Finite Group Databasebeta

← #33096275

Subgroups — #33096275

Order 18688.

1162 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988549C211yesmaximal, characteristic
2#22612310C211yesmaximal, characteristic
3#380×D73C211yesmaximal, characteristic
4#22610132C211yesmaximal, characteristic, complemented
5#22610130C211yesmaximal, characteristic, complemented
6#22610128C211yesmaximal, characteristic, complemented
7#22610125C211yesmaximal, characteristic, complemented
8#22610122C211yesmaximal, characteristic, complemented
9#22610120C211yesmaximal, characteristic, complemented
10#22610117C211yesmaximal, characteristic, complemented
11#22609965C211yesmaximal, characteristic, complemented
12#22609963C211yesmaximal, characteristic, complemented
13#22609963C211yesmaximal, characteristic, complemented
14#22609961C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C2×#14556550C2211yescharacteristic
20C2×C4⋊C4×D73C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C22⋊C4×D73—21no—
23C2×#14556525C2211yescharacteristic, complemented
24C2×#14556524C2211yescharacteristic, complemented
25C2×#14556524C2211yescharacteristic, complemented
26C2×#14556523C2211yescharacteristic, complemented
27C2×#14556522C2211yescharacteristic, complemented
28C2×#14556522C2211yescharacteristic, complemented
29#17988549C418yescomplemented
30C2×C22⋊#10596831C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33#17988448—21no—
34#17988447C2211yescharacteristic
35#17988446—21no—
36#17988445—21no—
37#17988444C2211yescharacteristic
38#17988444C2211yescharacteristic
39#17988444C2211yescharacteristic
40#17988444C2211yescharacteristic
41#17988444C2211yescharacteristic
42#17988444C2211yescharacteristic
43#17988442—21no—
44C4×#11924005—21no—
45C4×#11924005—21no—
46#95×D73—21no—
47#17988350C2211yescharacteristic, complemented
48#17988350C2211yescharacteristic, complemented
49#17988349C2211yescharacteristic, complemented
50#17988349C2211yescharacteristic, complemented
51#17988349C2211yescharacteristic, complemented
52#17988349C2211yescharacteristic, complemented
53C2×#117×C73C2211yescharacteristic
54C2×#107×C73C2211yescharacteristic, complemented
55C2×#106×C73C2211yescharacteristic, complemented
56C2×C22⋊C8×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic, complemented
59#340×C73C2211yescharacteristic, complemented
60C24×D73D411yescharacteristic
61C23×Dic73D411yescharacteristic
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73—41no—
65C22×C4×D73—41no—
66C22×C4×D73—41no—
67C22×C4×D73—41no—
68C22×C4×D73C2×C414yes—
69C22×C4×D73D411yescharacteristic
70C22×C4×D73D411yescharacteristic
71C22×C4×D73Q814yes—
72C22×C4×D73C2311yescharacteristic
73C22×C4×D73C2311yescharacteristic
74C2×#11924011—41no—
75C2×#11924011—41no—
76C2×#11924011—41no—
77C2×#11924011—41no—
78C2×#11924011C2×C414yescomplemented
79C2×#11924011C2×C414yescomplemented
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82#14556550—41no—
83#14556550—41no—
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×C4⋊Dic73C2311yescharacteristic
88C2×#11924007—21no—
89C2×#11924007—21no—
90C4⋊C4×D73—41no—
91C4⋊C4×D73—41no—
92C4⋊C4×D73—41no—
93C4⋊C4×D73—41no—
94C2×C22⋊Dic73—21no—
95C2×C22⋊Dic73—21no—
96C2×#11924005—21no—
97C2×#11924005—21no—
98C2×#11924005—21no—
99C2×#11924005—21no—
100C2×#11924005—21no—
101C2×#11924005—21no—
102C22⋊C4×D73—44no—
103C2×C4×Dic73—21no—
104#14556525—41no—
105#14556524—41no—
106#14556524—41no—
107#14556523—41no—
108#14556522—41no—
109#14556522—41no—
110C22⋊#10596831C2×C414yescomplemented
111#14556503C2×C414yes—
112#14556503C2×C414yes—
113#14556498—21no—
114#14556498—21no—
115#14556498—21no—
116#14556498—21no—
117#14556498—21no—
118#14556498—21no—
119#14556498—21no—
120C23×C4×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123#117×C73—41no—
124#117×C73—41no—
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C42×C73—21no—
132#107×C73—41no—
133#106×C73—41no—
134C22⋊C8×C73C2×C414yescomplemented
135#95×C73—21no—
136C23×D73—22no—
137C23×D73—22no—
138C23×D73—41no—
139C23×D73—41no—
140C23×D73—41no—
141C23×D73—41no—
142C23×D73C4⋊C414yes—
143C23×D73C2×D411yescharacteristic
144C23×D73C2×D411yescharacteristic
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—41no—
150C22×Dic73—41no—
151C22×Dic73C4⋊C414yes—
152C22×Dic73C2×D411yescharacteristic
153C22×Dic73C2×D411yescharacteristic
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—44no—
163C2×C4×D73—44no—
164C2×C4×D73—44no—
165C2×C4×D73—44no—
166C2×C4×D73—41no—
167C2×C4×D73—41no—
168C2×C4×D73—41no—
169C2×C4×D73—41no—
170C2×C4×D73—42no—
171C2×C4×D73—42no—
172C2×C4×D73—42no—
173C2×C4×D73—42no—
174C2×C4×D73—42no—
175C2×C4×D73—42no—
176C2×C4×D73C4⋊C414yes—
177C2×C4×D73C4⋊C414yes—
178C2×C4×D73C22×C412yes—
179C2×C4×D73C22×C412yes—
180C2×C4×D73C2×Q812yes—
181C2×C4×D73C2×Q812yes—
182#11924011—44no—
183#11924011—44no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831C22×C412yes—
189C2×#10596831C22×C412yes—
190C4⋊Dic73—21no—
191C4⋊Dic73—21no—
192C4⋊Dic73—21no—
193C4⋊Dic73—21no—
194C4⋊Dic73—21no—
195C4⋊Dic73—21no—
196C4⋊Dic73—21no—
197C4⋊Dic73—21no—
198#11924007—42no—
199#11924007—42no—
200C22⋊Dic73—42no—
201C22⋊Dic73—42no—
202#11924005—42no—
203#11924005—42no—
204#11924005—42no—
205#11924005—42no—
206#11924005—42no—
207#11924005—42no—
208C4×Dic73—42no—
209C24×C73C2×D411yescharacteristic
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73C22×C412yes—
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2×Q812yes—
221C22×C4×C73C2411yescharacteristic
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73C22×C412yes—
227C2×C8×C73C22×C412yes—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C42×C73—42no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73C2×C4⋊C412yes—
246C23×C73C22×D411yescharacteristic
247C22×D73—21no—
248C22×D73—21no—
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—28no—
258C22×D73—44no—
259C22×D73—44no—
260C22×D73—44no—
261C22×D73—44no—
262C22×D73—44no—
263C22×D73—44no—
264C22×D73C2×C4⋊C412yes—
265C22×D73C2×C4⋊C412yes—
266C22×D73AGL(1,ℤ/8)12yes—
267C22×D73#13712yes—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73C2×C4⋊C412yes—
287C2×C4×C73C23×C411yescharacteristic
288C2×C4×C73C22×Q811yescharacteristic
289C2×C4×C73H(5,𝔽2)11yescharacteristic
290C2×C4×C73H(5,𝔽2)11yescharacteristic
291C2×C4×C73H(5,𝔽2)11yescharacteristic
292C2×C4×C73H(5,𝔽2)11yescharacteristic
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—44no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73C2×C4⋊C412yes—
311C2×Dic73C2×C4⋊C412yes—
312C4×D73—22no—
313C4×D73—22no—
314C4×D73—22no—
315C4×D73—22no—
316C4×D73—22no—
317C4×D73—22no—
318C4×D73—22no—
319C4×D73—22no—
320C4×D73—44no—
321C4×D73—44no—
322C4×D73—84no—
323C4×D73—84no—
324C8×C73—22no—
325C8×C73—22no—
326#10596831—22no—
327#10596831—22no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73C22×C4⋊C411yescharacteristic
336C22×C73#53411yescharacteristic
337C22×C73#53411yescharacteristic
338C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C73C2×#13711yescharacteristic
340C22×C73#57511yescharacteristic
341C22×C73#57511yescharacteristic
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—22no—
345C2×D73—22no—
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—22no—
351C2×D73—416no—
352C2×D73—41no—
353C2×D73—41no—
354C2×D73—41no—
355C2×D73—41no—
356C2×D73#42814yes—
357C4×C73—22no—
358C4×C73—81no—
359C4×C73—81no—
360C4×C73—81no—
361C4×C73—81no—
362C4×C73#51811yescharacteristic
363C4×C73#51811yescharacteristic
364C4×C73#54311yescharacteristic
365C4×C73#54311yescharacteristic
366Dic73—22no—
367Dic73—22no—
368Dic73—81no—
369Dic73—81no—
370Dic73—81no—
371Dic73—81no—
372#21944—731nomaximal, Sylow
373C2×C73—42no—
374C2×C73#231511yescharacteristic
375C2×C73C2×#42811yescharacteristic
376C2×C73#291111yescharacteristic
377C2×C73#319411yescharacteristic
378C2×C73#319411yescharacteristic
379C2×C73#319611yescharacteristic
380C2×C73#319611yescharacteristic
381D73—24no—
382D73—42no—
383C2×#407—731no—
384#2280—731no—
385C2×#380—731no—
386#1854—731no—
387#1854—731no—
388#1854—731no—
389#1854D7311yescharacteristic, complemented
390#1853—731no—
391#1853—731no—
392#1852—731no—
393#1852—731no—
394#1809—731no—
395#1809—731no—
396#1809—731no—
397#1809—731no—
398C73#2194411yescharacteristic, complemented, Sylow
399C24×C4—731no—
400C22×M16—731no—
401C22×M16—731no—
402C2×#117—731no—
403C2×#117C2×D7311yescharacteristic
404C22×C4⋊C4—731no—
405C22×C4⋊C4—731no—
406C22×C22⋊C4—1461no—
407C2×#107—731no—
408C2×#107—731no—
409C2×#107—731no—
410C2×#107C2×D7311yescharacteristic, complemented
411C2×#106—731no—
412C2×#106—731no—
413C2×#106—731no—
414C2×#106C2×D7311yescharacteristic, complemented
415#407—738no—
416C2×C22⋊C8—731no—
417C2×C22⋊C8—731no—
418C2×C22⋊C8—731no—
419C2×C22⋊C8C2×D7311yescharacteristic
420#381—1461no—
421#380—731no—
422#380—731no—
423#380—731no—
424#380—731no—
425#380—731no—
426#380—731no—
427#380—731no—
428#380—1461no—
429#380—1461no—
430#380C2×D7311yescharacteristic
431#379—1461no—
432C4×C22⋊C4—1461no—
433C4×C22⋊C4—1461no—
434C2×#95—1461no—
435#340—731no—
436#340—731no—
437#340—731no—
438#340—731no—
439#340—731no—
440#340—731no—
441#340C2×D7311yescharacteristic, complemented
442#340C2×D7311yescharacteristic, complemented
443C25—731no—
444C23×C4—2921no—
445C23×C4—2921no—
446C23×C4—2921no—
447C23×C4—2921no—
448C23×C4—731no—
449C23×C4—734no—
450C23×C4—731no—
451C23×C4—731no—
452C23×C4—734no—
453C23×C4—731no—
454C23×C4—731no—
455C23×C4—1461no—
456C23×C4—1461no—
457C23×C4C22×D7311yescharacteristic
458C2×M16—2921no—
459C2×M16—2921no—
460C2×M16—2921no—
461C2×M16—2921no—
462C2×M16—734no—
463C2×M16—734no—
464C22×C8—731no—
465C22×C8—731no—
466C22×C8C22×D7311yescharacteristic
467C22×C8C22×D7311yescharacteristic
468#117—41no—
469#117—41no—
470#117—2921no—
471#117—2921no—
472C2×C4⋊C4—2921no—
473C2×C4⋊C4—2921no—
474C2×C4⋊C4—2921no—
475C2×C4⋊C4—2921no—
476C2×C4⋊C4—731no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—731no—
479C2×C4⋊C4—731no—
480C2×C4⋊C4—1461no—
481C2×C4⋊C4—1461no—
482C2×C4⋊C4C22×D7311yescharacteristic
483C2×C4⋊C4C22×D7311yescharacteristic
484C2×C4⋊C4C22×D7311yescharacteristic
485C2×C4⋊C4C22×D7311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—2924no—
489C2×C22⋊C4—1461no—
490C2×C22⋊C4—1461no—
491C2×C22⋊C4—1461no—
492C2×C22⋊C4—1461no—
493C2×C22⋊C4—1461no—
494C2×C22⋊C4—1461no—
495C2×C22⋊C4—1461no—
496C2×C22⋊C4—1461no—
497C2×C42—21no—
498C2×C42—1461no—
499#107—41no—
500#107—2921no—
501#107—2921no—
502#107—2921no—
503#106—41no—
504#106—2921no—
505#106—2921no—
506#106—2921no—
507C22⋊C8—734no—
508C22⋊C8—734no—
509C22⋊C8—734no—
510C22⋊C8C4×D7314yescomplemented
511#95—21no—
512#95—1461no—
513#95—1461no—
514#95—1461no—
515#95—1461no—
516#95—1461no—
517#95—1461no—
518#95—1461no—
519C24—2921no—
520C24—2921no—
521C24—2921no—
522C24—2921no—
523C24—734no—
524C24—731no—
525C24—731no—
526C24—1462no—
527C24—1462no—
528C24D4×D7311yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—2921no—
538C22×C4—2921no—
539C22×C4—2921no—
540C22×C4—2921no—
541C22×C4—2924no—
542C22×C4—2924no—
543C22×C4—2924no—
544C22×C4—2924no—
545C22×C4—2922no—
546C22×C4—2922no—
547C22×C4—2922no—
548C22×C4—2922no—
549C22×C4—2922no—
550C22×C4—2922no—
551C22×C4—2921no—
552C22×C4—2921no—
553C22×C4—734no—
554C22×C4—734no—
555C22×C4—734no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—732no—
559C22×C4—732no—
560C22×C4—732no—
561C22×C4—732no—
562C22×C4—1461no—
563C22×C4—1461no—
564C22×C4—1461no—
565C22×C4—1461no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4C2×C4×D7312yes—
575C22×C4D4×D7311yescharacteristic
576C22×C4Q8×D7312yes—
577C22×C4C23×D7311yescharacteristic
578M16—2924no—
579M16—2924no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—732no—
585C2×C8—732no—
586C2×C8—1461no—
587C2×C8—1461no—
588C2×C8—1461no—
589C2×C8—1461no—
590C2×C8C2×C4×D7312yes—
591C2×C8C2×C4×D7312yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—2922no—
601C4⋊C4—2922no—
602C4⋊C4—1461no—
603C4⋊C4—1461no—
604C4⋊C4—1461no—
605C4⋊C4—1461no—
606C4⋊C4—1461no—
607C4⋊C4—1461no—
608C4⋊C4—1461no—
609C4⋊C4—1461no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—2922no—
613C22⋊C4—2922no—
614C22⋊C4—2922no—
615C22⋊C4—2922no—
616C22⋊C4—2922no—
617C22⋊C4—2922no—
618C22⋊C4—2922no—
619C22⋊C4—2922no—
620C42—42no—
621C42—2922no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—2924no—
629C23—2924no—
630C23—2924no—
631C23—2924no—
632C23—2924no—
633C23—2924no—
634C23—732no—
635C23—732no—
636C23—732no—
637C23—732no—
638C23—1468no—
639C23—1461no—
640C23—1461no—
641C23—1461no—
642C23—1461no—
643C23—1461no—
644C23—1461no—
645C23—1461no—
646C23—1461no—
647C23—1461no—
648C23—1461no—
649C23C4⋊C4×D7312yes—
650C23C2×D4×D7311yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—2924no—
670C2×C4—2924no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—2921no—
680C2×C4—2921no—
681C2×C4—2921no—
682C2×C4—2921no—
683C2×C4—2924no—
684C2×C4—5844no—
685C2×C4—5844no—
686C2×C4—732no—
687C2×C4—732no—
688C2×C4—1461no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4C4⋊C4×D7312yes—
701C2×C4C22×C4×D7311yescharacteristic
702C2×C4C2×Q8×D7311yescharacteristic
703C2×C4#1455663611yescharacteristic
704C2×C4#1455663611yescharacteristic
705C2×C4#1455663711yescharacteristic
706C2×C4#1455663711yescharacteristic
707C8—22no—
708C8—22no—
709C8—1462no—
710C8—1462no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—29216no—
719C22—2921no—
720C22—2921no—
721C22—2921no—
722C22—2921no—
723C22—734no—
724C22—1462no—
725C22—1462no—
726C22—1462no—
727C22—1462no—
728C22—1462no—
729C22—1462no—
730C22—1462no—
731C22—1462no—
732C22—1462no—
733C22C2×C4⋊C4×D7311yescharacteristic
734C22#1798914711yescharacteristic
735C22#1798914811yescharacteristic
736C22AGL(1,ℤ/8)×D7311yescharacteristic
737C22#137×D7311yescharacteristic
738C22#1798938411yescharacteristic
739C22#1798938411yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—5841no—
746C4—5841no—
747C4—5841no—
748C4—5841no—
749C4—1462no—
750C4—1462no—
751C4#1798905911yescharacteristic
752C4#1798905911yescharacteristic
753C4#1798921211yescharacteristic
754C4#1798921211yescharacteristic
755C2—42no—
756C2—2922no—
757C2—1464no—
758C2#2261254211yescharacteristic
759C2#428×D7311yescharacteristic
760C2#2261851911yescharacteristic
761C2#2262074311yescharacteristic
762C2#2262074911yescharacteristic
763C2#2262075911yescharacteristic
764C2#2262076511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1854C2
socleC23×C73C22×D4
prime radicalC24×D73D4
cosocleC22×C4×C73C24
hypercenter#1854D73
hypocenterC73#21944
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #22610132C2semidirect
5. #22610130C2semidirect
6. #22610128C2semidirect
7. #22610125C2semidirect
8. #22610122C2semidirect
9. #22610120C2semidirect
10. #22610117C2semidirect
11. #22609965C2semidirect
12. #22609963C2semidirect
13. #22609963C2semidirect
14. #22609961C2semidirect
15. C73×#1854C2semidirect
23. C2×#14556525C22semidirect
24. C2×#14556524C22semidirect
25. C2×#14556524C22semidirect
26. C2×#14556523C22semidirect
27. C2×#14556522C22semidirect
28. C2×#14556522C22semidirect
29. #17988549C4semidirect
47. #17988350C22semidirect
48. #17988350C22semidirect
49. #17988349C22semidirect
50. #17988349C22semidirect
51. #17988349C22semidirect
52. #17988349C22semidirect
54. C2×#107×C73C22semidirect
55. C2×#106×C73C22semidirect
58. #340×C73C22semidirect
59. #340×C73C22semidirect
78. C2×#11924011C2×C4semidirect
79. C2×#11924011C2×C4semidirect
110. C22⋊#10596831C2×C4semidirect
134. C22⋊C8×C73C2×C4semidirect
389. #1854D73semidirect
398. C73#21944semidirect
410. C2×#107C2×D73semidirect
414. C2×#106C2×D73semidirect
441. #340C2×D73semidirect
442. #340C2×D73semidirect
510. C22⋊C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179885492
#226123102
#380×D732
#226101322
#226101302
#226101282
#226101252
#226101222
#226101202
#226101172
#226099652
#226099632
#226099612
C73×#18542
#2194473