Finite Group Databasebeta

← #34314574

Subgroups — #34314574

Order 20224.

770 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23766644C211yesmaximal, characteristic
2#23764196C211yesmaximal, characteristic, complemented
3#23764193C211yesmaximal, characteristic, complemented
4#23764012C211yesmaximal, characteristic, complemented
5#23764008C211yesmaximal, characteristic, complemented
6#23763961C211yesmaximal, characteristic, complemented
7#23763955C211yesmaximal, characteristic, complemented
8#23763697C211yesmaximal, characteristic, complemented
9#23763697C211yesmaximal, characteristic, complemented
10#23763696C211yesmaximal, characteristic, complemented
11#23763694C211yesmaximal, characteristic, complemented
12#23763584C211yesmaximal, characteristic, complemented
13#23763470C211yesmaximal, characteristic, complemented
14#23763381C211yesmaximal, characteristic, complemented
15C79×#1851C211yesmaximal, characteristic, complemented
16C22×#11929607C2211yescharacteristic
17C2×C4×D316C2211yescharacteristic
18C2×C4×C22⋊D79C2211yescharacteristic
19C2×C4×C22⋊D79C2211yescharacteristic
20C2×#14579118C2211yescharacteristic
21C2×C4⋊(C79⋊C8)C2211yescharacteristic
22C2×Dic79⋊C8C2211yescharacteristic
23C2×C22⋊(C79⋊C8)C2211yescharacteristic
24C2×C22⋊(C79⋊C8)C2211yescharacteristic
25C2×(C2×D79)⋊C8C2211yescharacteristic
26C2×(C2×D79)⋊C8C2211yescharacteristic
27C2×(C2×D79)⋊C8C2211yescharacteristic
28C2×(C2×D79)⋊C8C2211yescharacteristic
29C2×(C2×D79)⋊C8C2211yescharacteristic
30C2×(C2×D79)⋊C8C2211yescharacteristic
31C2×(C2×D79)⋊C8C2211yescharacteristic
32C2×#14579071C2211yescharacteristic
33C2×C4×C79⋊C8C2211yescharacteristic
34#19098497C411yescharacteristic
35#19098492C411yescharacteristic
36#19098487C411yescharacteristic
37#19098486C411yescharacteristic
38#19098481C411yescharacteristic
39#19098478C411yescharacteristic
40#19098478C411yescharacteristic
41#19098472C411yescharacteristic
42C4×Dic79⋊C4C2211yescharacteristic
43C4×(C2×D79)⋊C4C2211yescharacteristic
44#19098318C2211yescharacteristic
45#19098318C2211yescharacteristic
46#19098317C2211yescharacteristic
47#19098317C2211yescharacteristic
48#19098317C2211yescharacteristic
49#19098317C2211yescharacteristic
50#19098317C2211yescharacteristic
51#19098317C2211yescharacteristic
52C22×M16×C79C2211yescharacteristic
53C2×C4⋊C8×C79C2211yescharacteristic
54C2×C4⋊C8×C79C2211yescharacteristic
55C2×C22⋊C8×C79C2211yescharacteristic
56C4×C22⋊C4×C79C2211yescharacteristic
57#336×C79C2211yescharacteristic
58#336×C79C2211yescharacteristic
59C22×D316C2×C411yescharacteristic
60C22×C22⋊D79C2×C411yescharacteristic
61C22×C22⋊D79C2×C411yescharacteristic
62C22×C4×D79C2311yescharacteristic
63C22×C4×D79C2311yescharacteristic
64C2×#11929607—41no—
65C2×#11929607—41no—
66C2×#11929607—41no—
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71C4×D316—41no—
72C4×D316—41no—
73C4×C22⋊D79—41no—
74C4×C22⋊D79—41no—
75C4×C22⋊D79—41no—
76C4×C22⋊D79—41no—
77#14579118—41no—
78#14579118—41no—
79C2×C4⋊Dic79C2×C411yescharacteristic
80C2×Dic79⋊C4C2×C411yescharacteristic
81C2×Dic79⋊C4C2×C411yescharacteristic
82C2×Dic79⋊C4C2×C411yescharacteristic
83C2×Dic79⋊C4C2×C411yescharacteristic
84C2×Dic79⋊C4C2×C411yescharacteristic
85C2×Dic79⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic79C2×C411yescharacteristic
87C2×C22⋊Dic79C2×C411yescharacteristic
88C2×(C2×D79)⋊C4C2×C411yescharacteristic
89C2×(C2×D79)⋊C4C2×C411yescharacteristic
90C2×(C2×D79)⋊C4C2×C411yescharacteristic
91C2×(C2×D79)⋊C4C2×C411yescharacteristic
92C2×(C2×D79)⋊C4C2×C411yescharacteristic
93C2×(C2×D79)⋊C4C2×C411yescharacteristic
94C2×(C2×D79)⋊C4C2×C411yescharacteristic
95C2×(C2×D79)⋊C4C2×C411yescharacteristic
96C2×C4×Dic79C2311yescharacteristic
97C2×C4×Dic79C2311yescharacteristic
98C4⋊(C79⋊C8)—41no—
99Dic79⋊C8—41no—
100C22⋊(C79⋊C8)—41no—
101C22⋊(C79⋊C8)—41no—
102(C2×D79)⋊C8—41no—
103(C2×D79)⋊C8—41no—
104(C2×D79)⋊C8—41no—
105(C2×D79)⋊C8—41no—
106(C2×D79)⋊C8—41no—
107(C2×D79)⋊C8—41no—
108(C2×D79)⋊C8—41no—
109#14579071—41no—
110C4×C79⋊C8—41no—
111C79⋊#95C2×C411yescharacteristic
112C79⋊#95C2×C411yescharacteristic
113C79⋊#95C2×C411yescharacteristic
114C79⋊#95C2×C411yescharacteristic
115C23×C4×C79C2311yescharacteristic
116C2×M16×C79—41no—
117C2×M16×C79—41no—
118C2×M16×C79—41no—
119C22×C8×C79C2311yescharacteristic
120C22×C8×C79C2311yescharacteristic
121C22×C8×C79C2311yescharacteristic
122C22×C8×C79C2311yescharacteristic
123C2×C22⋊C4×C79C2×C411yescharacteristic
124C2×C22⋊C4×C79C2×C411yescharacteristic
125C2×C42×C79C2311yescharacteristic
126C2×C42×C79C2311yescharacteristic
127C4⋊C8×C79—41no—
128C4⋊C8×C79—41no—
129C22⋊C8×C79—41no—
130#95×C79C2×C411yescharacteristic
131#95×C79C2×C411yescharacteristic
132C23×D79C22×C411yescharacteristic
133C23×D79C22×C411yescharacteristic
134C2×D316—22no—
135C2×D316—41no—
136C2×D316—41no—
137C2×C22⋊D79—41no—
138C2×C22⋊D79—41no—
139C2×C22⋊D79—41no—
140C2×C22⋊D79—41no—
141C2×C22⋊D79—41no—
142C2×C22⋊D79—41no—
143C22×Dic79C22×C411yescharacteristic
144C22×Dic79C22×C411yescharacteristic
145C22×Dic79C22×C411yescharacteristic
146C22×Dic79C22×C411yescharacteristic
147C22×Dic79C22×C411yescharacteristic
148C22×Dic79C22×C411yescharacteristic
149C2×C4×D79—21no—
150C2×C4×D79—21no—
151C2×C4×D79—21no—
152C2×C4×D79—21no—
153C2×C4×D79—21no—
154C2×C4×D79—21no—
155C2×C4×D79—21no—
156C2×C4×D79—21no—
157C2×C4×D79—21no—
158C2×C4×D79—21no—
159C2×C4×D79—21no—
160C2×C4×D79—21no—
161#11929607—44no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8—21no—
168C2×C79⋊C8—21no—
169C2×C79⋊C8—21no—
170C2×C79⋊C8—21no—
171C2×C79⋊C8—21no—
172C2×C79⋊C8—21no—
173C2×C79⋊C8—21no—
174C4⋊Dic79—41no—
175Dic79⋊C4—22no—
176Dic79⋊C4—41no—
177Dic79⋊C4—41no—
178Dic79⋊C4—41no—
179Dic79⋊C4—41no—
180Dic79⋊C4—41no—
181C22⋊Dic79—41no—
182C22⋊Dic79—41no—
183(C2×D79)⋊C4—41no—
184(C2×D79)⋊C4—41no—
185(C2×D79)⋊C4—41no—
186(C2×D79)⋊C4—41no—
187(C2×D79)⋊C4—41no—
188(C2×D79)⋊C4—41no—
189(C2×D79)⋊C4—41no—
190(C2×D79)⋊C4—41no—
191C4×Dic79—21no—
192C4×Dic79—21no—
193C4×Dic79—21no—
194C4×Dic79—21no—
195C24×C79C22×C411yescharacteristic
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79C22×C411yescharacteristic
203C22×C4×C79C22×C411yescharacteristic
204C22×C4×C79C22×C411yescharacteristic
205C22×C4×C79C22×C411yescharacteristic
206C22×C4×C79C22×C411yescharacteristic
207C22×C4×C79C2411yescharacteristic
208M16×C79—44no—
209C2×C8×C79—21no—
210C2×C8×C79—21no—
211C2×C8×C79—21no—
212C2×C8×C79—21no—
213C2×C8×C79—21no—
214C2×C8×C79—21no—
215C2×C8×C79—21no—
216C2×C8×C79—21no—
217C2×C8×C79—21no—
218C2×C8×C79—21no—
219C2×C8×C79—21no—
220C2×C8×C79—21no—
221C22⋊C4×C79—22no—
222C22⋊C4×C79—41no—
223C42×C79—21no—
224C42×C79—21no—
225C42×C79—21no—
226C42×C79—21no—
227C23×C79—21no—
228C23×C79—21no—
229C23×C79—21no—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79—21no—
234C23×C79C23×C411yescharacteristic
235C22×D79—21no—
236C22×D79—21no—
237C22×D79—21no—
238C22×D79—21no—
239C22×D79—21no—
240C22×D79—21no—
241C22×D79—21no—
242C22×D79—21no—
243C22×D79—21no—
244C22×D79—21no—
245C22×D79—21no—
246C22×D79—21no—
247C22×D79—21no—
248C22×D79—21no—
249C2×C4×C79—21no—
250C2×C4×C79—21no—
251C2×C4×C79—21no—
252C2×C4×C79—21no—
253C2×C4×C79—21no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—21no—
263C2×C4×C79—41no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79—41no—
267C2×C4×C79#13112yes—
268C2×C4×C79H(5,𝔽2)11yescharacteristic
269C2×C4×C79H(5,𝔽2)11yescharacteristic
270C2×C4×C79H(5,𝔽2)11yescharacteristic
271C2×C4×C79H(5,𝔽2)11yescharacteristic
272C2×C4×C79H(5,𝔽2)11yescharacteristic
273C2×C4×C792−1+411yescharacteristic
274C22⋊D79—44no—
275C22⋊D79—44no—
276C2×Dic79—21no—
277C2×Dic79—21no—
278C2×Dic79—21no—
279C2×Dic79—21no—
280C2×Dic79—21no—
281C2×Dic79—21no—
282C2×Dic79—21no—
283C2×Dic79—21no—
284C2×Dic79—21no—
285C2×Dic79—21no—
286C2×Dic79—21no—
287C2×Dic79—21no—
288C2×Dic79—21no—
289C2×Dic79—21no—
290C2×Dic79—21no—
291C2×Dic79—21no—
292C2×Dic79—21no—
293C2×Dic79—21no—
294D316—44no—
295C4×D79—41no—
296C4×D79—41no—
297C4×D79—41no—
298C4×D79—41no—
299C4×D79—41no—
300C4×D79—41no—
301C4×D79—41no—
302C4×D79—41no—
303C8×C79—41no—
304C8×C79—41no—
305C8×C79—41no—
306C8×C79—41no—
307C79⋊C8—41no—
308C79⋊C8—41no—
309C79⋊C8—41no—
310C79⋊C8—41no—
311C22×C79—41no—
312C22×C79—41no—
313C22×C79—41no—
314C22×C79—41no—
315C22×C79—41no—
316C22×C79—41no—
317C22×C79—41no—
318C22×C79#51811yescharacteristic
319C22×C79#51811yescharacteristic
320C22×C79#52011yescharacteristic
321C22×C79C2×#13111yescharacteristic
322C22×C79#56811yescharacteristic
323C22×C79#56811yescharacteristic
324C22×C79#56811yescharacteristic
325C2×D79—41no—
326C2×D79—41no—
327C2×D79—41no—
328C2×D79—41no—
329C2×D79—41no—
330C2×D79—41no—
331C2×D79—41no—
332C2×D79—41no—
333C2×D79—41no—
334C2×D79—41no—
335C2×D79—41no—
336C2×D79—41no—
337C2×D79—41no—
338C2×D79—41no—
339C4×C79—22no—
340C4×C79—41no—
341C4×C79—41no—
342C4×C79—41no—
343C4×C79—41no—
344C4×C79#56011yescharacteristic
345C4×C79#56011yescharacteristic
346C4×C79#56211yescharacteristic
347C4×C79#56211yescharacteristic
348Dic79—41no—
349Dic79—41no—
350Dic79—41no—
351Dic79—41no—
352Dic79—41no—
353Dic79—41no—
354#23332—791nomaximal, Sylow
355C2×C79—81no—
356C2×C79#237711yescharacteristic
357C2×C79#297611yescharacteristic
358C2×C79#297811yescharacteristic
359C2×C79#297811yescharacteristic
360C2×C79#298111yescharacteristic
361C2×C79#299311yescharacteristic
362C2×C79#299511yescharacteristic
363D79—81no—
364D79—81no—
365#2392—791no—
366#1955—791no—
367#1954—791no—
368#1924—791no—
369#1923—791no—
370#1917—791no—
371#1916—791no—
372#1870—791no—
373#1870—791no—
374#1870—791no—
375#1870—791no—
376#1851—791no—
377#1851D7911yescharacteristic, complemented
378#1818—791no—
379#1798—791no—
380C79#2333211yescharacteristic, complemented, Sylow
381C22×M16—791no—
382C22×M16C2×D7911yescharacteristic
383C2×C4×D4—791no—
384C2×C4×D4—791no—
385C2×C4×D4—791no—
386C2×#117—791no—
387C2×C4⋊C8—791no—
388C2×C4⋊C8—791no—
389C2×C4⋊C8C2×D7911yescharacteristic
390C2×C4⋊C8C2×D7911yescharacteristic
391C2×C22⋊C8—791no—
392C2×C22⋊C8—791no—
393C2×C22⋊C8—791no—
394C2×C22⋊C8—791no—
395C2×C22⋊C8—791no—
396C2×C22⋊C8—791no—
397C2×C22⋊C8—791no—
398C2×C22⋊C8—791no—
399C2×C22⋊C8—791no—
400C2×C22⋊C8C2×D7911yescharacteristic
401C2×#97—791no—
402C2×C4×C8—791no—
403#398—791no—
404#397—791no—
405#396—791no—
406#396—791no—
407#394—791no—
408#394—791no—
409#394—791no—
410#392—791no—
411C4×C4⋊C4—791no—
412C4×C22⋊C4—791no—
413C4×C22⋊C4C2×D7911yescharacteristic
414#336—791no—
415#336—791no—
416#336—791no—
417#336—791no—
418#336—791no—
419#336—791no—
420#336—791no—
421#336—791no—
422#336C2×D7911yescharacteristic
423#336C2×D7911yescharacteristic
424C22×D4—791no—
425C22×D4—791no—
426C22×D4—791no—
427C23×C4—791no—
428C23×C4—791no—
429C23×C4C22×D7911yescharacteristic
430C2×M16—41no—
431C2×M16—41no—
432C2×M16—41no—
433C2×M16—3161no—
434C2×M16—3161no—
435C2×M16—3161no—
436C22×C8—791no—
437C22×C8—791no—
438C22×C8—791no—
439C22×C8—791no—
440C22×C8C22×D7911yescharacteristic
441C22×C8C22×D7911yescharacteristic
442C22×C8C22×D7911yescharacteristic
443C22×C8C22×D7911yescharacteristic
444C4×D4—3161no—
445C4×D4—3161no—
446C4×D4—3161no—
447C4×D4—3161no—
448C4×D4—3161no—
449C4×D4—3161no—
450#117—3161no—
451#117—3161no—
452C2×C4⋊C4—791no—
453C2×C4⋊C4—791no—
454C2×C4⋊C4—791no—
455C2×C4⋊C4—791no—
456C2×C4⋊C4—791no—
457C2×C4⋊C4—791no—
458C2×C4⋊C4—791no—
459C2×C22⋊C4—791no—
460C2×C22⋊C4—791no—
461C2×C22⋊C4—791no—
462C2×C22⋊C4—791no—
463C2×C22⋊C4—791no—
464C2×C22⋊C4—791no—
465C2×C22⋊C4—791no—
466C2×C22⋊C4—791no—
467C2×C22⋊C4—791no—
468C2×C22⋊C4—791no—
469C2×C22⋊C4C4×D7911yescharacteristic
470C2×C22⋊C4C4×D7911yescharacteristic
471C2×C42—791no—
472C2×C42—791no—
473C2×C42C22×D7911yescharacteristic
474C2×C42C22×D7911yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C4⋊C8—3161no—
478C4⋊C8—3161no—
479C22⋊C8—41no—
480C22⋊C8—3161no—
481C22⋊C8—3161no—
482C22⋊C8—3161no—
483C22⋊C8—3161no—
484C22⋊C8—3161no—
485C22⋊C8—3161no—
486C22⋊C8—3161no—
487C22⋊C8—3161no—
488C22⋊C8—3161no—
489#97—3161no—
490C4×C8—3161no—
491#95—791no—
492#95—791no—
493#95—791no—
494#95—791no—
495#95C4×D7911yescharacteristic
496#95C4×D7911yescharacteristic
497C24—791no—
498C24—791no—
499C24C2×C4×D7911yescharacteristic
500C2×D4—3161no—
501C2×D4—3161no—
502C2×D4—3161no—
503C2×D4—3161no—
504C2×D4—3161no—
505C2×D4—3161no—
506C2×D4—3161no—
507C2×D4—3161no—
508C2×D4—1582no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—791no—
516C22×C4—791no—
517C22×C4—791no—
518C22×C4—791no—
519C22×C4—791no—
520C22×C4—791no—
521C22×C4—1581no—
522C22×C4—1581no—
523C22×C4—1581no—
524C22×C4—1581no—
525C22×C4—1581no—
526C22×C4—1581no—
527C22×C4—1581no—
528C22×C4—1581no—
529C22×C4—1581no—
530C22×C4—1581no—
531C22×C4—1581no—
532C22×C4—1581no—
533C22×C4C2×C4×D7911yescharacteristic
534C22×C4C2×C4×D7911yescharacteristic
535C22×C4C2×C4×D7911yescharacteristic
536C22×C4C2×C4×D7911yescharacteristic
537C22×C4C2×C4×D7911yescharacteristic
538C22×C4C23×D7911yescharacteristic
539M16—44no—
540M16—3164no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—1581no—
554C2×C8—1581no—
555C2×C8—1581no—
556C2×C8—1581no—
557C2×C8—1581no—
558C2×C8—1581no—
559C2×C8—1581no—
560C2×C8—1581no—
561C2×C8—1581no—
562C2×C8—1581no—
563C2×C8—1581no—
564C2×C8—1581no—
565C4⋊C4—3161no—
566C4⋊C4—3161no—
567C4⋊C4—3161no—
568C4⋊C4—3161no—
569C4⋊C4—3161no—
570C4⋊C4—3161no—
571C4⋊C4—1582no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—3161no—
575C22⋊C4—3161no—
576C22⋊C4—3161no—
577C22⋊C4—3161no—
578C22⋊C4—3161no—
579C22⋊C4—3161no—
580C22⋊C4—3161no—
581C22⋊C4—3161no—
582C22⋊C4—3161no—
583C22⋊C4—3161no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—1581no—
589C42—1581no—
590C42—1581no—
591C42—1581no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—1581no—
600C23—1581no—
601C23—1581no—
602C23—1581no—
603C23—1581no—
604C23—1581no—
605C23—1581no—
606C23—1581no—
607C23—1581no—
608C23—1581no—
609C23—1581no—
610C23—1581no—
611C23—1581no—
612C23—1581no—
613C23C22×C4×D7911yescharacteristic
614D4—3164no—
615D4—3164no—
616D4—3164no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—3161no—
636C2×C4—3161no—
637C2×C4—3161no—
638C2×C4—3161no—
639C2×C4—3161no—
640C2×C4—3161no—
641C2×C4—3161no—
642C2×C4—3161no—
643C2×C4—1581no—
644C2×C4—1581no—
645C2×C4—1581no—
646C2×C4—1581no—
647C2×C4—1581no—
648C2×C4—1581no—
649C2×C4—1581no—
650C2×C4—1581no—
651C2×C4—1581no—
652C2×C4—1581no—
653C2×C4—1581no—
654C2×C4—1581no—
655C2×C4—1581no—
656C2×C4—1581no—
657C2×C4—1581no—
658C2×C4—1581no—
659C2×C4—1581no—
660C2×C4—1581no—
661C2×C4#1457916912yes—
662C2×C4#1457920611yescharacteristic
663C2×C4#1457920611yescharacteristic
664C2×C4#1457920611yescharacteristic
665C2×C4#1457920711yescharacteristic
666C2×C4#1457920711yescharacteristic
667C2×C4#1457920911yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—3161no—
673C8—3161no—
674C8—3161no—
675C8—3161no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—3161no—
684C22—3161no—
685C22—3161no—
686C22—3161no—
687C22—3161no—
688C22—3161no—
689C22—3161no—
690C22—3161no—
691C22—3161no—
692C22—3161no—
693C22—3161no—
694C22—3161no—
695C22—3161no—
696C22—3161no—
697C22#1909903511yescharacteristic
698C22#1909903511yescharacteristic
699C22#1909904411yescharacteristic
700C22C2×#1457916911yescharacteristic
701C22#1909932811yescharacteristic
702C22#1909932811yescharacteristic
703C22#1909932911yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—3161no—
710C4—3161no—
711C4—3161no—
712C4—3161no—
713C4—3161no—
714C4—3161no—
715C4#1909930211yescharacteristic
716C4#1909930311yescharacteristic
717C4#1909930911yescharacteristic
718C4#1909930911yescharacteristic
719C2—81no—
720C2—6321no—
721C2—6321no—
722C2#2376655611yescharacteristic
723C2#2377244911yescharacteristic
724C2#2377245711yescharacteristic
725C2#2377245911yescharacteristic
726C2#2377247711yescharacteristic
727C2#2377254511yescharacteristic
728C2#2377256811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D79
commutator, socleC23×C79C23×C4
FittingC79×#1851C2
prime radical#19098472C4
cosocleC22×C4×C79C24
hypercenter#1851D79
hypocenterC79#23332
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
2. #23764196C2semidirect
3. #23764193C2semidirect
4. #23764012C2semidirect
5. #23764008C2semidirect
6. #23763961C2semidirect
7. #23763955C2semidirect
8. #23763697C2semidirect
9. #23763697C2semidirect
10. #23763696C2semidirect
11. #23763694C2semidirect
12. #23763584C2semidirect
13. #23763470C2semidirect
14. #23763381C2semidirect
15. C79×#1851C2semidirect
377. #1851D79semidirect
380. C79#23332semidirect

Maximal subgroups

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

subgroupindex
#237666442
#237641962
#237641932
#237640122
#237640082
#237639612
#237639552
#237636972
#237636962
#237636942
#237635842
#237634702
#237633812
C79×#18512
#2333279