Finite Group Databasebeta

← C2×#23766468 #34447873

Subgroups — C2×#23766468 #34447873

Order 20224.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579147C211yesmaximal, characteristic
2C22×#14579126C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D79C211yesmaximal, characteristic
4#23766468C2116yesmaximal, direct product factor
5C2×#19098467C211yesmaximal, characteristic, complemented
6C2×#19098463C211yesmaximal, characteristic
7C2×#19098456C211yesmaximal, characteristic, complemented
8C2×#19098455C211yesmaximal, characteristic, complemented
9C2×#19098453C211yesmaximal, characteristic, complemented
10C2×#19098451C211yesmaximal, characteristic, complemented
11C2×#19098434C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098414C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic79C211yesmaximal, characteristic, complemented
15C2×#19098410C211yesmaximal, characteristic, complemented
16C2×#385×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C23×C22⋊D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C2×#14579147C4116yescomplemented
21C2×#14579147C2218yes—
22C2×#14579126—28no—
23C2×#14579126C2218yescomplemented
24C2×C4×C22⋊D79—28no—
25C2×C4×C22⋊D79C2218yes—
26C22×C4⋊Dic79C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×C22⋊Dic79C2211yescharacteristic
31C22×C22⋊Dic79C2211yescharacteristic
32C22×C22⋊Dic79C2211yescharacteristic
33C22×(C2×D79)⋊C4C2211yescharacteristic
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×(C2×D79)⋊C4C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43C22×C4×Dic79C2211yescharacteristic
44C22×C4×Dic79C2211yescharacteristic
45#19098467C2218yescomplemented
46#19098463C2218yes—
47#19098456C2218yescomplemented
48#19098455C2218yescomplemented
49#19098453C2218yescomplemented
50#19098451C2218yescomplemented
51#19098434C2218yescomplemented
52C4⋊C4×Dic79C2218yescomplemented
53#19098414C2218yescomplemented
54C4×C22⋊Dic79C2218yescomplemented
55#19098410C2218yescomplemented
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C2×C79⋊#95C2211yescharacteristic
62C24×C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C4⋊C4×C79C2211yescharacteristic
65C22×C22⋊C4×C79C2211yescharacteristic
66C22×C22⋊C4×C79C2211yescharacteristic
67#385×C79C2218yescomplemented
68C2×#95×C79C2211yescharacteristic
69C2×#95×C79C2211yescharacteristic
70C24×D79C2311yescharacteristic
71C22×Dic158—24no—
72C22×Dic158—24no—
73C22×Dic158C2×C418yescomplemented
74C22×Dic158C2314yes—
75C22×C22⋊D79—24no—
76C22×C22⋊D79—24no—
77C22×C22⋊D79C2×C418yes—
78C22×C22⋊D79C2314yes—
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2311yescharacteristic
83C23×Dic79C2311yescharacteristic
84C23×Dic79C2311yescharacteristic
85C23×Dic79C2311yescharacteristic
86C22×C4×D79—24no—
87C22×C4×D79—24no—
88C22×C4×D79—42no—
89C22×C4×D79C2314yes—
90#14579147C2×C4164yescomplemented
91#14579126—232no—
92C4×C22⋊D79—232no—
93C2×C4⋊Dic79—24no—
94C2×C4⋊Dic79C2314yes—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4—24no—
97C2×Dic79⋊C4D418yes—
98C2×Dic79⋊C4C2314yes—
99C2×Dic79⋊C4C2314yes—
100C2×Dic79⋊C4C2314yes—
101C2×C22⋊Dic79—24no—
102C2×C22⋊Dic79—24no—
103C2×C22⋊Dic79C2×C418yescomplemented
104C2×C22⋊Dic79C2314yes—
105C2×C22⋊Dic79C2314yes—
106C2×C22⋊Dic79C2314yes—
107C2×(C2×D79)⋊C4—24no—
108C2×(C2×D79)⋊C4—24no—
109C2×(C2×D79)⋊C4—42no—
110C2×(C2×D79)⋊C4C2×C418yescomplemented
111C2×(C2×D79)⋊C4C2×C418yescomplemented
112C2×(C2×D79)⋊C4C2314yes—
113C2×(C2×D79)⋊C4C2314yes—
114C2×(C2×D79)⋊C4C2314yes—
115C2×(C2×D79)⋊C4C2314yes—
116C2×(C2×D79)⋊C4C2314yes—
117C2×C4×Dic79—24no—
118C2×C4×Dic79—24no—
119C2×C4×Dic79—24no—
120C2×C4×Dic79—24no—
121C2×C4×Dic79—42no—
122C2×C4×Dic79—42no—
123C2×C4×Dic79C2×C418yescomplemented
124C2×C4×Dic79C2314yes—
125C2×C4×Dic79C2314yes—
126C2×C4×Dic79C2314yes—
127C2×C4×Dic79C2314yes—
128C2×C4×Dic79C2314yes—
129C2×C4×Dic79C2314yes—
130C2×C4×Dic79C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C79⋊#95C2314yes—
135C79⋊#95C2314yes—
136C79⋊#95C2314yes—
137C25×C79C2311yescharacteristic
138C23×C4×C79—24no—
139C23×C4×C79—24no—
140C23×C4×C79—42no—
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2314yes—
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C23×C4×C79C2311yescharacteristic
147C23×C4×C79C2311yescharacteristic
148C2×C4⋊C4×C79—24no—
149C2×C4⋊C4×C79—24no—
150C2×C4⋊C4×C79C2314yes—
151C2×C4⋊C4×C79C2314yes—
152C2×C22⋊C4×C79—42no—
153C2×C22⋊C4×C79C2×C418yescomplemented
154C2×C22⋊C4×C79C2314yes—
155C2×C22⋊C4×C79C2314yes—
156#95×C79C2314yes—
157#95×C79C2314yes—
158C23×D79—22no—
159C23×D79—22no—
160C23×D79—22no—
161C23×D79—22no—
162C23×D79—22no—
163C23×D79—22no—
164C23×D79C22×C414yes—
165C23×D79C2412yes—
166C2×Dic158—232no—
167C2×Dic158—28no—
168C2×Dic158—28no—
169C2×Dic158C22×C4116yescomplemented
170C2×C22⋊D79—232no—
171C2×C22⋊D79—28no—
172C2×C22⋊D79—28no—
173C2×C22⋊D79C22×C4116yes—
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×Dic79—22no—
186C22×Dic79—22no—
187C22×Dic79—22no—
188C22×Dic79C22×C414yes—
189C22×Dic79C22×C414yes—
190C22×Dic79C22×C414yes—
191C22×Dic79C2×D414yes—
192C22×Dic79C2×D414yes—
193C22×Dic79#4114yes—
194C22×Dic79#4114yes—
195C22×Dic79C2412yes—
196C22×Dic79C2412yes—
197C22×Dic79C2412yes—
198C22×Dic79C2412yes—
199C22×Dic79C2412yes—
200C22×Dic79C2412yes—
201C22×Dic79C2412yes—
202C2×C4×D79—28no—
203C2×C4×D79—28no—
204C2×C4×D79—44no—
205C2×C4×D79—416no—
206C4⋊Dic79—28no—
207Dic79⋊C4—28no—
208Dic79⋊C4—28no—
209Dic79⋊C4C2×D4116yes—
210C22⋊Dic79—28no—
211C22⋊Dic79—28no—
212C22⋊Dic79C22×C4116yescomplemented
213(C2×D79)⋊C4—28no—
214(C2×D79)⋊C4—28no—
215(C2×D79)⋊C4—44no—
216(C2×D79)⋊C4C22×C4116yescomplemented
217(C2×D79)⋊C4C22×C4116yescomplemented
218C4×Dic79—28no—
219C4×Dic79—28no—
220C4×Dic79—28no—
221C4×Dic79—28no—
222C4×Dic79—44no—
223C4×Dic79—44no—
224C4×Dic79C22×C4116yescomplemented
225C24×C79—22no—
226C24×C79—22no—
227C24×C79—22no—
228C24×C79—22no—
229C24×C79—22no—
230C24×C79—22no—
231C24×C79C22×C414yes—
232C24×C79C2412yes—
233C24×C79C2411yescharacteristic
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—22no—
248C22×C4×C79—28no—
249C22×C4×C79—28no—
250C22×C4×C79—44no—
251C22×C4×C79—416no—
252C22×C4×C79C22×C414yes—
253C22×C4×C79C22×C414yes—
254C22×C4×C79C2×D414yes—
255C22×C4×C79#4114yes—
256C22×C4×C79C2412yes—
257C22×C4×C79C2412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2412yes—
260C22×C4×C79C2412yes—
261C22×C4×C79C2412yes—
262C4⋊C4×C79—28no—
263C4⋊C4×C79—28no—
264C22⋊C4×C79—44no—
265C22⋊C4×C79C22×C4116yescomplemented
266C23×C79—28no—
267C23×C79—28no—
268C23×C79—28no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C79—22no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—44no—
276C23×C79—44no—
277C23×C79—44no—
278C23×C79—44no—
279C23×C79C23×C414yes—
280C23×C79C23×C412yes—
281C23×C79C22×D412yes—
282C23×C79C2×#4112yes—
283C23×C79C2×#4112yes—
284C23×C79C2×#4112yes—
285C23×C79H(5,𝔽2)12yes—
286C23×C792−1+412yes—
287C23×C79C2511yescharacteristic
288C22×D79—28no—
289C22×D79—28no—
290C22×D79—28no—
291C22×D79—22no—
292C22×D79—22no—
293C22×D79—22no—
294C22×D79—22no—
295C22×D79—22no—
296C22×D79—22no—
297C22×D79—44no—
298C22×D79—44no—
299C22×D79—44no—
300C22×D79—44no—
301C22×D79C23×C414yes—
302C2×C4×C79—28no—
303C2×C4×C79—28no—
304C2×C4×C79—28no—
305C2×C4×C79—28no—
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—22no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—416no—
321C2×C4×C79—44no—
322C2×C4×C79—44no—
323C2×C4×C79C23×C414yes—
324C2×C4×C79C23×C414yes—
325C2×C4×C79C22×D414yes—
326C2×C4×C79C2×#4114yes—
327C22⋊D79—232no—
328C2×Dic79—28no—
329C2×Dic79—28no—
330C2×Dic79—28no—
331C2×Dic79—28no—
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—22no—
344C2×Dic79—22no—
345C2×Dic79—22no—
346C2×Dic79—44no—
347C2×Dic79—44no—
348C2×Dic79C4×D4116yes—
349C2×Dic79C23×C414yes—
350C2×Dic79C23×C414yes—
351C2×Dic79C23×C414yes—
352C2×Dic79C22×D414yes—
353C2×Dic79C22×D414yes—
354C2×Dic79C2×#4114yes—
355C2×Dic79C2×#4114yes—
356C4×D79—416no—
357Dic158—232no—
358C22×C79—24no—
359C22×C79—24no—
360C22×C79—24no—
361C22×C79—416no—
362C22×C79—42no—
363C22×C79—42no—
364C22×C79—42no—
365C22×C79—42no—
366C22×C79C2×C4×D414yes—
367C22×C79C4×#4114yes—
368C22×C79#52014yes—
369C22×C79#54614yes—
370C22×C79#54814yes—
371C22×C79#55614yes—
372C22×C79#55914yes—
373C22×C79C24×C411yescharacteristic
374C22×C79C23×D411yescharacteristic
375C22×C79C22×#4111yescharacteristic
376C22×C79C22×#4111yescharacteristic
377C22×C79C22×#4111yescharacteristic
378C22×C79C2×H(5,𝔽2)11yescharacteristic
379C22×C79C2×2−1+411yescharacteristic
380C2×D79—24no—
381C2×D79—24no—
382C2×D79—24no—
383C2×D79—416no—
384C2×D79—42no—
385C2×D79—42no—
386C2×D79—42no—
387C2×D79—42no—
388C4×C79—24no—
389C4×C79—24no—
390C4×C79—24no—
391C4×C79—24no—
392C4×C79—42no—
393C4×C79—42no—
394Dic79—24no—
395Dic79—24no—
396Dic79—24no—
397Dic79—24no—
398Dic79—42no—
399Dic79—42no—
400Dic79C2×C4×D418yes—
401C2×#2367—791nomaximal, Sylow
402C2×C79—44no—
403C2×C79#236718yescomplemented
404C2×C79C22×C4×D411yescharacteristic
405C2×C79C2×C4×#4111yescharacteristic
406C2×C79C2×#52011yescharacteristic
407C2×C79C2×#54611yescharacteristic
408C2×C79C2×#54811yescharacteristic
409C2×C79C2×#55611yescharacteristic
410C2×C79C2×#55911yescharacteristic
411D79—44no—
412C22×#124—791no—
413C22×C4×Q8—791no—
414C22×C4×D4—791no—
415#2367—7916no—
416C2×#391—791no—
417C2×#390—791no—
418C2×#388—791no—
419C2×#388—791no—
420C2×#388—791no—
421C2×#388—791no—
422C2×#385—791no—
423C2×#385D7911yescharacteristic, complemented
424C2×C4×C4⋊C4—791no—
425C2×C4×C4⋊C4—791no—
426C2×C4×C22⋊C4—791no—
427C2×C4×C22⋊C4—791no—
428C79C2×#236711yescharacteristic, complemented, Sylow
429C23×Q8—791no—
430C23×D4—791no—
431C24×C4—791no—
432C24×C4C2×D7911yescharacteristic
433C2×#124—798no—
434C2×#124—7916no—
435C2×C4×Q8—798no—
436C2×C4×Q8—1588no—
437C2×C4×D4—798no—
438C2×C4×D4—1588no—
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—
458C22×C42—791no—
459C22×C42—791no—
460C22×C42—791no—
461C22×C42—791no—
462#391—798no—
463#390—798no—
464#388—798no—
465#388—798no—
466#388—798no—
467#388—798no—
468#385—798no—
469#385C2×D7918yescomplemented
470C4×C4⋊C4—798no—
471C4×C4⋊C4—798no—
472C4×C22⋊C4—798no—
473C4×C22⋊C4—798no—
474C2×#95—791no—
475C2×#95—791no—
476C2×#95—791no—
477C2×#95—791no—
478C2×#95—791no—
479C2×#95—791no—
480C2×#95C2×D7911yescharacteristic
481C2×#95C2×D7911yescharacteristic
482C25—791no—
483C25C22×D7911yescharacteristic
484C22×Q8—798no—
485C22×Q8—794no—
486C22×Q8—1584no—
487C22×Q8—1584no—
488C22×D4—798no—
489C22×D4—794no—
490C22×D4—1584no—
491C22×D4—1584no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—3162no—
496C23×C4—794no—
497C23×C4—791no—
498C23×C4—791no—
499C23×C4—791no—
500C23×C4—791no—
501C23×C4—791no—
502C23×C4—791no—
503C23×C4—791no—
504C23×C4—1584no—
505C23×C4—1584no—
506C23×C4C22×D7911yescharacteristic
507C23×C4C22×D7911yescharacteristic
508C23×C4C22×D7914yes—
509C23×C4C22×D7911yescharacteristic
510C23×C4C22×D7911yescharacteristic
511C23×C4C22×D7911yescharacteristic
512C23×C4C22×D7911yescharacteristic
513#124—7964no—
514C4×Q8—15832no—
515C4×D4—15832no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—798no—
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⋊C4C22×D7914yes—
527C2×C4⋊C4C22×D7914yes—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—3162no—
530C2×C22⋊C4—794no—
531C2×C22⋊C4—798no—
532C2×C22⋊C4—794no—
533C2×C22⋊C4—798no—
534C2×C22⋊C4—798no—
535C2×C22⋊C4—794no—
536C2×C22⋊C4—794no—
537C2×C22⋊C4—794no—
538C2×C22⋊C4—794no—
539C2×C22⋊C4—794no—
540C2×C22⋊C4—794no—
541C2×C22⋊C4—1584no—
542C2×C22⋊C4—1584no—
543C2×C22⋊C4—1584no—
544C2×C22⋊C4—1584no—
545C2×C22⋊C4C4×D7918yescomplemented
546C2×C22⋊C4C22×D7914yes—
547C2×C22⋊C4C22×D7914yes—
548C2×C42—3162no—
549C2×C42—3162no—
550C2×C42—794no—
551C2×C42—794no—
552C2×C42—798no—
553C2×C42—794no—
554C2×C42—794no—
555C2×C42—794no—
556C2×C42—794no—
557C2×C42—794no—
558C2×C42—1584no—
559C2×C42—1584no—
560C2×C42—1584no—
561C2×C42—1584no—
562#95—794no—
563#95—794no—
564#95—794no—
565#95—794no—
566#95—794no—
567#95—794no—
568#95C22×D7914yes—
569#95C22×D7914yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—792no—
577C24—794no—
578C24—1582no—
579C24—1582no—
580C24—1582no—
581C24—1582no—
582C24—1582no—
583C24—1582no—
584C24C2×C4×D7914yes—
585C24C23×D7912yes—
586C24C23×D7911yescharacteristic
587C2×Q8—7916no—
588C2×Q8—1588no—
589C2×Q8—15832no—
590C2×Q8—1588no—
591C2×D4—7916no—
592C2×D4—1588no—
593C2×D4—15832no—
594C2×D4—1588no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—44no—
612C22×C4—416no—
613C22×C4—31616no—
614C22×C4—3164no—
615C22×C4—794no—
616C22×C4—792no—
617C22×C4—794no—
618C22×C4—794no—
619C22×C4—794no—
620C22×C4—792no—
621C22×C4—792no—
622C22×C4—792no—
623C22×C4—792no—
624C22×C4—794no—
625C22×C4—794no—
626C22×C4—794no—
627C22×C4—792no—
628C22×C4—792no—
629C22×C4—1588no—
630C22×C4—1582no—
631C22×C4—1582no—
632C22×C4—1582no—
633C22×C4—1582no—
634C22×C4—1582no—
635C22×C4—1582no—
636C22×C4—1588no—
637C22×C4—1582no—
638C22×C4—1582no—
639C22×C4—1582no—
640C22×C4—1582no—
641C22×C4—1582no—
642C22×C4—1582no—
643C22×C4—1582no—
644C22×C4—1582no—
645C22×C4C2×C4×D7914yes—
646C22×C4C2×C4×D7914yes—
647C22×C4D4×D7914yes—
648C22×C4#1192962314yes—
649C22×C4C23×D7912yes—
650C22×C4C23×D7912yes—
651C22×C4C23×D7912yes—
652C22×C4C23×D7912yes—
653C22×C4C23×D7912yes—
654C22×C4C23×D7912yes—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—7916no—
658C4⋊C4—1588no—
659C4⋊C4—1588no—
660C4⋊C4—1588no—
661C22⋊C4—44no—
662C22⋊C4—3164no—
663C22⋊C4—7916no—
664C22⋊C4—7916no—
665C22⋊C4—7916no—
666C22⋊C4—1588no—
667C22⋊C4—1588no—
668C22⋊C4—1588no—
669C22⋊C4—1588no—
670C22⋊C4C2×C4×D79116yescomplemented
671C42—3164no—
672C42—3164no—
673C42—7916no—
674C42—1588no—
675C42—1588no—
676C42—1588no—
677C42—1588no—
678C23—22no—
679C23—22no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—3164no—
692C23—3164no—
693C23—3164no—
694C23—3164no—
695C23—794no—
696C23—1582no—
697C23—1582no—
698C23—1588no—
699C23—1588no—
700C23—1588no—
701C23—1582no—
702C23—1582no—
703C23—1582no—
704C23—1582no—
705C23C22×C4×D7914yes—
706C23C22×C4×D7912yes—
707C23C2×D4×D7912yes—
708C23#41×D7912yes—
709C23#41×D7912yes—
710C23C2×#1192962312yes—
711C23#1457920612yes—
712C23#1457920912yes—
713C23C24×D7911yescharacteristic
714Q8—15832no—
715D4—15832no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—31616no—
738C2×C4—3164no—
739C2×C4—3164no—
740C2×C4—7916no—
741C2×C4—794no—
742C2×C4—794no—
743C2×C4—794no—
744C2×C4—794no—
745C2×C4—794no—
746C2×C4—794no—
747C2×C4—794no—
748C2×C4—1582no—
749C2×C4—1582no—
750C2×C4—1582no—
751C2×C4—1582no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1582no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1588no—
759C2×C4—1588no—
760C2×C4—1588no—
761C2×C4—1588no—
762C2×C4—1582no—
763C2×C4—1582no—
764C2×C4—1582no—
765C2×C4—1582no—
766C2×C4C22×C4×D7914yes—
767C2×C4C22×C4×D7914yes—
768C2×C4C2×D4×D7914yes—
769C2×C4C2×#1192962314yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—3162no—
779C22—3162no—
780C22—3162no—
781C22—31616no—
782C22—3162no—
783C22—1584no—
784C22—1584no—
785C22—1584no—
786C22C4×D4×D7914yes—
787C22C4×#1192962314yes—
788C22#1909904414yes—
789C22#1909920014yes—
790C22#1909922314yes—
791C22#1909928414yes—
792C22#1909929714yes—
793C22C23×C4×D7911yescharacteristic
794C22C22×D4×D7911yescharacteristic
795C22C2×#41×D7911yescharacteristic
796C22C2×#41×D7911yescharacteristic
797C22C22×#1192962311yescharacteristic
798C22C2×#1457920611yescharacteristic
799C22C2×#1457920911yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—3162no—
807C4—3162no—
808C4—798no—
809C4—1584no—
810C4—1584no—
811C4—1584no—
812C4—1584no—
813C2—44no—
814C2—3164no—
815C2#2376646818yesdirect product factor
816C2C2×C4×D4×D7911yescharacteristic
817C2C2×C4×#1192962311yescharacteristic
818C2C2×#1909904411yescharacteristic
819C2C2×#1909920011yescharacteristic
820C2C2×#1909922311yescharacteristic
821C2C2×#1909928411yescharacteristic
822C2C2×#1909929711yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#385×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
cosocleC23×C79C25
hypercenterC2×#385D79
hypocenterC79C2×#2367
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14579126C2semidirect
4. #23766468C2direct (N × H)
5. C2×#19098467C2semidirect
7. C2×#19098456C2semidirect
8. C2×#19098455C2semidirect
9. C2×#19098453C2semidirect
10. C2×#19098451C2semidirect
11. C2×#19098434C2semidirect
12. C2×C4⋊C4×Dic79C2semidirect
13. C2×#19098414C2semidirect
14. C2×C4×C22⋊Dic79C2semidirect
15. C2×#19098410C2semidirect
16. C2×#385×C79C2semidirect
20. C2×#14579147C4semidirect
23. C2×#14579126C22semidirect
45. #19098467C22semidirect
47. #19098456C22semidirect
48. #19098455C22semidirect
49. #19098453C22semidirect
50. #19098451C22semidirect
51. #19098434C22semidirect
52. C4⋊C4×Dic79C22semidirect
53. #19098414C22semidirect
54. C4×C22⋊Dic79C22semidirect
55. #19098410C22semidirect
67. #385×C79C22semidirect
73. C22×Dic158C2×C4semidirect
90. #14579147C2×C4semidirect
103. C2×C22⋊Dic79C2×C4semidirect
110. C2×(C2×D79)⋊C4C2×C4semidirect
111. C2×(C2×D79)⋊C4C2×C4semidirect
123. C2×C4×Dic79C2×C4semidirect
153. C2×C22⋊C4×C79C2×C4semidirect
169. C2×Dic158C22×C4semidirect
212. C22⋊Dic79C22×C4semidirect
216. (C2×D79)⋊C4C22×C4semidirect
217. (C2×D79)⋊C4C22×C4semidirect
224. C4×Dic79C22×C4semidirect
265. C22⋊C4×C79C22×C4semidirect
403. C2×C79#2367semidirect
423. C2×#385D79semidirect
428. C79C2×#2367semidirect
469. #385C2×D79semidirect
545. C2×C22⋊C4C4×D79semidirect
670. C22⋊C4C2×C4×D79semidirect
815. C2#23766468direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791472
C22×#145791262
C22×C4×C22⋊D792
#237664682
C2×#190984672
C2×#190984632
C2×#190984562
C2×#190984552
C2×#190984532
C2×#190984512
C2×#190984342
C2×C4⋊C4×Dic792
C2×#190984142
C2×C4×C22⋊Dic792
C2×#190984102
C2×#385×C792
C2×#236779