Finite Group Databasebeta

← #33112229

Subgroups — #33112229

Order 18688.

796 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#22613175C211yesmaximal, characteristic
2#22610724C211yesmaximal, characteristic, complemented
3#22610723C211yesmaximal, characteristic, complemented
4#22610539C211yesmaximal, characteristic, complemented
5#22610536C211yesmaximal, characteristic, complemented
6#22610486C211yesmaximal, characteristic, complemented
7#22610485C211yesmaximal, characteristic, complemented
8#22610227C211yesmaximal, characteristic, complemented
9#22610225C211yesmaximal, characteristic, complemented
10#22610223C211yesmaximal, characteristic, complemented
11#22610223C211yesmaximal, characteristic, complemented
12#22610115C211yesmaximal, characteristic, complemented
13#22610001C211yesmaximal, characteristic, complemented
14#22609912C211yesmaximal, characteristic, complemented
15C73×#1850C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×#14556548C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34#17988521C411yescharacteristic
35#17988516C411yescharacteristic
36#17988511C411yescharacteristic
37#17988510C411yescharacteristic
38#17988505C411yescharacteristic
39#17988502C411yescharacteristic
40#17988502C411yescharacteristic
41#17988496C411yescharacteristic
42C4×#11924007C2211yescharacteristic
43C4×#11924005C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C23×C8×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C4×C22⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D292C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C22×C4×D73C2311yescharacteristic
64C2×#11924011—41no—
65C2×#11924011—41no—
66C2×#11924011—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C4×D292—41no—
72C4×D292—41no—
73C4×C22⋊D73—41no—
74C4×C22⋊D73—41no—
75C4×C22⋊D73—41no—
76C4×C22⋊D73—41no—
77#14556548—41no—
78#14556548—41no—
79C2×C4⋊Dic73C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×#11924005C2×C411yescharacteristic
95C2×#11924005C2×C411yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C4⋊#10596831—41no—
99#14556520—41no—
100C22⋊#10596831—41no—
101C22⋊#10596831—41no—
102#14556503—41no—
103#14556503—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556503—41no—
109C4×#10596831—41no—
110C8×Dic73—41no—
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C22×C8×C73—41no—
117C22×C8×C73—41no—
118C22×C8×C73—41no—
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C22⋊C4×C73C2×C411yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C4⋊C8×C73—41no—
128C4⋊C8×C73—41no—
129C22⋊C8×C73—41no—
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132C23×D73C22×C411yescharacteristic
133C23×D73C22×C411yescharacteristic
134C2×D292—22no—
135C2×D292—41no—
136C2×D292—41no—
137C2×C22⋊D73—22no—
138C2×C22⋊D73—22no—
139C2×C22⋊D73—22no—
140C2×C22⋊D73—41no—
141C2×C22⋊D73—41no—
142C2×C22⋊D73—41no—
143C22×Dic73C22×C411yescharacteristic
144C22×Dic73C22×C411yescharacteristic
145C22×Dic73C22×C411yescharacteristic
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161#11924011—44no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C4⋊Dic73—41no—
175#11924007—22no—
176#11924007—22no—
177#11924007—41no—
178#11924007—41no—
179#11924007—41no—
180#11924007—41no—
181C22⋊Dic73—41no—
182C22⋊Dic73—41no—
183#11924005—22no—
184#11924005—41no—
185#11924005—41no—
186#11924005—41no—
187#11924005—41no—
188#11924005—41no—
189#11924005—41no—
190#11924005—41no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C24×C73C22×C411yescharacteristic
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C2411yescharacteristic
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—44no—
221C22⋊C4×C73—22no—
222C22⋊C4×C73—22no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73#13112yes—
234C23×C73C23×C411yescharacteristic
235C22×D73—21no—
236C22×D73—21no—
237C22×D73—21no—
238C22×D73—21no—
239C22×D73—21no—
240C22×D73—21no—
241C22×D73—21no—
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73#13112yes—
268C2×C4×C73H(5,𝔽2)11yescharacteristic
269C2×C4×C73H(5,𝔽2)11yescharacteristic
270C2×C4×C73H(5,𝔽2)11yescharacteristic
271C2×C4×C73H(5,𝔽2)11yescharacteristic
272C2×C4×C73H(5,𝔽2)11yescharacteristic
273C2×C4×C732−1+411yescharacteristic
274C22⋊D73—44no—
275C22⋊D73—44no—
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73#13112yes—
294D292—44no—
295C4×D73—41no—
296C4×D73—41no—
297C4×D73—41no—
298C4×D73—41no—
299C4×D73—41no—
300C4×D73—41no—
301C4×D73—41no—
302C4×D73—41no—
303C8×C73—41no—
304C8×C73—41no—
305C8×C73—41no—
306C8×C73—41no—
307#10596831—41no—
308#10596831—41no—
309#10596831—41no—
310#10596831—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73#51811yescharacteristic
319C22×C73#51811yescharacteristic
320C22×C73#52011yescharacteristic
321C22×C73C2×#13111yescharacteristic
322C22×C73C2×#13111yescharacteristic
323C22×C73C2×#13111yescharacteristic
324C22×C73#56811yescharacteristic
325C2×D73—41no—
326C2×D73—41no—
327C2×D73—41no—
328C2×D73—41no—
329C2×D73—41no—
330C2×D73—41no—
331C2×D73—41no—
332C2×D73—41no—
333C2×D73—41no—
334C2×D73—41no—
335C2×D73—41no—
336C2×D73—41no—
337C2×D73—41no—
338C2×D73—41no—
339C4×C73—22no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—41no—
343C4×C73—41no—
344C4×C73#56011yescharacteristic
345C4×C73#56011yescharacteristic
346C4×C73#56211yescharacteristic
347C4×C73#56211yescharacteristic
348Dic73—22no—
349Dic73—41no—
350Dic73—41no—
351Dic73—41no—
352Dic73—41no—
353Dic73—41no—
354#23328—731nomaximal, Sylow
355C2×C73—42no—
356C2×C73#237711yescharacteristic
357C2×C73#297611yescharacteristic
358C2×C73#297611yescharacteristic
359C2×C73#297711yescharacteristic
360C2×C73#297911yescharacteristic
361C2×C73#299311yescharacteristic
362C2×C73#299411yescharacteristic
363D73—81no—
364D73—81no—
365#2392—731no—
366#1954—731no—
367#1954—731no—
368#1923—731no—
369#1923—731no—
370#1916—731no—
371#1916—731no—
372#1870—731no—
373#1870—731no—
374#1869—731no—
375#1869—731no—
376#1851—731no—
377#1850D7311yescharacteristic, complemented
378#1818—731no—
379#1798—731no—
380C73#2332811yescharacteristic, complemented, Sylow
381C22×M16—731no—
382C23×C8C2×D7311yescharacteristic
383C2×C4×D4—731no—
384C2×C4×D4—731no—
385C2×C4×D4—731no—
386C2×#117—731no—
387C2×C4⋊C8—731no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8C2×D7311yescharacteristic
390C2×C4⋊C8C2×D7311yescharacteristic
391C2×C22⋊C8—731no—
392C2×C22⋊C8—731no—
393C2×C22⋊C8—731no—
394C2×C22⋊C8—731no—
395C2×C22⋊C8—731no—
396C2×C22⋊C8—731no—
397C2×C22⋊C8—731no—
398C2×C22⋊C8—731no—
399C2×C22⋊C8—731no—
400C2×C22⋊C8C2×D7311yescharacteristic
401C2×C4×C8—731no—
402C2×C4×C8—731no—
403#398—731no—
404#397—731no—
405#396—731no—
406#396—731no—
407#394—731no—
408#394—731no—
409#394—731no—
410#392—731no—
411C4×C4⋊C4—731no—
412C4×C22⋊C4—731no—
413C4×C22⋊C4C2×D7311yescharacteristic
414#336—731no—
415#336—731no—
416#336—731no—
417#336—731no—
418#336—731no—
419#336—731no—
420#336—731no—
421#336—731no—
422#336C2×D7311yescharacteristic
423#336C2×D7311yescharacteristic
424C22×D4—731no—
425C22×D4—731no—
426C22×D4—731no—
427C23×C4—731no—
428C23×C4—731no—
429C23×C4C22×D7311yescharacteristic
430C2×M16—2921no—
431C2×M16—2921no—
432C2×M16—2921no—
433C22×C8—41no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8—731no—
437C22×C8—731no—
438C22×C8—731no—
439C22×C8—731no—
440C22×C8C22×D7311yescharacteristic
441C22×C8C22×D7311yescharacteristic
442C22×C8C22×D7311yescharacteristic
443C22×C8C22×D7311yescharacteristic
444C4×D4—2921no—
445C4×D4—2921no—
446C4×D4—2921no—
447C4×D4—2921no—
448C4×D4—2921no—
449C4×D4—2921no—
450#117—2921no—
451#117—2921no—
452C2×C4⋊C4—731no—
453C2×C4⋊C4—731no—
454C2×C4⋊C4—731no—
455C2×C4⋊C4—731no—
456C2×C4⋊C4—731no—
457C2×C4⋊C4—731no—
458C2×C4⋊C4—731no—
459C2×C22⋊C4—731no—
460C2×C22⋊C4—731no—
461C2×C22⋊C4—731no—
462C2×C22⋊C4—731no—
463C2×C22⋊C4—731no—
464C2×C22⋊C4—731no—
465C2×C22⋊C4—731no—
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4C4×D7311yescharacteristic
470C2×C22⋊C4C4×D7311yescharacteristic
471C2×C42—731no—
472C2×C42—731no—
473C2×C42C22×D7311yescharacteristic
474C2×C42C22×D7311yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C4⋊C8—2921no—
478C4⋊C8—2921no—
479C22⋊C8—41no—
480C22⋊C8—2921no—
481C22⋊C8—2921no—
482C22⋊C8—2921no—
483C22⋊C8—2921no—
484C22⋊C8—2921no—
485C22⋊C8—2921no—
486C22⋊C8—2921no—
487C22⋊C8—2921no—
488C22⋊C8—2921no—
489C4×C8—2921no—
490C4×C8—2921no—
491#95—731no—
492#95—731no—
493#95—731no—
494#95—731no—
495#95C4×D7311yescharacteristic
496#95C4×D7311yescharacteristic
497C24—731no—
498C24—731no—
499C24C2×C4×D7311yescharacteristic
500C2×D4—2921no—
501C2×D4—2921no—
502C2×D4—2921no—
503C2×D4—2921no—
504C2×D4—2921no—
505C2×D4—1462no—
506C2×D4—1462no—
507C2×D4—1462no—
508C2×D4—1462no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—731no—
516C22×C4—731no—
517C22×C4—731no—
518C22×C4—731no—
519C22×C4—731no—
520C22×C4—731no—
521C22×C4—1461no—
522C22×C4—1461no—
523C22×C4—1461no—
524C22×C4—1461no—
525C22×C4—1461no—
526C22×C4—1461no—
527C22×C4—1461no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4C2×C4×D7311yescharacteristic
534C22×C4C2×C4×D7311yescharacteristic
535C22×C4C2×C4×D7311yescharacteristic
536C22×C4C2×C4×D7311yescharacteristic
537C22×C4C2×C4×D7311yescharacteristic
538C22×C4C23×D7311yescharacteristic
539M16—2924no—
540C2×C8—21no—
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—44no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8—1461no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C2×C8—1461no—
564C2×C8—1461no—
565C4⋊C4—2921no—
566C4⋊C4—2921no—
567C4⋊C4—2921no—
568C4⋊C4—2921no—
569C4⋊C4—2921no—
570C4⋊C4—1462no—
571C4⋊C4—1462no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—2921no—
575C22⋊C4—2921no—
576C22⋊C4—2921no—
577C22⋊C4—2921no—
578C22⋊C4—2921no—
579C22⋊C4—2921no—
580C22⋊C4—2921no—
581C22⋊C4—2921no—
582C22⋊C4—2921no—
583C22⋊C4—1462no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—1461no—
589C42—1461no—
590C42—1461no—
591C42—1461no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—1461no—
599C23—1461no—
600C23—1461no—
601C23—1461no—
602C23—1461no—
603C23—1461no—
604C23—1461no—
605C23—1461no—
606C23—1461no—
607C23—1461no—
608C23—1461no—
609C23—1461no—
610C23—1461no—
611C23—1461no—
612C23#1455659912yes—
613C23C22×C4×D7311yescharacteristic
614D4—2924no—
615D4—2924no—
616D4—2924no—
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—2921no—
636C2×C4—2921no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—732no—
644C2×C4—1461no—
645C2×C4—1461no—
646C2×C4—1461no—
647C2×C4—1461no—
648C2×C4—1461no—
649C2×C4—1461no—
650C2×C4—1461no—
651C2×C4—1461no—
652C2×C4—1461no—
653C2×C4—1461no—
654C2×C4—1461no—
655C2×C4—1461no—
656C2×C4—1461no—
657C2×C4—1461no—
658C2×C4—1461no—
659C2×C4—1461no—
660C2×C4—1461no—
661C2×C4#1455659712yes—
662C2×C4#1455663611yescharacteristic
663C2×C4#1455663611yescharacteristic
664C2×C4#1455663611yescharacteristic
665C2×C4#1455663711yescharacteristic
666C2×C4#1455663711yescharacteristic
667C2×C4#1455663911yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—2921no—
673C8—2921no—
674C8—2921no—
675C8—2921no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—2921no—
684C22—2921no—
685C22—2921no—
686C22—2921no—
687C22—2921no—
688C22—2921no—
689C22—2921no—
690C22—2921no—
691C22—2921no—
692C22—2921no—
693C22—2921no—
694C22—2921no—
695C22—2921no—
696C22—2921no—
697C22#1798905911yescharacteristic
698C22#1798905911yescharacteristic
699C22#1798906811yescharacteristic
700C22#131×D7311yescharacteristic
701C22C2×#1455659711yescharacteristic
702C22C2×#1455659911yescharacteristic
703C22#1798935211yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—2921no—
710C4—2921no—
711C4—2921no—
712C4—2921no—
713C4—2921no—
714C4—1462no—
715C4#1798932611yescharacteristic
716C4#1798932711yescharacteristic
717C4#1798933311yescharacteristic
718C4#1798933311yescharacteristic
719C2—42no—
720C2—5841no—
721C2—5841no—
722C2#2261308711yescharacteristic
723C2#2261897311yescharacteristic
724C2#2261898011yescharacteristic
725C2#2261898211yescharacteristic
726C2#2261899411yescharacteristic
727C2#2261907811yescharacteristic
728C2#2261908711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1850C2
prime radical#17988496C4
cosocleC22×C4×C73C24
hypercenter#1850D73
hypocenterC73#23328
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #22610724C2semidirect
3. #22610723C2semidirect
4. #22610539C2semidirect
5. #22610536C2semidirect
6. #22610486C2semidirect
7. #22610485C2semidirect
8. #22610227C2semidirect
9. #22610225C2semidirect
10. #22610223C2semidirect
11. #22610223C2semidirect
12. #22610115C2semidirect
13. #22610001C2semidirect
14. #22609912C2semidirect
15. C73×#1850C2semidirect
377. #1850D73semidirect
380. C73#23328semidirect

Maximal subgroups

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

subgroupindex
#226131752
#226107242
#226107232
#226105392
#226105362
#226104862
#226104852
#226102272
#226102252
#226102232
#226101152
#226100012
#226099122
C73×#18502
#2332873