Finite Group Databasebeta

← C2×#23766339 #34447607

Subgroups — C2×#23766339 #34447607

Order 20224.

3374 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579123C211yesmaximal, characteristic
2#23766339C2116yesmaximal, direct product factor
3C2×#19098455C211yesmaximal, characteristic, complemented
4C2×#19098453C211yesmaximal, characteristic, complemented
5C2×#19098449C211yesmaximal, characteristic, complemented
6C2×#19098441C211yesmaximal, characteristic
7C2×#19098441C211yesmaximal, characteristic
8C2×#19098430C211yesmaximal, characteristic, complemented
9C2×#19098425C211yesmaximal, characteristic, complemented
10C2×#19098420C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
13C2×#19098410C211yesmaximal, characteristic, complemented
14C2×#19098408C211yesmaximal, characteristic, complemented
15C2×#95×D79C211yesmaximal, characteristic, complemented
16C2×#387×C79C211yesmaximal, characteristic, complemented
17C23×D316C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C23×C4×D79C2211yescharacteristic
21C23×C4×D79C2211yescharacteristic
22C2×#14579123C4116yescomplemented
23C2×#14579123C2218yes—
24C22×C4⋊Dic79C2211yescharacteristic
25C22×(C2×D79)⋊C4C2211yescharacteristic
26C22×(C2×D79)⋊C4C2211yescharacteristic
27C22×(C2×D79)⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×(C2×D79)⋊C4C2211yescharacteristic
32C22×(C2×D79)⋊C4C2211yescharacteristic
33C22×C4×Dic79C2211yescharacteristic
34C22×C4×Dic79C2211yescharacteristic
35C22×C4×Dic79C2211yescharacteristic
36C22×C4×Dic79C2211yescharacteristic
37#19098455C2218yescomplemented
38#19098453C2218yescomplemented
39#19098449C2218yescomplemented
40#19098441C2218yes—
41#19098441C2218yes—
42#19098430C2218yescomplemented
43#19098425C2218yescomplemented
44#19098420C2218yescomplemented
45C4×(C2×D79)⋊C4C2218yescomplemented
46C4×(C2×D79)⋊C4C2218yescomplemented
47#19098410C2218yescomplemented
48#19098408C2218yescomplemented
49C2×C79⋊#95C2211yescharacteristic
50C2×C79⋊#95C2211yescharacteristic
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59#95×D79C2218yescomplemented
60C22×C4⋊C4×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C42×C79C2211yescharacteristic
63#387×C79C2218yescomplemented
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C24×D79C2311yescharacteristic
69C24×D79C2311yescharacteristic
70C22×D316—24no—
71C22×D316—24no—
72C22×D316C2×C418yes—
73C22×D316C2314yes—
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C22×C4×D79—24no—
81C22×C4×D79—24no—
82C22×C4×D79—24no—
83C22×C4×D79—24no—
84C22×C4×D79—42no—
85C22×C4×D79—42no—
86C22×C4×D79—42no—
87C22×C4×D79—42no—
88C22×C4×D79—42no—
89C22×C4×D79—42no—
90C22×C4×D79C2×C418yes—
91C22×C4×D79C2×C418yescomplemented
92C22×C4×D79C2314yes—
93C22×C4×D79C2314yes—
94C22×C4×D79C2314yes—
95C22×C4×D79C2314yes—
96#14579123C2×C4164yescomplemented
97C2×C4⋊Dic79—42no—
98C2×C4⋊Dic79C2314yes—
99C2×(C2×D79)⋊C4—24no—
100C2×(C2×D79)⋊C4—24no—
101C2×(C2×D79)⋊C4—24no—
102C2×(C2×D79)⋊C4—24no—
103C2×(C2×D79)⋊C4—42no—
104C2×(C2×D79)⋊C4—42no—
105C2×(C2×D79)⋊C4C2×C418yes—
106C2×(C2×D79)⋊C4C2×C418yescomplemented
107C2×(C2×D79)⋊C4C2314yes—
108C2×(C2×D79)⋊C4C2314yes—
109C2×(C2×D79)⋊C4C2314yes—
110C2×(C2×D79)⋊C4C2314yes—
111C2×(C2×D79)⋊C4C2314yes—
112C2×(C2×D79)⋊C4C2314yes—
113C2×(C2×D79)⋊C4C2314yes—
114C2×(C2×D79)⋊C4C2314yes—
115C2×C4×Dic79—24no—
116C2×C4×Dic79—24no—
117C2×C4×Dic79—42no—
118C2×C4×Dic79C2×C418yescomplemented
119C2×C4×Dic79C2314yes—
120C2×C4×Dic79C2314yes—
121C2×C4×Dic79C2314yes—
122C2×C4×Dic79C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
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—42no—
141C2×C4⋊C4×C79C2×C418yescomplemented
142C2×C4⋊C4×C79C2314yes—
143C2×C4⋊C4×C79C2314yes—
144C2×C42×C79—42no—
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×D79—22no—
157C23×D79—22no—
158C23×D79—22no—
159C23×D79—22no—
160C23×D79C22×C414yes—
161C23×D79C22×C414yes—
162C23×D79#4114yes—
163C23×D79#4114yes—
164C23×D79C2412yes—
165C23×D79C2412yes—
166C2×D316—232no—
167C2×D316—28no—
168C2×D316—28no—
169C2×D316C22×C4116yes—
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×Dic79—22no—
185C22×Dic79C22×C414yes—
186C22×Dic79C22×C414yes—
187C22×Dic79#4114yes—
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—416no—
200C2×C4×D79—44no—
201C2×C4×D79—44no—
202C2×C4×D79—44no—
203C2×C4×D79—44no—
204C2×C4×D79—44no—
205C2×C4×D79—44no—
206C2×C4×D79—416no—
207C2×C4×D79—416no—
208C2×C4×D79C22×C4116yes—
209C2×C4×D79C22×C4116yescomplemented
210C4⋊Dic79—44no—
211(C2×D79)⋊C4—28no—
212(C2×D79)⋊C4—28no—
213(C2×D79)⋊C4—28no—
214(C2×D79)⋊C4—28no—
215(C2×D79)⋊C4—44no—
216(C2×D79)⋊C4—44no—
217(C2×D79)⋊C4C22×C4116yes—
218(C2×D79)⋊C4C22×C4116yescomplemented
219C4×Dic79—28no—
220C4×Dic79—28no—
221C4×Dic79—44no—
222C4×Dic79C22×C4116yescomplemented
223C24×C79C2411yescharacteristic
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×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×C79C22×C414yes—
242C22×C4×C79C22×C414yes—
243C22×C4×C79C22×C414yes—
244C22×C4×C79#4114yes—
245C22×C4×C79C2412yes—
246C22×C4×C79C2412yes—
247C22×C4×C79C2412yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2412yes—
250C22×C4×C79C2412yes—
251C22×C4×C79C2412yes—
252C4⋊C4×C79—44no—
253C4⋊C4×C79C22×C4116yescomplemented
254C42×C79—44no—
255C23×C79C23×C412yes—
256C23×C79C2×#4112yes—
257C23×C79C2×#4112yes—
258C23×C79C2×#4112yes—
259C23×C79C2×#4112yes—
260C23×C79H(5,𝔽2)12yes—
261C23×C79H(5,𝔽2)12yes—
262C23×C79C2511yescharacteristic
263C22×D79—28no—
264C22×D79—28no—
265C22×D79—28no—
266C22×D79—28no—
267C22×D79—28no—
268C22×D79—28no—
269C22×D79—22no—
270C22×D79—22no—
271C22×D79—22no—
272C22×D79—22no—
273C22×D79—28no—
274C22×D79—28no—
275C22×D79—28no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—22no—
281C22×D79—22no—
282C22×D79—44no—
283C22×D79—44no—
284C22×D79—44no—
285C22×D79—44no—
286C22×D79#117116yes—
287C22×D79C23×C414yes—
288C22×D79C23×C414yes—
289C22×D79C2×#4114yes—
290C22×D79C2×#4114yes—
291C2×C4×C79—28no—
292C2×C4×C79—28no—
293C2×C4×C79—28no—
294C2×C4×C79—28no—
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—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—44no—
313C2×C4×C79—44no—
314C2×C4×C79—44no—
315C2×C4×C79C23×C414yes—
316C2×C4×C79C23×C414yes—
317C2×C4×C79C23×C414yes—
318C2×C4×C79C2×#4114yes—
319C2×Dic79—28no—
320C2×Dic79—28no—
321C2×Dic79—28no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—22no—
332C2×Dic79—22no—
333C2×Dic79—22no—
334C2×Dic79—22no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—44no—
338C2×Dic79—44no—
339C2×Dic79—44no—
340C2×Dic79C23×C414yes—
341C2×Dic79C23×C414yes—
342C2×Dic79C2×#4114yes—
343D316—232no—
344C4×D79—416no—
345C4×D79—416no—
346C4×D79—416no—
347C4×D79—416no—
348C22×C79C2×#11714yes—
349C22×C79C4×#4114yes—
350C22×C79#51814yes—
351C22×C79#55114yes—
352C22×C79#55114yes—
353C22×C79#55314yes—
354C22×C79#55314yes—
355C22×C79C24×C411yescharacteristic
356C22×C79C22×#4111yescharacteristic
357C22×C79C22×#4111yescharacteristic
358C22×C79C22×#4111yescharacteristic
359C22×C79C22×#4111yescharacteristic
360C22×C79C2×H(5,𝔽2)11yescharacteristic
361C22×C79C2×H(5,𝔽2)11yescharacteristic
362C2×D79—232no—
363C2×D79—24no—
364C2×D79—24no—
365C2×D79—24no—
366C2×D79—24no—
367C2×D79—24no—
368C2×D79—24no—
369C2×D79—24no—
370C2×D79—24no—
371C2×D79—24no—
372C2×D79—416no—
373C2×D79—42no—
374C2×D79—42no—
375C2×D79—42no—
376C2×D79—42no—
377C2×D79C2×#11718yes—
378C4×C79—24no—
379C4×C79—24no—
380C4×C79—24no—
381C4×C79—24no—
382C4×C79—42no—
383C4×C79—42no—
384C4×C79—42no—
385Dic79—24no—
386Dic79—24no—
387Dic79—24no—
388Dic79—42no—
389Dic79—42no—
390Dic79—42no—
391C2×#2353—791nomaximal, Sylow
392C2×C79#235318yescomplemented
393C2×C79C22×#11711yescharacteristic
394C2×C79C2×C4×#4111yescharacteristic
395C2×C79C2×#51811yescharacteristic
396C2×C79C2×#55111yescharacteristic
397C2×C79C2×#55111yescharacteristic
398C2×C79C2×#55311yescharacteristic
399C2×C79C2×#55311yescharacteristic
400D79—28no—
401D79—44no—
402C22×C4×D4—791no—
403#2353—7916no—
404C2×#388—791no—
405C2×#388—791no—
406C2×#387—791no—
407C2×#387D7911yescharacteristic, complemented
408C2×#386—791no—
409C2×#386—791no—
410C2×#383—791no—
411C2×#381—791no—
412C2×#380—791no—
413C2×C4×C22⋊C4—791no—
414C2×C4×C22⋊C4—791no—
415C2×C4×C22⋊C4—791no—
416C2×#376—791no—
417C22×#95—791no—
418C79C2×#235311yescharacteristic, complemented, Sylow
419C23×D4—791no—
420C24×C4—791no—
421C24×C4—791no—
422C24×C4—791no—
423C24×C4—791no—
424C2×C4×D4—798no—
425C2×C4×D4—7916no—
426C22×C4⋊C4—791no—
427C22×C4⋊C4C2×D7911yescharacteristic
428C22×C4⋊C4C2×D7911yescharacteristic
429C22×C22⋊C4—791no—
430C22×C22⋊C4—791no—
431C22×C22⋊C4—791no—
432C22×C22⋊C4—791no—
433C22×C22⋊C4—791no—
434C22×C22⋊C4—791no—
435C22×C22⋊C4—791no—
436C22×C22⋊C4—791no—
437C22×C42—791no—
438C22×C42—791no—
439C22×C42—791no—
440C22×C42—791no—
441C22×C42C2×D7911yescharacteristic
442#388—798no—
443#388—798no—
444#387—798no—
445#387C2×D7918yescomplemented
446#386—798no—
447#386—798no—
448#383—798no—
449#381—798no—
450#380—798no—
451C4×C22⋊C4—798no—
452C4×C22⋊C4—798no—
453C4×C22⋊C4—798no—
454#376—798no—
455C2×#95—791no—
456C2×#95—791no—
457C2×#95—791no—
458C2×#95—791no—
459C2×#95—791no—
460C2×#95—791no—
461C2×#95—791no—
462C2×#95—791no—
463C2×#95—791no—
464C2×#95—791no—
465C2×#95—798no—
466C2×#95C2×D7911yescharacteristic
467C2×#95C2×D7911yescharacteristic
468C2×#95C2×D7911yescharacteristic
469C2×#95C2×D7911yescharacteristic
470C25—791no—
471C25—791no—
472C22×D4—798no—
473C22×D4—794no—
474C22×D4—1584no—
475C22×D4—1584no—
476C23×C4—3162no—
477C23×C4—3162no—
478C23×C4—3162no—
479C23×C4—3162no—
480C23×C4—3162no—
481C23×C4—3162no—
482C23×C4—798no—
483C23×C4—798no—
484C23×C4—794no—
485C23×C4—794no—
486C23×C4—794no—
487C23×C4—794no—
488C23×C4—791no—
489C23×C4—791no—
490C23×C4—791no—
491C23×C4—791no—
492C23×C4—791no—
493C23×C4—791no—
494C23×C4—1584no—
495C23×C4—1584no—
496C23×C4—1584no—
497C23×C4—1584no—
498C23×C4C22×D7911yescharacteristic
499C23×C4C22×D7911yescharacteristic
500C23×C4C22×D7911yescharacteristic
501C23×C4C22×D7911yescharacteristic
502C23×C4C22×D7911yescharacteristic
503C23×C4C22×D7911yescharacteristic
504C23×C4C22×D7911yescharacteristic
505C4×D4—7964no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—3162no—
508C2×C4⋊C4—794no—
509C2×C4⋊C4C4×D7918yescomplemented
510C2×C4⋊C4C22×D7914yes—
511C2×C4⋊C4C22×D7914yes—
512C2×C22⋊C4—3162no—
513C2×C22⋊C4—3162no—
514C2×C22⋊C4—794no—
515C2×C22⋊C4—794no—
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—794no—
523C2×C22⋊C4—794no—
524C2×C22⋊C4—1584no—
525C2×C22⋊C4—1584no—
526C2×C22⋊C4—1584no—
527C2×C22⋊C4—1584no—
528C2×C42—42no—
529C2×C42—3162no—
530C2×C42—794no—
531C2×C42—798no—
532C2×C42—794no—
533C2×C42—794no—
534C2×C42—794no—
535C2×C42—1584no—
536C2×C42—1584no—
537C2×C42C22×D7914yes—
538#95—794no—
539#95—794no—
540#95—794no—
541#95—794no—
542#95—794no—
543#95—794no—
544#95—794no—
545#95—794no—
546#95—794no—
547#95—794no—
548#95C22×D7914yes—
549#95C22×D7914yes—
550#95C22×D7914yes—
551#95C22×D7914yes—
552C24—794no—
553C24—794no—
554C24—792no—
555C24—794no—
556C24—792no—
557C24—794no—
558C24—1582no—
559C24—1582no—
560C24—1582no—
561C24—1582no—
562C24—1582no—
563C24—1582no—
564C24—1582no—
565C24—1582no—
566C24—1582no—
567C24—1582no—
568C24C23×D7911yescharacteristic
569C2×D4—7916no—
570C2×D4—15832no—
571C2×D4—1588no—
572C2×D4—1588no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—31616no—
591C22×C4—3164no—
592C22×C4—3164no—
593C22×C4—3164no—
594C22×C4—3164no—
595C22×C4—3164no—
596C22×C4—31616no—
597C22×C4—31616no—
598C22×C4—3164no—
599C22×C4—31616no—
600C22×C4—7916no—
601C22×C4—7916no—
602C22×C4—794no—
603C22×C4—792no—
604C22×C4—792no—
605C22×C4—792no—
606C22×C4—794no—
607C22×C4—794no—
608C22×C4—792no—
609C22×C4—792no—
610C22×C4—792no—
611C22×C4—1588no—
612C22×C4—1588no—
613C22×C4—1588no—
614C22×C4—1582no—
615C22×C4—1582no—
616C22×C4—1582no—
617C22×C4—1582no—
618C22×C4—1582no—
619C22×C4—1582no—
620C22×C4—1582no—
621C22×C4—1582no—
622C22×C4—1582no—
623C22×C4—1588no—
624C22×C4—1582no—
625C22×C4—1582no—
626C22×C4—1582no—
627C22×C4—1582no—
628C22×C4—1582no—
629C22×C4—1582no—
630C22×C4C2×C4×D7914yes—
631C22×C4C2×C4×D7914yes—
632C22×C4C2×C4×D7914yes—
633C22×C4#1192962514yes—
634C22×C4C23×D7912yes—
635C22×C4C23×D7912yes—
636C22×C4C23×D7912yes—
637C22×C4C23×D7912yes—
638C22×C4C23×D7912yes—
639C22×C4C23×D7912yes—
640C22×C4C23×D7912yes—
641C4⋊C4—44no—
642C4⋊C4—3164no—
643C4⋊C4C2×C4×D79116yescomplemented
644C22⋊C4—3164no—
645C22⋊C4—3164no—
646C22⋊C4—7916no—
647C22⋊C4—7916no—
648C22⋊C4—1588no—
649C22⋊C4—1588no—
650C22⋊C4—1588no—
651C22⋊C4—1588no—
652C42—44no—
653C42—3164no—
654C42—7916no—
655C42—1588no—
656C42—1588no—
657C23—3164no—
658C23—3164no—
659C23—3164no—
660C23—3164no—
661C23—7916no—
662C23—794no—
663C23—794no—
664C23—794no—
665C23—794no—
666C23—1582no—
667C23—1582no—
668C23—1588no—
669C23—1588no—
670C23—1588no—
671C23—1582no—
672C23—1582no—
673C23—1582no—
674C23—1582no—
675C23—1582no—
676C23—1582no—
677C23—1588no—
678C23—1588no—
679C23—1588no—
680C23—1588no—
681C23—1588no—
682C23—1588no—
683C23—1582no—
684C23—1582no—
685C23C22×C4×D7912yes—
686C23#41×D7912yes—
687C23#41×D7912yes—
688C23#41×D7912yes—
689C23C2×#1192962512yes—
690C23#1457920612yes—
691C23#1457920712yes—
692C23C24×D7911yescharacteristic
693D4—15832no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—31616no—
719C2×C4—31616no—
720C2×C4—31616no—
721C2×C4—31616no—
722C2×C4—3164no—
723C2×C4—3164no—
724C2×C4—3164no—
725C2×C4—794no—
726C2×C4—794no—
727C2×C4—794no—
728C2×C4—1582no—
729C2×C4—1582no—
730C2×C4—1582no—
731C2×C4—1582no—
732C2×C4—1582no—
733C2×C4—1582no—
734C2×C4—1582no—
735C2×C4—1582no—
736C2×C4—1582no—
737C2×C4—1582no—
738C2×C4—1582no—
739C2×C4—1582no—
740C2×C4—1588no—
741C2×C4—1588no—
742C2×C4—1588no—
743C2×C4—1582no—
744C2×C4—1582no—
745C2×C4—1582no—
746C2×C4C22×C4×D7914yes—
747C2×C4C22×C4×D7914yes—
748C2×C4C22×C4×D7914yes—
749C2×C4C2×#1192962514yes—
750C22—31616no—
751C22—3162no—
752C22—3162no—
753C22—3162no—
754C22—3162no—
755C22—798no—
756C22—1584no—
757C22—1584no—
758C22—1584no—
759C22—15832no—
760C22—1584no—
761C22—1584no—
762C22—1584no—
763C22—1584no—
764C22—1584no—
765C22—1584no—
766C22#117×D7914yes—
767C22C4×#1192962514yes—
768C22#1909903514yes—
769C22#1909923814yes—
770C22#1909924014yes—
771C22#1909925814yes—
772C22#1909926614yes—
773C22C23×C4×D7911yescharacteristic
774C22C2×#41×D7911yescharacteristic
775C22C2×#41×D7911yescharacteristic
776C22C2×#41×D7911yescharacteristic
777C22C22×#1192962511yescharacteristic
778C22C2×#1457920611yescharacteristic
779C22C2×#1457920711yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—3162no—
788C4—3162no—
789C4—3162no—
790C4—1584no—
791C4—1584no—
792C4—1584no—
793C2—3164no—
794C2—1588no—
795C2#2376633918yesdirect product factor
796C2C2×#117×D7911yescharacteristic
797C2C2×C4×#1192962511yescharacteristic
798C2C2×#1909903511yescharacteristic
799C2C2×#1909923811yescharacteristic
800C2C2×#1909924011yescharacteristic
801C2C2×#1909925811yescharacteristic
802C2C2×#1909926611yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#387×C79C2
socleC24×C79C24
prime radicalC23×D316C22
cosocleC23×C79C25
hypercenterC2×#387D79
hypocenterC79C2×#2353
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #23766339C2direct (N × H)
3. C2×#19098455C2semidirect
4. C2×#19098453C2semidirect
5. C2×#19098449C2semidirect
8. C2×#19098430C2semidirect
9. C2×#19098425C2semidirect
10. C2×#19098420C2semidirect
11. C2×C4×(C2×D79)⋊C4C2semidirect
12. C2×C4×(C2×D79)⋊C4C2semidirect
13. C2×#19098410C2semidirect
14. C2×#19098408C2semidirect
15. C2×#95×D79C2semidirect
16. C2×#387×C79C2semidirect
22. C2×#14579123C4semidirect
37. #19098455C22semidirect
38. #19098453C22semidirect
39. #19098449C22semidirect
42. #19098430C22semidirect
43. #19098425C22semidirect
44. #19098420C22semidirect
45. C4×(C2×D79)⋊C4C22semidirect
46. C4×(C2×D79)⋊C4C22semidirect
47. #19098410C22semidirect
48. #19098408C22semidirect
59. #95×D79C22semidirect
63. #387×C79C22semidirect
91. C22×C4×D79C2×C4semidirect
96. #14579123C2×C4semidirect
106. C2×(C2×D79)⋊C4C2×C4semidirect
118. C2×C4×Dic79C2×C4semidirect
141. C2×C4⋊C4×C79C2×C4semidirect
209. C2×C4×D79C22×C4semidirect
218. (C2×D79)⋊C4C22×C4semidirect
222. C4×Dic79C22×C4semidirect
253. C4⋊C4×C79C22×C4semidirect
392. C2×C79#2353semidirect
407. C2×#387D79semidirect
418. C79C2×#2353semidirect
445. #387C2×D79semidirect
509. C2×C4⋊C4C4×D79semidirect
643. C4⋊C4C2×C4×D79semidirect
795. C2#23766339direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791232
#237663392
C2×#190984552
C2×#190984532
C2×#190984492
C2×#190984412
C2×#190984302
C2×#190984252
C2×#190984202
C2×C4×(C2×D79)⋊C42
C2×#190984102
C2×#190984082
C2×#95×D792
C2×#387×C792
C2×#235379