Finite Group Databasebeta

← #33112205

Subgroups — #33112205

Order 18688.

888 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×#14556566C211yesmaximal, characteristic
2#22610725C211yesmaximal, characteristic, complemented
3#22610724C211yesmaximal, characteristic, complemented
4#22610537C211yesmaximal, characteristic, complemented
5#22610535C211yesmaximal, characteristic, complemented
6#22610490C211yesmaximal, characteristic, complemented
7#22610222C211yesmaximal, characteristic, complemented
8#22610222C211yesmaximal, characteristic, complemented
9#22610222C211yesmaximal, characteristic, complemented
10#22610222C211yesmaximal, characteristic, complemented
11#22610110C211yesmaximal, characteristic, complemented
12#22610107C211yesmaximal, characteristic, complemented
13#22609998C211yesmaximal, characteristic, complemented
14#22609910C211yesmaximal, characteristic, complemented
15C73×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556566C411yescharacteristic
19C2×C4×D292C2211yescharacteristic
20C2×C4×D292C2211yescharacteristic
21C2×C4×D292C2211yescharacteristic
22C2×C42×D73C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556503C2211yescharacteristic
36C2×C4×#10596831C2211yescharacteristic
37#17988488C411yescharacteristic
38#17988486C411yescharacteristic
39#17988479C411yescharacteristic
40#17988479C411yescharacteristic
41#17988465C411yescharacteristic
42#17988465C411yescharacteristic
43#17988444C411yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×#11924005C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C4×C8×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D292C2×C411yescharacteristic
60C22×D292C2×C411yescharacteristic
61C22×D292C2×C411yescharacteristic
62C22×C4×D73C2×C411yescharacteristic
63C22×C4×D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C22×C4×D73C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C2×C8×D73—41no—
72C2×C8×D73—41no—
73C2×C8×D73—41no—
74C2×C8×D73—41no—
75C2×C8×D73—41no—
76C2×C8×D73—41no—
77#14556566C818yescomplemented
78C4×D292—41no—
79C4×D292—41no—
80C4×D292—41no—
81C4×D292—41no—
82C4×D292—41no—
83C4×D292—41no—
84C2×C4⋊Dic73C2×C411yescharacteristic
85C2×C4⋊Dic73C2×C411yescharacteristic
86C2×C4⋊Dic73C2×C411yescharacteristic
87C2×#11924005C2×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×#11924005C2×C411yescharacteristic
97C2×C4×Dic73C2×C411yescharacteristic
98C2×C4×Dic73C2×C411yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C42×D73—41no—
101C42×D73—41no—
102C4⋊#10596831—41no—
103#14556520—41no—
104#14556520—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556503—41no—
109#14556503—41no—
110#14556503—41no—
111#14556503—41no—
112#14556503—41no—
113#14556503—41no—
114#14556503—41no—
115C4×#10596831—41no—
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2×C411yescharacteristic
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—41no—
130C4×C8×C73—41no—
131#95×C73C2×C411yescharacteristic
132#95×C73C2×C411yescharacteristic
133C23×D73C22×C411yescharacteristic
134C23×D73C22×C411yescharacteristic
135C23×D73C22×C411yescharacteristic
136C2×D292—41no—
137C2×D292—41no—
138C2×D292—41no—
139C2×D292—41no—
140C2×D292—41no—
141C2×D292—41no—
142C2×D292C2×C814yes—
143C2×D292C2×C814yescomplemented
144C2×D292C2×C814yescomplemented
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—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168C2×C4×D73—41no—
169C2×C4×D73—41no—
170C2×C4×D73—41no—
171C2×C4×D73—41no—
172C2×C4×D73—41no—
173C2×C4×D73C2×C814yescomplemented
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C8×D73—44no—
187C8×D73—44no—
188C4⋊Dic73—41no—
189C4⋊Dic73—41no—
190C4⋊Dic73—41no—
191#11924005—41no—
192#11924005—41no—
193#11924005—41no—
194#11924005—41no—
195#11924005—41no—
196#11924005—41no—
197#11924005—41no—
198#11924005—41no—
199#11924005C2×C814yescomplemented
200#11924005C2×C814yescomplemented
201C4×Dic73—21no—
202C4×Dic73—21no—
203C4×Dic73—41no—
204C4×Dic73—41no—
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C2411yescharacteristic
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—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C4⋊C4×C73—41no—
225C4⋊C4×C73C2×C814yescomplemented
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C23×C73C23×C411yescharacteristic
233C22×D73—21no—
234C22×D73—21no—
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—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73C22×C812yes—
252C22×D73C22×C812yes—
253C22×D73C22×C812yes—
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—21no—
269C2×C4×C73C22×C812yes—
270C2×C4×C73C22×C812yes—
271C2×C4×C73C22×C812yes—
272C2×C4×C73H(5,𝔽2)11yescharacteristic
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×C732−1+411yescharacteristic
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×Dic73C22×C812yes—
293D292—44no—
294D292—44no—
295D292—44no—
296C4×D73—44no—
297C4×D73—44no—
298C4×D73—41no—
299C4×D73—41no—
300C4×D73—41no—
301C4×D73—41no—
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#51811yescharacteristic
319C22×C73#51811yescharacteristic
320C22×C73#52011yescharacteristic
321C22×C73C23×C811yescharacteristic
322C22×C73#56811yescharacteristic
323C22×C73#56811yescharacteristic
324C22×C73#56811yescharacteristic
325C2×D73—22no—
326C2×D73—22no—
327C2×D73—22no—
328C2×D73—22no—
329C2×D73—22no—
330C2×D73—22no—
331C2×D73—22no—
332C2×D73—22no—
333C2×D73—22no—
334C2×D73—41no—
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—22no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—41no—
352C4×C73#56011yescharacteristic
353C4×C73#56011yescharacteristic
354C4×C73#56211yescharacteristic
355C4×C73#56211yescharacteristic
356Dic73—22no—
357Dic73—41no—
358Dic73—41no—
359Dic73—41no—
360Dic73—41no—
361#23326—731nomaximal, Sylow
362C2×C73#237711yescharacteristic
363C2×C73#297211yescharacteristic
364C2×C73#297211yescharacteristic
365C2×C73#297811yescharacteristic
366C2×C73#298011yescharacteristic
367C2×C73#298811yescharacteristic
368C2×C73#299511yescharacteristic
369D73—42no—
370D73—42no—
371D73—42no—
372C4×#121—731no—
373#1954—731no—
374#1954—731no—
375#1923—731no—
376#1923—731no—
377#1916—731no—
378#1916D7311yescharacteristic, complemented
379#1869—731no—
380#1869—731no—
381#1869—731no—
382#1869—731no—
383#1850—731no—
384#1850—731no—
385#1817—731no—
386#1797—731no—
387C73#2332611yescharacteristic, complemented, Sylow
388C23×C8—731no—
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⋊C8—731no—
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⋊C8—731no—
409C2×C4×C8—731no—
410C2×C4×C8C2×D7311yescharacteristic
411#390—731no—
412#389—731no—
413#388—731no—
414#388—731no—
415#386—731no—
416#386—731no—
417#380—731no—
418C4×C4⋊C4C2×D7311yescharacteristic
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×C4—731no—
437C23×C4—731no—
438C23×C4—731no—
439C22×C8—2921no—
440C22×C8—2921no—
441C22×C8—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—738no—
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⋊C4C4×D7311yescharacteristic
464C2×C4⋊C4C4×D7311yescharacteristic
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—2921no—
476C2×C42—2921no—
477C2×C42—731no—
478C2×C42—731no—
479C2×C42—731no—
480C2×C42C22×D7311yescharacteristic
481C2×C42C22×D7311yescharacteristic
482C2×C42C22×D7311yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—2921no—
485C4⋊C8—2921no—
486C4⋊C8—2921no—
487C22⋊C8—2921no—
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—
497C4×C8—41no—
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—
507C24—731no—
508C2×D4—2921no—
509C2×D4—2921no—
510C2×D4—2921no—
511C2×D4—2921no—
512C2×D4—2921no—
513C2×D4—2921no—
514C2×D4—734no—
515C2×D4—734no—
516C2×D4—734no—
517C22×C4—2921no—
518C22×C4—2921no—
519C22×C4—2921no—
520C22×C4—2921no—
521C22×C4—2921no—
522C22×C4—734no—
523C22×C4—731no—
524C22×C4—731no—
525C22×C4—731no—
526C22×C4—731no—
527C22×C4—731no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4—1461no—
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×C4C2×C4×D7311yescharacteristic
547C22×C4C2×C4×D7311yescharacteristic
548C22×C4C2×C4×D7311yescharacteristic
549C22×C4C2×C4×D7311yescharacteristic
550C22×C4C2×C4×D7311yescharacteristic
551C22×C4C2×C4×D7311yescharacteristic
552C22×C4C23×D7311yescharacteristic
553C2×C8—21no—
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—2924no—
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—41no—
580C4⋊C4—2921no—
581C4⋊C4—2921no—
582C4⋊C4—2921no—
583C4⋊C4C8×D7314yescomplemented
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—734no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—2921no—
601C42—2921no—
602C42—1461no—
603C42—1461no—
604C23—732no—
605C23—732no—
606C23—732no—
607C23—1461no—
608C23—1461no—
609C23—1461no—
610C23—1461no—
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—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—21no—
644C2×C4—2924no—
645C2×C4—2924no—
646C2×C4—2921no—
647C2×C4—2921no—
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—2921no—
657C2×C4—2921no—
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×C4C2×C8×D7312yes—
674C2×C4C2×C8×D7312yes—
675C2×C4C2×C8×D7312yes—
676C2×C4#1455663611yescharacteristic
677C2×C4#1455663711yescharacteristic
678C2×C4#1455663711yescharacteristic
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—2921no—
691C22—2921no—
692C22—2921no—
693C22—2921no—
694C22—2921no—
695C22—2921no—
696C22—2921no—
697C22—2921no—
698C22—2921no—
699C22—2921no—
700C22—2921no—
701C22—2921no—
702C22—1462no—
703C22—1462no—
704C22—1462no—
705C22—1462no—
706C22—1462no—
707C22—1462no—
708C22—1462no—
709C22—1462no—
710C22—1462no—
711C22#1798905911yescharacteristic
712C22#1798906111yescharacteristic
713C22#1798906911yescharacteristic
714C22C22×C8×D7311yescharacteristic
715C22#1798935211yescharacteristic
716C22#1798935211yescharacteristic
717C22#1798935311yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—2921no—
725C4—2921no—
726C4—2921no—
727C4—2921no—
728C4—1462no—
729C4#1798932711yescharacteristic
730C4#1798932811yescharacteristic
731C4#1798933311yescharacteristic
732C4#1798933511yescharacteristic
733C2—2922no—
734C2—2922no—
735C2—2922no—
736C2#2261308611yescharacteristic
737C2#2261895211yescharacteristic
738C2#2261895411yescharacteristic
739C2#2261899211yescharacteristic
740C2#2261899911yescharacteristic
741C2#2261904111yescharacteristic
742C2#2261910011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutatorC22×C73C23×C8
FittingC73×#1916C2
socleC23×C73C23×C4
prime radicalC2×#14556566C4
cosocleC22×C4×C73C24
hypercenter#1916D73
hypocenterC73#23326
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #22610725C2semidirect
3. #22610724C2semidirect
4. #22610537C2semidirect
5. #22610535C2semidirect
6. #22610490C2semidirect
7. #22610222C2semidirect
8. #22610222C2semidirect
9. #22610222C2semidirect
10. #22610222C2semidirect
11. #22610110C2semidirect
12. #22610107C2semidirect
13. #22609998C2semidirect
14. #22609910C2semidirect
15. C73×#1916C2semidirect
77. #14556566C8semidirect
143. C2×D292C2×C8semidirect
144. C2×D292C2×C8semidirect
173. C2×C4×D73C2×C8semidirect
199. #11924005C2×C8semidirect
200. #11924005C2×C8semidirect
225. C4⋊C4×C73C2×C8semidirect
378. #1916D73semidirect
387. C73#23326semidirect
583. C4⋊C4C8×D73semidirect

Maximal subgroups

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

subgroupindex
C4×#145565662
#226107252
#226107242
#226105372
#226105352
#226104902
#226102222
#226101102
#226101072
#226099982
#226099102
C73×#19162
#2332673