Finite Group Databasebeta

← C2×#23768405 #34458307

Subgroups — C2×#23768405 #34458307

Order 20224.

3094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579141C211yesmaximal, characteristic
2C22×#14579137C211yesmaximal, characteristic
3#23768405C2116yesmaximal, direct product factor
4C2×#19098496C211yesmaximal, characteristic, complemented
5C2×#19098495C211yesmaximal, characteristic, complemented
6C2×#19098484C211yesmaximal, characteristic, complemented
7C2×#19098470C211yesmaximal, characteristic, complemented
8C2×#19098467C211yesmaximal, characteristic, complemented
9C2×#19098462C211yesmaximal, characteristic, complemented
10C2×#19098458C211yesmaximal, characteristic, complemented
11C2×#19098437C211yesmaximal, characteristic
12C2×#19098434C211yesmaximal, characteristic
13C2×#19098420C211yesmaximal, characteristic
14C2×#19098410C211yesmaximal, characteristic
15C2×#95×D79C211yesmaximal, characteristic
16C2×#395×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C23×C4×D79C2211yescharacteristic
21C2×#14579141—28no—
22C2×#14579141C2218yes—
23C2×#14579137—28no—
24C2×#14579137C2218yes—
25C22×C4⋊Dic79C2211yescharacteristic
26C22×C4⋊Dic79C2211yescharacteristic
27C22×C4⋊Dic79C2211yescharacteristic
28C22×C4⋊Dic79C2211yescharacteristic
29C22×C4⋊Dic79C2211yescharacteristic
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×C4×Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40#19098496C2218yescomplemented
41#19098495C2218yescomplemented
42#19098484C2218yescomplemented
43#19098470C2218yescomplemented
44#19098467C2218yescomplemented
45#19098462C2218yescomplemented
46#19098458C2218yescomplemented
47#19098437C2218yes—
48#19098434C2218yes—
49#19098420C2218yes—
50#19098410C2218yes—
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60#95×D79C2218yes—
61C23×Q8×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C4⋊C4×C79C2211yescharacteristic
65#395×C79C2218yescomplemented
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—24no—
84C22×C4×D79—24no—
85C22×C4×D79—42no—
86C22×C4×D79—42no—
87C22×C4×D79—42no—
88C22×C4×D79—42no—
89C22×C4×D79Q818yescomplemented
90C22×C4×D79C2314yes—
91C22×C4×D79C2314yes—
92C22×C4×D79C2314yes—
93#14579141—232no—
94#14579137—232no—
95C2×C4⋊Dic79—24no—
96C2×C4⋊Dic79—24no—
97C2×C4⋊Dic79—24no—
98C2×C4⋊Dic79—42no—
99C2×C4⋊Dic79—42no—
100C2×C4⋊Dic79C2314yes—
101C2×C4⋊Dic79C2314yes—
102C2×C4⋊Dic79C2314yes—
103C2×C4⋊Dic79C2314yes—
104C2×C4⋊Dic79C2314yes—
105C2×Dic79⋊C4—24no—
106C2×Dic79⋊C4—24no—
107C2×Dic79⋊C4—24no—
108C2×Dic79⋊C4—42no—
109C2×Dic79⋊C4C2314yes—
110C2×Dic79⋊C4C2314yes—
111C2×Dic79⋊C4C2314yes—
112C2×Dic79⋊C4C2314yes—
113C2×(C2×D79)⋊C4—24no—
114C2×(C2×D79)⋊C4—24no—
115C2×(C2×D79)⋊C4D418yes—
116C2×(C2×D79)⋊C4Q818yescomplemented
117C2×(C2×D79)⋊C4C2314yes—
118C2×(C2×D79)⋊C4C2314yes—
119C2×(C2×D79)⋊C4C2314yes—
120C2×(C2×D79)⋊C4C2314yes—
121C2×C4×Dic79—42no—
122C2×C4×Dic79—42no—
123C2×C4×Dic79C2314yes—
124C2×C4×Dic79C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C22×Q8×C79—24no—
135C22×Q8×C79—24no—
136C22×Q8×C79—42no—
137C22×Q8×C79C2314yes—
138C23×C4×C79C2311yescharacteristic
139C23×C4×C79C2311yescharacteristic
140C23×C4×C79C2311yescharacteristic
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2311yescharacteristic
144C23×C4×C79C2311yescharacteristic
145C2×C4⋊C4×C79—24no—
146C2×C4⋊C4×C79—24no—
147C2×C4⋊C4×C79—42no—
148C2×C4⋊C4×C79C2314yes—
149C2×C4⋊C4×C79C2314yes—
150C2×C4⋊C4×C79C2314yes—
151#95×C79C2314yes—
152#95×C79C2314yes—
153#95×C79C2314yes—
154C23×D79—22no—
155C23×D79—22no—
156C23×D79—22no—
157C23×D79—22no—
158C23×D79C2×D414yes—
159C23×D79C2×Q814yes—
160C23×D79C2×Q814yes—
161C23×D79C2412yes—
162C2×Dic158—28no—
163C2×Dic158—28no—
164C2×Dic158—44no—
165C2×Dic158—416no—
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×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79—22no—
181C22×Dic79—22no—
182C22×Dic79—22no—
183C22×Dic79—22no—
184C22×Dic79C2×D414yes—
185C22×Dic79C2×Q814yes—
186C22×Dic79C2×Q814yes—
187C22×Dic79C2412yes—
188C22×Dic79C2412yes—
189C22×Dic79C2412yes—
190C22×Dic79C2412yes—
191C22×Dic79C2412yes—
192C22×Dic79C2412yes—
193C22×Dic79C2412yes—
194C2×C4×D79—28no—
195C2×C4×D79—28no—
196C2×C4×D79—28no—
197C2×C4×D79—28no—
198C2×C4×D79—416no—
199C2×C4×D79—44no—
200C2×C4×D79—44no—
201C2×C4×D79—44no—
202C2×C4×D79—44no—
203C2×C4×D79—416no—
204C2×C4×D79—416no—
205C2×C4×D79C2×Q8116yescomplemented
206C4⋊Dic79—28no—
207C4⋊Dic79—28no—
208C4⋊Dic79—28no—
209C4⋊Dic79—44no—
210C4⋊Dic79—44no—
211Dic79⋊C4—28no—
212Dic79⋊C4—28no—
213Dic79⋊C4—28no—
214Dic79⋊C4—44no—
215(C2×D79)⋊C4—28no—
216(C2×D79)⋊C4—28no—
217(C2×D79)⋊C4C2×D4116yes—
218(C2×D79)⋊C4C2×Q8116yescomplemented
219C4×Dic79—44no—
220C4×Dic79—44no—
221C24×C79C2411yescharacteristic
222C2×Q8×C79—28no—
223C2×Q8×C79—28no—
224C2×Q8×C79—44no—
225C2×Q8×C79—416no—
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×C79—22no—
234C22×C4×C79—22no—
235C22×C4×C79—22no—
236C22×C4×C79—22no—
237C22×C4×C79—22no—
238C22×C4×C79—22no—
239C22×C4×C79—22no—
240C22×C4×C79—22no—
241C22×C4×C79—22no—
242C22×C4×C79C2×D414yes—
243C22×C4×C79C2×Q814yes—
244C22×C4×C79C2×Q814yes—
245C22×C4×C79#4114yes—
246C22×C4×C79#4114yes—
247C22×C4×C79C2412yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2412yes—
250C22×C4×C79C2412yes—
251C22×C4×C79C2412yes—
252C22×C4×C79C2412yes—
253C22×C4×C79C2412yes—
254C4⋊C4×C79—28no—
255C4⋊C4×C79—28no—
256C4⋊C4×C79—44no—
257C23×C79C22×D412yes—
258C23×C79C22×Q812yes—
259C23×C79C22×Q812yes—
260C23×C79C2×#4112yes—
261C23×C79C2×#4112yes—
262C23×C79H(5,𝔽2)12yes—
263C23×C79H(5,𝔽2)12yes—
264C23×C79C2511yescharacteristic
265C22×D79—28no—
266C22×D79—28no—
267C22×D79—28no—
268C22×D79—28no—
269C22×D79—28no—
270C22×D79—28no—
271C22×D79—22no—
272C22×D79—22no—
273C22×D79—22no—
274C22×D79—22no—
275C22×D79C4⋊Q8116yes—
276C22×D79C22×D414yes—
277C22×D79C22×Q814yes—
278C22×D79C22×Q814yes—
279Q8×C79—416no—
280C2×C4×C79—28no—
281C2×C4×C79—28no—
282C2×C4×C79—28no—
283C2×C4×C79—28no—
284C2×C4×C79—28no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
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—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—44no—
302C2×C4×C79—44no—
303C2×C4×C79C22×D414yes—
304C2×C4×C79C22×Q814yes—
305C2×C4×C79C22×Q814yes—
306C2×C4×C79C2×#4114yes—
307C2×C4×C79C2×#4114yes—
308C2×Dic79—28no—
309C2×Dic79—28no—
310C2×Dic79—28no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—44no—
330C2×Dic79—44no—
331C2×Dic79—44no—
332C2×Dic79—44no—
333C2×Dic79C22×D414yes—
334C2×Dic79C22×Q814yes—
335C2×Dic79C22×Q814yes—
336C4×D79—416no—
337C4×D79—416no—
338C4×D79—416no—
339Dic158—416no—
340C22×C79C2×C4⋊Q814yes—
341C22×C79#53314yes—
342C22×C79#54314yes—
343C22×C79#54614yes—
344C22×C79#54614yes—
345C22×C79#55414yes—
346C22×C79#55414yes—
347C22×C79C23×D411yescharacteristic
348C22×C79C23×Q811yescharacteristic
349C22×C79C23×Q811yescharacteristic
350C22×C79C22×#4111yescharacteristic
351C22×C79C22×#4111yescharacteristic
352C22×C79C2×H(5,𝔽2)11yescharacteristic
353C22×C79C2×H(5,𝔽2)11yescharacteristic
354C2×D79—24no—
355C2×D79—24no—
356C2×D79—24no—
357C2×D79—24no—
358C2×D79—24no—
359C2×D79—24no—
360C2×D79—232no—
361C2×D79C2×C4⋊Q818yes—
362C4×C79—24no—
363C4×C79—24no—
364C4×C79—24no—
365C4×C79—24no—
366C4×C79—24no—
367C4×C79—42no—
368C4×C79—42no—
369Dic79—24no—
370Dic79—24no—
371Dic79—24no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376C2×#2549—791nomaximal, Sylow
377C2×C79#254918yescomplemented
378C2×C79C22×C4⋊Q811yescharacteristic
379C2×C79C2×#53311yescharacteristic
380C2×C79C2×#54311yescharacteristic
381C2×C79C2×#54611yescharacteristic
382C2×C79C2×#54611yescharacteristic
383C2×C79C2×#55411yescharacteristic
384C2×C79C2×#55411yescharacteristic
385D79—28no—
386C22×C22⋊Q8—791no—
387C22×C22⋊Q8—791no—
388#2549—7916no—
389C2×#398—791no—
390C2×#398—791no—
391C2×#395—791no—
392C2×#395D7911yescharacteristic, complemented
393C2×#391—791no—
394C2×#391—791no—
395C2×#389—791no—
396C2×#389—791no—
397C2×#385—791no—
398C2×#385—791no—
399C2×#380—791no—
400C2×C4×C22⋊C4—791no—
401C22×#95—791no—
402C79C2×#254911yescharacteristic, complemented, Sylow
403C23×Q8—791no—
404C23×Q8C2×D7911yescharacteristic
405C24×C4—791no—
406C24×C4—791no—
407C24×C4—791no—
408C2×C22⋊Q8—798no—
409C2×C22⋊Q8—798no—
410C2×C22⋊Q8—1588no—
411C2×C22⋊Q8—1588no—
412C22×C4⋊C4—791no—
413C22×C4⋊C4—791no—
414C22×C4⋊C4—791no—
415C22×C4⋊C4—791no—
416C22×C4⋊C4—791no—
417C22×C4⋊C4—791no—
418C22×C4⋊C4—791no—
419C22×C4⋊C4—791no—
420C22×C4⋊C4—791no—
421C22×C4⋊C4C2×D7911yescharacteristic
422C22×C4⋊C4C2×D7911yescharacteristic
423C22×C4⋊C4C2×D7911yescharacteristic
424C22×C22⋊C4—791no—
425C22×C22⋊C4—791no—
426C22×C22⋊C4—791no—
427C22×C22⋊C4—791no—
428C22×C42—791no—
429C22×C42—791no—
430#398—798no—
431#398—798no—
432#395—798no—
433#395C2×D7918yescomplemented
434#391—798no—
435#391—798no—
436#389—798no—
437#389—798no—
438#385—798no—
439#385—798no—
440#380—798no—
441C4×C22⋊C4—798no—
442C2×#95—791no—
443C2×#95—791no—
444C2×#95—791no—
445C2×#95—791no—
446C2×#95—791no—
447C2×#95—791no—
448C2×#95—791no—
449C2×#95—791no—
450C2×#95—791no—
451C2×#95—798no—
452C2×#95C2×D7911yescharacteristic
453C2×#95C2×D7911yescharacteristic
454C2×#95C2×D7911yescharacteristic
455C25—791no—
456C22×Q8—24no—
457C22×Q8—24no—
458C22×Q8—42no—
459C22×Q8—3162no—
460C22×Q8—794no—
461C22×Q8—1584no—
462C22×Q8—1584no—
463C22×Q8C22×D7914yes—
464C23×C4—3162no—
465C23×C4—3162no—
466C23×C4—3162no—
467C23×C4—3162no—
468C23×C4—798no—
469C23×C4—794no—
470C23×C4—794no—
471C23×C4—794no—
472C23×C4—791no—
473C23×C4—791no—
474C23×C4—791no—
475C23×C4—791no—
476C23×C4—791no—
477C23×C4—791no—
478C23×C4—791no—
479C23×C4—1584no—
480C23×C4—1584no—
481C23×C4—1584no—
482C23×C4—1584no—
483C23×C4C22×D7911yescharacteristic
484C23×C4C22×D7911yescharacteristic
485C23×C4C22×D7911yescharacteristic
486C23×C4C22×D7911yescharacteristic
487C23×C4C22×D7911yescharacteristic
488C23×C4C22×D7911yescharacteristic
489C23×C4C22×D7911yescharacteristic
490C22⋊Q8—15832no—
491C22⋊Q8—15832no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—3162no—
496C2×C4⋊C4—3162no—
497C2×C4⋊C4—3162no—
498C2×C4⋊C4—794no—
499C2×C4⋊C4—794no—
500C2×C4⋊C4—794no—
501C2×C4⋊C4—794no—
502C2×C4⋊C4—794no—
503C2×C4⋊C4—794no—
504C2×C4⋊C4—794no—
505C2×C4⋊C4—794no—
506C2×C4⋊C4—794no—
507C2×C4⋊C4—1584no—
508C2×C4⋊C4—1584no—
509C2×C4⋊C4—1584no—
510C2×C4⋊C4—1584no—
511C2×C4⋊C4—1584no—
512C2×C4⋊C4—1584no—
513C2×C4⋊C4C22×D7914yes—
514C2×C4⋊C4C22×D7914yes—
515C2×C4⋊C4C22×D7914yes—
516C2×C22⋊C4—798no—
517C2×C22⋊C4—798no—
518C2×C22⋊C4—794no—
519C2×C22⋊C4—794no—
520C2×C22⋊C4—794no—
521C2×C22⋊C4—794no—
522C2×C22⋊C4—1584no—
523C2×C22⋊C4—1584no—
524C2×C42—3162no—
525C2×C42—3162no—
526C2×C42—794no—
527C2×C42—794no—
528#95—794no—
529#95—794no—
530#95—794no—
531#95—794no—
532#95—794no—
533#95—794no—
534#95—794no—
535#95—794no—
536#95—794no—
537#95C22×D7914yes—
538#95C22×D7914yes—
539#95C22×D7914yes—
540C24—794no—
541C24—794no—
542C24—792no—
543C24—794no—
544C24—1582no—
545C24—1582no—
546C24—1582no—
547C24—1582no—
548C24C23×D7911yescharacteristic
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8—44no—
552C2×Q8—416no—
553C2×Q8—31616no—
554C2×Q8—3164no—
555C2×Q8—1588no—
556C2×Q8—1588no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—31616no—
574C22×C4—31616no—
575C22×C4—3164no—
576C22×C4—3164no—
577C22×C4—3164no—
578C22×C4—3164no—
579C22×C4—31616no—
580C22×C4—7916no—
581C22×C4—794no—
582C22×C4—794no—
583C22×C4—792no—
584C22×C4—792no—
585C22×C4—792no—
586C22×C4—794no—
587C22×C4—792no—
588C22×C4—792no—
589C22×C4—792no—
590C22×C4—792no—
591C22×C4—1588no—
592C22×C4—1588no—
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4—1582no—
600C22×C4—1582no—
601C22×C4—1582no—
602C22×C4—1582no—
603C22×C4—1582no—
604C22×C4—1582no—
605C22×C4—1588no—
606C22×C4—1588no—
607C22×C4—1582no—
608C22×C4—1582no—
609C22×C4—1582no—
610C22×C4—1582no—
611C22×C4—1582no—
612C22×C4—1582no—
613C22×C4D4×D7914yes—
614C22×C4Q8×D7914yes—
615C22×C4Q8×D7914yes—
616C22×C4#1192962314yes—
617C22×C4#1192962514yes—
618C22×C4C23×D7912yes—
619C22×C4C23×D7912yes—
620C22×C4C23×D7912yes—
621C22×C4C23×D7912yes—
622C22×C4C23×D7912yes—
623C22×C4C23×D7912yes—
624C22×C4C23×D7912yes—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—44no—
628C4⋊C4—3164no—
629C4⋊C4—3164no—
630C4⋊C4—3164no—
631C4⋊C4—1588no—
632C4⋊C4—1588no—
633C4⋊C4—1588no—
634C4⋊C4—1588no—
635C4⋊C4—1588no—
636C4⋊C4—1588no—
637C22⋊C4—7916no—
638C22⋊C4—7916no—
639C22⋊C4—1588no—
640C22⋊C4—1588no—
641C42—3164no—
642C42—3164no—
643C23—7916no—
644C23—794no—
645C23—794no—
646C23—794no—
647C23—1582no—
648C23—1582no—
649C23—1588no—
650C23—1588no—
651C23—1588no—
652C23—1588no—
653C23—1588no—
654C23—1588no—
655C23—1582no—
656C23—1582no—
657C23C2×D4×D7912yes—
658C23C2×Q8×D7912yes—
659C23C2×Q8×D7912yes—
660C23C2×#1192962312yes—
661C23C2×#1192962512yes—
662C23#1457920612yes—
663C23#1457920712yes—
664C23C24×D7911yescharacteristic
665Q8—416no—
666Q8—31616no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—31616no—
691C2×C4—31616no—
692C2×C4—31616no—
693C2×C4—3164no—
694C2×C4—3164no—
695C2×C4—3164no—
696C2×C4—3164no—
697C2×C4—794no—
698C2×C4—794no—
699C2×C4—794no—
700C2×C4—1582no—
701C2×C4—1582no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4—1582no—
711C2×C4—1582no—
712C2×C4—1582no—
713C2×C4—1582no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1588no—
717C2×C4—1588no—
718C2×C4—1588no—
719C2×C4—1582no—
720C2×C4—1582no—
721C2×C4C2×D4×D7914yes—
722C2×C4C2×Q8×D7914yes—
723C2×C4C2×Q8×D7914yes—
724C2×C4C2×#1192962314yes—
725C2×C4C2×#1192962514yes—
726C22—798no—
727C22—1584no—
728C22—1584no—
729C22—1584no—
730C22—15832no—
731C22—1584no—
732C22—1584no—
733C22—1584no—
734C22C4⋊Q8×D7914yes—
735C22#1909911814yes—
736C22#1909918814yes—
737C22#1909920014yes—
738C22#1909920414yes—
739C22#1909927114yes—
740C22#1909927414yes—
741C22C22×D4×D7911yescharacteristic
742C22C22×Q8×D7911yescharacteristic
743C22C22×Q8×D7911yescharacteristic
744C22C22×#1192962311yescharacteristic
745C22C22×#1192962511yescharacteristic
746C22C2×#1457920611yescharacteristic
747C22C2×#1457920711yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—42no—
755C4—3162no—
756C4—3162no—
757C4—3162no—
758C4—3162no—
759C4—1584no—
760C4—1584no—
761C4—1584no—
762C2—1588no—
763C2#2376840518yesdirect product factor
764C2C2×C4⋊Q8×D7911yescharacteristic
765C2C2×#1909911811yescharacteristic
766C2C2×#1909918811yescharacteristic
767C2C2×#1909920011yescharacteristic
768C2C2×#1909920411yescharacteristic
769C2C2×#1909927111yescharacteristic
770C2C2×#1909927411yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#395×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#395D79
hypocenterC79C2×#2549
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #23768405C2direct (N × H)
4. C2×#19098496C2semidirect
5. C2×#19098495C2semidirect
6. C2×#19098484C2semidirect
7. C2×#19098470C2semidirect
8. C2×#19098467C2semidirect
9. C2×#19098462C2semidirect
10. C2×#19098458C2semidirect
16. C2×#395×C79C2semidirect
40. #19098496C22semidirect
41. #19098495C22semidirect
42. #19098484C22semidirect
43. #19098470C22semidirect
44. #19098467C22semidirect
45. #19098462C22semidirect
46. #19098458C22semidirect
65. #395×C79C22semidirect
89. C22×C4×D79Q8semidirect
116. C2×(C2×D79)⋊C4Q8semidirect
205. C2×C4×D79C2×Q8semidirect
218. (C2×D79)⋊C4C2×Q8semidirect
377. C2×C79#2549semidirect
392. C2×#395D79semidirect
402. C79C2×#2549semidirect
433. #395C2×D79semidirect
763. C2#23768405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791412
C22×#145791372
#237684052
C2×#190984962
C2×#190984952
C2×#190984842
C2×#190984702
C2×#190984672
C2×#190984622
C2×#190984582
C2×#190984372
C2×#190984342
C2×#190984202
C2×#190984102
C2×#95×D792
C2×#395×C792
C2×#254979