Finite Group Databasebeta

← #33112240

Subgroups — #33112240

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×#14556564C211yesmaximal, characteristic
2#22610728C211yesmaximal, characteristic, complemented
3#22610723C211yesmaximal, characteristic, complemented
4#22610546C211yesmaximal, characteristic, complemented
5#22610536C211yesmaximal, characteristic, complemented
6#22610493C211yesmaximal, characteristic, complemented
7#22610485C211yesmaximal, characteristic, complemented
8#22610228C211yesmaximal, characteristic, complemented
9#22610228C211yesmaximal, characteristic, complemented
10#22610222C211yesmaximal, characteristic, complemented
11#22610220C211yesmaximal, characteristic, complemented
12#22610110C211yesmaximal, characteristic, complemented
13#22609998C211yesmaximal, characteristic, complemented
14#22609908C211yesmaximal, characteristic, complemented
15C73×#1851C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C2×#14556564C411yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C42×D73C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556502C2211yescharacteristic
34C2×C8×Dic73C2211yescharacteristic
35#17988487C411yescharacteristic
36#17988484C411yescharacteristic
37#17988480C411yescharacteristic
38#17988476C411yescharacteristic
39#17988465C411yescharacteristic
40#17988463C411yescharacteristic
41#17988446C411yescharacteristic
42C4×#11924007C2211yescharacteristic
43C4×#11924005C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C22×M16×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×D73C2×C411yescharacteristic
63C22×C4×D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C8×D73—41no—
71C2×C8×D73—41no—
72C2×C8×D73—41no—
73#14556564—24no—
74C4×D292—41no—
75C4×D292—41no—
76C4×C22⋊D73—41no—
77C4×C22⋊D73—41no—
78C4×C22⋊D73—41no—
79C4×C22⋊D73—41no—
80C2×C4⋊Dic73C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×#11924007C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C42×D73—41no—
98C42×D73—41no—
99C4⋊#10596831—41no—
100#14556520—41no—
101C22⋊#10596831—41no—
102C22⋊#10596831—41no—
103#14556503—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556503—41no—
109#14556503—41no—
110#14556502—41no—
111C8×Dic73—41no—
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116C23×C4×C73C2311yescharacteristic
117C2×M16×C73—41no—
118C2×M16×C73—41no—
119C2×M16×C73—41no—
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C2×C22⋊C4×C73C2×C411yescharacteristic
125C2×C22⋊C4×C73C2×C411yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—41no—
129C4⋊C8×C73—41no—
130C22⋊C8×C73—41no—
131#95×C73C2×C411yescharacteristic
132#95×C73C2×C411yescharacteristic
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—22no—
151C2×C4×D73—22no—
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—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—22no—
165C2×C4×D73—41no—
166C2×C4×D73—41no—
167C2×C4×D73—41no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C8×D73—44no—
181C4⋊Dic73—41no—
182#11924007—22no—
183#11924007—22no—
184#11924007—41no—
185#11924007—41no—
186C22⋊Dic73—41no—
187C22⋊Dic73—41no—
188#11924005—41no—
189#11924005—41no—
190#11924005—41no—
191#11924005—41no—
192#11924005—41no—
193#11924005M1614yescomplemented
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—41no—
199C4×Dic73—41no—
200C24×C73C22×C411yescharacteristic
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C2411yescharacteristic
213M16×C73—44no—
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—
226C22⋊C4×C73—22no—
227C22⋊C4×C73—41no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
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×D73C2×M1612yes—
253C22×D73#13112yes—
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—21no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73C2×M1612yes—
273C2×C4×C73H(5,𝔽2)11yescharacteristic
274C2×C4×C73H(5,𝔽2)11yescharacteristic
275C2×C4×C73H(5,𝔽2)11yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C2×C4×C73H(5,𝔽2)11yescharacteristic
278C2×C4×C732−1+411yescharacteristic
279C22⋊D73—44no—
280C22⋊D73—44no—
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—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73C2×M1612yes—
298C2×Dic73#13112yes—
299D292—44no—
300C4×D73—44no—
301C4×D73—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—41no—
319C22×C73—41no—
320C22×C73—41no—
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—22no—
336C2×D73—22no—
337C2×D73—22no—
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—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73#56011yescharacteristic
352C4×C73#56011yescharacteristic
353C4×C73#56211yescharacteristic
354C4×C73#56211yescharacteristic
355Dic73—22no—
356Dic73—22no—
357Dic73—41no—
358Dic73—41no—
359Dic73—41no—
360Dic73—41no—
361#23329—731nomaximal, Sylow
362C2×C73—81no—
363C2×C73#237711yescharacteristic
364C2×C73#297411yescharacteristic
365C2×C73#297411yescharacteristic
366C2×C73#297611yescharacteristic
367C2×C73#298111yescharacteristic
368C2×C73#298911yescharacteristic
369C2×C73#299411yescharacteristic
370D73—42no—
371D73—42no—
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#1851D7311yescharacteristic, complemented
384#1850—731no—
385#1817—731no—
386#1797—731no—
387C73#2332911yescharacteristic, complemented, Sylow
388C22×M16C2×D7311yescharacteristic
389C23×C8—731no—
390C2×#121—731no—
391C2×C4×D4—731no—
392C2×C4×D4—731no—
393C2×C4×D4—731no—
394C22×C42—731no—
395C2×C4⋊C8—731no—
396C2×C4⋊C8—731no—
397C2×C4⋊C8C2×D7311yescharacteristic
398C2×C4⋊C8C2×D7311yescharacteristic
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⋊C8—731no—
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⋊C4C2×D7311yescharacteristic
421#336—731no—
422#336—731no—
423#336—731no—
424#336—731no—
425#336—731no—
426#336—731no—
427#336—731no—
428#336—731no—
429#336C2×D7311yescharacteristic
430#336C2×D7311yescharacteristic
431C22×D4—731no—
432C22×D4—731no—
433C22×D4—731no—
434C23×C4—731no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4—731no—
438C23×C4C22×D7311yescharacteristic
439C2×M16—41no—
440C2×M16—41no—
441C2×M16—41no—
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⋊C4C4×D7311yescharacteristic
474C2×C22⋊C4C4×D7311yescharacteristic
475C2×C42—2921no—
476C2×C42—2921no—
477C2×C42—731no—
478C2×C42—731no—
479C2×C42—731no—
480C2×C42—731no—
481C2×C42C22×D7311yescharacteristic
482C2×C42C22×D7311yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C4⋊C8—2921no—
486C4⋊C8—2921no—
487C22⋊C8—41no—
488C22⋊C8—2921no—
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#95C4×D7311yescharacteristic
504#95C4×D7311yescharacteristic
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—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—2921no—
524C22×C4—2921no—
525C22×C4—2921no—
526C22×C4—731no—
527C22×C4—731no—
528C22×C4—731no—
529C22×C4—731no—
530C22×C4—731no—
531C22×C4—731no—
532C22×C4—1462no—
533C22×C4—1462no—
534C22×C4—1462no—
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—44no—
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—22no—
585C22⋊C4—41no—
586C22⋊C4—2921no—
587C22⋊C4—2921no—
588C22⋊C4—2921no—
589C22⋊C4—2921no—
590C22⋊C4—2921no—
591C22⋊C4—2921no—
592C22⋊C4—2921no—
593C22⋊C4—734no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—2921no—
599C42—2921no—
600C42—1461no—
601C42—1461no—
602C42—1461no—
603C42—1461no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—732no—
612C23—732no—
613C23—1461no—
614C23—1461no—
615C23—1461no—
616C23—1461no—
617C23—1461no—
618C23—1461no—
619C23—1461no—
620C23—1461no—
621C23—1461no—
622C23—1461no—
623C23—1461no—
624C23—1461no—
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—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—2924no—
648C2×C4—2924no—
649C2×C4—2921no—
650C2×C4—2921no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—732no—
658C2×C4—732no—
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×C4—1461no—
675C2×C4M16×D7312yes—
676C2×C4#1455663611yescharacteristic
677C2×C4#1455663611yescharacteristic
678C2×C4#1455663611yescharacteristic
679C2×C4#1455663711yescharacteristic
680C2×C4#1455663711yescharacteristic
681C2×C4#1455663911yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—2921no—
687C8—2921no—
688C8—2921no—
689C8—2921no—
690C22—41no—
691C22—41no—
692C22—41no—
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—1462no—
706C22—1462no—
707C22—1462no—
708C22—1462no—
709C22—1462no—
710C22—1462no—
711C22#1798905911yescharacteristic
712C22#1798905911yescharacteristic
713C22#1798906811yescharacteristic
714C22C2×M16×D7311yescharacteristic
715C22#131×D7311yescharacteristic
716C22#131×D7311yescharacteristic
717C22#1798935311yescharacteristic
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—2921no—
724C4—2921no—
725C4—2921no—
726C4—2921no—
727C4—1462no—
728C4—1462no—
729C4#1798932611yescharacteristic
730C4#1798932711yescharacteristic
731C4#1798933311yescharacteristic
732C4#1798933311yescharacteristic
733C2—81no—
734C2—2922no—
735C2—2922no—
736C2#2261308711yescharacteristic
737C2#2261896111yescharacteristic
738C2#2261896311yescharacteristic
739C2#2261897511yescharacteristic
740C2#2261900311yescharacteristic
741C2#2261904511yescharacteristic
742C2#2261908911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1851C2
prime radicalC2×#14556564C4
cosocleC22×C4×C73C24
hypercenter#1851D73
hypocenterC73#23329
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
2. #22610728C2semidirect
3. #22610723C2semidirect
4. #22610546C2semidirect
5. #22610536C2semidirect
6. #22610493C2semidirect
7. #22610485C2semidirect
8. #22610228C2semidirect
9. #22610228C2semidirect
10. #22610222C2semidirect
11. #22610220C2semidirect
12. #22610110C2semidirect
13. #22609998C2semidirect
14. #22609908C2semidirect
15. C73×#1851C2semidirect
193. #11924005M16semidirect
383. #1851D73semidirect
387. C73#23329semidirect

Maximal subgroups

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

subgroupindex
C4×#145565642
#226107282
#226107232
#226105462
#226105362
#226104932
#226104852
#226102282
#226102222
#226102202
#226101102
#226099982
#226099082
C73×#18512
#2332973