Finite Group Databasebeta

← #34447664

Subgroups — #34447664

Order 20224.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D79)⋊C4C211yesmaximal, characteristic
2C22×#14579117C211yesmaximal, characteristic, complemented
3C2×#117×D79C211yesmaximal, characteristic, complemented
4#23766346C212yesmaximal, complemented
5#23766328C212yesmaximal, complemented
6#23766323C212yesmaximal, complemented
7#23766298C212yesmaximal, complemented
8#23766270C211yesmaximal, characteristic, complemented
9#23766264C211yesmaximal, characteristic, complemented
10#23766252C211yesmaximal, characteristic, complemented
11#23766249C211yesmaximal, characteristic, complemented
12#23766246C211yesmaximal, characteristic, complemented
13C22⋊C4×C22⋊D79C211yesmaximal, characteristic
14#23766216C211yesmaximal, characteristic
15#23765860C212yesmaximal, complemented
16#23765842C212yesmaximal, complemented
17#23765836C212yesmaximal, complemented
18#23765802C211yesmaximal, characteristic, complemented
19#23765780C211yesmaximal, characteristic, complemented
20#23765778C211yesmaximal, characteristic, complemented
21C4×(C22⋊D79)⋊C4C212yesmaximal, complemented
22C4×#14579117C211yesmaximal, characteristic, complemented
23C79×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D79C2211yescharacteristic
25C24×Dic79C2211yescharacteristic
26C23×C4×D79C2211yescharacteristic
27C2×C4×C22⋊D79C2212yes—
28C2×(C22⋊D79)⋊C4C4116yescomplemented
29C2×(C22⋊D79)⋊C4C2212yes—
30C2×(C22⋊D79)⋊C4C2211yescharacteristic
31C2×(C22⋊D79)⋊C4C2211yescharacteristic
32C2×(C22⋊D79)⋊C4C2211yescharacteristic
33C2×(C22⋊D79)⋊C4C2211yescharacteristic
34C2×(C22⋊D79)⋊C4C2211yescharacteristic
35C2×(C22⋊D79)⋊C4C2211yescharacteristic
36C2×(C22⋊D79)⋊C4C2211yescharacteristic
37C2×(C22⋊D79)⋊C4C2211yescharacteristic
38C2×#14579120C2211yescharacteristic
39C2×#14579119C2212yescomplemented
40C2×#14579118C2212yescomplemented
41C2×#14579117—28no—
42C2×#14579117C2211yescharacteristic
43C2×#14579117C2211yescharacteristic
44C2×#14579117C2211yescharacteristic
45C2×#14579117C2211yescharacteristic
46C2×#14579117C2211yescharacteristic
47C2×#14579117C2211yescharacteristic
48C2×#14579117C2212yescomplemented
49C2×#14579117C2212yescomplemented
50#117×D79—28no—
51C22×Dic79⋊C4C2211yescharacteristic
52C22×Dic79⋊C4C2212yescomplemented
53C2×C4⋊C4×D79C2212yescomplemented
54C22×C22⋊Dic79C2211yescharacteristic
55C22×(C2×D79)⋊C4C2211yescharacteristic
56C2×C22⋊C4×D79C2211yescharacteristic
57C2×C22⋊C4×D79C2211yescharacteristic
58C22×C4×Dic79C2211yescharacteristic
59C22×C4×Dic79C2212yescomplemented
60C2×C42×D79C2212yescomplemented
61#19098463C2212yes—
62#19098463C2212yes—
63#19098460C2212yescomplemented
64#19098458C2212yescomplemented
65#19098456C2212yescomplemented
66#19098456C2212yescomplemented
67#19098455C2212yescomplemented
68#19098454C2212yescomplemented
69#19098453C2212yescomplemented
70#19098452C2212yescomplemented
71#19098450C2212yescomplemented
72#19098447C2212yescomplemented
73#19098445C2212yescomplemented
74#19098444C2212yescomplemented
75#19098442C2212yes—
76#19098440C2212yes—
77#19098439C2212yes—
78#19098439C2212yes—
79#19098438C2212yescomplemented
80#19098437C2212yescomplemented
81#19098434C2212yescomplemented
82#19098432C2212yescomplemented
83#19098427C2212yescomplemented
84#19098426C2211yescharacteristic
85#19098424C2211yescharacteristic
86#19098424C2211yescharacteristic
87#19098423C2211yescharacteristic
88#19098422C2212yescomplemented
89#19098422C2212yescomplemented
90#19098421C2211yescharacteristic
91#19098421C2211yescharacteristic
92#19098421C2212yescomplemented
93#19098421C2212yescomplemented
94#19098419C2211yescharacteristic
95#19098418C2211yescharacteristic
96#19098418C2211yescharacteristic
97C4⋊C4×Dic79C2212yescomplemented
98C4×Dic79⋊C4C2212yescomplemented
99C4×Dic79⋊C4C2212yescomplemented
100#19098414C2212yescomplemented
101#19098414C2212yescomplemented
102#19098414C2212yescomplemented
103C22⋊C4×Dic79C2211yescharacteristic
104C22⋊C4×Dic79C2211yescharacteristic
105C22⋊C4×Dic79C2212yescomplemented
106C22⋊C4×Dic79C2212yescomplemented
107C22⋊C4×Dic79C2212yescomplemented
108C4×(C2×D79)⋊C4C2212yescomplemented
109C4×C22⋊Dic79C2211yescharacteristic
110#19098410C2212yescomplemented
111#19098410C2212yescomplemented
112#19098410C2212yescomplemented
113#19098408C2212yescomplemented
114C42×Dic79C2212yescomplemented
115C2×#117×C79C2211yescharacteristic
116C22×C22⋊C4×C79C2211yescharacteristic
117C22×C22⋊C4×C79C2211yescharacteristic
118#388×C79C2212yescomplemented
119#388×C79C2212yescomplemented
120#385×C79C2212yescomplemented
121#381×C79C2211yescharacteristic
122#380×C79C2211yescharacteristic
123#379×C79C2211yescharacteristic
124C4×C22⋊C4×C79C2211yescharacteristic
125C4×C22⋊C4×C79C2212yescomplemented
126C24×D79C2311yescharacteristic
127C22×C22⋊D79—28no—
128C22×C22⋊D79C2×C418yes—
129C22×C22⋊D79C2311yescharacteristic
130C22×C22⋊D79C2311yescharacteristic
131C22×C22⋊D79C2311yescharacteristic
132C22×C22⋊D79C2311yescharacteristic
133C23×Dic79—24no—
134C23×Dic79—24no—
135C23×Dic79C2×C418yescomplemented
136C23×Dic79C2312yes—
137C23×Dic79C2311yescharacteristic
138C23×Dic79C2311yescharacteristic
139C23×Dic79C2311yescharacteristic
140C23×Dic79C2311yescharacteristic
141C23×Dic79C2311yescharacteristic
142C23×Dic79C2311yescharacteristic
143C23×Dic79C2311yescharacteristic
144C22×C4×D79—24no—
145C22×C4×D79—24no—
146C22×C4×D79C2×C418yescomplemented
147C22×C4×D79C2312yes—
148C22×C4×D79C2312yes—
149C22×C4×D79C2311yescharacteristic
150C22×C4×D79C2311yescharacteristic
151C22×C4×D79C2311yescharacteristic
152C22×C4×D79C2311yescharacteristic
153C4×C22⋊D79—28no—
154(C22⋊D79)⋊C4—28no—
155(C22⋊D79)⋊C4C2×C418yes—
156(C22⋊D79)⋊C4C2×C418yes—
157(C22⋊D79)⋊C4C2×C418yescomplemented
158(C22⋊D79)⋊C4C2×C418yescomplemented
159(C22⋊D79)⋊C4C2×C418yescomplemented
160(C22⋊D79)⋊C4C2×C418yescomplemented
161(C22⋊D79)⋊C4C2×C418yescomplemented
162(C22⋊D79)⋊C4C2×C418yescomplemented
163#14579120—24no—
164#14579119—28no—
165#14579118—28no—
166#14579117—24no—
167#14579117—24no—
168#14579117—24no—
169#14579117—24no—
170#14579117—28no—
171#14579117—24no—
172#14579117—28no—
173#14579117D418yescomplemented
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2312yes—
176C2×Dic79⋊C4—28no—
177C2×Dic79⋊C4C2×C418yescomplemented
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2311yescharacteristic
186C2×Dic79⋊C4C2311yescharacteristic
187C2×Dic79⋊C4C2311yescharacteristic
188C2×Dic79⋊C4C2311yescharacteristic
189C2×Dic79⋊C4C2312yes—
190C4⋊C4×D79—28no—
191C2×C22⋊Dic79—24no—
192C2×C22⋊Dic79C2311yescharacteristic
193C2×C22⋊Dic79C2312yes—
194C2×C22⋊Dic79C2311yescharacteristic
195C2×C22⋊Dic79C2311yescharacteristic
196C2×C22⋊Dic79C2312yes—
197C2×C22⋊Dic79C2312yes—
198C2×C22⋊Dic79C2311yescharacteristic
199C2×(C2×D79)⋊C4C2×C418yescomplemented
200C2×(C2×D79)⋊C4C2312yes—
201C2×(C2×D79)⋊C4C2312yes—
202C2×(C2×D79)⋊C4C2312yes—
203C2×(C2×D79)⋊C4C2312yes—
204C2×(C2×D79)⋊C4C2312yes—
205C2×(C2×D79)⋊C4C2312yes—
206C2×(C2×D79)⋊C4C2311yescharacteristic
207C2×(C2×D79)⋊C4C2311yescharacteristic
208C2×(C2×D79)⋊C4C2311yescharacteristic
209C2×(C2×D79)⋊C4C2311yescharacteristic
210C22⋊C4×D79—24no—
211C22⋊C4×D79—24no—
212C2×C4×Dic79—28no—
213C2×C4×Dic79C2×C418yescomplemented
214C2×C4×Dic79C2312yes—
215C2×C4×Dic79C2312yes—
216C2×C4×Dic79C2312yes—
217C2×C4×Dic79C2312yes—
218C2×C4×Dic79C2312yes—
219C2×C4×Dic79C2312yes—
220C2×C4×Dic79C2312yes—
221C2×C4×Dic79C2312yes—
222C2×C4×Dic79C2312yes—
223C2×C4×Dic79C2311yescharacteristic
224C2×C4×Dic79C2311yescharacteristic
225C2×C4×Dic79C2311yescharacteristic
226C2×C4×Dic79C2311yescharacteristic
227C2×C4×Dic79C2312yes—
228C42×D79—28no—
229C79⋊#95C2312yes—
230C79⋊#95C2312yes—
231C79⋊#95C2312yes—
232C79⋊#95C2312yes—
233C79⋊#95C2312yes—
234C79⋊#95C2312yes—
235C79⋊#95C2312yes—
236C79⋊#95C2312yes—
237C79⋊#95C2312yes—
238C79⋊#95C2312yes—
239C79⋊#95C2312yes—
240C79⋊#95C2312yes—
241C25×C79C2311yescharacteristic
242C23×C4×C79C2312yes—
243C23×C4×C79C2311yescharacteristic
244C23×C4×C79C2311yescharacteristic
245#117×C79—24no—
246C2×C4⋊C4×C79C2312yes—
247C2×C4⋊C4×C79C2312yes—
248C2×C22⋊C4×C79—24no—
249C2×C22⋊C4×C79C2×C418yescomplemented
250C2×C22⋊C4×C79C2311yescharacteristic
251C2×C22⋊C4×C79C2312yes—
252C2×C22⋊C4×C79C2311yescharacteristic
253C2×C22⋊C4×C79C2311yescharacteristic
254C2×C22⋊C4×C79C2312yes—
255C2×C22⋊C4×C79C2312yes—
256C2×C22⋊C4×C79C2311yescharacteristic
257C2×C22⋊C4×C79C2311yescharacteristic
258C2×C22⋊C4×C79C2311yescharacteristic
259C2×C22⋊C4×C79C2311yescharacteristic
260C2×C22⋊C4×C79C2311yescharacteristic
261C2×C42×C79C2312yes—
262C2×C42×C79C2312yes—
263#95×C79C2312yes—
264#95×C79C2312yes—
265#95×C79C2312yes—
266#95×C79C2312yes—
267C23×D79—22no—
268C23×D79—22no—
269C23×D79—24no—
270C23×D79—42no—
271C23×D79C22×C414yes—
272C23×D79C2411yescharacteristic
273C23×D79C2411yescharacteristic
274C2×C22⋊D79—24no—
275C2×C22⋊D79—24no—
276C2×C22⋊D79—24no—
277C2×C22⋊D79—232no—
278C2×C22⋊D79C22×C414yes—
279C2×C22⋊D79C22×C414yes—
280C2×C22⋊D79C22×C414yes—
281C2×C22⋊D79C22×C414yes—
282C2×C22⋊D79#4118yes—
283C22×Dic79—232no—
284C22×Dic79—22no—
285C22×Dic79—22no—
286C22×Dic79—22no—
287C22×Dic79—22no—
288C22×Dic79—22no—
289C22×Dic79—22no—
290C22×Dic79—22no—
291C22×Dic79—22no—
292C22×Dic79—24no—
293C22×Dic79—24no—
294C22×Dic79—22no—
295C22×Dic79—22no—
296C22×Dic79—24no—
297C22×Dic79—42no—
298C22×Dic79C22×C414yes—
299C22×Dic79C22×C414yes—
300C22×Dic79C22×C414yes—
301C22×Dic79C22×C414yes—
302C22×Dic79C22×C414yes—
303C22×Dic79C22×C414yes—
304C22×Dic79C22×C414yes—
305C22×Dic79C2×D414yes—
306C22×Dic79#4114yes—
307C22×Dic79C2412yes—
308C22×Dic79C2412yes—
309C22×Dic79C2412yes—
310C22×Dic79C2411yescharacteristic
311C22×Dic79C2411yescharacteristic
312C22×Dic79C2411yescharacteristic
313C22×Dic79C2412yes—
314C22×Dic79C2411yescharacteristic
315C22×Dic79C2411yescharacteristic
316C22×Dic79C2411yescharacteristic
317C2×C4×D79—232no—
318C2×C4×D79—22no—
319C2×C4×D79—22no—
320C2×C4×D79—22no—
321C2×C4×D79—22no—
322C2×C4×D79—22no—
323C2×C4×D79—22no—
324C2×C4×D79—22no—
325C2×C4×D79—22no—
326C2×C4×D79—24no—
327C2×C4×D79—24no—
328C2×C4×D79—24no—
329C2×C4×D79—24no—
330C2×C4×D79—42no—
331C2×C4×D79—42no—
332C2×C4×D79C22×C414yes—
333C2×C4×D79C22×C414yes—
334C2×C4×D79C22×C414yes—
335C2×C4×D79C22×C414yes—
336C4⋊Dic79—24no—
337C4⋊Dic79—42no—
338Dic79⋊C4—24no—
339Dic79⋊C4—24no—
340Dic79⋊C4—24no—
341Dic79⋊C4—24no—
342Dic79⋊C4—24no—
343Dic79⋊C4—24no—
344Dic79⋊C4—24no—
345Dic79⋊C4C22×C414yes—
346Dic79⋊C4C22×C414yes—
347Dic79⋊C4C22×C414yes—
348Dic79⋊C4C22×C414yes—
349Dic79⋊C4C2×D418yescomplemented
350C22⋊Dic79—24no—
351C22⋊Dic79—22no—
352C22⋊Dic79—22no—
353C22⋊Dic79—22no—
354C22⋊Dic79—24no—
355C22⋊Dic79—42no—
356C22⋊Dic79C2×D414yes—
357(C2×D79)⋊C4—24no—
358(C2×D79)⋊C4—24no—
359(C2×D79)⋊C4—24no—
360(C2×D79)⋊C4—24no—
361(C2×D79)⋊C4—42no—
362(C2×D79)⋊C4—42no—
363(C2×D79)⋊C4C22×C414yes—
364(C2×D79)⋊C4C22×C414yes—
365(C2×D79)⋊C4C22×C414yes—
366(C2×D79)⋊C4C22×C414yes—
367C4×Dic79—24no—
368C4×Dic79—24no—
369C4×Dic79—24no—
370C4×Dic79—24no—
371C4×Dic79—24no—
372C4×Dic79—24no—
373C4×Dic79—24no—
374C4×Dic79—24no—
375C4×Dic79—42no—
376C4×Dic79C22×C414yes—
377C4×Dic79C22×C414yes—
378C4×Dic79C22×C414yes—
379C4×Dic79C22×C414yes—
380C4×Dic79C2×D418yescomplemented
381C24×C79—22no—
382C24×C79—22no—
383C24×C79—24no—
384C24×C79—42no—
385C24×C79C22×C414yes—
386C24×C79C2411yescharacteristic
387C24×C79C2411yescharacteristic
388C24×C79C2411yescharacteristic
389C22×C4×C79—22no—
390C22×C4×C79—22no—
391C22×C4×C79—24no—
392C22×C4×C79—24no—
393C22×C4×C79—42no—
394C22×C4×C79—42no—
395C22×C4×C79C22×C414yes—
396C22×C4×C79C22×C414yes—
397C22×C4×C79C2412yes—
398C22×C4×C79C2412yes—
399C22×C4×C79C2412yes—
400C22×C4×C79C2411yescharacteristic
401C22×C4×C79C2411yescharacteristic
402C22×C4×C79C2411yescharacteristic
403C22×C4×C79C2411yescharacteristic
404C22×C4×C79C2412yes—
405C4⋊C4×C79—24no—
406C4⋊C4×C79—42no—
407C22⋊C4×C79—22no—
408C22⋊C4×C79—22no—
409C22⋊C4×C79—22no—
410C22⋊C4×C79—24no—
411C22⋊C4×C79—24no—
412C22⋊C4×C79—42no—
413C22⋊C4×C79C22×C414yes—
414C22⋊C4×C79C22×C414yes—
415C22⋊C4×C79C22×C414yes—
416C22⋊C4×C79C22×C414yes—
417C22⋊C4×C79C2×D414yes—
418C42×C79—24no—
419C42×C79—42no—
420C23×C79—21no—
421C23×C79—21no—
422C23×C79—22no—
423C23×C79—22no—
424C23×C79—22no—
425C23×C79—28no—
426C23×C79—28no—
427C23×C79—21no—
428C23×C79—21no—
429C23×C79—22no—
430C23×C79—22no—
431C23×C79—44no—
432C23×C79—48no—
433C23×C79—48no—
434C23×C79C23×C412yes—
435C23×C79C23×C412yes—
436C23×C79C23×C412yes—
437C23×C79C22×D412yes—
438C23×C79C2×#4114yes—
439C23×C79C2×#4112yes—
440C23×C79C2511yescharacteristic
441C22×D79—21no—
442C22×D79—21no—
443C22×D79—22no—
444C22×D79—28no—
445C22×D79—21no—
446C22×D79—21no—
447C22×D79—22no—
448C22×D79—22no—
449C22×D79—28no—
450C22×D79—44no—
451C22×D79—48no—
452C22×D79—48no—
453C22×D79C23×C412yes—
454C22×D79C23×C412yes—
455C22×D79C2×#4114yes—
456C2×C4×C79—28no—
457C2×C4×C79—21no—
458C2×C4×C79—21no—
459C2×C4×C79—22no—
460C2×C4×C79—21no—
461C2×C4×C79—21no—
462C2×C4×C79—22no—
463C2×C4×C79—22no—
464C2×C4×C79—22no—
465C2×C4×C79—22no—
466C2×C4×C79—22no—
467C2×C4×C79—22no—
468C2×C4×C79—22no—
469C2×C4×C79—22no—
470C2×C4×C79—22no—
471C2×C4×C79—22no—
472C2×C4×C79—22no—
473C2×C4×C79—22no—
474C2×C4×C79—44no—
475C2×C4×C79—48no—
476C2×C4×C79C23×C412yes—
477C2×C4×C79C23×C412yes—
478C2×C4×C79C23×C412yes—
479C2×C4×C79C23×C412yes—
480C2×C4×C79C22×D414yes—
481C22⋊D79—28no—
482C22⋊D79—28no—
483C22⋊D79—28no—
484C22⋊D79#117116yescomplemented
485C2×Dic79—28no—
486C2×Dic79—21no—
487C2×Dic79—21no—
488C2×Dic79—22no—
489C2×Dic79—21no—
490C2×Dic79—21no—
491C2×Dic79—22no—
492C2×Dic79—22no—
493C2×Dic79—28no—
494C2×Dic79—28no—
495C2×Dic79—28no—
496C2×Dic79—28no—
497C2×Dic79—28no—
498C2×Dic79—22no—
499C2×Dic79—22no—
500C2×Dic79—22no—
501C2×Dic79—22no—
502C2×Dic79—22no—
503C2×Dic79—22no—
504C2×Dic79—22no—
505C2×Dic79—22no—
506C2×Dic79—22no—
507C2×Dic79—48no—
508C2×Dic79C4×D4116yescomplemented
509C2×Dic79C23×C412yes—
510C2×Dic79C23×C412yes—
511C2×Dic79C23×C412yes—
512C2×Dic79C23×C412yes—
513C2×Dic79C23×C412yes—
514C2×Dic79C23×C412yes—
515C2×Dic79C22×D414yes—
516C2×Dic79C22×D412yes—
517C2×Dic79C22×D412yes—
518C2×Dic79C2×#4114yes—
519C2×Dic79C2×#4112yes—
520C2×Dic79C2×#4112yes—
521C4×D79—28no—
522C4×D79—28no—
523C4×D79—28no—
524C4×D79—28no—
525C4×D79—48no—
526C4×D79—48no—
527C22×C79—22no—
528C22×C79—22no—
529C22×C79—22no—
530C22×C79—22no—
531C22×C79—24no—
532C22×C79—24no—
533C22×C79—24no—
534C22×C79—24no—
535C22×C79—22no—
536C22×C79—22no—
537C22×C79—22no—
538C22×C79—416no—
539C22×C79—42no—
540C22×C79—42no—
541C22×C79C2×#11714yescomplemented
542C22×C79C2×C4×D414yes—
543C22×C79C24×C411yescharacteristic
544C22×C79C23×D411yescharacteristic
545C22×C79C22×#4112yes—
546C22×C79C22×#4111yescharacteristic
547C22×C79#58512yes—
548C2×D79—22no—
549C2×D79—22no—
550C2×D79—24no—
551C2×D79—24no—
552C2×D79—22no—
553C2×D79—22no—
554C2×D79—22no—
555C2×D79—416no—
556C2×D79—42no—
557C2×D79—42no—
558C2×D79C2×#11714yescomplemented
559C4×C79—22no—
560C4×C79—22no—
561C4×C79—22no—
562C4×C79—22no—
563C4×C79—24no—
564C4×C79—42no—
565C4×C79—42no—
566C4×C79—42no—
567Dic79—22no—
568Dic79—22no—
569Dic79—22no—
570Dic79—24no—
571Dic79—42no—
572Dic79—42no—
573Dic79—42no—
574Dic79C2×#11714yescomplemented
575Dic79C2×C4×D414yes—
576Dic79C2×C4×D414yes—
577D4×#117—791nomaximal, Sylow
578C2×C79—24no—
579C2×C79—24no—
580C2×C79—42no—
581C2×C79C22×#11711yescharacteristic
582C2×C79C22×C4×D411yescharacteristic
583C2×C79#342811yescharacteristic
584C2×C79D4×#4112yes—
585C2×C79#347512yes—
586D79—24no—
587D79—42no—
588C22×C4×D4—791no—
589C22×#117—791no—
590C22×#117—791no—
591#2354—792no—
592#2352—792no—
593#2352—792no—
594D4×C4⋊C4—792no—
595#2344—791no—
596#2344—791no—
597#2342—791no—
598#2342—791no—
599#2342—791no—
600#2342D7911yescharacteristic, complemented
601D4×C22⋊C4—791no—
602D4×C22⋊C4—791no—
603#2293—792no—
604#2290—792no—
605#2290—792no—
606#2285—791no—
607#2280—791no—
608#2280—791no—
609C42×D4—792no—
610C4×#117—791no—
611C79D4×#11711yescharacteristic, complemented, Sylow
612C23×D4—791no—
613C24×C4—791no—
614C24×C4—791no—
615C2×C4×D4—792no—
616C2×C4×D4—791no—
617C2×C4×D4—791no—
618C2×C4×D4—791no—
619C2×C4×D4—791no—
620C2×C4×D4—791no—
621C2×C4×D4—791no—
622C2×C4×D4—791no—
623C2×C4×D4—791no—
624C2×C4×D4—792no—
625C2×C4×D4—7916no—
626C2×#117—791no—
627C2×#117—792no—
628C2×#117—791no—
629C2×#117—791no—
630C2×#117—791no—
631C2×#117—792no—
632C2×#117—791no—
633C2×#117—791no—
634C2×#117—792no—
635C2×#117—791no—
636C2×#117—792no—
637C2×#117—1588no—
638C2×#117—1588no—
639C2×#117C2×D7911yescharacteristic
640C22×C4⋊C4—791no—
641C22×C4⋊C4—792no—
642C22×C4⋊C4—792no—
643C22×C22⋊C4—791no—
644C22×C22⋊C4—791no—
645C22×C22⋊C4—791no—
646C22×C22⋊C4—791no—
647C22×C22⋊C4C2×D7911yescharacteristic
648C22×C22⋊C4C2×D7911yescharacteristic
649C22×C42—791no—
650C22×C42—792no—
651C22×C42—792no—
652#390—792no—
653#390—792no—
654#389—792no—
655#389—792no—
656#388—792no—
657#388—792no—
658#388—792no—
659#388—792no—
660#388—792no—
661#388—792no—
662#388C2×D7912yescomplemented
663#388C2×D7912yescomplemented
664#387—792no—
665#387—792no—
666#387—792no—
667#387—792no—
668#386—792no—
669#386—792no—
670#386—792no—
671#386—792no—
672#385—792no—
673#385—792no—
674#385—792no—
675#385C2×D7912yescomplemented
676#384—792no—
677#382—792no—
678#381—791no—
679#381—791no—
680#381—791no—
681#381C2×D7911yescharacteristic
682#380—791no—
683#380—791no—
684#380—791no—
685#380—792no—
686#380—792no—
687#380—792no—
688#380—792no—
689#380C2×D7911yescharacteristic
690#379—791no—
691#379—791no—
692#379—791no—
693#379C2×D7911yescharacteristic
694C4×C4⋊C4—792no—
695C4×C4⋊C4—792no—
696C4×C4⋊C4—792no—
697C4×C4⋊C4—792no—
698C4×C4⋊C4—792no—
699C4×C4⋊C4—792no—
700C4×C22⋊C4—791no—
701C4×C22⋊C4—791no—
702C4×C22⋊C4—791no—
703C4×C22⋊C4—792no—
704C4×C22⋊C4—792no—
705C4×C22⋊C4—792no—
706C4×C22⋊C4—792no—
707C4×C22⋊C4—792no—
708C4×C22⋊C4—792no—
709C4×C22⋊C4—792no—
710C4×C22⋊C4C2×D7911yescharacteristic
711C4×C22⋊C4C2×D7912yescomplemented
712#376—792no—
713C43—792no—
714C25—791no—
715C25C22×D7911yescharacteristic
716C22×D4—791no—
717C22×D4—798no—
718C22×D4—791no—
719C22×D4—791no—
720C22×D4—791no—
721C22×D4—1588no—
722C23×C4—792no—
723C23×C4—792no—
724C23×C4—792no—
725C23×C4—791no—
726C23×C4—798no—
727C23×C4—791no—
728C23×C4—791no—
729C23×C4—791no—
730C23×C4—791no—
731C23×C4—791no—
732C23×C4—791no—
733C23×C4—798no—
734C23×C4—791no—
735C23×C4—791no—
736C23×C4—791no—
737C23×C4—791no—
738C23×C4—1584no—
739C23×C4—1584no—
740C23×C4—1584no—
741C23×C4—1584no—
742C23×C4C22×D7912yes—
743C23×C4C22×D7911yescharacteristic
744C23×C4C22×D7911yescharacteristic
745C4×D4—798no—
746C4×D4—798no—
747C4×D4—798no—
748C4×D4—798no—
749C4×D4—798no—
750C4×D4—798no—
751C4×D4—798no—
752C4×D4—798no—
753C4×D4—1588no—
754C4×D4—1588no—
755#117—24no—
756#117—798no—
757#117—1588no—
758#117—1588no—
759#117—1588no—
760#117—1584no—
761#117—1588no—
762#117—1584no—
763#117—1584no—
764#117—1584no—
765#117—1584no—
766#117—1584no—
767C2×C4⋊C4—792no—
768C2×C4⋊C4—798no—
769C2×C4⋊C4—792no—
770C2×C4⋊C4—791no—
771C2×C4⋊C4—791no—
772C2×C4⋊C4—791no—
773C2×C4⋊C4—791no—
774C2×C4⋊C4—792no—
775C2×C4⋊C4—792no—
776C2×C4⋊C4—792no—
777C2×C4⋊C4—792no—
778C2×C4⋊C4—792no—
779C2×C4⋊C4—792no—
780C2×C4⋊C4—792no—
781C2×C4⋊C4—792no—
782C2×C4⋊C4—1588no—
783C2×C4⋊C4—1588no—
784C2×C4⋊C4C22×D7912yes—
785C2×C4⋊C4C22×D7912yes—
786C2×C22⋊C4—24no—
787C2×C22⋊C4—792no—
788C2×C22⋊C4—792no—
789C2×C22⋊C4—792no—
790C2×C22⋊C4—791no—
791C2×C22⋊C4—798no—
792C2×C22⋊C4—791no—
793C2×C22⋊C4—791no—
794C2×C22⋊C4—791no—
795C2×C22⋊C4—791no—
796C2×C22⋊C4—791no—
797C2×C22⋊C4—791no—
798C2×C22⋊C4—792no—
799C2×C22⋊C4—791no—
800C2×C22⋊C4—792no—
801C2×C22⋊C4—792no—
802C2×C22⋊C4—792no—
803C2×C22⋊C4—792no—
804C2×C22⋊C4—792no—
805C2×C22⋊C4—1584no—
806C2×C22⋊C4—1584no—
807C2×C22⋊C4—1584no—
808C2×C22⋊C4C4×D7918yescomplemented
809C2×C22⋊C4C22×D7911yescharacteristic
810C2×C22⋊C4C22×D7911yescharacteristic
811C2×C22⋊C4C22×D7912yes—
812C2×C22⋊C4C22×D7911yescharacteristic
813C2×C22⋊C4C22×D7912yes—
814C2×C22⋊C4C22×D7912yes—
815C2×C22⋊C4C22×D7911yescharacteristic
816C2×C22⋊C4C22×D7911yescharacteristic
817C2×C22⋊C4C22×D7911yescharacteristic
818C2×C22⋊C4C22×D7911yescharacteristic
819C2×C22⋊C4C22×D7911yescharacteristic
820C2×C42—792no—
821C2×C42—798no—
822C2×C42—792no—
823C2×C42—791no—
824C2×C42—791no—
825C2×C42—791no—
826C2×C42—791no—
827C2×C42—792no—
828C2×C42—792no—
829C2×C42—792no—
830C2×C42—792no—
831C2×C42—792no—
832C2×C42—792no—
833C2×C42—792no—
834C2×C42—792no—
835C2×C42—1588no—
836C2×C42—1588no—
837C2×C42C22×D7912yes—
838C2×C42C22×D7912yes—
839#95—792no—
840#95—792no—
841#95—792no—
842#95—792no—
843#95—792no—
844#95—792no—
845#95—792no—
846#95—792no—
847#95—792no—
848#95—792no—
849#95—792no—
850#95—792no—
851#95C22×D7912yes—
852#95C22×D7912yes—
853#95C22×D7912yes—
854#95C22×D7912yes—
855C24—22no—
856C24—24no—
857C24—22no—
858C24—42no—
859C24—3162no—
860C24—794no—
861C24—791no—
862C24—791no—
863C24—1584no—
864C24—1582no—
865C24—1582no—
866C24C2×C4×D7914yes—
867C24C23×D7911yescharacteristic
868C24C23×D7911yescharacteristic
869C24C23×D7911yescharacteristic
870C2×D4—798no—
871C2×D4—794no—
872C2×D4—794no—
873C2×D4—794no—
874C2×D4—794no—
875C2×D4—1584no—
876C2×D4—15832no—
877C2×D4—1584no—
878C2×D4—1584no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—3162no—
886C22×C4—3162no—
887C22×C4—3162no—
888C22×C4—794no—
889C22×C4—791no—
890C22×C4—791no—
891C22×C4—791no—
892C22×C4—794no—
893C22×C4—794no—
894C22×C4—791no—
895C22×C4—791no—
896C22×C4—791no—
897C22×C4—792no—
898C22×C4—794no—
899C22×C4—794no—
900C22×C4—794no—
901C22×C4—794no—
902C22×C4—794no—
903C22×C4—794no—
904C22×C4—794no—
905C22×C4—794no—
906C22×C4—794no—
907C22×C4—794no—
908C22×C4—792no—
909C22×C4—792no—
910C22×C4—792no—
911C22×C4—1584no—
912C22×C4—1584no—
913C22×C4—1584no—
914C22×C4—1582no—
915C22×C4—1582no—
916C22×C4—1582no—
917C22×C4—1582no—
918C22×C4—15832no—
919C22×C4—1582no—
920C22×C4—1582no—
921C22×C4—1582no—
922C22×C4—1582no—
923C22×C4—1584no—
924C22×C4—1584no—
925C22×C4—1584no—
926C22×C4—1582no—
927C22×C4—1582no—
928C22×C4—1582no—
929C22×C4—1582no—
930C22×C4—15832no—
931C22×C4—1582no—
932C22×C4—1582no—
933C22×C4—1582no—
934C22×C4—1582no—
935C22×C4—1584no—
936C22×C4—1582no—
937C22×C4—1582no—
938C22×C4C2×C4×D7914yes—
939C22×C4C2×C4×D7914yes—
940C22×C4C23×D7912yes—
941C22×C4C23×D7912yes—
942C22×C4C23×D7912yes—
943C22×C4C23×D7911yescharacteristic
944C22×C4C23×D7911yescharacteristic
945C22×C4C23×D7911yescharacteristic
946C22×C4C23×D7911yescharacteristic
947C22×C4C23×D7912yes—
948C4⋊C4—24no—
949C4⋊C4—42no—
950C4⋊C4—3162no—
951C4⋊C4—794no—
952C4⋊C4—794no—
953C4⋊C4—794no—
954C4⋊C4—794no—
955C4⋊C4—798no—
956C4⋊C4—1584no—
957C4⋊C4—1584no—
958C4⋊C4—1584no—
959C4⋊C4—1584no—
960C4⋊C4—1584no—
961C4⋊C4—1584no—
962C4⋊C4—1584no—
963C4⋊C4—1584no—
964C22⋊C4—22no—
965C22⋊C4—24no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—24no—
969C22⋊C4—42no—
970C22⋊C4—3162no—
971C22⋊C4—3162no—
972C22⋊C4—3162no—
973C22⋊C4—794no—
974C22⋊C4—794no—
975C22⋊C4—794no—
976C22⋊C4—794no—
977C22⋊C4—794no—
978C22⋊C4—1584no—
979C22⋊C4—1584no—
980C22⋊C4—1584no—
981C22⋊C4—1584no—
982C22⋊C4—1582no—
983C22⋊C4—1584no—
984C22⋊C4—1582no—
985C22⋊C4—1582no—
986C22⋊C4—1584no—
987C22⋊C4C2×C4×D7914yes—
988C22⋊C4C2×C4×D7914yes—
989C22⋊C4C2×C4×D7914yes—
990C22⋊C4C2×C4×D7914yes—
991C22⋊C4D4×D7914yes—
992C42—24no—
993C42—42no—
994C42—3162no—
995C42—794no—
996C42—794no—
997C42—794no—
998C42—794no—
999C42—798no—
1000C42—1584no—
1001C42—1584no—
1002C42—1584no—
1003C42—1584no—
1004C42—1584no—
1005C42—1584no—
1006C42—1584no—
1007C42—1584no—
1008C23—22no—
1009C23—22no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—22no—
1014C23—28no—
1015C23—28no—
1016C23—21no—
1017C23—21no—
1018C23—22no—
1019C23—44no—
1020C23—48no—
1021C23—48no—
1022C23—3168no—
1023C23—3168no—
1024C23—3164no—
1025C23—792no—
1026C23—794no—
1027C23—792no—
1028C23—1588no—
1029C23—1582no—
1030C23—1588no—
1031C23—1581no—
1032C23—1581no—
1033C23—1582no—
1034C23—1582no—
1035C23—1581no—
1036C23—1581no—
1037C23C22×C4×D7912yes—
1038C23C22×C4×D7912yes—
1039C23C22×C4×D7912yes—
1040C23C2×D4×D7912yes—
1041C23#41×D7914yes—
1042C23#41×D7912yes—
1043C23C24×D7911yescharacteristic
1044D4—7916no—
1045D4—1588no—
1046D4—1588no—
1047D4—1588no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—28no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—44no—
1067C2×C4—48no—
1068C2×C4—3168no—
1069C2×C4—3168no—
1070C2×C4—3168no—
1071C2×C4—7916no—
1072C2×C4—792no—
1073C2×C4—792no—
1074C2×C4—792no—
1075C2×C4—792no—
1076C2×C4—792no—
1077C2×C4—794no—
1078C2×C4—792no—
1079C2×C4—792no—
1080C2×C4—792no—
1081C2×C4—792no—
1082C2×C4—792no—
1083C2×C4—794no—
1084C2×C4—1588no—
1085C2×C4—1588no—
1086C2×C4—1588no—
1087C2×C4—1588no—
1088C2×C4—1582no—
1089C2×C4—1582no—
1090C2×C4—1582no—
1091C2×C4—1582no—
1092C2×C4—1582no—
1093C2×C4—1582no—
1094C2×C4—1582no—
1095C2×C4—1582no—
1096C2×C4—1582no—
1097C2×C4—1588no—
1098C2×C4—1588no—
1099C2×C4—1588no—
1100C2×C4—1588no—
1101C2×C4—1588no—
1102C2×C4—1582no—
1103C2×C4—1588no—
1104C2×C4—1581no—
1105C2×C4—1581no—
1106C2×C4—1582no—
1107C2×C4—1581no—
1108C2×C4—1581no—
1109C2×C4—1582no—
1110C2×C4C22×C4×D7912yes—
1111C2×C4C22×C4×D7912yes—
1112C2×C4C22×C4×D7912yes—
1113C2×C4C22×C4×D7912yes—
1114C2×C4C2×D4×D7914yes—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—416no—
1127C22—42no—
1128C22—42no—
1129C22—31616no—
1130C22—3162no—
1131C22—3162no—
1132C22—794no—
1133C22—1582no—
1134C22—1582no—
1135C22—1582no—
1136C22—1582no—
1137C22—1582no—
1138C22—1584no—
1139C22—1584no—
1140C22#117×D7914yescomplemented
1141C22C4×D4×D7914yes—
1142C22C23×C4×D7911yescharacteristic
1143C22C22×D4×D7911yescharacteristic
1144C22C2×#41×D7912yes—
1145C22C2×#41×D7911yescharacteristic
1146C22#1909939812yes—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—24no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—3162no—
1156C4—3162no—
1157C4—3162no—
1158C4—794no—
1159C4—794no—
1160C4—794no—
1161C4—1582no—
1162C4—1582no—
1163C4—1582no—
1164C4—1584no—
1165C2—24no—
1166C2—24no—
1167C2—42no—
1168C2—3162no—
1169C2—1584no—
1170C2C2×#117×D7911yescharacteristic
1171C2C2×C4×D4×D7911yescharacteristic
1172C2#2377659811yescharacteristic
1173C2#2377688412yes—
1174C2#2377695512yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2342C2
socle, cosocleC23×C79C25
prime radicalC23×C22⋊D79C22
hypercenter#2342D79
hypocenterC79D4×#117
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. C22×#14579117C2semidirect
3. C2×#117×D79C2semidirect
4. #23766346C2semidirect
5. #23766328C2semidirect
6. #23766323C2semidirect
7. #23766298C2semidirect
8. #23766270C2semidirect
9. #23766264C2semidirect
10. #23766252C2semidirect
11. #23766249C2semidirect
12. #23766246C2semidirect
15. #23765860C2semidirect
16. #23765842C2semidirect
17. #23765836C2semidirect
18. #23765802C2semidirect
19. #23765780C2semidirect
20. #23765778C2semidirect
21. C4×(C22⋊D79)⋊C4C2semidirect
22. C4×#14579117C2semidirect
23. C79×#2342C2semidirect
28. C2×(C22⋊D79)⋊C4C4semidirect
39. C2×#14579119C22semidirect
40. C2×#14579118C22semidirect
48. C2×#14579117C22semidirect
49. C2×#14579117C22semidirect
52. C22×Dic79⋊C4C22semidirect
53. C2×C4⋊C4×D79C22semidirect
59. C22×C4×Dic79C22semidirect
60. C2×C42×D79C22semidirect
63. #19098460C22semidirect
64. #19098458C22semidirect
65. #19098456C22semidirect
66. #19098456C22semidirect
67. #19098455C22semidirect
68. #19098454C22semidirect
69. #19098453C22semidirect
70. #19098452C22semidirect
71. #19098450C22semidirect
72. #19098447C22semidirect
73. #19098445C22semidirect
74. #19098444C22semidirect
79. #19098438C22semidirect
80. #19098437C22semidirect
81. #19098434C22semidirect
82. #19098432C22semidirect
83. #19098427C22semidirect
88. #19098422C22semidirect
89. #19098422C22semidirect
92. #19098421C22semidirect
93. #19098421C22semidirect
97. C4⋊C4×Dic79C22semidirect
98. C4×Dic79⋊C4C22semidirect
99. C4×Dic79⋊C4C22semidirect
100. #19098414C22semidirect
101. #19098414C22semidirect
102. #19098414C22semidirect
105. C22⋊C4×Dic79C22semidirect
106. C22⋊C4×Dic79C22semidirect
107. C22⋊C4×Dic79C22semidirect
108. C4×(C2×D79)⋊C4C22semidirect
110. #19098410C22semidirect
111. #19098410C22semidirect
112. #19098410C22semidirect
113. #19098408C22semidirect
114. C42×Dic79C22semidirect
118. #388×C79C22semidirect
119. #388×C79C22semidirect
120. #385×C79C22semidirect
125. C4×C22⋊C4×C79C22semidirect
135. C23×Dic79C2×C4semidirect
146. C22×C4×D79C2×C4semidirect
157. (C22⋊D79)⋊C4C2×C4semidirect
158. (C22⋊D79)⋊C4C2×C4semidirect
159. (C22⋊D79)⋊C4C2×C4semidirect
160. (C22⋊D79)⋊C4C2×C4semidirect
161. (C22⋊D79)⋊C4C2×C4semidirect
162. (C22⋊D79)⋊C4C2×C4semidirect
173. #14579117D4semidirect
177. C2×Dic79⋊C4C2×C4semidirect
199. C2×(C2×D79)⋊C4C2×C4semidirect
213. C2×C4×Dic79C2×C4semidirect
249. C2×C22⋊C4×C79C2×C4semidirect
349. Dic79⋊C4C2×D4semidirect
380. C4×Dic79C2×D4semidirect
484. C22⋊D79#117semidirect
508. C2×Dic79C4×D4semidirect
541. C22×C79C2×#117semidirect
558. C2×D79C2×#117semidirect
574. Dic79C2×#117semidirect
600. #2342D79semidirect
611. C79D4×#117semidirect
662. #388C2×D79semidirect
663. #388C2×D79semidirect
675. #385C2×D79semidirect
711. C4×C22⋊C4C2×D79semidirect
808. C2×C22⋊C4C4×D79semidirect
1140. C22#117×D79semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D79)⋊C42
C22×#145791172
C2×#117×D792
#237663462
#237663282
#237663232
#237662982
#237662702
#237662642
#237662522
#237662492
#237662462
C22⋊C4×C22⋊D792
#237662162
#237658602
#237658422
#237658362
#237658022
#237657802
#237657782
C4×(C22⋊D79)⋊C42
C4×#145791172
C79×#23422
D4×#11779