Finite Group Databasebeta

← #34314412

Subgroups — #34314412

Order 20224.

706 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23764195C211yesmaximal, characteristic
2#23764124C211yesmaximal, characteristic, complemented
3#23764119C211yesmaximal, characteristic, complemented
4#23764015C211yesmaximal, characteristic, complemented
5#23764015C211yesmaximal, characteristic, complemented
6#23764008C211yesmaximal, characteristic, complemented
7#23764008C211yesmaximal, characteristic, complemented
8#23763959C211yesmaximal, characteristic, complemented
9#23763959C211yesmaximal, characteristic, complemented
10#23763693C211yesmaximal, characteristic
11#23763580C211yesmaximal, characteristic, complemented
12#23763580C211yesmaximal, characteristic, complemented
13#23763384C211yesmaximal, characteristic, complemented
14#23763384C211yesmaximal, characteristic, complemented
15C79×#2395C211yesmaximal, characteristic
16C23×C79⋊C8C2211yescharacteristic
17C2×C4⋊(C79⋊C8)C2211yescharacteristic
18C2×C4⋊(C79⋊C8)C2211yescharacteristic
19C2×C4⋊(C79⋊C8)C2211yescharacteristic
20C2×C4⋊(C79⋊C8)C2211yescharacteristic
21C2×C4⋊(C79⋊C8)C2211yescharacteristic
22C2×C4⋊(C79⋊C8)C2211yescharacteristic
23C2×C4⋊(C79⋊C8)C2211yescharacteristic
24C2×C22⋊(C79⋊C8)C2211yescharacteristic
25C2×C22⋊(C79⋊C8)C2211yescharacteristic
26C2×C22⋊(C79⋊C8)C2211yescharacteristic
27C2×C22⋊(C79⋊C8)C2211yescharacteristic
28C2×C22⋊(C79⋊C8)C2211yescharacteristic
29C2×C22⋊(C79⋊C8)C2211yescharacteristic
30C2×C22⋊(C79⋊C8)C2211yescharacteristic
31C2×#14579072C2211yescharacteristic
32C2×C4×C79⋊C8C2211yescharacteristic
33C2×C4×C79⋊C8C2211yescharacteristic
34#19098318C2211yescharacteristic
35#19098318C2211yescharacteristic
36#19098318C2211yescharacteristic
37#19098318C2211yescharacteristic
38#19098318C2211yescharacteristic
39#19098318C2211yescharacteristic
40#19098318C2211yescharacteristic
41#19098318C2211yescharacteristic
42#19098318C2211yescharacteristic
43#19098318C2211yescharacteristic
44C2×C4×D4×C79C2211yescharacteristic
45C2×#117×C79C2211yescharacteristic
46#400×C79C411yescharacteristic
47#399×C79C411yescharacteristic
48#398×C79C411yescharacteristic
49#397×C79C411yescharacteristic
50#397×C79C411yescharacteristic
51#397×C79C411yescharacteristic
52#394×C79C411yescharacteristic
53#394×C79C411yescharacteristic
54C4×C4⋊C4×C79C2211yescharacteristic
55C4×C4⋊C4×C79C2211yescharacteristic
56C4×C22⋊C4×C79C2211yescharacteristic
57C4×C22⋊C4×C79C2211yescharacteristic
58C4×C22⋊C4×C79C2211yescharacteristic
59C22×C79⋊C8—41no—
60C22×C79⋊C8—41no—
61C22×C79⋊C8—41no—
62C22×C79⋊C8C2311yescharacteristic
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65C22×C79⋊C8C2311yescharacteristic
66C22×C79⋊C8C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C4⋊(C79⋊C8)—41no—
71C4⋊(C79⋊C8)—41no—
72C4⋊(C79⋊C8)—41no—
73C4⋊(C79⋊C8)—41no—
74C4⋊(C79⋊C8)—41no—
75C4⋊(C79⋊C8)—41no—
76C4⋊(C79⋊C8)—41no—
77C22⋊(C79⋊C8)—41no—
78C22⋊(C79⋊C8)—41no—
79C22⋊(C79⋊C8)—41no—
80C22⋊(C79⋊C8)—41no—
81C22⋊(C79⋊C8)—41no—
82C22⋊(C79⋊C8)—41no—
83C22⋊(C79⋊C8)—41no—
84#14579072—41no—
85C4×C79⋊C8—41no—
86C4×C79⋊C8—41no—
87C22×D4×C79C2×C411yescharacteristic
88C23×C4×C79C2311yescharacteristic
89C23×C4×C79C2311yescharacteristic
90C4×D4×C79—41no—
91C4×D4×C79—41no—
92#117×C79—41no—
93#117×C79—41no—
94C2×C4⋊C4×C79C2×C411yescharacteristic
95C2×C4⋊C4×C79C2×C411yescharacteristic
96C2×C4⋊C4×C79C2×C411yescharacteristic
97C2×C4⋊C4×C79C2×C411yescharacteristic
98C2×C4⋊C4×C79C2×C411yescharacteristic
99C2×C4⋊C4×C79C2×C411yescharacteristic
100C2×C4⋊C4×C79C2×C411yescharacteristic
101C2×C22⋊C4×C79C2×C411yescharacteristic
102C2×C22⋊C4×C79C2×C411yescharacteristic
103C2×C22⋊C4×C79C2×C411yescharacteristic
104C2×C22⋊C4×C79C2×C411yescharacteristic
105C2×C22⋊C4×C79C2×C411yescharacteristic
106C2×C22⋊C4×C79C2×C411yescharacteristic
107C2×C22⋊C4×C79C2×C411yescharacteristic
108C2×C22⋊C4×C79C2×C411yescharacteristic
109C2×C22⋊C4×C79C2×C411yescharacteristic
110C2×C22⋊C4×C79C2×C411yescharacteristic
111C2×C42×C79C2311yescharacteristic
112C2×C42×C79C2311yescharacteristic
113C2×C42×C79C2311yescharacteristic
114C2×C42×C79C2311yescharacteristic
115C2×C42×C79C2311yescharacteristic
116#95×C79C2×C411yescharacteristic
117#95×C79C2×C411yescharacteristic
118#95×C79C2×C411yescharacteristic
119#95×C79C2×C411yescharacteristic
120#95×C79C2×C411yescharacteristic
121#95×C79C2×C411yescharacteristic
122#95×C79C2×C411yescharacteristic
123#95×C79C2×C411yescharacteristic
124#95×C79C2×C411yescharacteristic
125#95×C79C2×C411yescharacteristic
126C2×C79⋊C8—21no—
127C2×C79⋊C8—21no—
128C2×C79⋊C8—21no—
129C2×C79⋊C8—21no—
130C2×C79⋊C8—21no—
131C2×C79⋊C8—21no—
132C2×C79⋊C8—21no—
133C2×C79⋊C8—21no—
134C2×C79⋊C8—21no—
135C2×C79⋊C8—21no—
136C2×C79⋊C8—21no—
137C2×C79⋊C8—21no—
138C2×C79⋊C8—21no—
139C2×C79⋊C8—21no—
140C2×C79⋊C8—21no—
141C2×C79⋊C8—21no—
142C2×C79⋊C8—21no—
143C2×C79⋊C8—21no—
144C2×C79⋊C8—21no—
145C2×C79⋊C8—21no—
146C2×C79⋊C8—21no—
147C2×C79⋊C8—21no—
148C2×C79⋊C8—21no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—44no—
151C24×C79C22×C411yescharacteristic
152C24×C79C22×C411yescharacteristic
153C2×D4×C79—22no—
154C2×D4×C79—22no—
155C2×D4×C79—41no—
156C22×C4×C79—21no—
157C22×C4×C79—21no—
158C22×C4×C79—21no—
159C22×C4×C79—21no—
160C22×C4×C79—21no—
161C22×C4×C79—21no—
162C22×C4×C79—21no—
163C22×C4×C79—21no—
164C22×C4×C79—21no—
165C22×C4×C79—21no—
166C22×C4×C79—21no—
167C22×C4×C79—21no—
168C22×C4×C79C22×C411yescharacteristic
169C22×C4×C79C22×C411yescharacteristic
170C22×C4×C79C22×C411yescharacteristic
171C22×C4×C79C22×C411yescharacteristic
172C22×C4×C79C22×C411yescharacteristic
173C22×C4×C79C22×C411yescharacteristic
174C22×C4×C79C22×C411yescharacteristic
175C22×C4×C79C22×C411yescharacteristic
176C22×C4×C79C22×C411yescharacteristic
177C22×C4×C79C22×C411yescharacteristic
178C22×C4×C79C22×C411yescharacteristic
179C22×C4×C79C22×C411yescharacteristic
180C22×C4×C79C2411yescharacteristic
181C4⋊C4×C79—22no—
182C4⋊C4×C79—22no—
183C4⋊C4×C79—22no—
184C4⋊C4×C79—41no—
185C4⋊C4×C79—41no—
186C4⋊C4×C79—41no—
187C4⋊C4×C79—41no—
188C22⋊C4×C79—22no—
189C22⋊C4×C79—22no—
190C22⋊C4×C79—22no—
191C22⋊C4×C79—22no—
192C22⋊C4×C79—41no—
193C22⋊C4×C79—41no—
194C22⋊C4×C79—41no—
195C22⋊C4×C79—41no—
196C22⋊C4×C79—41no—
197C22⋊C4×C79—41no—
198C42×C79—21no—
199C42×C79—21no—
200C42×C79—21no—
201C42×C79—21no—
202C42×C79—21no—
203C42×C79—21no—
204C42×C79—21no—
205C42×C79—21no—
206C42×C79—21no—
207C42×C79—21no—
208C23×C79—21no—
209C23×C79—21no—
210C23×C79—21no—
211C23×C79—21no—
212C23×C79—21no—
213C23×C79—21no—
214C23×C79—21no—
215C23×C79—21no—
216C23×C79—21no—
217C23×C79—21no—
218C23×C79—21no—
219C23×C79—21no—
220C23×C79—21no—
221C23×C79#13112yes—
222C23×C79C23×C411yescharacteristic
223D4×C79—44no—
224C2×C4×C79—21no—
225C2×C4×C79—21no—
226C2×C4×C79—21no—
227C2×C4×C79—21no—
228C2×C4×C79—21no—
229C2×C4×C79—21no—
230C2×C4×C79—21no—
231C2×C4×C79—21no—
232C2×C4×C79—21no—
233C2×C4×C79—21no—
234C2×C4×C79—21no—
235C2×C4×C79—21no—
236C2×C4×C79—21no—
237C2×C4×C79—21no—
238C2×C4×C79—21no—
239C2×C4×C79—21no—
240C2×C4×C79—21no—
241C2×C4×C79—21no—
242C2×C4×C79—21no—
243C2×C4×C79—21no—
244C2×C4×C79—21no—
245C2×C4×C79—21no—
246C2×C4×C79—21no—
247C2×C4×C79—21no—
248C2×C4×C79—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—41no—
259C2×C4×C79—41no—
260C2×C4×C79—41no—
261C2×C4×C79—41no—
262C2×C4×C79—41no—
263C2×C4×C79—41no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79#13112yes—
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×C792−1+411yescharacteristic
273C2×C4×C792−1+411yescharacteristic
274C79⋊C8—41no—
275C79⋊C8—41no—
276C79⋊C8—41no—
277C79⋊C8—41no—
278C79⋊C8—41no—
279C79⋊C8—41no—
280C79⋊C8—41no—
281C79⋊C8—41no—
282C22×C79—22no—
283C22×C79—22no—
284C22×C79—22no—
285C22×C79—41no—
286C22×C79—41no—
287C22×C79—41no—
288C22×C79—41no—
289C22×C79—41no—
290C22×C79—41no—
291C22×C79—41no—
292C22×C79—41no—
293C22×C79—41no—
294C22×C79—41no—
295C22×C79—41no—
296C22×C79#51811yescharacteristic
297C22×C79#52011yescharacteristic
298C22×C79#52011yescharacteristic
299C22×C79C2×#13111yescharacteristic
300C22×C79C2×#13111yescharacteristic
301C22×C79C2×#13111yescharacteristic
302C22×C79#56811yescharacteristic
303C4×C79—22no—
304C4×C79—22no—
305C4×C79—41no—
306C4×C79—41no—
307C4×C79—41no—
308C4×C79—41no—
309C4×C79—41no—
310C4×C79—41no—
311C4×C79—41no—
312C4×C79—41no—
313C4×C79—41no—
314C4×C79—41no—
315C4×C79#56011yescharacteristic
316C4×C79#56211yescharacteristic
317C4×C79#56211yescharacteristic
318C4×C79#56311yescharacteristic
319#23319—791nomaximal, Sylow
320C2×C79—42no—
321C2×C79—81no—
322C2×C79#237611yescharacteristic
323C2×C79#297711yescharacteristic
324C2×C79#298111yescharacteristic
325C2×C79#299211yescharacteristic
326C2×C79#299311yescharacteristic
327C2×C79#299411yescharacteristic
328C2×C79#299411yescharacteristic
329#2395D7911yescharacteristic
330#1954—791no—
331#1940—791no—
332#1939—791no—
333#1924—791no—
334#1924—791no—
335#1923—791no—
336#1923—791no—
337#1916—791no—
338#1916—791no—
339#1869—791no—
340#1850—791no—
341#1850—791no—
342#1798—791no—
343#1798—791no—
344C79#2331911yescharacteristic, complemented, Sylow
345C23×C8—791no—
346C2×C4×D4C2×D7911yescharacteristic
347C2×#117C2×D7911yescharacteristic
348C2×C4⋊C8—791no—
349C2×C4⋊C8—791no—
350C2×C4⋊C8—791no—
351C2×C4⋊C8—791no—
352C2×C4⋊C8—791no—
353C2×C4⋊C8—791no—
354C2×C4⋊C8—791no—
355C2×C22⋊C8—791no—
356C2×C22⋊C8—791no—
357C2×C22⋊C8—791no—
358C2×C22⋊C8—791no—
359C2×C22⋊C8—791no—
360C2×C22⋊C8—791no—
361C2×C22⋊C8—791no—
362C2×#97—791no—
363C2×C4×C8—791no—
364C2×C4×C8—791no—
365#400Dic7911yescharacteristic
366#399Dic7911yescharacteristic
367#398Dic7911yescharacteristic
368#397Dic7911yescharacteristic
369#397Dic7911yescharacteristic
370#397Dic7911yescharacteristic
371#394Dic7911yescharacteristic
372#394Dic7911yescharacteristic
373C4×C4⋊C4C2×D7911yescharacteristic
374C4×C4⋊C4C2×D7911yescharacteristic
375C4×C22⋊C4C2×D7911yescharacteristic
376C4×C22⋊C4C2×D7911yescharacteristic
377C4×C22⋊C4C2×D7911yescharacteristic
378#336—791no—
379#336—791no—
380#336—791no—
381#336—791no—
382#336—791no—
383#336—791no—
384#336—791no—
385#336—791no—
386#336—791no—
387#336—791no—
388C22×D4C2×Dic7911yescharacteristic
389C23×C4C22×D7911yescharacteristic
390C23×C4C22×D7911yescharacteristic
391C22×C8—3161no—
392C22×C8—3161no—
393C22×C8—3161no—
394C22×C8—791no—
395C22×C8—791no—
396C22×C8—791no—
397C22×C8—791no—
398C22×C8—791no—
399C22×C8—791no—
400C22×C8—791no—
401C22×C8—791no—
402C4×D4—41no—
403C4×D4—41no—
404#117—41no—
405#117—41no—
406C2×C4⋊C4C2×Dic7911yescharacteristic
407C2×C4⋊C4C2×Dic7911yescharacteristic
408C2×C4⋊C4C2×Dic7911yescharacteristic
409C2×C4⋊C4C2×Dic7911yescharacteristic
410C2×C4⋊C4C2×Dic7911yescharacteristic
411C2×C4⋊C4C2×Dic7911yescharacteristic
412C2×C4⋊C4C2×Dic7911yescharacteristic
413C2×C22⋊C4C2×Dic7911yescharacteristic
414C2×C22⋊C4C2×Dic7911yescharacteristic
415C2×C22⋊C4C2×Dic7911yescharacteristic
416C2×C22⋊C4C2×Dic7911yescharacteristic
417C2×C22⋊C4C2×Dic7911yescharacteristic
418C2×C22⋊C4C2×Dic7911yescharacteristic
419C2×C22⋊C4C2×Dic7911yescharacteristic
420C2×C22⋊C4C2×Dic7911yescharacteristic
421C2×C22⋊C4C2×Dic7911yescharacteristic
422C2×C22⋊C4C2×Dic7911yescharacteristic
423C2×C42C22×D7911yescharacteristic
424C2×C42C22×D7911yescharacteristic
425C2×C42C22×D7911yescharacteristic
426C2×C42C22×D7911yescharacteristic
427C2×C42C22×D7911yescharacteristic
428C4⋊C8—3161no—
429C4⋊C8—3161no—
430C4⋊C8—3161no—
431C4⋊C8—3161no—
432C4⋊C8—3161no—
433C4⋊C8—3161no—
434C4⋊C8—3161no—
435C22⋊C8—3161no—
436C22⋊C8—3161no—
437C22⋊C8—3161no—
438C22⋊C8—3161no—
439C22⋊C8—3161no—
440C22⋊C8—3161no—
441C22⋊C8—3161no—
442#97—3161no—
443C4×C8—3161no—
444C4×C8—3161no—
445#95C2×Dic7911yescharacteristic
446#95C2×Dic7911yescharacteristic
447#95C2×Dic7911yescharacteristic
448#95C2×Dic7911yescharacteristic
449#95C2×Dic7911yescharacteristic
450#95C2×Dic7911yescharacteristic
451#95C2×Dic7911yescharacteristic
452#95C2×Dic7911yescharacteristic
453#95C2×Dic7911yescharacteristic
454#95C2×Dic7911yescharacteristic
455C24C22×Dic7911yescharacteristic
456C24C22×Dic7911yescharacteristic
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—41no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4C22×Dic7911yescharacteristic
473C22×C4C22×Dic7911yescharacteristic
474C22×C4C22×Dic7911yescharacteristic
475C22×C4C22×Dic7911yescharacteristic
476C22×C4C22×Dic7911yescharacteristic
477C22×C4C22×Dic7911yescharacteristic
478C22×C4C22×Dic7911yescharacteristic
479C22×C4C22×Dic7911yescharacteristic
480C22×C4C22×Dic7911yescharacteristic
481C22×C4C22×Dic7911yescharacteristic
482C22×C4C22×Dic7911yescharacteristic
483C22×C4C22×Dic7911yescharacteristic
484C22×C4C23×D7911yescharacteristic
485C2×C8—3164no—
486C2×C8—1581no—
487C2×C8—1581no—
488C2×C8—1581no—
489C2×C8—1581no—
490C2×C8—1581no—
491C2×C8—1581no—
492C2×C8—1581no—
493C2×C8—1581no—
494C2×C8—1581no—
495C2×C8—1581no—
496C2×C8—1581no—
497C2×C8—1581no—
498C2×C8—1581no—
499C2×C8—1581no—
500C2×C8—1581no—
501C2×C8—1581no—
502C2×C8—1581no—
503C2×C8—1581no—
504C2×C8—1581no—
505C2×C8—1581no—
506C2×C8—1581no—
507C2×C8—1581no—
508C2×C8—1581no—
509C2×C8—1581no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23#1457916812yes—
551C23C23×Dic7911yescharacteristic
552D4—44no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4#1457916812yes—
596C2×C4#1457916812yes—
597C2×C4#1457920611yescharacteristic
598C2×C4#1457920611yescharacteristic
599C2×C4#1457920711yescharacteristic
600C2×C4#1457920711yescharacteristic
601C2×C4#1457920811yescharacteristic
602C2×C4#1457920811yescharacteristic
603C8—3161no—
604C8—3161no—
605C8—3161no—
606C8—3161no—
607C8—3161no—
608C8—3161no—
609C8—3161no—
610C8—3161no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22#1909903811yescharacteristic
626C22#1909904611yescharacteristic
627C22#1909904611yescharacteristic
628C22C2×#1457916811yescharacteristic
629C22C2×#1457916811yescharacteristic
630C22C2×#1457916811yescharacteristic
631C22#1909933011yescharacteristic
632C4—22no—
633C4—22no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4#1909930311yescharacteristic
645C4#1909931011yescharacteristic
646C4#1909931011yescharacteristic
647C4#1909931611yescharacteristic
648C2—42no—
649C2—81no—
650C2#2376654811yescharacteristic
651C2#2377245611yescharacteristic
652C2#2377247611yescharacteristic
653C2#2377253911yescharacteristic
654C2#2377254911yescharacteristic
655C2#2377256011yescharacteristic
656C2#2377256011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D79
commutator, socleC23×C79C23×C4
FittingC79×#2395C2
prime radicalC22×D4×C79C2×C4
cosocleC22×C4×C79C24
hypercenter#2395D79
hypocenterC79#23319
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. #23764124C2semidirect
3. #23764119C2semidirect
4. #23764015C2semidirect
5. #23764015C2semidirect
6. #23764008C2semidirect
7. #23764008C2semidirect
8. #23763959C2semidirect
9. #23763959C2semidirect
11. #23763580C2semidirect
12. #23763580C2semidirect
13. #23763384C2semidirect
14. #23763384C2semidirect
344. C79#23319semidirect

Maximal subgroups

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

subgroupindex
#237641952
#237641242
#237641192
#237640152
#237640082
#237639592
#237636932
#237635802
#237633842
C79×#23952
#2331979