Finite Group Databasebeta

← #11806087

Subgroups — #11806087

Order 1152.

1392 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C9C211yesmaximal, characteristic, complemented
2C2×#63499C211yesmaximal, characteristic
3C2×C4×#611C211yesmaximal, characteristic, complemented
4C22×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D9C211yesmaximal, characteristic, complemented
6#10588900C211yesmaximal, characteristic, complemented
7#10588893C211yesmaximal, characteristic, complemented
8#10588890C211yesmaximal, characteristic, complemented
9#10588670C211yesmaximal, characteristic, complemented
10#10588669C211yesmaximal, characteristic, complemented
11#10588637C211yesmaximal, characteristic, complemented
12#10588636C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic9C211yesmaximal, characteristic, complemented
14#10588620C211yesmaximal, characteristic, complemented
15C4×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
16#82398—31nomaximal
17C24×D9C2211yescharacteristic
18C22×D4×C9C2211yescharacteristic
19C23×C4×C9C2211yescharacteristic
20C23×C4×C9C2211yescharacteristic, complemented
21C22×#611C2211yescharacteristic
22C22×#611C2211yescharacteristic
23C23×Dic9C2211yescharacteristic
24C22×C4×D9C2211yescharacteristic
25C22×C4×D9C2211yescharacteristic
26C4×D4×C9—24no—
27C2×C9×C4⋊C4C2211yescharacteristic, complemented
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C9×C22⋊C4C2211yescharacteristic, complemented
30C2×C42×C9C2211yescharacteristic, complemented
31C2×#3676C2211yescharacteristic
32C2×#3676C2211yescharacteristic
33C2×#3676C2211yescharacteristic, complemented
34C2×#3676C2211yescharacteristic, complemented
35#63499C418yescomplemented
36C4×#611—24no—
37C2×(C2×D9)⋊C4—24no—
38C2×(C2×D9)⋊C4C2211yescharacteristic
39C2×(C2×D9)⋊C4C2211yescharacteristic
40C2×(C2×D9)⋊C4C2211yescharacteristic
41C2×(C2×D9)⋊C4C2211yescharacteristic
42C2×(C2×D9)⋊C4C2211yescharacteristic
43C2×(C2×D9)⋊C4C2211yescharacteristic
44C2×(C2×D9)⋊C4C2211yescharacteristic
45C2×(C2×D9)⋊C4C2211yescharacteristic
46C2×Dic9⋊C4C2211yescharacteristic, complemented
47C2×Dic9⋊C4C2211yescharacteristic, complemented
48C2×C4×Dic9C2211yescharacteristic, complemented
49C2×C4×Dic9C2211yescharacteristic, complemented
50C22⋊C4×D9—24no—
51C9⋊#95C2211yescharacteristic, complemented
52C9⋊#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C9⋊#95C2211yescharacteristic, complemented
57C2×C3×C4×D4D311yescharacteristic
58C2×#937—31no—
59C2×C4×#67—31no—
60C22×(C2×D3)⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62#5220—31no—
63#5213—31no—
64#5210—31no—
65#4990—31no—
66#4989—31no—
67#4957—31no—
68#4956—31no—
69Dic3×C22⋊C4—31no—
70#4940—31no—
71C4×(C2×D3)⋊C4—31no—
72C24×C9C2311yescharacteristic
73C24×C9C2311yescharacteristic
74C23×D9—22no—
75C23×D9—22no—
76C23×D9—22no—
77C23×D9—22no—
78C23×D9—41no—
79C23×D9—41no—
80C23×D9C2×C414yescomplemented
81C23×D9C2311yescharacteristic
82C23×D9C2311yescharacteristic
83C2×D4×C9—22no—
84C2×D4×C9—22no—
85C2×D4×C9C2×C414yescomplemented
86C22×C4×C9—22no—
87C22×C4×C9—22no—
88C22×C4×C9—22no—
89C22×C4×C9—22no—
90C22×C4×C9—41no—
91C22×C4×C9—41no—
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2311yescharacteristic
94C22×C4×C9C2311yescharacteristic
95C22×C4×C9C2311yescharacteristic
96C22×C4×C9C2311yescharacteristic
97C2×#611—22no—
98C2×#611—22no—
99C2×#611—41no—
100C2×#611—41no—
101C2×#611C2×C414yescomplemented
102C2×#611C2×C414yescomplemented
103C22×Dic9—22no—
104C22×Dic9—22no—
105C22×Dic9—41no—
106C22×Dic9C2311yescharacteristic
107C22×Dic9C2311yescharacteristic
108C22×Dic9C2311yescharacteristic
109C22×Dic9C2311yescharacteristic
110C22×Dic9C2311yescharacteristic
111C22×Dic9C2311yescharacteristic
112C2×C4×D9—22no—
113C2×C4×D9—22no—
114C2×C4×D9—22no—
115C2×C4×D9—22no—
116C2×C4×D9—41no—
117C2×C4×D9—41no—
118C9×C4⋊C4—22no—
119C9×C22⋊C4—22no—
120C9×C22⋊C4D414yescomplemented
121C42×C9—22no—
122#3676—22no—
123#3676—22no—
124#3676—41no—
125#3676C2×C414yescomplemented
126(C2×D9)⋊C4—22no—
127(C2×D9)⋊C4—22no—
128(C2×D9)⋊C4—22no—
129(C2×D9)⋊C4—22no—
130(C2×D9)⋊C4—22no—
131(C2×D9)⋊C4C2×C414yescomplemented
132(C2×D9)⋊C4C2×C414yescomplemented
133(C2×D9)⋊C4D414yescomplemented
134Dic9⋊C4—22no—
135Dic9⋊C4—41no—
136C4×Dic9—22no—
137C4×Dic9—41no—
138#2358—91noSylow
139C24×D3—31no—
140C22×C3×D4C2×D311yescharacteristic
141C23×C3×C4C2×D311yescharacteristic
142C23×C3×C4C2×D311yescharacteristic
143C22×#67—31no—
144C22×#67—31no—
145C23×Dic3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C3×C4×D4—24no—
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C22⋊C4C2×D311yescharacteristic
151C2×C3×C22⋊C4C2×D311yescharacteristic
152C2×C3×C42C2×D311yescharacteristic
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157#937—38no—
158C4×#67—64no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—64no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172D3×C22⋊C4—64no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C23×C9—21no—
180C23×C9—21no—
181C23×C9—21no—
182C23×C9—21no—
183C23×C9—21no—
184C23×C9—21no—
185C23×C9—21no—
186C23×C9—21no—
187C23×C9—21no—
188C23×C9—21no—
189C23×C9C22×C412yes—
190C23×C9C22×C412yes—
191C23×C9C2×D412yes—
192C23×C9#4112yes—
193C23×C9C2411yescharacteristic
194C22×D9—21no—
195C22×D9—21no—
196C22×D9—21no—
197C22×D9—21no—
198C22×D9—28no—
199C22×D9—21no—
200C22×D9—21no—
201C22×D9—21no—
202C22×D9—21no—
203C22×D9—21no—
204C22×D9—21no—
205C22×D9—28no—
206C22×D9—44no—
207C22×D9—44no—
208C22×D9—44no—
209C22×D9—44no—
210C22×D9—44no—
211C22×D9C22×C412yes—
212C22×D9C22×C412yes—
213C22×D9C2×D412yes—
214C22×D9#4112yes—
215D4×C9—28no—
216C2×C4×C9—21no—
217C2×C4×C9—21no—
218C2×C4×C9—21no—
219C2×C4×C9—21no—
220C2×C4×C9—21no—
221C2×C4×C9—21no—
222C2×C4×C9—21no—
223C2×C4×C9—21no—
224C2×C4×C9—21no—
225C2×C4×C9—21no—
226C2×C4×C9—21no—
227C2×C4×C9—44no—
228C2×C4×C9—44no—
229C2×C4×C9C22×C412yes—
230C2×C4×C9C2×D412yes—
231C2×C4×C9C2×D412yes—
232C2×C4×C9C2×D412yes—
233#611—28no—
234#611—44no—
235C2×Dic9—21no—
236C2×Dic9—21no—
237C2×Dic9—21no—
238C2×Dic9—21no—
239C2×Dic9—21no—
240C2×Dic9—21no—
241C2×Dic9—21no—
242C2×Dic9—21no—
243C2×Dic9—21no—
244C2×Dic9—21no—
245C2×Dic9—21no—
246C2×Dic9—21no—
247C2×Dic9—21no—
248C2×Dic9—21no—
249C2×Dic9—21no—
250C2×Dic9—44no—
251C2×Dic9C22×C412yes—
252C2×Dic9C22×C412yes—
253C2×Dic9C2×D412yes—
254C4×D9—44no—
255C4×D9—44no—
256C2×#120—91no—
257C2×C4×D4—91no—
258C2×C4×D4D911yescharacteristic, complemented
259C22×C22⋊C4—91no—
260C22×C22⋊C4—91no—
261#390—91no—
262#388—91no—
263#388—91no—
264#386—91no—
265#386—91no—
266#386—91no—
267#385—91no—
268#385—91no—
269C4×C22⋊C4—91no—
270C4×C22⋊C4—91no—
271C24×C3C22×D311yescharacteristic
272C24×C3C22×D311yescharacteristic
273C23×D3—31no—
274C23×D3—31no—
275C23×D3—34no—
276C23×D3—62no—
277C23×D3—62no—
278C23×D3—62no—
279C23×D3—62no—
280C23×D3—121no—
281C23×D3—121no—
282C2×C3×D4—22no—
283C2×C3×D4—22no—
284C2×C3×D4C4×D314yes—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—41no—
290C22×C3×C4—41no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C2×#67—34no—
297C2×#67—34no—
298C2×#67—62no—
299C2×#67—62no—
300C2×#67—121no—
301C2×#67—121no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—62no—
309C22×Dic3—62no—
310C22×Dic3—121no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—62no—
315C2×C4×D3—121no—
316C2×C4×D3—121no—
317C3×C4⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4#6714yes—
320C3×C42—22no—
321#217—34no—
322#217—62no—
323#217—62no—
324#217—121no—
325(C2×D3)⋊C4—34no—
326(C2×D3)⋊C4—34no—
327(C2×D3)⋊C4—34no—
328(C2×D3)⋊C4—62no—
329(C2×D3)⋊C4—62no—
330(C2×D3)⋊C4—62no—
331(C2×D3)⋊C4—62no—
332(C2×D3)⋊C4—62no—
333Dic3⋊C4—62no—
334Dic3⋊C4—121no—
335C4×Dic3—62no—
336C4×Dic3—121no—
337C22×C9—22no—
338C22×C9—22no—
339C22×C9—22no—
340C22×C9—22no—
341C22×C9—22no—
342C22×C9—22no—
343C22×C9—22no—
344C22×C9—22no—
345C22×C9—22no—
346C22×C9—41no—
347C22×C9—41no—
348C22×C9—41no—
349C22×C9—41no—
350C22×C9C4×D414yescomplemented
351C22×C9C23×C411yescharacteristic
352C22×C9C22×D411yescharacteristic
353C22×C9C22×D411yescharacteristic
354C22×C9C2×#4111yescharacteristic
355C22×C9C2×#4111yescharacteristic
356C22×C9H(5,𝔽2)11yescharacteristic
357C22×C9H(5,𝔽2)11yescharacteristic
358C2×D9—22no—
359C2×D9—22no—
360C2×D9—22no—
361C2×D9—22no—
362C2×D9—22no—
363C2×D9—22no—
364C2×D9—22no—
365C2×D9—22no—
366C2×D9—22no—
367C2×D9—416no—
368C2×D9—41no—
369C2×D9—41no—
370C2×D9—41no—
371C2×D9—41no—
372C2×D9C4×D414yescomplemented
373C4×C9—22no—
374C4×C9—22no—
375C4×C9—22no—
376C4×C9—22no—
377C4×C9—41no—
378Dic9—22no—
379Dic9—22no—
380Dic9—22no—
381Dic9—41no—
382Dic9—41no—
383Dic9—41no—
384C25—91no—
385C22×D4—91no—
386C22×D4—91no—
387C22×D4C2×D911yescharacteristic
388C23×C4—91no—
389C23×C4—91no—
390C23×C4—91no—
391C23×C4C2×D911yescharacteristic
392C23×C4C2×D911yescharacteristic, complemented
393#120—98no—
394C4×D4—24no—
395C4×D4—184no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4C2×D911yescharacteristic, complemented
399C2×C22⋊C4—91no—
400C2×C22⋊C4—91no—
401C2×C22⋊C4—91no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—91no—
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C22⋊C4—91no—
411C2×C22⋊C4—184no—
412C2×C22⋊C4—184no—
413C2×C22⋊C4C2×D911yescharacteristic
414C2×C22⋊C4C2×D911yescharacteristic, complemented
415C2×C42—91no—
416C2×C42—91no—
417C2×C42C2×D911yescharacteristic, complemented
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3C2×C4×D312yes—
435C23×C3C2×C4×D312yes—
436C23×C3#23512yes—
437C23×C3C2×#6712yes—
438C23×C3C23×D311yescharacteristic
439C22×D3—32no—
440C22×D3—32no—
441C22×D3—32no—
442C22×D3—32no—
443C22×D3—68no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—68no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—61no—
454C22×D3—61no—
455C22×D3—124no—
456C22×D3—124no—
457C22×D3—124no—
458C22×D3—124no—
459C22×D3—124no—
460C3×D4—28no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—44no—
473C2×C3×C4—44no—
474C2×C3×C4C2×C4×D312yes—
475C2×C3×C4D3×D412yes—
476C2×C3×C4C2×#6712yes—
477C2×C3×C4C2×#6712yes—
478#67—68no—
479#67—124no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—32no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—124no—
499C4×D3—124no—
500C4×D3—124no—
501C2×C9—24no—
502C2×C9—42no—
503C2×C9C2×C4×D411yescharacteristic
504C2×C9C2×C4×D411yescharacteristic
505C2×C9#51811yescharacteristic
506C2×C9D4211yescharacteristic
507C2×C9#54611yescharacteristic
508C2×C9#54611yescharacteristic
509C2×C9#55111yescharacteristic
510D9—24no—
511D9—42no—
512C24—91no—
513C24—91no—
514C24—94no—
515C24—182no—
516C24—182no—
517C24—182no—
518C24—182no—
519C24—361no—
520C24—361no—
521C24C22×D911yescharacteristic
522C24C22×D911yescharacteristic
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—94no—
526C2×D4—94no—
527C2×D4—182no—
528C2×D4—182no—
529C2×D4—361no—
530C2×D4—361no—
531C2×D4C4×D914yescomplemented
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4—91no—
542C22×C4—91no—
543C22×C4—91no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—182no—
548C22×C4—182no—
549C22×C4—182no—
550C22×C4—361no—
551C22×C4—361no—
552C22×C4—361no—
553C22×C4C22×D911yescharacteristic
554C22×C4C22×D911yescharacteristic
555C22×C4C22×D911yescharacteristic
556C22×C4C22×D911yescharacteristic
557C22×C4C22×D911yescharacteristic
558C4⋊C4—22no—
559C4⋊C4—182no—
560C4⋊C4—361no—
561C22⋊C4—22no—
562C22⋊C4—94no—
563C22⋊C4—94no—
564C22⋊C4—94no—
565C22⋊C4—94no—
566C22⋊C4—182no—
567C22⋊C4—182no—
568C22⋊C4—182no—
569C22⋊C4—182no—
570C22⋊C4—182no—
571C22⋊C4—182no—
572C22⋊C4—182no—
573C22⋊C4—361no—
574C22⋊C4#61114yescomplemented
575C42—22no—
576C42—182no—
577C42—361no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3C4×#6714yes—
592C22×C3C22×C4×D311yescharacteristic
593C22×C3C2×#23511yescharacteristic
594C22×C3C2×D3×D411yescharacteristic
595C22×C3#100411yescharacteristic
596C22×C3D3×#4111yescharacteristic
597C22×C3#100911yescharacteristic
598C22×C3C22×#6711yescharacteristic
599C2×D3—34no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—62no—
604C2×D3—62no—
605C2×D3—62no—
606C2×D3—62no—
607C2×D3—62no—
608C2×D3—62no—
609C2×D3—1216no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—41no—
619Dic3—62no—
620Dic3—62no—
621Dic3—62no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625C9#235811yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—92no—
637C23—92no—
638C23—92no—
639C23—92no—
640C23—188no—
641C23—181no—
642C23—181no—
643C23—181no—
644C23—181no—
645C23—188no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23—364no—
653C23—364no—
654C23—364no—
655C23—364no—
656C23—364no—
657C23C2×C4×D912yes—
658C23C2×C4×D912yes—
659C23#369712yes—
660C23C2×#61112yes—
661C23C23×D911yescharacteristic
662D4—28no—
663D4—188no—
664D4—364no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—92no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—364no—
697C2×C4—364no—
698C2×C4—364no—
699C2×C4C2×C4×D912yes—
700C2×C4D4×D912yes—
701C2×C4C2×#61112yes—
702C2×C4C2×#61112yes—
703C2×C3—24no—
704C2×C3—42no—
705C2×C3C4×D3×D411yescharacteristic
706C2×C3#554511yescharacteristic
707C2×C3#555011yescharacteristic
708C2×C3#555611yescharacteristic
709C2×C3C2×C4×#6711yescharacteristic
710C2×C3D4×#6711yescharacteristic
711C2×C3#582911yescharacteristic
712D3—64no—
713D3—122no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—94no—
728C22—182no—
729C22—182no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22—182no—
734C22—182no—
735C22—182no—
736C22—182no—
737C22—3616no—
738C22—361no—
739C22—361no—
740C22—361no—
741C22—361no—
742C22C4×#61114yescomplemented
743C22C22×C4×D911yescharacteristic
744C22C2×#369711yescharacteristic
745C22C2×D4×D911yescharacteristic
746C22#6371011yescharacteristic
747C22#41×D911yescharacteristic
748C22#6371511yescharacteristic
749C22C22×#61111yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—41no—
755C4—182no—
756C4—182no—
757C4—182no—
758C4—361no—
759C4—361no—
760C4—361no—
761C3#8239811yescharacteristic
762C2—24no—
763C2—42no—
764C2—184no—
765C2—362no—
766C2C4×D4×D911yescharacteristic
767C2#1058964711yescharacteristic
768C2#1058965211yescharacteristic
769C2#1058965811yescharacteristic
770C2C2×C4×#61111yescharacteristic
771C2D4×#61111yescharacteristic
772C2#1058993111yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC2×C4×D4×C9C2
prime radicalC2×#63499C2
cosocleC23×C9C24
hypercenterC2×C4×D4D9
hypocenterC9#2358
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C9C2semidirect
3. C2×C4×#611C2semidirect
4. C22×(C2×D9)⋊C4C2semidirect
5. C2×C22⋊C4×D9C2semidirect
6. #10588900C2semidirect
7. #10588893C2semidirect
8. #10588890C2semidirect
9. #10588670C2semidirect
10. #10588669C2semidirect
11. #10588637C2semidirect
12. #10588636C2semidirect
13. C22⋊C4×Dic9C2semidirect
14. #10588620C2semidirect
15. C4×(C2×D9)⋊C4C2semidirect
20. C23×C4×C9C22semidirect
27. C2×C9×C4⋊C4C22semidirect
29. C2×C9×C22⋊C4C22semidirect
30. C2×C42×C9C22semidirect
33. C2×#3676C22semidirect
34. C2×#3676C22semidirect
35. #63499C4semidirect
46. C2×Dic9⋊C4C22semidirect
47. C2×Dic9⋊C4C22semidirect
48. C2×C4×Dic9C22semidirect
49. C2×C4×Dic9C22semidirect
51. C9⋊#95C22semidirect
52. C9⋊#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
56. C9⋊#95C22semidirect
80. C23×D9C2×C4semidirect
85. C2×D4×C9C2×C4semidirect
101. C2×#611C2×C4semidirect
102. C2×#611C2×C4semidirect
120. C9×C22⋊C4D4semidirect
125. #3676C2×C4semidirect
131. (C2×D9)⋊C4C2×C4semidirect
132. (C2×D9)⋊C4C2×C4semidirect
133. (C2×D9)⋊C4D4semidirect
258. C2×C4×D4D9semidirect
350. C22×C9C4×D4semidirect
372. C2×D9C4×D4semidirect
392. C23×C4C2×D9semidirect
398. C2×C4⋊C4C2×D9semidirect
414. C2×C22⋊C4C2×D9semidirect
417. C2×C42C2×D9semidirect
531. C2×D4C4×D9semidirect
574. C22⋊C4#611semidirect
625. C9#2358semidirect
742. C22C4×#611semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
C2×#634992
C2×C4×#6112
C22×(C2×D9)⋊C42
C2×C22⋊C4×D92
#105889002
#105888932
#105888902
#105886702
#105886692
#105886372
#105886362
C22⋊C4×Dic92
#105886202
C4×(C2×D9)⋊C42
#823983