Finite Group Databasebeta

← #33103027

Subgroups — #33103027

Order 18688.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988645C211yesmaximal, characteristic, complemented
2C2×#17988552C211yesmaximal, characteristic
3#22612421C211yesmaximal, characteristic
4#22610545C211yesmaximal, characteristic, complemented
5#22610544C211yesmaximal, characteristic, complemented
6#22610544C211yesmaximal, characteristic, complemented
7#22610538C211yesmaximal, characteristic, complemented
8#22610115C211yesmaximal, characteristic, complemented
9#22610110C211yesmaximal, characteristic, complemented
10#22610000C211yesmaximal, characteristic, complemented
11#22609911C211yesmaximal, characteristic, complemented
12#22609842C211yesmaximal, characteristic
13#22609716C211yesmaximal, characteristic, complemented
14#22609708C211yesmaximal, characteristic, complemented
15C73×#1749C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19C2×#14556550C2211yescharacteristic
20#17988645—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25#17988552—24no—
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556501C2211yescharacteristic
35C2×C8×Dic73C2211yescharacteristic
36#17988493C411yescharacteristic
37#17988493C411yescharacteristic
38#17988489C411yescharacteristic
39#17988489C411yescharacteristic
40#17988466C411yescharacteristic
41#17988466C411yescharacteristic
42#17988466C411yescharacteristic
43#17988466C411yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×#11924005C2211yescharacteristic
46C4×#11924005C2211yescharacteristic
47C4×#11924005C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×C42×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×#97×C73C2211yescharacteristic
58C2×#97×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C2×#11924028—22no—
62C2×#11924028—22no—
63C2×#11924028—22no—
64C2×#11924028—22no—
65C2×#11924028—41no—
66C2×#11924028—41no—
67C22×Dic146C2×C411yescharacteristic
68C22×D292C2×C411yescharacteristic
69C22×C22⋊D73C2×C411yescharacteristic
70C22×C22⋊D73C2×C411yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C22×C4×D73C2311yescharacteristic
73C2×#11924011—22no—
74C2×#11924011—22no—
75C2×#11924011—41no—
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C2×C8×D73—22no—
81C2×C8×D73—22no—
82C2×C8×D73—41no—
83#14556550—22no—
84#14556550—22no—
85C2×C4⋊Dic73C2×C411yescharacteristic
86C2×C4⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×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×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C4⋊#10596831—41no—
100C4⋊#10596831—41no—
101#14556520—22no—
102#14556520—22no—
103C22⋊#10596831—22no—
104C22⋊#10596831—22no—
105#14556503—22no—
106#14556503—22no—
107#14556503—22no—
108#14556503—22no—
109#14556503—41no—
110#14556503—41no—
111#14556501—22no—
112C8×Dic73—22no—
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121C23×C4×C73C2×C411yescharacteristic
122C23×C4×C73C2×C411yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C22×C8×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C2×C42×C73—41no—
129C2×C42×C73—41no—
130C2×C42×C73C2×C411yescharacteristic
131C2×C42×C73C2×C411yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134C22⋊C8×C73—22no—
135C22⋊C8×C73D414yes—
136#97×C73—41no—
137#97×C73—41no—
138C23×D73C22×C411yescharacteristic
139C23×D73C22×C411yescharacteristic
140#11924028—44no—
141#11924028—44no—
142#11924028—44no—
143#11924028—44no—
144C2×Dic146—22no—
145C2×Dic146—22no—
146C2×Dic146—41no—
147C2×D292—22no—
148C2×D292—22no—
149C2×D292—41no—
150C2×C22⋊D73—22no—
151C2×C22⋊D73—22no—
152C2×C22⋊D73—22no—
153C2×C22⋊D73—22no—
154C2×C22⋊D73—41no—
155C2×C22⋊D73—41no—
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C22×Dic73C22×C411yescharacteristic
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—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73#4112yes—
173C2×C4×D73#4112yes—
174#11924011—44no—
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—
186C2×#10596831—21no—
187C8×D73—44no—
188C4⋊Dic73—22no—
189C4⋊Dic73—22no—
190C22⋊Dic73—22no—
191C22⋊Dic73—22no—
192#11924005—22no—
193#11924005—22no—
194#11924005—41no—
195#11924005—41no—
196#11924005—41no—
197#11924005—41no—
198#11924005—41no—
199#11924005—41no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C4×Dic73—21no—
203C4×Dic73—21no—
204C24×C73C22×C411yescharacteristic
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—22no—
210C22×C4×C73—41no—
211C22×C4×C73—41no—
212C22×C4×C73—41no—
213C22×C4×C73—41no—
214C22×C4×C73—41no—
215C22×C4×C73C22×C411yescharacteristic
216C22×C4×C73C22×C411yescharacteristic
217C22×C4×C73C22×C411yescharacteristic
218C22×C4×C73C22×C411yescharacteristic
219C22×C4×C73C22×C411yescharacteristic
220C22×C4×C73C2×D412yes—
221C22×C4×C73#4112yes—
222C22×C4×C73C2411yescharacteristic
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73C2×D412yes—
234C2×C8×C73C2×D412yes—
235C42×C73—21no—
236C42×C73—21no—
237C42×C73—21no—
238C42×C73—21no—
239C42×C73—41no—
240C42×C73—41no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73C4×D412yes—
248C23×C73C23×C411yescharacteristic
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73—21no—
254C22×D73—21no—
255C22×D73—21no—
256C22×D73—21no—
257C22×D73—21no—
258C22×D73—21no—
259C22×D73—21no—
260C22×D73—21no—
261C22×D73—21no—
262C22×D73#11712yes—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—44no—
281C2×C4×C73—44no—
282C2×C4×C73C4×D412yes—
283C2×C4×C73#13112yes—
284C2×C4×C73C22×D411yescharacteristic
285C2×C4×C73C2×#4111yescharacteristic
286C2×C4×C73C2×#4111yescharacteristic
287C2×C4×C73C2×#4111yescharacteristic
288C2×C4×C73H(5,𝔽2)11yescharacteristic
289C2×C4×C73H(5,𝔽2)11yescharacteristic
290C22⋊D73—44no—
291C22⋊D73—44no—
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×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—21no—
308C2×Dic73—21no—
309C2×Dic73#11712yes—
310D292—44no—
311C4×D73—22no—
312C4×D73—22no—
313C4×D73—22no—
314C4×D73—22no—
315C4×D73—41no—
316C4×D73—41no—
317C4×D73—41no—
318C4×D73—41no—
319Dic146—44no—
320C8×C73—22no—
321C8×C73—22no—
322C8×C73—41no—
323C8×C73—41no—
324#10596831—41no—
325#10596831—41no—
326#10596831—41no—
327#10596831—41no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73C2×#11711yescharacteristic
336C22×C73C2×C4×D411yescharacteristic
337C22×C73#51811yescharacteristic
338C22×C73C2×#13111yescharacteristic
339C22×C73#56811yescharacteristic
340C22×C73#56811yescharacteristic
341C22×C73#56811yescharacteristic
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—22no—
345C2×D73—41no—
346C2×D73—41no—
347C2×D73—41no—
348C2×D73—41no—
349C2×D73—41no—
350C2×D73—41no—
351C2×D73—41no—
352C2×D73—41no—
353C2×D73—41no—
354C2×D73—41no—
355C2×D73—41no—
356C4×C73—22no—
357C4×C73—22no—
358C4×C73—41no—
359C4×C73—41no—
360C4×C73—41no—
361C4×C73#54611yescharacteristic
362C4×C73#54611yescharacteristic
363C4×C73#55111yescharacteristic
364C4×C73#55111yescharacteristic
365Dic73—22no—
366Dic73—41no—
367Dic73—41no—
368Dic73—41no—
369Dic73—41no—
370Dic73—41no—
371#22561—731nomaximal, Sylow
372C2×C73—42no—
373C2×C73#234211yescharacteristic
374C2×C73#292311yescharacteristic
375C2×C73#292511yescharacteristic
376C2×C73#293211yescharacteristic
377C2×C73#293511yescharacteristic
378C2×C73#297611yescharacteristic
379C2×C73#297811yescharacteristic
380D73—42no—
381D73—81no—
382C2×#433—731no—
383C2×#408—731no—
384#2297—731no—
385#1924—731no—
386#1924—731no—
387#1924—731no—
388#1923—731no—
389#1851—731no—
390#1850—731no—
391#1818—731no—
392#1797—731no—
393#1780—731no—
394#1753—731no—
395#1752—731no—
396#1749D7311yescharacteristic, complemented
397C73#2256111yescharacteristic, complemented, Sylow
398C22×#41—731no—
399C22×M16—731no—
400C23×C8—731no—
401C2×#117—731no—
402C22×C42C2×D7311yescharacteristic
403#433—1464no—
404C2×C4⋊C8—731no—
405C2×C4⋊C8—731no—
406C2×C4⋊C8—731no—
407C2×C4⋊C8—731no—
408#408—1464no—
409C2×C22⋊C8—731no—
410C2×C22⋊C8—731no—
411C2×C22⋊C8—731no—
412C2×C22⋊C8—731no—
413C2×C22⋊C8—731no—
414C2×C22⋊C8—731no—
415C2×C22⋊C8—731no—
416C2×C22⋊C8—731no—
417C2×C22⋊C8C2×D7311yescharacteristic
418C2×C22⋊C8C2×D7311yescharacteristic
419C2×#97—731no—
420C2×#97C2×D7311yescharacteristic
421C2×#97C2×D7311yescharacteristic
422C2×C4×C8—731no—
423#391—731no—
424#391—731no—
425#390—731no—
426#390—731no—
427#386—731no—
428#386—731no—
429#386—731no—
430#386—731no—
431C4×C22⋊C4—731no—
432C4×C22⋊C4—731no—
433C4×C22⋊C4—731no—
434C4×C22⋊C4—731no—
435#336—731no—
436#336—731no—
437#336—731no—
438#336—731no—
439#336—731no—
440#336—731no—
441#336C2×D7311yescharacteristic
442#336C2×D7311yescharacteristic
443C2×#41—2921no—
444C2×#41—2921no—
445C2×#41—1462no—
446C2×#41—1462no—
447C2×#41—1462no—
448C2×#41—1462no—
449C22×Q8—731no—
450C22×D4—731no—
451C22×D4—731no—
452C22×D4—731no—
453C23×C4—731no—
454C23×C4—731no—
455C23×C4C4×D7311yescharacteristic
456C23×C4C4×D7311yescharacteristic
457C23×C4C22×D7311yescharacteristic
458C2×M16—2921no—
459C2×M16—1462no—
460C2×M16—1462no—
461C22×C8—2921no—
462C22×C8—731no—
463C22×C8—731no—
464C22×C8—731no—
465C22×C8—731no—
466C22×C8—1462no—
467C22×C8—1462no—
468C22×C8C22×D7311yescharacteristic
469C22×C8C22×D7311yescharacteristic
470C22×C8C22×D7311yescharacteristic
471C22×C8C22×D7311yescharacteristic
472#117—1462no—
473#117—1462no—
474C2×C4⋊C4—731no—
475C2×C4⋊C4—731no—
476C2×C22⋊C4—731no—
477C2×C22⋊C4—731no—
478C2×C22⋊C4—731no—
479C2×C22⋊C4—731no—
480C2×C22⋊C4—731no—
481C2×C22⋊C4—731no—
482C2×C22⋊C4—731no—
483C2×C22⋊C4—731no—
484C2×C22⋊C4—731no—
485C2×C22⋊C4—731no—
486C2×C42—41no—
487C2×C42—41no—
488C2×C42—731no—
489C2×C42—731no—
490C2×C42C4×D7311yescharacteristic
491C2×C42C4×D7311yescharacteristic
492C2×C42C22×D7311yescharacteristic
493C2×C42C22×D7311yescharacteristic
494C4⋊C8—2921no—
495C4⋊C8—2921no—
496C4⋊C8—1462no—
497C4⋊C8—1462no—
498C22⋊C8—22no—
499C22⋊C8—2921no—
500C22⋊C8—2921no—
501C22⋊C8—1462no—
502C22⋊C8—1462no—
503C22⋊C8—1462no—
504C22⋊C8—1462no—
505C22⋊C8—1462no—
506C22⋊C8—1462no—
507C22⋊C8D29214yes—
508#97—41no—
509#97—41no—
510#97—1462no—
511C4×C8—1462no—
512#95—731no—
513#95—731no—
514#95—731no—
515#95—731no—
516#95—731no—
517#95—731no—
518#95—731no—
519#95—731no—
520C24—731no—
521C24—731no—
522C24C2×C4×D7311yescharacteristic
523#41—2924no—
524#41—2924no—
525#41—2924no—
526#41—2924no—
527C2×Q8—2921no—
528C2×Q8—1462no—
529C2×Q8—1462no—
530C2×D4—2921no—
531C2×D4—2921no—
532C2×D4—2921no—
533C2×D4—1462no—
534C2×D4—1462no—
535C2×D4—1462no—
536C2×D4—1462no—
537C2×D4—1462no—
538C2×D4—1462no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—731no—
550C22×C4—732no—
551C22×C4—732no—
552C22×C4—731no—
553C22×C4—731no—
554C22×C4—731no—
555C22×C4—731no—
556C22×C4—731no—
557C22×C4—1461no—
558C22×C4—1461no—
559C22×C4—1461no—
560C22×C4—1461no—
561C22×C4—1461no—
562C22×C4—1461no—
563C22×C4—1461no—
564C22×C4—1461no—
565C22×C4—1461no—
566C22×C4—1461no—
567C22×C4C2×C4×D7311yescharacteristic
568C22×C4C2×C4×D7311yescharacteristic
569C22×C4C2×C4×D7311yescharacteristic
570C22×C4C2×C4×D7311yescharacteristic
571C22×C4C2×C4×D7311yescharacteristic
572C22×C4C2×D29212yes—
573C22×C4#1192402812yes—
574C22×C4C23×D7311yescharacteristic
575M16—2924no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—2924no—
587C2×C8—1461no—
588C2×C8—1461no—
589C2×C8—1461no—
590C2×C8—1461no—
591C2×C8—1461no—
592C2×C8—1461no—
593C2×C8—1461no—
594C2×C8—1461no—
595C2×C8—1461no—
596C2×C8—1461no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8C2×D29212yes—
600C2×C8C2×D29212yes—
601C4⋊C4—1462no—
602C4⋊C4—1462no—
603C22⋊C4—2921no—
604C22⋊C4—2921no—
605C22⋊C4—2921no—
606C22⋊C4—2921no—
607C22⋊C4—2921no—
608C22⋊C4—2921no—
609C22⋊C4—1462no—
610C22⋊C4—1462no—
611C22⋊C4—1462no—
612C22⋊C4—1462no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—41no—
618C42—41no—
619C42—1461no—
620C42—1461no—
621C42—1461no—
622C42—1461no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—732no—
630C23—1461no—
631C23—1461no—
632C23—1461no—
633C23—1461no—
634C23—1461no—
635C23—1461no—
636C23—1461no—
637C23—1461no—
638C23—1461no—
639C23—1461no—
640C23—1461no—
641C23—1461no—
642C23—1461no—
643C23C4×D29212yes—
644C23C22×C4×D7311yescharacteristic
645Q8—2924no—
646D4—2924no—
647D4—2924no—
648D4—2924no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—732no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4—1461no—
679C2×C4—1461no—
680C2×C4—1461no—
681C2×C4—1461no—
682C2×C4—1461no—
683C2×C4—1461no—
684C2×C4—1461no—
685C2×C4—1461no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4—1461no—
689C2×C4—1461no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4C4×D29212yes—
695C2×C4#1455659912yes—
696C2×C4C22×D29211yescharacteristic
697C2×C4#41×D7311yescharacteristic
698C2×C4#41×D7311yescharacteristic
699C2×C4C2×#1192402811yescharacteristic
700C2×C4#1455663611yescharacteristic
701C2×C4#1455663611yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—2921no—
707C8—2921no—
708C8—2921no—
709C8—2921no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—2921no—
718C22—2921no—
719C22—2921no—
720C22—2921no—
721C22—2921no—
722C22—2921no—
723C22—2921no—
724C22—2921no—
725C22—2921no—
726C22—2921no—
727C22—2921no—
728C22—1462no—
729C22—1462no—
730C22—1462no—
731C22#117×D7311yescharacteristic
732C22C2×C4×D29211yescharacteristic
733C22#1798906011yescharacteristic
734C22C2×#1455659911yescharacteristic
735C22#1798935311yescharacteristic
736C22#1798935311yescharacteristic
737C22#1798935311yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—2921no—
744C4—2921no—
745C4—2921no—
746C4—2921no—
747C4—2921no—
748C4—1462no—
749C4#1798923211yescharacteristic
750C4#1798923211yescharacteristic
751C4#1798926611yescharacteristic
752C4#1798926611yescharacteristic
753C2—42no—
754C2—2922no—
755C2—5841no—
756C2#2261278311yescharacteristic
757C2#2261857711yescharacteristic
758C2#2261859811yescharacteristic
759C2#2261865011yescharacteristic
760C2#2261867711yescharacteristic
761C2#2261898111yescharacteristic
762C2#2261899111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1749C2
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenter#1749D73
hypocenterC73#22561
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#17988645C2semidirect
4. #22610545C2semidirect
5. #22610544C2semidirect
6. #22610544C2semidirect
7. #22610538C2semidirect
8. #22610115C2semidirect
9. #22610110C2semidirect
10. #22610000C2semidirect
11. #22609911C2semidirect
13. #22609716C2semidirect
14. #22609708C2semidirect
15. C73×#1749C2semidirect
396. #1749D73semidirect
397. C73#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#179886452
C2×#179885522
#226124212
#226105452
#226105442
#226105382
#226101152
#226101102
#226100002
#226099112
#226098422
#226097162
#226097082
C73×#17492
#2256173