Finite Group Databasebeta

← C2×#23766073 #34447001

Subgroups — C2×#23766073 #34447001

Order 20224.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579146C211yesmaximal, characteristic
2C22×C4×D316C211yesmaximal, characteristic
3C22×C4⋊C4×D79C211yesmaximal, characteristic, complemented
4#23766073C2116yesmaximal, direct product factor
5C2×#19098462C211yesmaximal, characteristic, complemented
6C2×#19098460C211yesmaximal, characteristic, complemented
7C2×#19098455C211yesmaximal, characteristic, complemented
8C2×#19098452C211yesmaximal, characteristic, complemented
9C2×#19098447C211yesmaximal, characteristic, complemented
10C2×#19098441C211yesmaximal, characteristic
11C2×#19098437C211yesmaximal, characteristic, complemented
12C2×#19098437C211yesmaximal, characteristic, complemented
13C2×#19098434C211yesmaximal, characteristic, complemented
14C2×#19098425C211yesmaximal, characteristic, complemented
15C2×#19098410C211yesmaximal, characteristic, complemented
16C2×#387×C79C211yesmaximal, characteristic, complemented
17C23×D316C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C23×C4×D79C2211yescharacteristic
21C23×C4×D79C2211yescharacteristic
22C2×#14579146C4116yescomplemented
23C2×#14579146C2218yes—
24C2×C4×D316—28no—
25C2×C4×D316C2218yes—
26C22×C4⋊Dic79C2211yescharacteristic
27C22×C4⋊Dic79C2211yescharacteristic
28C22×C4⋊Dic79C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2211yescharacteristic
32C22×Dic79⋊C4C2211yescharacteristic
33C2×C4⋊C4×D79—28no—
34C2×C4⋊C4×D79C2218yescomplemented
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×(C2×D79)⋊C4C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×(C2×D79)⋊C4C2211yescharacteristic
39C22×(C2×D79)⋊C4C2211yescharacteristic
40C22×(C2×D79)⋊C4C2211yescharacteristic
41C22×(C2×D79)⋊C4C2211yescharacteristic
42C22×(C2×D79)⋊C4C2211yescharacteristic
43C22×C4×Dic79C2211yescharacteristic
44C22×C4×Dic79C2211yescharacteristic
45#19098462C2218yescomplemented
46#19098460C2218yescomplemented
47#19098455C2218yescomplemented
48#19098452C2218yescomplemented
49#19098447C2218yescomplemented
50#19098441C2218yes—
51#19098437C2218yescomplemented
52#19098437C2218yescomplemented
53#19098434C2218yescomplemented
54#19098425C2218yescomplemented
55#19098410C2218yescomplemented
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C2×C79⋊#95C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C42×C79C2211yescharacteristic
65#387×C79C2218yescomplemented
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C2×#95×C79C2211yescharacteristic
69C2×#95×C79C2211yescharacteristic
70C24×D79C2311yescharacteristic
71C24×D79C2311yescharacteristic
72C22×D316—24no—
73C22×D316—24no—
74C22×D316C2×C418yes—
75C22×D316C2314yes—
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C22×C4×D79—24no—
83C22×C4×D79—24no—
84C22×C4×D79—24no—
85C22×C4×D79—24no—
86C22×C4×D79—42no—
87C22×C4×D79—42no—
88C22×C4×D79—42no—
89C22×C4×D79—42no—
90C22×C4×D79—42no—
91C22×C4×D79—42no—
92C22×C4×D79C2×C418yescomplemented
93C22×C4×D79D418yes—
94C22×C4×D79C2314yes—
95C22×C4×D79C2314yes—
96C22×C4×D79C2314yes—
97C22×C4×D79C2314yes—
98#14579146C2×C4164yescomplemented
99C4×D316—232no—
100C2×C4⋊Dic79—24no—
101C2×C4⋊Dic79—24no—
102C2×C4⋊Dic79—42no—
103C2×C4⋊Dic79C2314yes—
104C2×C4⋊Dic79C2314yes—
105C2×C4⋊Dic79C2314yes—
106C2×Dic79⋊C4—24no—
107C2×Dic79⋊C4—24no—
108C2×Dic79⋊C4—42no—
109C2×Dic79⋊C4C2×C418yescomplemented
110C2×Dic79⋊C4C2314yes—
111C2×Dic79⋊C4C2314yes—
112C2×Dic79⋊C4C2314yes—
113C2×Dic79⋊C4C2314yes—
114C4⋊C4×D79—232no—
115C2×(C2×D79)⋊C4—24no—
116C2×(C2×D79)⋊C4—24no—
117C2×(C2×D79)⋊C4—24no—
118C2×(C2×D79)⋊C4—42no—
119C2×(C2×D79)⋊C4—42no—
120C2×(C2×D79)⋊C4C2×C418yescomplemented
121C2×(C2×D79)⋊C4C2×C418yescomplemented
122C2×(C2×D79)⋊C4C2×C418yescomplemented
123C2×(C2×D79)⋊C4C2314yes—
124C2×(C2×D79)⋊C4C2314yes—
125C2×(C2×D79)⋊C4C2314yes—
126C2×(C2×D79)⋊C4C2314yes—
127C2×(C2×D79)⋊C4C2314yes—
128C2×(C2×D79)⋊C4C2314yes—
129C2×(C2×D79)⋊C4C2314yes—
130C2×(C2×D79)⋊C4C2314yes—
131C2×C4×Dic79—42no—
132C2×C4×Dic79—42no—
133C2×C4×Dic79C2314yes—
134C2×C4×Dic79C2314yes—
135C79⋊#95C2314yes—
136C79⋊#95C2314yes—
137C79⋊#95C2314yes—
138C79⋊#95C2314yes—
139C79⋊#95C2314yes—
140C79⋊#95C2314yes—
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2311yescharacteristic
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C23×C4×C79C2311yescharacteristic
147C23×C4×C79C2311yescharacteristic
148C2×C4⋊C4×C79—24no—
149C2×C4⋊C4×C79C2×C418yescomplemented
150C2×C4⋊C4×C79C2314yes—
151C2×C4⋊C4×C79C2314yes—
152C2×C42×C79—24no—
153C2×C42×C79C2314yes—
154#95×C79C2314yes—
155#95×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×D79—22no—
165C23×D79—22no—
166C23×D79—22no—
167C23×D79—22no—
168C23×D79C22×C414yes—
169C23×D79C22×C414yes—
170C23×D79C2×D414yes—
171C23×D79#4114yes—
172C23×D79C2412yes—
173C23×D79C2412yes—
174C2×D316—232no—
175C2×D316—28no—
176C2×D316—28no—
177C2×D316C22×C4116yes—
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×Dic79—22no—
189C22×Dic79—22no—
190C22×Dic79—22no—
191C22×Dic79—22no—
192C22×Dic79—22no—
193C22×Dic79C22×C414yes—
194C22×Dic79C22×C414yes—
195C22×Dic79C2×D414yes—
196C22×Dic79C2412yes—
197C22×Dic79C2412yes—
198C22×Dic79C2412yes—
199C22×Dic79C2412yes—
200C22×Dic79C2412yes—
201C22×Dic79C2412yes—
202C2×C4×D79—232no—
203C2×C4×D79—28no—
204C2×C4×D79—28no—
205C2×C4×D79—28no—
206C2×C4×D79—28no—
207C2×C4×D79—416no—
208C2×C4×D79—44no—
209C2×C4×D79—44no—
210C2×C4×D79—44no—
211C2×C4×D79—44no—
212C2×C4×D79—44no—
213C2×C4×D79—44no—
214C2×C4×D79—416no—
215C2×C4×D79—416no—
216C2×C4×D79C22×C4116yescomplemented
217C2×C4×D79C2×D4116yes—
218C4⋊Dic79—28no—
219C4⋊Dic79—28no—
220C4⋊Dic79—44no—
221Dic79⋊C4—28no—
222Dic79⋊C4—28no—
223Dic79⋊C4—44no—
224Dic79⋊C4C22×C4116yescomplemented
225(C2×D79)⋊C4—28no—
226(C2×D79)⋊C4—28no—
227(C2×D79)⋊C4—28no—
228(C2×D79)⋊C4—44no—
229(C2×D79)⋊C4—44no—
230(C2×D79)⋊C4C22×C4116yescomplemented
231(C2×D79)⋊C4C22×C4116yescomplemented
232(C2×D79)⋊C4C22×C4116yescomplemented
233C4×Dic79—44no—
234C4×Dic79—44no—
235C24×C79C2411yescharacteristic
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—22no—
249C22×C4×C79—22no—
250C22×C4×C79—22no—
251C22×C4×C79—22no—
252C22×C4×C79—22no—
253C22×C4×C79C22×C414yes—
254C22×C4×C79C22×C414yes—
255C22×C4×C79C22×C414yes—
256C22×C4×C79C2×D414yes—
257C22×C4×C79C2412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2412yes—
260C22×C4×C79C2412yes—
261C22×C4×C79C2412yes—
262C22×C4×C79C2412yes—
263C22×C4×C79C2412yes—
264C4⋊C4×C79—28no—
265C4⋊C4×C79C22×C4116yescomplemented
266C42×C79—28no—
267C23×C79C23×C412yes—
268C23×C79C22×D412yes—
269C23×C79C2×#4112yes—
270C23×C79H(5,𝔽2)12yes—
271C23×C79H(5,𝔽2)12yes—
272C23×C792−1+412yes—
273C23×C792−1+412yes—
274C23×C79C2511yescharacteristic
275C22×D79—28no—
276C22×D79—28no—
277C22×D79—28no—
278C22×D79—28no—
279C22×D79—28no—
280C22×D79—28no—
281C22×D79—22no—
282C22×D79—22no—
283C22×D79—22no—
284C22×D79—22no—
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×D79C4×D4116yes—
299C22×D79C23×C414yes—
300C22×D79C23×C414yes—
301C22×D79C22×D414yes—
302C22×D79C2×#4114yes—
303C2×C4×C79—28no—
304C2×C4×C79—28no—
305C2×C4×C79—28no—
306C2×C4×C79—28no—
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—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—44no—
325C2×C4×C79—44no—
326C2×C4×C79—44no—
327C2×C4×C79C23×C414yes—
328C2×C4×C79C23×C414yes—
329C2×C4×C79C23×C414yes—
330C2×C4×C79C22×D414yes—
331C2×Dic79—28no—
332C2×Dic79—28no—
333C2×Dic79—28no—
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—22no—
347C2×Dic79—22no—
348C2×Dic79—22no—
349C2×Dic79—44no—
350C2×Dic79—44no—
351C2×Dic79—44no—
352C2×Dic79C23×C414yes—
353C2×Dic79C23×C414yes—
354C2×Dic79C22×D414yes—
355D316—232no—
356C4×D79—232no—
357C4×D79—416no—
358C4×D79—416no—
359C4×D79—416no—
360C22×C79C2×C4×D414yes—
361C22×C79#52014yes—
362C22×C79#52014yes—
363C22×C79#53414yes—
364C22×C79#53614yes—
365C22×C79#53914yes—
366C22×C79#53914yes—
367C22×C79C24×C411yescharacteristic
368C22×C79C23×D411yescharacteristic
369C22×C79C22×#4111yescharacteristic
370C22×C79C2×H(5,𝔽2)11yescharacteristic
371C22×C79C2×H(5,𝔽2)11yescharacteristic
372C22×C79C2×2−1+411yescharacteristic
373C22×C79C2×2−1+411yescharacteristic
374C2×D79—232no—
375C2×D79—24no—
376C2×D79—24no—
377C2×D79—24no—
378C2×D79—24no—
379C2×D79—24no—
380C2×D79—24no—
381C2×D79—24no—
382C2×D79—24no—
383C2×D79—24no—
384C2×D79—416no—
385C2×D79—42no—
386C2×D79—42no—
387C2×D79—42no—
388C2×D79—42no—
389C2×D79C2×C4×D418yes—
390C4×C79—24no—
391C4×C79—24no—
392C4×C79—24no—
393C4×C79—24no—
394C4×C79—42no—
395C4×C79—42no—
396C4×C79—42no—
397Dic79—24no—
398Dic79—24no—
399Dic79—24no—
400Dic79—42no—
401Dic79—42no—
402Dic79—42no—
403C2×#2322—791nomaximal, Sylow
404C2×C79#232218yescomplemented
405C2×C79C22×C4×D411yescharacteristic
406C2×C79C2×#52011yescharacteristic
407C2×C79C2×#52011yescharacteristic
408C2×C79C2×#53411yescharacteristic
409C2×C79C2×#53611yescharacteristic
410C2×C79C2×#53911yescharacteristic
411C2×C79C2×#53911yescharacteristic
412D79—28no—
413D79—44no—
414C22×#123—791no—
415C22×C4×D4—791no—
416C23×C4⋊C4—791no—
417#2322—7916no—
418C2×#389—791no—
419C2×#389—791no—
420C2×#388—791no—
421C2×#388—791no—
422C2×#387—791no—
423C2×#387D7911yescharacteristic, complemented
424C2×#386—791no—
425C2×#385—791no—
426C2×#385—791no—
427C2×#385—791no—
428C2×#381—791no—
429C2×C4×C22⋊C4—791no—
430C79C2×#232211yescharacteristic, complemented, Sylow
431C23×D4—791no—
432C24×C4—791no—
433C24×C4—791no—
434C24×C4—791no—
435C24×C4—791no—
436C2×#123—798no—
437C2×#123—7916no—
438C2×C4×D4—798no—
439C2×C4×D4—1588no—
440C22×C4⋊C4—791no—
441C22×C4⋊C4—791no—
442C22×C4⋊C4—791no—
443C22×C4⋊C4—791no—
444C22×C4⋊C4—791no—
445C22×C4⋊C4—791no—
446C22×C4⋊C4—791no—
447C22×C4⋊C4—798no—
448C22×C4⋊C4—1588no—
449C22×C4⋊C4C2×D7911yescharacteristic
450C22×C4⋊C4C2×D7911yescharacteristic
451C22×C22⋊C4—791no—
452C22×C22⋊C4—791no—
453C22×C22⋊C4—791no—
454C22×C22⋊C4—791no—
455C22×C22⋊C4—791no—
456C22×C22⋊C4—791no—
457C22×C22⋊C4—791no—
458C22×C22⋊C4—791no—
459C22×C42—791no—
460C22×C42—791no—
461C22×C42C2×D7911yescharacteristic
462#389—798no—
463#389—798no—
464#388—798no—
465#388—798no—
466#387—798no—
467#387C2×D7918yescomplemented
468#386—798no—
469#385—798no—
470#385—798no—
471#385—798no—
472#381—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
482C2×#95C2×D7911yescharacteristic
483C2×#95C2×D7911yescharacteristic
484C25—791no—
485C25—791no—
486C22×D4—798no—
487C22×D4—794no—
488C22×D4—1584no—
489C22×D4—1584no—
490C23×C4—3162no—
491C23×C4—3162no—
492C23×C4—3162no—
493C23×C4—3162no—
494C23×C4—3162no—
495C23×C4—3162no—
496C23×C4—798no—
497C23×C4—794no—
498C23×C4—794no—
499C23×C4—794no—
500C23×C4—791no—
501C23×C4—791no—
502C23×C4—791no—
503C23×C4—798no—
504C23×C4—794no—
505C23×C4—791no—
506C23×C4—791no—
507C23×C4—791no—
508C23×C4—1584no—
509C23×C4—1584no—
510C23×C4—1584no—
511C23×C4—1584no—
512C23×C4C22×D7911yescharacteristic
513C23×C4C22×D7911yescharacteristic
514C23×C4C22×D7911yescharacteristic
515C23×C4C22×D7911yescharacteristic
516C23×C4C22×D7911yescharacteristic
517C23×C4C22×D7911yescharacteristic
518C23×C4C22×D7911yescharacteristic
519#123—7964no—
520C4×D4—15832no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—3162no—
523C2×C4⋊C4—3162no—
524C2×C4⋊C4—794no—
525C2×C4⋊C4—794no—
526C2×C4⋊C4—798no—
527C2×C4⋊C4—794no—
528C2×C4⋊C4—794no—
529C2×C4⋊C4—794no—
530C2×C4⋊C4—794no—
531C2×C4⋊C4—794no—
532C2×C4⋊C4—15832no—
533C2×C4⋊C4—1584no—
534C2×C4⋊C4—1584no—
535C2×C4⋊C4—1584no—
536C2×C4⋊C4—1584no—
537C2×C4⋊C4C4×D7918yescomplemented
538C2×C4⋊C4C22×D7914yes—
539C2×C4⋊C4C22×D7914yes—
540C2×C22⋊C4—3162no—
541C2×C22⋊C4—3162no—
542C2×C22⋊C4—794no—
543C2×C22⋊C4—794no—
544C2×C22⋊C4—798no—
545C2×C22⋊C4—798no—
546C2×C22⋊C4—798no—
547C2×C22⋊C4—794no—
548C2×C22⋊C4—794no—
549C2×C22⋊C4—794no—
550C2×C22⋊C4—794no—
551C2×C22⋊C4—794no—
552C2×C22⋊C4—794no—
553C2×C22⋊C4—1584no—
554C2×C22⋊C4—1584no—
555C2×C22⋊C4—1584no—
556C2×C42—24no—
557C2×C42—3162no—
558C2×C42—3162no—
559C2×C42—794no—
560C2×C42—794no—
561C2×C42C22×D7914yes—
562#95—794no—
563#95—794no—
564#95—794no—
565#95—794no—
566#95—794no—
567#95—794no—
568#95C22×D7914yes—
569#95C22×D7914yes—
570#95C22×D7914yes—
571#95C22×D7914yes—
572C24—794no—
573C24—792no—
574C24—794no—
575C24—794no—
576C24—792no—
577C24—794no—
578C24—1582no—
579C24—1582no—
580C24—1582no—
581C24—1582no—
582C24—1582no—
583C24—1582no—
584C24—1582no—
585C24—1582no—
586C24—1582no—
587C24—1582no—
588C24C23×D7911yescharacteristic
589C2×D4—7916no—
590C2×D4—1588no—
591C2×D4—15832no—
592C2×D4—1588no—
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—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—31616no—
611C22×C4—3164no—
612C22×C4—3164no—
613C22×C4—3164no—
614C22×C4—3164no—
615C22×C4—31616no—
616C22×C4—3164no—
617C22×C4—3164no—
618C22×C4—31616no—
619C22×C4—7916no—
620C22×C4—792no—
621C22×C4—792no—
622C22×C4—792no—
623C22×C4—794no—
624C22×C4—794no—
625C22×C4—794no—
626C22×C4—7916no—
627C22×C4—792no—
628C22×C4—792no—
629C22×C4—792no—
630C22×C4—1588no—
631C22×C4—1588no—
632C22×C4—15832no—
633C22×C4—1588no—
634C22×C4—1582no—
635C22×C4—1582no—
636C22×C4—1582no—
637C22×C4—1582no—
638C22×C4—1582no—
639C22×C4—1582no—
640C22×C4—1582no—
641C22×C4—1582no—
642C22×C4—1582no—
643C22×C4—1588no—
644C22×C4—1582no—
645C22×C4—1582no—
646C22×C4—1582no—
647C22×C4—1582no—
648C22×C4—1582no—
649C22×C4—1582no—
650C22×C4C2×C4×D7914yes—
651C22×C4C2×C4×D7914yes—
652C22×C4C2×C4×D7914yes—
653C22×C4D4×D7914yes—
654C22×C4C23×D7912yes—
655C22×C4C23×D7912yes—
656C22×C4C23×D7912yes—
657C22×C4C23×D7912yes—
658C22×C4C23×D7912yes—
659C22×C4C23×D7912yes—
660C22×C4C23×D7912yes—
661C4⋊C4—28no—
662C4⋊C4—3164no—
663C4⋊C4—3164no—
664C4⋊C4—7916no—
665C4⋊C4—1588no—
666C4⋊C4—1588no—
667C4⋊C4—1588no—
668C4⋊C4—1588no—
669C4⋊C4C2×C4×D79116yescomplemented
670C22⋊C4—3164no—
671C22⋊C4—3164no—
672C22⋊C4—7916no—
673C22⋊C4—7916no—
674C22⋊C4—7916no—
675C22⋊C4—1588no—
676C22⋊C4—1588no—
677C22⋊C4—1588no—
678C42—28no—
679C42—3164no—
680C42—3164no—
681C23—3164no—
682C23—3164no—
683C23—3164no—
684C23—3164no—
685C23—7916no—
686C23—794no—
687C23—794no—
688C23—794no—
689C23—794no—
690C23—1582no—
691C23—1582no—
692C23—1582no—
693C23—1582no—
694C23—1588no—
695C23—1588no—
696C23—1588no—
697C23—1582no—
698C23—1582no—
699C23—1588no—
700C23—1582no—
701C23—1582no—
702C23—1582no—
703C23—1582no—
704C23—1588no—
705C23—1588no—
706C23—1588no—
707C23—1588no—
708C23—1588no—
709C23C22×C4×D7912yes—
710C23C2×D4×D7912yes—
711C23#41×D7912yes—
712C23#1457920712yes—
713C23#1457920712yes—
714C23#1457920812yes—
715C23#1457920912yes—
716C23C24×D7911yescharacteristic
717D4—15832no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—28no—
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—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—31616no—
743C2×C4—31616no—
744C2×C4—31616no—
745C2×C4—3164no—
746C2×C4—3164no—
747C2×C4—3164no—
748C2×C4—794no—
749C2×C4—794no—
750C2×C4—794no—
751C2×C4—15832no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1582no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1582no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4—1582no—
763C2×C4—1582no—
764C2×C4—1582no—
765C2×C4—1588no—
766C2×C4—1588no—
767C2×C4—1588no—
768C2×C4—1582no—
769C2×C4—1582no—
770C2×C4C22×C4×D7914yes—
771C2×C4C22×C4×D7914yes—
772C2×C4C22×C4×D7914yes—
773C2×C4C2×D4×D7914yes—
774C22—31616no—
775C22—3162no—
776C22—3162no—
777C22—3162no—
778C22—3162no—
779C22—798no—
780C22—1584no—
781C22—1584no—
782C22—1584no—
783C22—15832no—
784C22—1584no—
785C22—1584no—
786C22—1584no—
787C22—1584no—
788C22—1584no—
789C22—1584no—
790C22C4×D4×D7914yes—
791C22#1909904314yes—
792C22#1909904514yes—
793C22#1909912414yes—
794C22#1909913614yes—
795C22#1909915414yes—
796C22#1909916114yes—
797C22C23×C4×D7911yescharacteristic
798C22C22×D4×D7911yescharacteristic
799C22C2×#41×D7911yescharacteristic
800C22C2×#1457920711yescharacteristic
801C22C2×#1457920711yescharacteristic
802C22C2×#1457920811yescharacteristic
803C22C2×#1457920911yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—3162no—
812C4—3162no—
813C4—3162no—
814C4—1584no—
815C4—1584no—
816C4—1584no—
817C2—3164no—
818C2—1588no—
819C2#2376607318yesdirect product factor
820C2C2×C4×D4×D7911yescharacteristic
821C2C2×#1909904311yescharacteristic
822C2C2×#1909904511yescharacteristic
823C2C2×#1909912411yescharacteristic
824C2C2×#1909913611yescharacteristic
825C2C2×#1909915411yescharacteristic
826C2C2×#1909916111yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#387×C79C2
socleC24×C79C24
prime radicalC23×D316C22
cosocleC23×C79C25
hypercenterC2×#387D79
hypocenterC79C2×#2322
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D79C2semidirect
4. #23766073C2direct (N × H)
5. C2×#19098462C2semidirect
6. C2×#19098460C2semidirect
7. C2×#19098455C2semidirect
8. C2×#19098452C2semidirect
9. C2×#19098447C2semidirect
11. C2×#19098437C2semidirect
12. C2×#19098437C2semidirect
13. C2×#19098434C2semidirect
14. C2×#19098425C2semidirect
15. C2×#19098410C2semidirect
16. C2×#387×C79C2semidirect
22. C2×#14579146C4semidirect
34. C2×C4⋊C4×D79C22semidirect
45. #19098462C22semidirect
46. #19098460C22semidirect
47. #19098455C22semidirect
48. #19098452C22semidirect
49. #19098447C22semidirect
51. #19098437C22semidirect
52. #19098437C22semidirect
53. #19098434C22semidirect
54. #19098425C22semidirect
55. #19098410C22semidirect
65. #387×C79C22semidirect
92. C22×C4×D79C2×C4semidirect
98. #14579146C2×C4semidirect
109. C2×Dic79⋊C4C2×C4semidirect
120. C2×(C2×D79)⋊C4C2×C4semidirect
121. C2×(C2×D79)⋊C4C2×C4semidirect
122. C2×(C2×D79)⋊C4C2×C4semidirect
149. C2×C4⋊C4×C79C2×C4semidirect
216. C2×C4×D79C22×C4semidirect
224. Dic79⋊C4C22×C4semidirect
230. (C2×D79)⋊C4C22×C4semidirect
231. (C2×D79)⋊C4C22×C4semidirect
232. (C2×D79)⋊C4C22×C4semidirect
265. C4⋊C4×C79C22×C4semidirect
404. C2×C79#2322semidirect
423. C2×#387D79semidirect
430. C79C2×#2322semidirect
467. #387C2×D79semidirect
537. C2×C4⋊C4C4×D79semidirect
669. C4⋊C4C2×C4×D79semidirect
819. C2#23766073direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791462
C22×C4×D3162
C22×C4⋊C4×D792
#237660732
C2×#190984622
C2×#190984602
C2×#190984552
C2×#190984522
C2×#190984472
C2×#190984412
C2×#190984372
C2×#190984342
C2×#190984252
C2×#190984102
C2×#387×C792
C2×#232279