharacteristic
76C2×C4×C8×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—24no—
79C2×#11929624—24no—
80C2×#11929624C2314yes—
81C22×Dic158C2311yescharacteristic
82C22×Dic158C2311yescharacteristic
83C22×Dic158C2311yescharacteristic
84C22×D316C2311yescharacteristic
85C22×C22⋊D79—21no—
86C23×Dic79—21no—
87C22×C4×D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79—21no—
90C2×Dic316—24no—
91C2×Dic316—24no—
92C2×Dic316C2314yes—
93C2×Dic316C2314yes—
94C2×#11929613—24no—
95C2×#11929613—24no—
96C2×#11929613C2314yes—
97C2×#11929613C2314yes—
98#14579161—22no—
99#14579161C2314yes—
100#14579154—28no—
101#14579154—28no—
102#14579153—22no—
103#14579153C2314yes—
104#14579151—28no—
105#14579151—28no—
106#14579140—22no—
107#14579140—22no—
108#14579140C2314yes—
109#14579140C2314yes—
110C4×Dic158—22no—
111C4×Dic158—22no—
112C4×Dic158—22no—
113C4×Dic158—22no—
114C4×Dic158C2314yes—
115C4×Dic158C2314yes—
116C4×Dic158C2314yes—
117C4×Dic158C2314yes—
118C4×D316—22no—
119C4×D316—22no—
120C4×D316C2314yes—
121C4×D316C2314yes—
122(C22⋊D79)⋊C4—28no—
123(C22⋊D79)⋊C4—28no—
124#14579119—28no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79—22no—
127C2×C4⋊Dic79—21no—
128C2×C4⋊Dic79—21no—
129C2×C4⋊Dic79C2314yes—
130C2×C4⋊Dic79C2311yescharacteristic
131C2×C4⋊Dic79C2311yescharacteristic
132C2×C4⋊Dic79C2311yescharacteristic
133C2×C4⋊Dic79C2311yescharacteristic
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4—21no—
140C2×Dic79⋊C4—21no—
141C2×Dic79⋊C4—21no—
142C4⋊C4×D79—28no—
143C2×C22⋊Dic79—21no—
144C2×C22⋊Dic79—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×C4×Dic79—21no—
148C2×C4×Dic79—21no—
149C2×C4×Dic79—21no—
150C2×C4×Dic79—21no—
151#14579095C2314yes—
152#14579095C2314yes—
153#14579093C2314yes—
154#14579093C2314yes—
155#14579086C2314yes—
156#14579086C2314yes—
157#14579086C2314yes—
158#14579086C2314yes—
159#14579086C2314yes—
160#14579086C2314yes—
161#14579083C2314yes—
162#14579083C2314yes—
163C23×C4×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168#117×C79D414yes—
169#117×C79C2314yes—
170C2×C4⋊C4×C79D411yescharacteristic
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C22⋊C4×C79D411yescharacteristic
173C2×C22⋊C4×C79D411yescharacteristic
174C2×C42×C79C2311yescharacteristic
175C2×C42×C79C2311yescharacteristic
176C4⋊C8×C79C2314yes—
177C4⋊C8×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C22⋊C8×C79C2314yes—
180#97×C79C2314yes—
181C4×C8×C79C2314yes—
182C23×D79—21no—
183#11929624—216no—
184#11929624—28no—
185#11929624—28no—
186C2×Dic158—21no—
187C2×Dic158—21no—
188C2×Dic158—21no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158—22no—
193C2×Dic158—22no—
194C2×Dic158#4114yes—
195C2×Dic158C2412yes—
196C2×Dic158C2412yes—
197C2×Dic158C2412yes—
198C2×D316—21no—
199C2×D316—22no—
200C2×D316#4114yes—
201C2×D316C2412yes—
202C2×C22⋊D79—28no—
203C2×C22⋊D79—24no—
204C22×Dic79—21no—
205C22×Dic79—21no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—21no—
210C22×Dic79—21no—
211C22×Dic79—24no—
212C22×Dic79—82no—
213C2×C4×D79—28no—
214C2×C4×D79—24no—
215C2×C4×D79—24no—
216C2×C4×D79—24no—
217C2×C4×D79—82no—
218C2×C4×D79—82no—
219Dic316—28no—
220Dic316—28no—
221#11929613—28no—
222#11929613—28no—
223C4⋊Dic79—24no—
224C4⋊Dic79—21no—
225C4⋊Dic79—21no—
226C4⋊Dic79—24no—
227C4⋊Dic79—24no—
228C4⋊Dic79—21no—
229C4⋊Dic79—21no—
230C4⋊Dic79C2412yes—
231C4⋊Dic79C2412yes—
232C4⋊Dic79C2412yes—
233C4⋊Dic79C2412yes—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236Dic79⋊C4—24no—
237Dic79⋊C4—24no—
238Dic79⋊C4—24no—
239Dic79⋊C4—24no—
240Dic79⋊C4—24no—
241Dic79⋊C4—24no—
242C22⋊Dic79—24no—
243C22⋊Dic79—24no—
244(C2×D79)⋊C4—24no—
245(C2×D79)⋊C4—24no—
246C4×Dic79—24no—
247C4×Dic79—24no—
248C4×Dic79—24no—
249C4×Dic79—24no—
250C24×C79C2×D411yescharacteristic
251C22×C4×C79—22no—
252C22×C4×C79—22no—
253C22×C4×C79C2×D412yes—
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2412yes—
260C22×C4×C79C2411yescharacteristic
261C2×C8×C79—22no—
262C2×C8×C79—22no—
263C2×C8×C79—22no—
264C2×C8×C79—22no—
265C2×C8×C79C2412yes—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C2×C8×C79C2412yes—
269C4⋊C4×C79C2×D414yes—
270C4⋊C4×C79C2×D414yes—
271C22⋊C4×C79C2×D414yes—
272C22⋊C4×C79C2×D414yes—
273C42×C79C2×D412yes—
274C42×C79C2×D412yes—
275C42×C79C2412yes—
276C42×C79C2412yes—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—22no—
280C23×C79C22×D412yes—
281C23×C79C22×D411yescharacteristic
282C22×D79—24no—
283C22×D79—22no—
284C22×D79—42no—
285C22×D79—42no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—24no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D412yes—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D411yescharacteristic
300C2×C4×C79C2×#4112yes—
301C2×C4×C79C2×#4112yes—
302C2×C4×C79C2511yescharacteristic
303C22⋊D79—216no—
304C2×Dic79—24no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—84no—
319D316—24no—
320D316—22no—
321D316C2×#4114yes—
322C4×D79—216no—
323C4×D79—84no—
324C4×D79—84no—
325Dic158—24no—
326Dic158—22no—
327Dic158—22no—
328Dic158—22no—
329Dic158—22no—
330Dic158—22no—
331Dic158—42no—
332Dic158—42no—
333Dic158C2×#4114yes—
334C8×C79—22no—
335C8×C79—22no—
336C8×C79—22no—
337C8×C79—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—24no—
347C2×D79—48no—
348C2×D79—42no—
349C2×D79—42no—
350C4×C79—22no—
351C4×C79—22no—
352C4×C79—22no—
353C4×C79—22no—
354C4×C79—22no—
355C4×C79#52512yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C22×#4111yescharacteristic
358Dic79—24no—
359Dic79—42no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365C2×#3120—791nomaximal, Sylow
366C2×C79—42no—
367C2×C79#312014yescomplemented
368C2×C79C2×#52511yescharacteristic
369C2×C79C2×#57711yescharacteristic
370C2×C79C2×#57811yescharacteristic
371D79—44no—
372C2×#541—791no—
373C2×#520—791no—
374#3120—7916no—
375C2×#484—791no—
376C2×#483—791no—
377C2×#479—791no—
378C2×#478—791no—
379C2×#462—791no—
380C2×#461—791no—
381C2×#452—791no—
382C2×#452—791no—
383C2×#441—791no—
384C2×#440—791no—
385C2×C4×Q16—791no—
386C2×C4×SD16—791no—
387C2×#433D7911yescharacteristic, complemented
388C79C2×#312011yescharacteristic, complemented, Sylow
389C22×#41—791no—
390C22×Q16—791no—
391C22×Q16—791no—
392C22×SD16—791no—
393C22×SD16—791no—
394#541—798no—
395#541—1584no—
396C2×C4⋊Q8—791no—
397C2×#126—1581no—
398C2×#126—1581no—
399C2×#125—791no—
400C2×#125—1581no—
401C2×#125—1581no—
402C2×C22⋊Q8—791no—
403C2×C22⋊Q8—791no—
404#520—798no—
405#520—1584no—
406C2×C4×Q8—791no—
407C2×C4×Q8—791no—
408C2×C4×Q8—791no—
409C2×C4×Q8—791no—
410C2×C4×D4—791no—
411C2×C4×D4—791no—
412C2×C4×D4—1581no—
413C2×C4×D4—1581no—
414C2×#117—1581no—
415C2×#117C2×D7911yescharacteristic
416C22×C4⋊C4—791no—
417C22×C4⋊C4—1581no—
418#484—798no—
419#483—798no—
420#479—798no—
421#478—798no—
422#462—798no—
423#461—798no—
424#452—798no—
425#452—798no—
426#441—798no—
427#440—798no—
428C4×Q16—798no—
429C4×SD16—798no—
430#433C2×D7918yescomplemented
431C2×#107—791no—
432C2×#107—791no—
433C2×#106—791no—
434C2×#106—791no—
435C2×C4⋊C8C2×D7911yescharacteristic
436C2×C4⋊C8C2×D7911yescharacteristic
437C2×#103—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103—791no—
443C2×#102—791no—
444C2×#102—791no—
445C2×C22⋊C8C2×D7911yescharacteristic
446C2×C22⋊C8C2×D7911yescharacteristic
447C2×#97C2×D7911yescharacteristic
448C2×C4×C8C2×D7911yescharacteristic
449C2×#41—794no—
450C2×#41—1584no—
451C2×#41—1584no—
452C2×#41—1582no—
453C22×Q8—791no—
454C22×Q8—791no—
455C22×Q8—791no—
456C22×D4—791no—
457C22×D4—1581no—
458C23×C4—1581no—
459C23×C4—1581no—
460C23×C4—1581no—
461C23×C4—1581no—
462C23×C4C22×D7911yescharacteristic
463C2×Q16—794no—
464C2×Q16—794no—
465C2×Q16—1584no—
466C2×Q16—1584no—
467C2×SD16—794no—
468C2×SD16—794no—
469C2×SD16—1584no—
470C2×SD16—1584no—
471C22×C8C22×D7911yescharacteristic
472C22×C8C22×D7911yescharacteristic
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—794no—
476C4⋊Q8—1582no—
477#126—1588no—
478#126—1588no—
479#125—794no—
480#125—1588no—
481#125—1588no—
482#125—1582no—
483C22⋊Q8—794no—
484C22⋊Q8—794no—
485C22⋊Q8—1582no—
486C22⋊Q8—1582no—
487C4×Q8—794no—
488C4×Q8—794no—
489C4×Q8—794no—
490C4×Q8—794no—
491C4×Q8—1582no—
492C4×Q8—1582no—
493C4×Q8—1582no—
494C4×Q8—1582no—
495C4×D4—794no—
496C4×D4—794no—
497C4×D4—1588no—
498C4×D4—1588no—
499C4×D4—1582no—
500C4×D4—1582no—
501#117—1588no—
502#117D31614yes—
503#117C22×D7914yes—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—794no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1582no—
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⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4—1581no—
521C2×C4⋊C4—1588no—
522C2×C4⋊C4D31611yescharacteristic
523C2×C4⋊C4D31611yescharacteristic
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4D31611yescharacteristic
529C2×C22⋊C4D31611yescharacteristic
530C2×C42—1581no—
531C2×C42—1581no—
532C2×C42—1581no—
533C2×C42—1581no—
534C2×C42C22×D7911yescharacteristic
535C2×C42C22×D7911yescharacteristic
536#107—794no—
537#107—794no—
538#106—794no—
539#106—794no—
540C4⋊C8C22×D7914yes—
541C4⋊C8C22×D7914yes—
542#103—794no—
543#103—794no—
544#103—794no—
545#103—794no—
546#103—794no—
547#103—794no—
548#102—794no—
549#102—794no—
550C22⋊C8C22×D7914yes—
551C22⋊C8C22×D7914yes—
552#97C22×D7914yes—
553C4×C8C22×D7914yes—
554C24—1581no—
555C24C2×D31611yescharacteristic
556#41—1588no—
557#41—1588no—
558#41—15816no—
559C2×Q8—794no—
560C2×Q8—792no—
561C2×Q8—792no—
562C2×Q8—792no—
563C2×Q8—1582no—
564C2×Q8—1582no—
565C2×Q8—1582no—
566C2×Q8—1582no—
567C2×Q8—1582no—
568C2×Q8—1581no—
569C2×Q8—1581no—
570C2×Q8—1581no—
571C2×D4—794no—
572C2×D4—792no—
573C2×D4—1588no—
574C2×D4—1584no—
575C2×D4—1582no—
576C2×D4—1581no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—6322no—
580C22×C4—6322no—
581C22×C4—6322no—
582C22×C4—1588no—
583C22×C4—1581no—
584C22×C4—1581no—
585C22×C4—1581no—
586C22×C4—1581no—
587C22×C4—1581no—
588C22×C4—1581no—
589C22×C4—1584no—
590C22×C4—1584no—
591C22×C4—1584no—
592C22×C4—1581no—
593C22×C4—1584no—
594C22×C4C2×D31612yes—
595C22×C4C2×D31611yescharacteristic
596C22×C4C2×D31611yescharacteristic
597C22×C4C2×D31611yescharacteristic
598C22×C4C2×D31611yescharacteristic
599C22×C4C2×D31611yescharacteristic
600C22×C4C23×D7912yes—
601C22×C4C23×D7911yescharacteristic
602Q16—1588no—
603Q16—1588no—
604SD16—1588no—
605SD16—1588no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D7912yes—
611C2×C8C23×D7912yes—
612C2×C8C23×D7912yes—
613C2×C8C23×D7912yes—
614C4⋊C4—792no—
615C4⋊C4—792no—
616C4⋊C4—792no—
617C4⋊C4—792no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
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⋊C4—1581no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4C2×D31614yes—
634C4⋊C4C2×D31614yes—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C22⋊C4C2×D31614yes—
640C22⋊C4C2×D31614yes—
641C42—1584no—
642C42—1584no—
643C42—1584no—
644C42—1584no—
645C42C2×D31612yes—
646C42C2×D31612yes—
647C42C23×D7912yes—
648C42C23×D7912yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—3162no—
653C23—3162no—
654C23—1584no—
655C23—1582no—
656C23C22×D31612yes—
657C23C22×D31611yescharacteristic
658Q8—3162no—
659Q8—3162no—
660Q8—794no—
661Q8—1582no—
662Q8—1582no—
663Q8—1582no—
664Q8—1582no—
665Q8—1584no—
666Q8—1582no—
667D4—794no—
668D4—15816no—
669D4—1584no—
670D4—1582no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—3162no—
680C2×C4—3162no—
681C2×C4—3162no—
682C2×C4—3162no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—6324no—
686C2×C4—6324no—
687C2×C4—6324no—
688C2×C4—15816no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1584no—
696C2×C4—1582no—
697C2×C4C22×D31612yes—
698C2×C4C22×D31612yes—
699C2×C4C22×D31612yes—
700C2×C4C22×D31612yes—
701C2×C4C22×D31612yes—
702C2×C4C22×D31611yescharacteristic
703C2×C4#41×D7912yes—
704C2×C4#41×D7912yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—3162no—
715C22—3162no—
716C22—3168no—
717C22—1584no—
718C22#1909907512yes—
719C22#1909937512yes—
720C22#1909938012yes—
721C22C23×D31611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—3162no—
731C4—3162no—
732C4—3162no—
733C4—1584no—
734C4#1909907512yes—
735C4C2×#41×D7911yescharacteristic
736C4C2×#41×D7911yescharacteristic
737C2—42no—
738C2—3164no—
739C2#2377361614yesdirect product factor
740C2C2×#1909907511yescharacteristic
741C2C2×#1909937511yescharacteristic
742C2C2×#1909938011yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#433×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929624C22
hypercenterC2×#433D79
hypocenterC79C2×#3120
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#19099175C2semidirect
3. #23773616C2direct (N × H)
4. C2×#19098899C2semidirect
5. C2×#19098894C2semidirect
6. C2×#19098871C2semidirect
7. C2×#19098864C2semidirect
8. C2×#19098774C2semidirect
9. C2×#19098769C2semidirect
12. C2×#19098671C2semidirect
13. C2×#19098665C2semidirect
14. C2×C4×Dic316C2semidirect
15. C2×C4×#11929613C2semidirect
16. C2×#433×C79C2semidirect
23. #19099175C22semidirect
45. #19098899C22semidirect
46. #19098894C22semidirect
47. #19098871C22semidirect
48. #19098864C22semidirect
49. #19098774C22semidirect
50. #19098769C22semidirect
53. #19098671C22semidirect
54. #19098665C22semidirect
55. C4×Dic316C22semidirect
56. C4×#11929613C22semidirect
70. #433×C79C22semidirect
367. C2×C79#3120semidirect
387. C2×#433D79semidirect
388. C79C2×#3120semidirect
430. #433C2×D79semidirect
739. C2#23773616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991752
C2×#190990432
#237736162
C2×#190988992
C2×#190988942
C2×#190988712
C2×#190988642
C2×#190987742
C2×#190987692
C2×#190987272
C2×#190986712
C2×#190986652
C2×C4×Dic3162
C2×C4×#119296132
C2×#433×C792
C2×#312079