Finite Group Databasebeta

← C2×#23768488 #34458372

Subgroups — C2×#23768488 #34458372

Order 20224.

2726 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
1C22×#14579153C211yesmaximal, characteristic, complemented
2C22×#14579139C211yesmaximal, characteristic
3#23768488C2116yesmaximal, direct product factor
4C2×#19098498C211yesmaximal, characteristic
5C2×#19098497C211yesmaximal, characteristic, complemented
6C2×#19098487C211yesmaximal, characteristic
7C2×#19098484C211yesmaximal, characteristic, complemented
8C2×#19098467C211yesmaximal, characteristic, complemented
9C2×#19098459C211yesmaximal, characteristic, complemented
10C2×#19098458C211yesmaximal, characteristic, complemented
11C2×#19098455C211yesmaximal, characteristic
12C2×#19098455C211yesmaximal, characteristic
13C2×#19098437C211yesmaximal, characteristic
14C2×#19098414C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic
16C2×#387×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C2×#14579153—28no—
20C2×#14579153C2218yescomplemented
21C2×#14579139—28no—
22C2×#14579139C2218yes—
23C22×C4⋊Dic79C2211yescharacteristic
24C22×C4⋊Dic79C2211yescharacteristic
25C22×C4⋊Dic79C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2211yescharacteristic
32C22×Dic79⋊C4C2211yescharacteristic
33C22×Dic79⋊C4C2211yescharacteristic
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×(C2×D79)⋊C4C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×(C2×D79)⋊C4C2211yescharacteristic
39C22×(C2×D79)⋊C4C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098498C2218yes—
44#19098497C2218yescomplemented
45#19098487C2218yes—
46#19098484C2218yescomplemented
47#19098467C2218yescomplemented
48#19098459C2218yescomplemented
49#19098458C2218yescomplemented
50#19098455C2218yes—
51#19098455C2218yes—
52#19098437C2218yes—
53#19098414C2218yescomplemented
54C4×(C2×D79)⋊C4C2218yes—
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C42×C79C2211yescharacteristic
64#387×C79C2218yescomplemented
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C2×#95×C79C2211yescharacteristic
69C24×D79C2311yescharacteristic
70C22×Dic158—24no—
71C22×Dic158—24no—
72C22×Dic158—42no—
73C22×Dic158C2314yes—
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2311yescharacteristic
81C22×C4×D79—24no—
82C22×C4×D79—24no—
83C22×C4×D79—42no—
84C22×C4×D79C2314yes—
85#14579153—232no—
86#14579139—232no—
87C2×C4⋊Dic79—24no—
88C2×C4⋊Dic79—24no—
89C2×C4⋊Dic79—24no—
90C2×C4⋊Dic79C2314yes—
91C2×C4⋊Dic79C2314yes—
92C2×C4⋊Dic79C2314yes—
93C2×Dic79⋊C4—24no—
94C2×Dic79⋊C4—24no—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4—24no—
97C2×Dic79⋊C4—24no—
98C2×Dic79⋊C4—24no—
99C2×Dic79⋊C4—42no—
100C2×Dic79⋊C4D418yes—
101C2×Dic79⋊C4C2314yes—
102C2×Dic79⋊C4C2314yes—
103C2×Dic79⋊C4C2314yes—
104C2×Dic79⋊C4C2314yes—
105C2×Dic79⋊C4C2314yes—
106C2×Dic79⋊C4C2314yes—
107C2×Dic79⋊C4C2314yes—
108C2×Dic79⋊C4C2314yes—
109C2×(C2×D79)⋊C4—24no—
110C2×(C2×D79)⋊C4—24no—
111C2×(C2×D79)⋊C4—24no—
112C2×(C2×D79)⋊C4—24no—
113C2×(C2×D79)⋊C4—42no—
114C2×(C2×D79)⋊C4Q818yescomplemented
115C2×(C2×D79)⋊C4C2314yes—
116C2×(C2×D79)⋊C4C2314yes—
117C2×(C2×D79)⋊C4C2314yes—
118C2×(C2×D79)⋊C4C2314yes—
119C2×(C2×D79)⋊C4C2314yes—
120C2×(C2×D79)⋊C4C2314yes—
121C2×C4×Dic79—24no—
122C2×C4×Dic79—42no—
123C2×C4×Dic79—42no—
124C2×C4×Dic79C2314yes—
125C2×C4×Dic79C2314yes—
126C2×C4×Dic79C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C23×C4×C79C2311yescharacteristic
139C23×C4×C79C2311yescharacteristic
140C2×C4⋊C4×C79—24no—
141C2×C4⋊C4×C79—24no—
142C2×C4⋊C4×C79C2314yes—
143C2×C4⋊C4×C79C2314yes—
144C2×C42×C79—24no—
145C2×C42×C79C2314yes—
146#95×C79C2314yes—
147#95×C79C2314yes—
148#95×C79C2314yes—
149#95×C79C2314yes—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79—22no—
153C23×D79—22no—
154C23×D79—22no—
155C23×D79—22no—
156C23×D79C2×Q814yes—
157C23×D79C2412yes—
158C2×Dic158—28no—
159C2×Dic158—28no—
160C2×Dic158—44no—
161C2×Dic158—416no—
162C22×Dic79—22no—
163C22×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—22no—
178C22×Dic79C2×D414yes—
179C22×Dic79C2×D414yes—
180C22×Dic79C2×Q814yes—
181C22×Dic79#4114yes—
182C22×Dic79#4114yes—
183C22×Dic79C2412yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C22×Dic79C2412yes—
189C22×Dic79C2412yes—
190C2×C4×D79—28no—
191C2×C4×D79—28no—
192C2×C4×D79—44no—
193C2×C4×D79—416no—
194C4⋊Dic79—28no—
195C4⋊Dic79—28no—
196C4⋊Dic79—28no—
197Dic79⋊C4—28no—
198Dic79⋊C4—28no—
199Dic79⋊C4—28no—
200Dic79⋊C4—28no—
201Dic79⋊C4—28no—
202Dic79⋊C4—28no—
203Dic79⋊C4—44no—
204Dic79⋊C4C2×D4116yes—
205(C2×D79)⋊C4—28no—
206(C2×D79)⋊C4—28no—
207(C2×D79)⋊C4—28no—
208(C2×D79)⋊C4—28no—
209(C2×D79)⋊C4—44no—
210(C2×D79)⋊C4C2×Q8116yescomplemented
211C4×Dic79—28no—
212C4×Dic79—44no—
213C4×Dic79—44no—
214C24×C79C2411yescharacteristic
215C22×C4×C79—22no—
216C22×C4×C79—22no—
217C22×C4×C79—22no—
218C22×C4×C79—22no—
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—22no—
223C22×C4×C79—22no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—22no—
231C22×C4×C79—22no—
232C22×C4×C79—22no—
233C22×C4×C79C2×D414yes—
234C22×C4×C79C2×Q814yes—
235C22×C4×C79#4114yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C22×C4×C79C2412yes—
241C22×C4×C79C2412yes—
242C22×C4×C79C2412yes—
243C4⋊C4×C79—28no—
244C4⋊C4×C79—28no—
245C42×C79—28no—
246C23×C79C22×D412yes—
247C23×C79C22×Q812yes—
248C23×C79C2×#4112yes—
249C23×C79C2×#4112yes—
250C23×C79C2×#4112yes—
251C23×C79H(5,𝔽2)12yes—
252C23×C792−1+412yes—
253C23×C79C2511yescharacteristic
254C22×D79—28no—
255C22×D79—28no—
256C22×D79—28no—
257C22×D79—22no—
258C22×D79—22no—
259C22×D79—22no—
260C22×D79—22no—
261C22×D79—22no—
262C22×D79—22no—
263C22×D79—44no—
264C22×D79—44no—
265C22×D79—44no—
266C22×D79—44no—
267C22×D79C22×Q814yes—
268C2×C4×C79—28no—
269C2×C4×C79—28no—
270C2×C4×C79—28no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—44no—
290C2×C4×C79—44no—
291C2×C4×C79—44no—
292C2×C4×C79—44no—
293C2×C4×C79C22×D414yes—
294C2×C4×C79C22×Q814yes—
295C2×C4×C79C2×#4114yes—
296C2×Dic79—28no—
297C2×Dic79—28no—
298C2×Dic79—28no—
299C2×Dic79—28no—
300C2×Dic79—28no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—44no—
318C2×Dic79—44no—
319C2×Dic79C22×D414yes—
320C2×Dic79C22×D414yes—
321C2×Dic79C22×Q814yes—
322C2×Dic79C2×#4114yes—
323C2×Dic79C2×#4114yes—
324C4×D79—416no—
325Dic158—416no—
326C22×C79#53214yes—
327C22×C79#53314yes—
328C22×C79#53914yes—
329C22×C79#54614yes—
330C22×C79D4×Q814yes—
331C22×C79#55214yes—
332C22×C79#55414yes—
333C22×C79C23×D411yescharacteristic
334C22×C79C23×Q811yescharacteristic
335C22×C79C22×#4111yescharacteristic
336C22×C79C22×#4111yescharacteristic
337C22×C79C22×#4111yescharacteristic
338C22×C79C2×H(5,𝔽2)11yescharacteristic
339C22×C79C2×2−1+411yescharacteristic
340C2×D79—24no—
341C2×D79—24no—
342C2×D79—24no—
343C2×D79—42no—
344C2×D79—42no—
345C2×D79—42no—
346C2×D79—42no—
347C2×D79—416no—
348C4×C79—24no—
349C4×C79—24no—
350C4×C79—24no—
351C4×C79—42no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79—42no—
355Dic79—24no—
356Dic79—24no—
357Dic79—24no—
358Dic79—24no—
359Dic79—24no—
360Dic79—42no—
361Dic79—42no—
362C2×#2556—791nomaximal, Sylow
363C2×C79#255618yescomplemented
364C2×C79C2×#53211yescharacteristic
365C2×C79C2×#53311yescharacteristic
366C2×C79C2×#53911yescharacteristic
367C2×C79C2×#54611yescharacteristic
368C2×C79C2×D4×Q811yescharacteristic
369C2×C79C2×#55211yescharacteristic
370C2×C79C2×#55411yescharacteristic
371D79—44no—
372C22×#125—791no—
373C22×C22⋊Q8—791no—
374#2556—7916no—
375C2×#399—791no—
376C2×#398—791no—
377C2×#396—791no—
378C2×#395—791no—
379C2×#391—791no—
380C2×#389—791no—
381C2×#389—791no—
382C2×#388—791no—
383C2×#388—791no—
384C2×#387D7911yescharacteristic, complemented
385C2×#385—791no—
386C2×C4×C4⋊C4—791no—
387C2×C4×C22⋊C4—791no—
388C79C2×#255611yescharacteristic, complemented, Sylow
389C23×Q8—791no—
390C24×C4—791no—
391C2×#125—798no—
392C2×#125—1588no—
393C2×C22⋊Q8—798no—
394C2×C22⋊Q8—1588no—
395C22×C4⋊C4—791no—
396C22×C4⋊C4—791no—
397C22×C4⋊C4—791no—
398C22×C4⋊C4—791no—
399C22×C4⋊C4—791no—
400C22×C4⋊C4—791no—
401C22×C4⋊C4—791no—
402C22×C4⋊C4—791no—
403C22×C4⋊C4—791no—
404C22×C4⋊C4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4C2×D7911yescharacteristic
407C22×C4⋊C4C2×D7911yescharacteristic
408C22×C22⋊C4—791no—
409C22×C22⋊C4—791no—
410C22×C22⋊C4—791no—
411C22×C22⋊C4—791no—
412C22×C22⋊C4—791no—
413C22×C22⋊C4—791no—
414C22×C42—791no—
415C22×C42—791no—
416C22×C42—791no—
417C22×C42C2×D7911yescharacteristic
418#399—798no—
419#398—798no—
420#396—798no—
421#395—798no—
422#391—798no—
423#389—798no—
424#389—798no—
425#388—798no—
426#388—798no—
427#387C2×D7918yescomplemented
428#385—798no—
429C4×C4⋊C4—798no—
430C4×C22⋊C4—798no—
431C2×#95—791no—
432C2×#95—791no—
433C2×#95—791no—
434C2×#95—791no—
435C2×#95—791no—
436C2×#95—791no—
437C2×#95C2×D7911yescharacteristic
438C2×#95C2×D7911yescharacteristic
439C2×#95C2×D7911yescharacteristic
440C2×#95C2×D7911yescharacteristic
441C25—791no—
442C22×Q8—3162no—
443C22×Q8—794no—
444C22×Q8—1584no—
445C22×Q8—1584no—
446C23×C4—3162no—
447C23×C4—794no—
448C23×C4—791no—
449C23×C4—791no—
450C23×C4—791no—
451C23×C4—791no—
452C23×C4—791no—
453C23×C4—791no—
454C23×C4—791no—
455C23×C4—1584no—
456C23×C4—1584no—
457C23×C4C22×D7911yescharacteristic
458C23×C4C22×D7911yescharacteristic
459C23×C4C22×D7911yescharacteristic
460C23×C4C22×D7911yescharacteristic
461C23×C4C22×D7911yescharacteristic
462C23×C4C22×D7911yescharacteristic
463C23×C4C22×D7911yescharacteristic
464#125—15832no—
465C22⋊Q8—15832no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—3162no—
469C2×C4⋊C4—794no—
470C2×C4⋊C4—798no—
471C2×C4⋊C4—794no—
472C2×C4⋊C4—794no—
473C2×C4⋊C4—794no—
474C2×C4⋊C4—794no—
475C2×C4⋊C4—794no—
476C2×C4⋊C4—794no—
477C2×C4⋊C4—794no—
478C2×C4⋊C4—794no—
479C2×C4⋊C4—794no—
480C2×C4⋊C4—794no—
481C2×C4⋊C4—1584no—
482C2×C4⋊C4—1584no—
483C2×C4⋊C4—1584no—
484C2×C4⋊C4—1584no—
485C2×C4⋊C4—1584no—
486C2×C4⋊C4—1584no—
487C2×C4⋊C4—1584no—
488C2×C4⋊C4—1584no—
489C2×C4⋊C4—1584no—
490C2×C4⋊C4C22×D7914yes—
491C2×C4⋊C4C22×D7914yes—
492C2×C22⋊C4—3162no—
493C2×C22⋊C4—794no—
494C2×C22⋊C4—798no—
495C2×C22⋊C4—794no—
496C2×C22⋊C4—794no—
497C2×C22⋊C4—794no—
498C2×C22⋊C4—794no—
499C2×C22⋊C4—794no—
500C2×C22⋊C4—1584no—
501C2×C22⋊C4—1584no—
502C2×C22⋊C4—1584no—
503C2×C22⋊C4—1584no—
504C2×C42—24no—
505C2×C42—3162no—
506C2×C42—3162no—
507C2×C42—794no—
508C2×C42—794no—
509C2×C42—794no—
510C2×C42—1584no—
511C2×C42C22×D7914yes—
512#95—794no—
513#95—794no—
514#95—794no—
515#95—794no—
516#95—794no—
517#95—794no—
518#95C22×D7914yes—
519#95C22×D7914yes—
520#95C22×D7914yes—
521#95C22×D7914yes—
522C24—794no—
523C24—792no—
524C24—1582no—
525C24—1582no—
526C24—1582no—
527C24—1582no—
528C24—1582no—
529C24—1582no—
530C24C23×D7911yescharacteristic
531C2×Q8—3164no—
532C2×Q8—31616no—
533C2×Q8—1588no—
534C2×Q8—1588no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—31616no—
554C22×C4—3164no—
555C22×C4—794no—
556C22×C4—794no—
557C22×C4—794no—
558C22×C4—792no—
559C22×C4—792no—
560C22×C4—792no—
561C22×C4—792no—
562C22×C4—792no—
563C22×C4—794no—
564C22×C4—794no—
565C22×C4—792no—
566C22×C4—792no—
567C22×C4—1588no—
568C22×C4—1582no—
569C22×C4—1582no—
570C22×C4—1582no—
571C22×C4—1582no—
572C22×C4—1582no—
573C22×C4—1582no—
574C22×C4—1588no—
575C22×C4—1582no—
576C22×C4—1582no—
577C22×C4—1582no—
578C22×C4—1582no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4—1582no—
582C22×C4—1582no—
583C22×C4—1582no—
584C22×C4—1582no—
585C22×C4D4×D7914yes—
586C22×C4Q8×D7914yes—
587C22×C4#1192962414yes—
588C22×C4C23×D7912yes—
589C22×C4C23×D7912yes—
590C22×C4C23×D7912yes—
591C22×C4C23×D7912yes—
592C22×C4C23×D7912yes—
593C22×C4C23×D7912yes—
594C22×C4C23×D7912yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—3164no—
598C4⋊C4—7916no—
599C4⋊C4—1588no—
600C4⋊C4—1588no—
601C4⋊C4—1588no—
602C4⋊C4—1588no—
603C4⋊C4—1588no—
604C4⋊C4—1588no—
605C4⋊C4—1588no—
606C4⋊C4—1588no—
607C4⋊C4—1588no—
608C22⋊C4—3164no—
609C22⋊C4—7916no—
610C22⋊C4—1588no—
611C22⋊C4—1588no—
612C22⋊C4—1588no—
613C22⋊C4—1588no—
614C42—28no—
615C42—3164no—
616C42—3164no—
617C42—1588no—
618C23—3164no—
619C23—3164no—
620C23—3164no—
621C23—3164no—
622C23—794no—
623C23—1582no—
624C23—1582no—
625C23—1588no—
626C23—1588no—
627C23—1588no—
628C23—1582no—
629C23—1582no—
630C23—1582no—
631C23—1582no—
632C23C2×D4×D7912yes—
633C23C2×Q8×D7912yes—
634C23#41×D7912yes—
635C23#41×D7912yes—
636C23C2×#1192962412yes—
637C23#1457920712yes—
638C23#1457920812yes—
639C23C24×D7911yescharacteristic
640Q8—31616no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—31616no—
667C2×C4—3164no—
668C2×C4—3164no—
669C2×C4—794no—
670C2×C4—794no—
671C2×C4—794no—
672C2×C4—794no—
673C2×C4—794no—
674C2×C4—1582no—
675C2×C4—1582no—
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—1582no—
685C2×C4—1588no—
686C2×C4—1588no—
687C2×C4—1588no—
688C2×C4—1588no—
689C2×C4—1588no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4C2×D4×D7914yes—
696C2×C4C2×Q8×D7914yes—
697C2×C4C2×#1192962414yes—
698C22—3162no—
699C22—3162no—
700C22—31616no—
701C22—3162no—
702C22—3162no—
703C22—1584no—
704C22—1584no—
705C22—1584no—
706C22#1909911014yes—
707C22#1909911914yes—
708C22#1909915414yes—
709C22#1909920514yes—
710C22#1909922614yes—
711C22#1909924614yes—
712C22#1909927314yes—
713C22C22×D4×D7911yescharacteristic
714C22C22×Q8×D7911yescharacteristic
715C22C2×#41×D7911yescharacteristic
716C22C2×#41×D7911yescharacteristic
717C22C22×#1192962411yescharacteristic
718C22C2×#1457920711yescharacteristic
719C22C2×#1457920811yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—3162no—
728C4—3162no—
729C4—1584no—
730C4—1584no—
731C4—1584no—
732C4—1584no—
733C4—1584no—
734C2—3164no—
735C2#2376848818yesdirect product factor
736C2C2×#1909911011yescharacteristic
737C2C2×#1909911911yescharacteristic
738C2C2×#1909915411yescharacteristic
739C2C2×#1909920511yescharacteristic
740C2C2×#1909922611yescharacteristic
741C2C2×#1909924611yescharacteristic
742C2C2×#1909927311yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#387×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#387D79
hypocenterC79C2×#2556
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#14579153C2semidirect
3. #23768488C2direct (N × H)
5. C2×#19098497C2semidirect
7. C2×#19098484C2semidirect
8. C2×#19098467C2semidirect
9. C2×#19098459C2semidirect
10. C2×#19098458C2semidirect
14. C2×#19098414C2semidirect
16. C2×#387×C79C2semidirect
20. C2×#14579153C22semidirect
44. #19098497C22semidirect
46. #19098484C22semidirect
47. #19098467C22semidirect
48. #19098459C22semidirect
49. #19098458C22semidirect
53. #19098414C22semidirect
64. #387×C79C22semidirect
114. C2×(C2×D79)⋊C4Q8semidirect
210. (C2×D79)⋊C4C2×Q8semidirect
363. C2×C79#2556semidirect
384. C2×#387D79semidirect
388. C79C2×#2556semidirect
427. #387C2×D79semidirect
735. C2#23768488direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791532
C22×#145791392
#237684882
C2×#190984982
C2×#190984972
C2×#190984872
C2×#190984842
C2×#190984672
C2×#190984592
C2×#190984582
C2×#190984552
C2×#190984372
C2×#190984142
C2×C4×(C2×D79)⋊C42
C2×#387×C792
C2×#255679