Finite Group Databasebeta

← C2×#23767271 #34456430

Subgroups — C2×#23767271 #34456430

Order 20224.

3094 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579151C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D79C211yesmaximal, characteristic
3#23767271C2116yesmaximal, direct product factor
4C2×#19098499C211yesmaximal, characteristic, complemented
5C2×#19098498C211yesmaximal, characteristic, complemented
6C2×#19098486C211yesmaximal, characteristic, complemented
7C2×#19098485C211yesmaximal, characteristic, complemented
8C2×#19098463C211yesmaximal, characteristic
9C2×#19098463C211yesmaximal, characteristic
10C2×#19098460C211yesmaximal, characteristic, complemented
11C2×#19098458C211yesmaximal, characteristic, complemented
12C2×#19098437C211yesmaximal, characteristic, complemented
13C2×#19098436C211yesmaximal, characteristic, complemented
14C2×#19098422C211yesmaximal, characteristic, complemented
15C2×#19098414C211yesmaximal, characteristic, complemented
16C2×#380×C79C211yesmaximal, characteristic, complemented
17C23×C22⋊D79C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C2×#14579151—28no—
20C2×#14579151C2218yescomplemented
21C2×C4×C22⋊D79—28no—
22C2×C4×C22⋊D79C2218yes—
23C22×C4⋊Dic79C2211yescharacteristic
24C22×C4⋊Dic79C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
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×C22⋊Dic79C2211yescharacteristic
35C22×C22⋊Dic79C2211yescharacteristic
36C22×C22⋊Dic79C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×(C2×D79)⋊C4C2211yescharacteristic
39C22×(C2×D79)⋊C4C2211yescharacteristic
40C22×(C2×D79)⋊C4C2211yescharacteristic
41C22×(C2×D79)⋊C4C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43C22×C4×Dic79C2211yescharacteristic
44C22×C4×Dic79C2211yescharacteristic
45#19098499C2218yescomplemented
46#19098498C2218yescomplemented
47#19098486C2218yescomplemented
48#19098485C2218yescomplemented
49#19098463C2218yes—
50#19098463C2218yes—
51#19098460C2218yescomplemented
52#19098458C2218yescomplemented
53#19098437C2218yescomplemented
54#19098436C2218yescomplemented
55#19098422C2218yescomplemented
56#19098414C2218yescomplemented
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C24×C4×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C22⋊C4×C79C2211yescharacteristic
65C22×C22⋊C4×C79C2211yescharacteristic
66#380×C79C2218yescomplemented
67C2×#95×C79C2211yescharacteristic
68C2×#95×C79C2211yescharacteristic
69C24×D79C2311yescharacteristic
70C22×C22⋊D79—24no—
71C22×C22⋊D79—24no—
72C22×C22⋊D79Q818yes—
73C22×C22⋊D79C2314yes—
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#14579151—232no—
86C4×C22⋊D79—232no—
87C2×C4⋊Dic79—24no—
88C2×C4⋊Dic79—42no—
89C2×C4⋊Dic79C2314yes—
90C2×C4⋊Dic79C2314yes—
91C2×Dic79⋊C4—24no—
92C2×Dic79⋊C4—24no—
93C2×Dic79⋊C4—24no—
94C2×Dic79⋊C4—24no—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4—24no—
97C2×Dic79⋊C4—42no—
98C2×Dic79⋊C4—42no—
99C2×Dic79⋊C4D418yes—
100C2×Dic79⋊C4C2314yes—
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×C22⋊Dic79—24no—
110C2×C22⋊Dic79—24no—
111C2×C22⋊Dic79—42no—
112C2×C22⋊Dic79C2314yes—
113C2×C22⋊Dic79C2314yes—
114C2×C22⋊Dic79C2314yes—
115C2×(C2×D79)⋊C4—24no—
116C2×(C2×D79)⋊C4—24no—
117C2×(C2×D79)⋊C4—42no—
118C2×(C2×D79)⋊C4—42no—
119C2×(C2×D79)⋊C4—42no—
120C2×(C2×D79)⋊C4C2314yes—
121C2×(C2×D79)⋊C4C2314yes—
122C2×(C2×D79)⋊C4C2314yes—
123C2×(C2×D79)⋊C4C2314yes—
124C2×(C2×D79)⋊C4C2314yes—
125C2×C4×Dic79—24no—
126C2×C4×Dic79—24no—
127C2×C4×Dic79—24no—
128C2×C4×Dic79C2314yes—
129C2×C4×Dic79C2314yes—
130C2×C4×Dic79C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C79⋊#95C2314yes—
135C25×C79C2311yescharacteristic
136C23×C4×C79—24no—
137C23×C4×C79—24no—
138C23×C4×C79—42no—
139C23×C4×C79C2311yescharacteristic
140C23×C4×C79C2311yescharacteristic
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2314yes—
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C2×C4⋊C4×C79—24no—
147C2×C4⋊C4×C79—42no—
148C2×C4⋊C4×C79C2314yes—
149C2×C4⋊C4×C79C2314yes—
150C2×C22⋊C4×C79—42no—
151C2×C22⋊C4×C79—42no—
152C2×C22⋊C4×C79C2314yes—
153C2×C22⋊C4×C79C2314yes—
154#95×C79C2314yes—
155#95×C79C2314yes—
156C23×D79—22no—
157C23×D79—22no—
158C23×D79—22no—
159C23×D79—22no—
160C23×D79—22no—
161C23×D79—22no—
162C23×D79C2×Q814yes—
163C23×D79C2412yes—
164C2×C22⋊D79—232no—
165C2×C22⋊D79—28no—
166C2×C22⋊D79—28no—
167C2×C22⋊D79C2×Q8116yes—
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×D414yes—
186C22×Dic79C2×Q814yes—
187C22×Dic79#4114yes—
188C22×Dic79#4114yes—
189C22×Dic79C2412yes—
190C22×Dic79C2412yes—
191C22×Dic79C2412yes—
192C22×Dic79C2412yes—
193C22×Dic79C2412yes—
194C22×Dic79C2412yes—
195C22×Dic79C2412yes—
196C2×C4×D79—28no—
197C2×C4×D79—28no—
198C2×C4×D79—44no—
199C2×C4×D79—416no—
200C4⋊Dic79—28no—
201C4⋊Dic79—44no—
202Dic79⋊C4—28no—
203Dic79⋊C4—28no—
204Dic79⋊C4—28no—
205Dic79⋊C4—28no—
206Dic79⋊C4—28no—
207Dic79⋊C4—28no—
208Dic79⋊C4—44no—
209Dic79⋊C4—44no—
210Dic79⋊C4C2×D4116yes—
211C22⋊Dic79—28no—
212C22⋊Dic79—28no—
213C22⋊Dic79—44no—
214(C2×D79)⋊C4—28no—
215(C2×D79)⋊C4—28no—
216(C2×D79)⋊C4—44no—
217(C2×D79)⋊C4—44no—
218(C2×D79)⋊C4—44no—
219C4×Dic79—28no—
220C4×Dic79—28no—
221C4×Dic79—28no—
222C24×C79—22no—
223C24×C79—22no—
224C24×C79—22no—
225C24×C79—22no—
226C24×C79—22no—
227C24×C79—22no—
228C24×C79C2×Q814yes—
229C24×C79C2412yes—
230C24×C79C2411yescharacteristic
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×C79—22no—
243C22×C4×C79—22no—
244C22×C4×C79—22no—
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79—28no—
248C22×C4×C79—28no—
249C22×C4×C79—44no—
250C22×C4×C79—416no—
251C22×C4×C79C2×D414yes—
252C22×C4×C79#4114yes—
253C22×C4×C79C2412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2412yes—
256C22×C4×C79C2412yes—
257C22×C4×C79C2412yes—
258C22×C4×C79C2412yes—
259C4⋊C4×C79—28no—
260C4⋊C4×C79—44no—
261C22⋊C4×C79—44no—
262C22⋊C4×C79—44no—
263C23×C79—28no—
264C23×C79—28no—
265C23×C79—28no—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79—22no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C79—22no—
272C23×C79—44no—
273C23×C79—44no—
274C23×C79—44no—
275C23×C79—44no—
276C23×C79C22×D412yes—
277C23×C79C22×Q814yes—
278C23×C79C22×Q812yes—
279C23×C79C2×#4112yes—
280C23×C79C2×#4112yes—
281C23×C79C2×#4112yes—
282C23×C79H(5,𝔽2)12yes—
283C23×C79H(5,𝔽2)12yes—
284C23×C79C2511yescharacteristic
285C22×D79—28no—
286C22×D79—28no—
287C22×D79—28no—
288C22×D79—22no—
289C22×D79—22no—
290C22×D79—22no—
291C22×D79—22no—
292C22×D79—22no—
293C22×D79—22no—
294C22×D79—44no—
295C22×D79—44no—
296C22×D79—44no—
297C22×D79—44no—
298C22×D79C22×Q814yes—
299C2×C4×C79—28no—
300C2×C4×C79—28no—
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—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—22no—
316C2×C4×C79—22no—
317C2×C4×C79—416no—
318C2×C4×C79—44no—
319C2×C4×C79—44no—
320C2×C4×C79—44no—
321C2×C4×C79—44no—
322C2×C4×C79C22×D414yes—
323C2×C4×C79C2×#4114yes—
324C22⋊D79—232no—
325C2×Dic79—28no—
326C2×Dic79—28no—
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—22no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—22no—
342C2×Dic79—22no—
343C2×Dic79—44no—
344C2×Dic79—44no—
345C2×Dic79—44no—
346C2×Dic79—44no—
347C2×Dic79C22⋊Q8116yes—
348C2×Dic79C22×D414yes—
349C2×Dic79C22×D414yes—
350C2×Dic79C22×Q814yes—
351C2×Dic79C2×#4114yes—
352C2×Dic79C2×#4114yes—
353C4×D79—416no—
354C22×C79—24no—
355C22×C79—24no—
356C22×C79—24no—
357C22×C79—42no—
358C22×C79—42no—
359C22×C79—42no—
360C22×C79—42no—
361C22×C79—416no—
362C22×C79C2×C22⋊Q814yes—
363C22×C79#52914yes—
364C22×C79#54014yes—
365C22×C79#54614yes—
366C22×C79#55014yes—
367C22×C79#55414yes—
368C22×C79#55414yes—
369C22×C79C23×D411yescharacteristic
370C22×C79C23×Q811yescharacteristic
371C22×C79C22×#4111yescharacteristic
372C22×C79C22×#4111yescharacteristic
373C22×C79C22×#4111yescharacteristic
374C22×C79C2×H(5,𝔽2)11yescharacteristic
375C22×C79C2×H(5,𝔽2)11yescharacteristic
376C2×D79—24no—
377C2×D79—24no—
378C2×D79—24no—
379C2×D79—42no—
380C2×D79—42no—
381C2×D79—42no—
382C2×D79—42no—
383C2×D79—416no—
384C4×C79—24no—
385C4×C79—24no—
386C4×C79—42no—
387C4×C79—42no—
388C4×C79—42no—
389C4×C79—42no—
390Dic79—24no—
391Dic79—24no—
392Dic79—42no—
393Dic79—42no—
394Dic79—42no—
395Dic79—42no—
396Dic79C2×C22⋊Q818yes—
397C2×#2454—791nomaximal, Sylow
398C2×C79—44no—
399C2×C79#245418yescomplemented
400C2×C79C22×C22⋊Q811yescharacteristic
401C2×C79C2×#52911yescharacteristic
402C2×C79C2×#54011yescharacteristic
403C2×C79C2×#54611yescharacteristic
404C2×C79C2×#55011yescharacteristic
405C2×C79C2×#55411yescharacteristic
406C2×C79C2×#55411yescharacteristic
407D79—44no—
408C22×#125—791no—
409C22×C4×D4—791no—
410#2454—7916no—
411C2×#399—791no—
412C2×#399—791no—
413C2×#396—791no—
414C2×#396—791no—
415C2×#390—791no—
416C2×#390—791no—
417C2×#389—791no—
418C2×#389—791no—
419C2×#385—791no—
420C2×#385—791no—
421C2×#380—791no—
422C2×#380D7911yescharacteristic, complemented
423C2×C4×C4⋊C4—791no—
424C79C2×#245411yescharacteristic, complemented, Sylow
425C23×D4—791no—
426C24×C4—791no—
427C24×C4C2×D7911yescharacteristic
428C2×#125—798no—
429C2×#125—1588no—
430C2×C4×D4—798no—
431C2×C4×D4—1588no—
432C22×C4⋊C4—791no—
433C22×C4⋊C4—791no—
434C22×C4⋊C4—791no—
435C22×C4⋊C4—791no—
436C22×C4⋊C4—791no—
437C22×C4⋊C4—791no—
438C22×C4⋊C4—791no—
439C22×C4⋊C4—791no—
440C22×C4⋊C4—791no—
441C22×C4⋊C4—791no—
442C22×C4⋊C4—791no—
443C22×C4⋊C4C2×D7911yescharacteristic
444C22×C4⋊C4C2×D7911yescharacteristic
445C22×C22⋊C4—791no—
446C22×C22⋊C4—791no—
447C22×C22⋊C4—791no—
448C22×C22⋊C4—791no—
449C22×C22⋊C4—791no—
450C22×C22⋊C4—791no—
451C22×C22⋊C4—791no—
452C22×C22⋊C4—791no—
453C22×C22⋊C4C2×D7911yescharacteristic
454C22×C22⋊C4C2×D7911yescharacteristic
455C22×C42—791no—
456C22×C42—791no—
457C22×C42—791no—
458#399—798no—
459#399—798no—
460#396—798no—
461#396—798no—
462#390—798no—
463#390—798no—
464#389—798no—
465#389—798no—
466#385—798no—
467#385—798no—
468#380—798no—
469#380C2×D7918yescomplemented
470C4×C4⋊C4—798no—
471C2×#95—791no—
472C2×#95—791no—
473C2×#95—791no—
474C2×#95—791no—
475C2×#95C2×D7911yescharacteristic
476C2×#95C2×D7911yescharacteristic
477C25—791no—
478C25C22×D7911yescharacteristic
479C22×D4—798no—
480C22×D4—794no—
481C22×D4—1584no—
482C22×D4—1584no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—42no—
486C23×C4—3162no—
487C23×C4—794no—
488C23×C4—791no—
489C23×C4—791no—
490C23×C4—791no—
491C23×C4—791no—
492C23×C4—791no—
493C23×C4—791no—
494C23×C4—791no—
495C23×C4—1584no—
496C23×C4—1584no—
497C23×C4C22×D7911yescharacteristic
498C23×C4C22×D7911yescharacteristic
499C23×C4C22×D7911yescharacteristic
500C23×C4C22×D7911yescharacteristic
501C23×C4C22×D7914yes—
502C23×C4C22×D7911yescharacteristic
503C23×C4C22×D7911yescharacteristic
504#125—15832no—
505C4×D4—15832no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—3162no—
509C2×C4⋊C4—3162no—
510C2×C4⋊C4—3162no—
511C2×C4⋊C4—794no—
512C2×C4⋊C4—794no—
513C2×C4⋊C4—794no—
514C2×C4⋊C4—798no—
515C2×C4⋊C4—794no—
516C2×C4⋊C4—794no—
517C2×C4⋊C4—794no—
518C2×C4⋊C4—794no—
519C2×C4⋊C4—794no—
520C2×C4⋊C4—794no—
521C2×C4⋊C4—794no—
522C2×C4⋊C4—794no—
523C2×C4⋊C4—1584no—
524C2×C4⋊C4—1584no—
525C2×C4⋊C4—1584no—
526C2×C4⋊C4—1584no—
527C2×C4⋊C4—1584no—
528C2×C4⋊C4—1584no—
529C2×C4⋊C4—1584no—
530C2×C4⋊C4C22×D7914yes—
531C2×C4⋊C4C22×D7914yes—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—3162no—
535C2×C22⋊C4—3162no—
536C2×C22⋊C4—3162no—
537C2×C22⋊C4—3162no—
538C2×C22⋊C4—794no—
539C2×C22⋊C4—794no—
540C2×C22⋊C4—794no—
541C2×C22⋊C4—794no—
542C2×C22⋊C4—794no—
543C2×C22⋊C4—794no—
544C2×C22⋊C4—794no—
545C2×C22⋊C4—794no—
546C2×C22⋊C4—1584no—
547C2×C22⋊C4—1584no—
548C2×C22⋊C4—1584no—
549C2×C22⋊C4—1584no—
550C2×C22⋊C4C22×D7914yes—
551C2×C22⋊C4C22×D7914yes—
552C2×C42—794no—
553C2×C42—794no—
554C2×C42—794no—
555C2×C42—1584no—
556C2×C42—1584no—
557C2×C42—1584no—
558#95—794no—
559#95—794no—
560#95—794no—
561#95—794no—
562#95C22×D7914yes—
563#95C22×D7914yes—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—794no—
571C24—792no—
572C24—1582no—
573C24—1582no—
574C24—1582no—
575C24—1582no—
576C24—1582no—
577C24—1582no—
578C24Q8×D7914yes—
579C24C23×D7912yes—
580C24C23×D7911yescharacteristic
581C2×D4—7916no—
582C2×D4—1588no—
583C2×D4—15832no—
584C2×D4—1588no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—44no—
604C22×C4—416no—
605C22×C4—31616no—
606C22×C4—3164no—
607C22×C4—794no—
608C22×C4—794no—
609C22×C4—792no—
610C22×C4—794no—
611C22×C4—794no—
612C22×C4—792no—
613C22×C4—792no—
614C22×C4—794no—
615C22×C4—792no—
616C22×C4—792no—
617C22×C4—792no—
618C22×C4—792no—
619C22×C4—1588no—
620C22×C4—1582no—
621C22×C4—1582no—
622C22×C4—1582no—
623C22×C4—1582no—
624C22×C4—1582no—
625C22×C4—1582no—
626C22×C4—1582no—
627C22×C4—1582no—
628C22×C4—1582no—
629C22×C4—1582no—
630C22×C4—1582no—
631C22×C4—1582no—
632C22×C4—1588no—
633C22×C4—1582no—
634C22×C4—1582no—
635C22×C4—1582no—
636C22×C4—1582no—
637C22×C4D4×D7914yes—
638C22×C4#1192962414yes—
639C22×C4C23×D7912yes—
640C22×C4C23×D7912yes—
641C22×C4C23×D7912yes—
642C22×C4C23×D7912yes—
643C22×C4C23×D7912yes—
644C22×C4C23×D7912yes—
645C4⋊C4—28no—
646C4⋊C4—44no—
647C4⋊C4—3164no—
648C4⋊C4—3164no—
649C4⋊C4—3164no—
650C4⋊C4—7916no—
651C4⋊C4—1588no—
652C4⋊C4—1588no—
653C4⋊C4—1588no—
654C4⋊C4—1588no—
655C4⋊C4—1588no—
656C4⋊C4—1588no—
657C4⋊C4—1588no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—3164no—
661C22⋊C4—3164no—
662C22⋊C4—3164no—
663C22⋊C4—3164no—
664C22⋊C4—1588no—
665C22⋊C4—1588no—
666C22⋊C4—1588no—
667C22⋊C4—1588no—
668C42—1588no—
669C42—1588no—
670C42—1588no—
671C23—22no—
672C23—22no—
673C23—28no—
674C23—28no—
675C23—28no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—3164no—
685C23—3164no—
686C23—3164no—
687C23—3164no—
688C23—794no—
689C23—1582no—
690C23—1582no—
691C23—1588no—
692C23—1588no—
693C23—1588no—
694C23—1582no—
695C23—1582no—
696C23—1582no—
697C23—1582no—
698C23C2×D4×D7912yes—
699C23C2×Q8×D7914yes—
700C23C2×Q8×D7912yes—
701C23#41×D7912yes—
702C23#41×D7912yes—
703C23C2×#1192962412yes—
704C23#1457920612yes—
705C23#1457920612yes—
706C23C24×D7911yescharacteristic
707D4—15832no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—416no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—31616no—
732C2×C4—3164no—
733C2×C4—3164no—
734C2×C4—3164no—
735C2×C4—3164no—
736C2×C4—7916no—
737C2×C4—794no—
738C2×C4—794no—
739C2×C4—794no—
740C2×C4—794no—
741C2×C4—794no—
742C2×C4—1582no—
743C2×C4—1582no—
744C2×C4—1582no—
745C2×C4—1582no—
746C2×C4—1582no—
747C2×C4—1582no—
748C2×C4—1582no—
749C2×C4—1582no—
750C2×C4—1582no—
751C2×C4—1582no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1588no—
756C2×C4—1588no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1582no—
760C2×C4C2×D4×D7914yes—
761C2×C4C2×#1192962414yes—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—416no—
769C22—42no—
770C22—3162no—
771C22—3162no—
772C22—3162no—
773C22—31616no—
774C22—3162no—
775C22—1584no—
776C22—1584no—
777C22—1584no—
778C22C22⋊Q8×D7914yes—
779C22#1909909114yes—
780C22#1909916314yes—
781C22#1909920314yes—
782C22#1909923114yes—
783C22#1909926714yes—
784C22#1909926814yes—
785C22C22×D4×D7911yescharacteristic
786C22C22×Q8×D7911yescharacteristic
787C22C2×#41×D7911yescharacteristic
788C22C2×#41×D7911yescharacteristic
789C22C22×#1192962411yescharacteristic
790C22C2×#1457920611yescharacteristic
791C22C2×#1457920611yescharacteristic
792C4—24no—
793C4—24no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—3162no—
799C4—3162no—
800C4—3162no—
801C4—3162no—
802C4—798no—
803C4—1584no—
804C4—1584no—
805C2—44no—
806C2—3164no—
807C2#2376727118yesdirect product factor
808C2C2×C22⋊Q8×D7911yescharacteristic
809C2C2×#1909909111yescharacteristic
810C2C2×#1909916311yescharacteristic
811C2C2×#1909920311yescharacteristic
812C2C2×#1909923111yescharacteristic
813C2C2×#1909926711yescharacteristic
814C2C2×#1909926811yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#380×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
hypercenterC2×#380D79
hypocenterC79C2×#2454
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#14579151C2semidirect
3. #23767271C2direct (N × H)
4. C2×#19098499C2semidirect
5. C2×#19098498C2semidirect
6. C2×#19098486C2semidirect
7. C2×#19098485C2semidirect
10. C2×#19098460C2semidirect
11. C2×#19098458C2semidirect
12. C2×#19098437C2semidirect
13. C2×#19098436C2semidirect
14. C2×#19098422C2semidirect
15. C2×#19098414C2semidirect
16. C2×#380×C79C2semidirect
20. C2×#14579151C22semidirect
45. #19098499C22semidirect
46. #19098498C22semidirect
47. #19098486C22semidirect
48. #19098485C22semidirect
51. #19098460C22semidirect
52. #19098458C22semidirect
53. #19098437C22semidirect
54. #19098436C22semidirect
55. #19098422C22semidirect
56. #19098414C22semidirect
66. #380×C79C22semidirect
399. C2×C79#2454semidirect
422. C2×#380D79semidirect
424. C79C2×#2454semidirect
469. #380C2×D79semidirect
807. C2#23767271direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791512
C22×C4×C22⋊D792
#237672712
C2×#190984992
C2×#190984982
C2×#190984862
C2×#190984852
C2×#190984632
C2×#190984602
C2×#190984582
C2×#190984372
C2×#190984362
C2×#190984222
C2×#190984142
C2×#380×C792
C2×#245479