Finite Group Databasebeta

← #33112245

Subgroups — #33112245

Order 18688.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556565C211yesmaximal, characteristic
2#22610727C211yesmaximal, characteristic, complemented
3#22610723C211yesmaximal, characteristic, complemented
4#22610545C211yesmaximal, characteristic, complemented
5#22610538C211yesmaximal, characteristic, complemented
6#22610494C211yesmaximal, characteristic, complemented
7#22610487C211yesmaximal, characteristic, complemented
8#22610227C211yesmaximal, characteristic, complemented
9#22610225C211yesmaximal, characteristic, complemented
10#22610222C211yesmaximal, characteristic, complemented
11#22610220C211yesmaximal, characteristic, complemented
12#22610115C211yesmaximal, characteristic, complemented
13#22610110C211yesmaximal, characteristic, complemented
14#22609911C211yesmaximal, characteristic, complemented
15C73×#1817C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556565C411yescharacteristic
19C2×C4×D292C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556501C2211yescharacteristic
35C2×C8×Dic73C2211yescharacteristic
36#17988489C411yescharacteristic
37#17988485C411yescharacteristic
38#17988478C411yescharacteristic
39#17988478C411yescharacteristic
40#17988466C411yescharacteristic
41#17988466C411yescharacteristic
42#17988447C411yescharacteristic
43C4×C4⋊Dic73C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×#11924005C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C22×C42×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×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
71C2×C8×D73—41no—
72C2×C8×D73—41no—
73C2×C8×D73—41no—
74#14556565—24no—
75C4×D292—41no—
76C4×D292—41no—
77C4×C22⋊D73—41no—
78C4×C22⋊D73—41no—
79C4×C22⋊D73—41no—
80C4×C22⋊D73—41no—
81C2×C4⋊Dic73C2×C411yescharacteristic
82C2×C4⋊Dic73C2×C411yescharacteristic
83C2×C4⋊Dic73C2×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—
99C4⋊#10596831—41no—
100#14556520—41no—
101#14556520—41no—
102C22⋊#10596831—41no—
103C22⋊#10596831—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556503—41no—
109#14556503—41no—
110#14556501—41no—
111C8×Dic73—41no—
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118C23×C4×C73C2×C411yescharacteristic
119C23×C4×C73C2×C411yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C2×C42×C73—41no—
126C2×C42×C73—41no—
127C2×C42×C73C2×C411yescharacteristic
128C2×C42×C73C2×C411yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C2×C42×C73C2311yescharacteristic
131C22⋊C8×C73—41no—
132C22⋊C8×C73—41no—
133C23×D73C22×C411yescharacteristic
134C23×D73C22×C411yescharacteristic
135C2×D292—22no—
136C2×D292—22no—
137C2×D292—41no—
138C2×C22⋊D73—22no—
139C2×C22⋊D73—22no—
140C2×C22⋊D73—22no—
141C2×C22⋊D73—22no—
142C2×C22⋊D73—41no—
143C2×C22⋊D73—41no—
144C22×Dic73C22×C411yescharacteristic
145C22×Dic73C22×C411yescharacteristic
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
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—
161C2×C4×D73—21no—
162#11924011—44no—
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—
174C2×#10596831—21no—
175C8×D73—44no—
176C4⋊Dic73—22no—
177C4⋊Dic73—22no—
178C4⋊Dic73—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#11924005M1614yescomplemented
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C24×C73C22×C411yescharacteristic
196C22×C4×C73—22no—
197C22×C4×C73—22no—
198C22×C4×C73—22no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—41no—
206C22×C4×C73—41no—
207C22×C4×C73—41no—
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C22×C411yescharacteristic
213C22×C4×C73C2411yescharacteristic
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—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—41no—
231C42×C73—41no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73#13112yes—
239C23×C73C23×C411yescharacteristic
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—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73C2×M1612yes—
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—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—44no—
268C2×C4×C73—44no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73C2×M1612yes—
274C2×C4×C73#13112yes—
275C2×C4×C73H(5,𝔽2)11yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C2×C4×C73H(5,𝔽2)11yescharacteristic
278C2×C4×C73H(5,𝔽2)11yescharacteristic
279C2×C4×C73H(5,𝔽2)11yescharacteristic
280C2×C4×C732−1+411yescharacteristic
281C22⋊D73—44no—
282C22⋊D73—44no—
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—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73C2×M1612yes—
301D292—44no—
302C4×D73—41no—
303C4×D73—41no—
304C4×D73—41no—
305C4×D73—41no—
306C4×D73—41no—
307C4×D73—41no—
308C4×D73—41no—
309C4×D73—41no—
310C8×C73—41no—
311C8×C73—41no—
312C8×C73—41no—
313C8×C73—41no—
314#10596831—41no—
315#10596831—41no—
316#10596831—41no—
317#10596831—41no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73#51811yescharacteristic
326C22×C73#51811yescharacteristic
327C22×C73#52011yescharacteristic
328C22×C73C22×M1611yescharacteristic
329C22×C73C2×#13111yescharacteristic
330C22×C73C2×#13111yescharacteristic
331C22×C73#56811yescharacteristic
332C2×D73—22no—
333C2×D73—22no—
334C2×D73—22no—
335C2×D73—41no—
336C2×D73—41no—
337C2×D73—41no—
338C2×D73—41no—
339C2×D73—41no—
340C2×D73—41no—
341C2×D73—41no—
342C2×D73—41no—
343C2×D73—41no—
344C2×D73—41no—
345C2×D73—41no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73#56011yescharacteristic
352C4×C73#56011yescharacteristic
353C4×C73#56211yescharacteristic
354C4×C73#56211yescharacteristic
355Dic73—22no—
356Dic73—41no—
357Dic73—41no—
358Dic73—41no—
359Dic73—41no—
360Dic73—41no—
361#23329—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73#237711yescharacteristic
364C2×C73#297411yescharacteristic
365C2×C73#297411yescharacteristic
366C2×C73#297611yescharacteristic
367C2×C73#298111yescharacteristic
368C2×C73#298911yescharacteristic
369C2×C73#299411yescharacteristic
370D73—42no—
371D73—81no—
372C4×#121—731no—
373#1955—731no—
374#1954—731no—
375#1924—731no—
376#1923—731no—
377#1917—731no—
378#1916—731no—
379#1870—731no—
380#1870—731no—
381#1869—731no—
382#1869—731no—
383#1851—731no—
384#1850—731no—
385#1817D7311yescharacteristic, complemented
386#1797—731no—
387C73#2332911yescharacteristic, complemented, Sylow
388C22×M16—731no—
389C23×C8—731no—
390C2×#121—731no—
391C2×C4×D4—731no—
392C2×C4×D4—731no—
393C2×C4×D4—731no—
394C22×C42C2×D7311yescharacteristic
395C2×C4⋊C8—731no—
396C2×C4⋊C8—731no—
397C2×C4⋊C8—731no—
398C2×C4⋊C8—731no—
399C2×C22⋊C8—731no—
400C2×C22⋊C8—731no—
401C2×C22⋊C8—731no—
402C2×C22⋊C8—731no—
403C2×C22⋊C8—731no—
404C2×C22⋊C8—731no—
405C2×C22⋊C8—731no—
406C2×C22⋊C8—731no—
407C2×C22⋊C8C2×D7311yescharacteristic
408C2×C22⋊C8C2×D7311yescharacteristic
409C2×#97—731no—
410C2×C4×C8—731no—
411#390—731no—
412#389—731no—
413#388—731no—
414#388—731no—
415#386—731no—
416#386—731no—
417#380—731no—
418C4×C4⋊C4—731no—
419C4×C22⋊C4—731no—
420C4×C22⋊C4—731no—
421#336—731no—
422#336—731no—
423#336—731no—
424#336—731no—
425#336—731no—
426#336—731no—
427#336C2×D7311yescharacteristic
428#336C2×D7311yescharacteristic
429#336C2×D7311yescharacteristic
430#336C2×D7311yescharacteristic
431C22×D4—731no—
432C22×D4—731no—
433C22×D4—731no—
434C23×C4—731no—
435C23×C4—731no—
436C23×C4C4×D7311yescharacteristic
437C23×C4C4×D7311yescharacteristic
438C23×C4C22×D7311yescharacteristic
439C2×M16—2921no—
440C2×M16—2921no—
441C2×M16—2921no—
442C22×C8—2921no—
443C22×C8—2921no—
444C22×C8—2921no—
445C22×C8—731no—
446C22×C8—731no—
447C22×C8—731no—
448C22×C8—731no—
449C22×C8C22×D7311yescharacteristic
450C22×C8C22×D7311yescharacteristic
451C22×C8C22×D7311yescharacteristic
452C22×C8C22×D7311yescharacteristic
453#121—1464no—
454C4×D4—2921no—
455C4×D4—2921no—
456C4×D4—2921no—
457C4×D4—2921no—
458C4×D4—2921no—
459C4×D4—2921no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4—731no—
465C2×C22⋊C4—731no—
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4—731no—
470C2×C22⋊C4—731no—
471C2×C22⋊C4—731no—
472C2×C22⋊C4—731no—
473C2×C22⋊C4—731no—
474C2×C22⋊C4—731no—
475C2×C42—41no—
476C2×C42—41no—
477C2×C42—731no—
478C2×C42—731no—
479C2×C42C4×D7311yescharacteristic
480C2×C42C4×D7311yescharacteristic
481C2×C42C22×D7311yescharacteristic
482C2×C42C22×D7311yescharacteristic
483C4⋊C8—2921no—
484C4⋊C8—2921no—
485C4⋊C8—2921no—
486C4⋊C8—2921no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—2921no—
490C22⋊C8—2921no—
491C22⋊C8—2921no—
492C22⋊C8—2921no—
493C22⋊C8—2921no—
494C22⋊C8—2921no—
495C22⋊C8—2921no—
496C22⋊C8—2921no—
497#97—2921no—
498C4×C8—2921no—
499#95—731no—
500#95—731no—
501#95—731no—
502#95—731no—
503#95—731no—
504#95—731no—
505C24—731no—
506C24—731no—
507C24C2×C4×D7311yescharacteristic
508C2×D4—2921no—
509C2×D4—2921no—
510C2×D4—2921no—
511C2×D4—1462no—
512C2×D4—1462no—
513C2×D4—1462no—
514C2×D4—1462no—
515C2×D4—1462no—
516C2×D4—1462no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—731no—
530C22×C4—731no—
531C22×C4—731no—
532C22×C4—731no—
533C22×C4—731no—
534C22×C4—731no—
535C22×C4—1461no—
536C22×C4—1461no—
537C22×C4—1461no—
538C22×C4—1461no—
539C22×C4—1461no—
540C22×C4—1461no—
541C22×C4—1461no—
542C22×C4—1461no—
543C22×C4—1461no—
544C22×C4—1461no—
545C22×C4—1461no—
546C22×C4—1461no—
547C22×C4C2×C4×D7311yescharacteristic
548C22×C4C2×C4×D7311yescharacteristic
549C22×C4C2×C4×D7311yescharacteristic
550C22×C4C2×C4×D7311yescharacteristic
551C22×C4C2×C4×D7311yescharacteristic
552C22×C4C23×D7311yescharacteristic
553M16—2924no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—2924no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C4⋊C4—2921no—
580C4⋊C4—2921no—
581C4⋊C4—2921no—
582C4⋊C4—1462no—
583C4⋊C4—1462no—
584C22⋊C4—2921no—
585C22⋊C4—2921no—
586C22⋊C4—2921no—
587C22⋊C4—2921no—
588C22⋊C4—2921no—
589C22⋊C4—2921no—
590C22⋊C4—2921no—
591C22⋊C4—2921no—
592C22⋊C4—734no—
593C22⋊C4—1462no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—41no—
599C42—41no—
600C42—1461no—
601C42—1461no—
602C42—1461no—
603C42—1461no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—732no—
611C23—1461no—
612C23—1461no—
613C23—1461no—
614C23—1461no—
615C23—1461no—
616C23—1461no—
617C23—1461no—
618C23—1461no—
619C23—1461no—
620C23—1461no—
621C23—1461no—
622C23—1461no—
623C23—1461no—
624C23#1455659712yes—
625C23C22×C4×D7311yescharacteristic
626D4—2924no—
627D4—2924no—
628D4—2924no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—2921no—
649C2×C4—2921no—
650C2×C4—2921no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—732no—
657C2×C4—1461no—
658C2×C4—1461no—
659C2×C4—1461no—
660C2×C4—1461no—
661C2×C4—1461no—
662C2×C4—1461no—
663C2×C4—1461no—
664C2×C4—1461no—
665C2×C4—1461no—
666C2×C4—1461no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4M16×D7312yes—
675C2×C4#1455659912yes—
676C2×C4#1455663611yescharacteristic
677C2×C4#1455663611yescharacteristic
678C2×C4#1455663711yescharacteristic
679C2×C4#1455663711yescharacteristic
680C2×C4#1455663711yescharacteristic
681C2×C4#1455663811yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—2921no—
687C8—2921no—
688C8—2921no—
689C8—2921no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—2921no—
698C22—2921no—
699C22—2921no—
700C22—2921no—
701C22—2921no—
702C22—2921no—
703C22—2921no—
704C22—2921no—
705C22—2921no—
706C22—2921no—
707C22—2921no—
708C22—1462no—
709C22—1462no—
710C22—1462no—
711C22#1798906011yescharacteristic
712C22#1798906111yescharacteristic
713C22#1798906711yescharacteristic
714C22C2×M16×D7311yescharacteristic
715C22C2×#1455659711yescharacteristic
716C22C2×#1455659911yescharacteristic
717C22#1798935311yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—2921no—
724C4—2921no—
725C4—2921no—
726C4—2921no—
727C4—2921no—
728C4—1462no—
729C4#1798932711yescharacteristic
730C4#1798932711yescharacteristic
731C4#1798933411yescharacteristic
732C4#1798933411yescharacteristic
733C2—42no—
734C2—2922no—
735C2—5841no—
736C2#2261309011yescharacteristic
737C2#2261896511yescharacteristic
738C2#2261896711yescharacteristic
739C2#2261897611yescharacteristic
740C2#2261900911yescharacteristic
741C2#2261905011yescharacteristic
742C2#2261909311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1817C2
prime radicalC2×#14556565C4
cosocleC22×C4×C73C24
hypercenter#1817D73
hypocenterC73#23329
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #22610727C2semidirect
3. #22610723C2semidirect
4. #22610545C2semidirect
5. #22610538C2semidirect
6. #22610494C2semidirect
7. #22610487C2semidirect
8. #22610227C2semidirect
9. #22610225C2semidirect
10. #22610222C2semidirect
11. #22610220C2semidirect
12. #22610115C2semidirect
13. #22610110C2semidirect
14. #22609911C2semidirect
15. C73×#1817C2semidirect
190. #11924005M16semidirect
385. #1817D73semidirect
387. C73#23329semidirect

Maximal subgroups

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

subgroupindex
C4×#145565652
#226107272
#226107232
#226105452
#226105382
#226104942
#226104872
#226102272
#226102252
#226102222
#226102202
#226101152
#226101102
#226099112
C73×#18172
#2332973