Finite Group Databasebeta

← #11806084

Subgroups — #11806084

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×#611C211yesmaximal, characteristic, complemented
2C22×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
3C2×#63455C211yesmaximal, characteristic, complemented
4C2×#63444C211yesmaximal, characteristic
5C2×C22⋊C4×D9C211yesmaximal, characteristic, complemented
6C9×#385C211yesmaximal, characteristic, complemented
7#10588670C211yesmaximal, characteristic, complemented
8#10588669C211yesmaximal, characteristic, complemented
9#10588668C211yesmaximal, characteristic, complemented
10#10588638C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic9C211yesmaximal, characteristic, complemented
12#10588349C211yesmaximal, characteristic, complemented
13#10588346C211yesmaximal, characteristic, complemented
14#10588345C211yesmaximal, characteristic, complemented
15#10588345C211yesmaximal, characteristic, complemented
16#74596—31nomaximal
17C24×D9C2211yescharacteristic
18C23×C4×C9C2211yescharacteristic
19C22×#611C2211yescharacteristic
20C23×Dic9C2211yescharacteristic
21C22×D36C2211yescharacteristic
22C22×D36C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic
24C22×C4×D9C2211yescharacteristic
25C22×C4×D9C2211yescharacteristic, complemented
26C2×C9×C4⋊C4C2211yescharacteristic, complemented
27C2×C9×C4⋊C4C2211yescharacteristic, complemented
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C9×C22⋊C4C2211yescharacteristic
30C2×#3676C2211yescharacteristic
31C4×#611—24no—
32C2×(C2×D9)⋊C4—24no—
33C2×(C2×D9)⋊C4C2211yescharacteristic
34C2×(C2×D9)⋊C4C2211yescharacteristic
35C2×(C2×D9)⋊C4C2211yescharacteristic
36C2×(C2×D9)⋊C4C2211yescharacteristic
37C2×(C2×D9)⋊C4C2211yescharacteristic
38C2×(C2×D9)⋊C4C2211yescharacteristic
39C2×(C2×D9)⋊C4C2211yescharacteristic
40C2×(C2×D9)⋊C4C2211yescharacteristic
41C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C2×Dic9⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic9C2211yescharacteristic, complemented
46C2×C4×Dic9C2211yescharacteristic, complemented
47C2×C4×Dic9C2211yescharacteristic, complemented
48#63455—24no—
49#63444C418yescomplemented
50C22⋊C4×D9—24no—
51C9×#95C2211yescharacteristic, complemented
52C9×#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C9⋊#95C2211yescharacteristic, complemented
57C2×C4×#67—31no—
58C22×(C2×D3)⋊C4—31no—
59C2×#893—31no—
60C2×#882—31no—
61C2×D3×C22⋊C4—31no—
62C3×#385D311yescharacteristic
63#4990—31no—
64#4989—31no—
65#4988—31no—
66#4958—31no—
67Dic3×C22⋊C4—31no—
68#4669—31no—
69#4666—31no—
70#4665—31no—
71#4665—31no—
72C24×C9C2311yescharacteristic
73C23×D9—22no—
74C23×D9—22no—
75C23×D9—22no—
76C23×D9—22no—
77C23×D9—41no—
78C23×D9—41no—
79C23×D9C2×C414yescomplemented
80C23×D9C2311yescharacteristic
81C23×D9C2311yescharacteristic
82C23×D9C2311yescharacteristic
83C22×C4×C9—22no—
84C22×C4×C9—22no—
85C22×C4×C9—41no—
86C22×C4×C9C2311yescharacteristic
87C22×C4×C9C2311yescharacteristic
88C22×C4×C9C2311yescharacteristic
89C22×C4×C9C2311yescharacteristic
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C2×#611—22no—
93C2×#611—22no—
94C2×#611C2×C414yescomplemented
95C22×Dic9—22no—
96C22×Dic9—22no—
97C22×Dic9—41no—
98C22×Dic9C2311yescharacteristic
99C22×Dic9C2311yescharacteristic
100C22×Dic9C2311yescharacteristic
101C22×Dic9C2311yescharacteristic
102C22×Dic9C2311yescharacteristic
103C2×D36—22no—
104C2×D36—22no—
105C2×D36—41no—
106C2×D36—41no—
107C2×D36C2×C414yescomplemented
108C2×D36C2×C414yescomplemented
109C2×C4×D9—22no—
110C2×C4×D9—22no—
111C2×C4×D9—22no—
112C2×C4×D9—22no—
113C2×C4×D9—22no—
114C2×C4×D9—22no—
115C2×C4×D9—41no—
116C2×C4×D9—41no—
117C2×C4×D9—41no—
118C9×C4⋊C4—22no—
119C9×C4⋊C4—41no—
120C9×C22⋊C4—22no—
121C9×C22⋊C4C2×C414yescomplemented
122#3676D414yescomplemented
123(C2×D9)⋊C4—22no—
124(C2×D9)⋊C4—22no—
125(C2×D9)⋊C4—22no—
126(C2×D9)⋊C4—22no—
127(C2×D9)⋊C4—22no—
128(C2×D9)⋊C4—22no—
129(C2×D9)⋊C4—22no—
130(C2×D9)⋊C4—41no—
131(C2×D9)⋊C4C2×C414yescomplemented
132(C2×D9)⋊C4C2×C414yescomplemented
133(C2×D9)⋊C4D414yescomplemented
134Dic9⋊C4—22no—
135C4×Dic9—22no—
136C4×Dic9—22no—
137C4×Dic9—41no—
138#2358—91noSylow
139C24×D3—31no—
140C23×C3×C4C2×D311yescharacteristic
141C22×#67—31no—
142C23×Dic3—31no—
143C22×D12—31no—
144C22×D12—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C22⋊C4C2×D311yescharacteristic
151C2×C3×C22⋊C4C2×D311yescharacteristic
152C2×#217—31no—
153C4×#67—64no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
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—64no—
166C2×Dic3⋊C4—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170#893—64no—
171#882—38no—
172D3×C22⋊C4—64no—
173C3×#95C2×D311yescharacteristic
174C3×#95C2×D311yescharacteristic
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×C9C22×C412yes—
184C23×C9C2×D412yes—
185C23×C9#4112yes—
186C23×C9C2411yescharacteristic
187C22×D9—21no—
188C22×D9—21no—
189C22×D9—21no—
190C22×D9—21no—
191C22×D9—28no—
192C22×D9—21no—
193C22×D9—21no—
194C22×D9—21no—
195C22×D9—21no—
196C22×D9—21no—
197C22×D9—21no—
198C22×D9—21no—
199C22×D9—21no—
200C22×D9—21no—
201C22×D9—21no—
202C22×D9—21no—
203C22×D9—21no—
204C22×D9—28no—
205C22×D9—44no—
206C22×D9—44no—
207C22×D9—44no—
208C22×D9—44no—
209C22×D9—44no—
210C22×D9C22×C412yes—
211C22×D9C22×C412yes—
212C22×D9C22×C412yes—
213C22×D9C2×D412yes—
214C22×D9#4112yes—
215C2×C4×C9—21no—
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—21no—
228C2×C4×C9—21no—
229C2×C4×C9—21no—
230C2×C4×C9—44no—
231C2×C4×C9C22×C412yes—
232C2×C4×C9C22×C412yes—
233C2×C4×C9C2×D412yes—
234#611—28no—
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—44no—
247C2×Dic9C22×C412yes—
248C2×Dic9C2×D412yes—
249C2×Dic9C2×D412yes—
250C2×Dic9C2×D412yes—
251D36—28no—
252D36—44no—
253C4×D9—44no—
254C4×D9—44no—
255C4×D9—44no—
256C2×#120—91no—
257C2×C4×D4—91no—
258C2×C4×D4—91no—
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#385D911yescharacteristic, complemented
269C4×C22⋊C4—91no—
270C4×C22⋊C4—91no—
271C24×C3C22×D311yescharacteristic
272C23×D3—31no—
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—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—41no—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C2×#67—34no—
292C2×#67—62no—
293C2×#67—62no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—62no—
300C22×Dic3—62no—
301C22×Dic3—121no—
302C2×D12—34no—
303C2×D12—34no—
304C2×D12—62no—
305C2×D12—62no—
306C2×D12—121no—
307C2×D12—121no—
308C2×C4×D3—62no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—121no—
315C2×C4×D3—121no—
316C2×C4×D3—121no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—41no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4C4×D314yes—
321#217—34no—
322(C2×D3)⋊C4—34no—
323(C2×D3)⋊C4—34no—
324(C2×D3)⋊C4—34no—
325(C2×D3)⋊C4—62no—
326(C2×D3)⋊C4—62no—
327(C2×D3)⋊C4—62no—
328(C2×D3)⋊C4—62no—
329(C2×D3)⋊C4—62no—
330(C2×D3)⋊C4—62no—
331(C2×D3)⋊C4—62no—
332(C2×D3)⋊C4—121no—
333Dic3⋊C4—62no—
334C4×Dic3—62no—
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×C9C4×D414yescomplemented
344C22×C9C23×C411yescharacteristic
345C22×C9C22×D411yescharacteristic
346C22×C9C22×D411yescharacteristic
347C22×C9C2×#4111yescharacteristic
348C22×C9C2×#4111yescharacteristic
349C22×C9H(5,𝔽2)11yescharacteristic
350C22×C9H(5,𝔽2)11yescharacteristic
351C2×D9—22no—
352C2×D9—22no—
353C2×D9—22no—
354C2×D9—22no—
355C2×D9—22no—
356C2×D9—22no—
357C2×D9—22no—
358C2×D9—22no—
359C2×D9—22no—
360C2×D9—22no—
361C2×D9—22no—
362C2×D9—22no—
363C2×D9—416no—
364C2×D9—41no—
365C2×D9—41no—
366C2×D9—41no—
367C2×D9—41no—
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—41no—
377C4×C9—41no—
378C4×C9—41no—
379Dic9—22no—
380Dic9—22no—
381Dic9—22no—
382Dic9—22no—
383Dic9—41no—
384C25—91no—
385C22×D4—91no—
386C22×D4—91no—
387C22×D4—91no—
388C23×C4—91no—
389C23×C4—91no—
390C23×C4—91no—
391C23×C4—91no—
392C23×C4C2×D911yescharacteristic
393#120—98no—
394C4×D4—184no—
395C4×D4—184no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4C2×D911yescharacteristic, complemented
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
415C2×C42—91no—
416C2×C42—91no—
417C2×C42—91no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95C2×D911yescharacteristic, complemented
423#95C2×D911yescharacteristic, complemented
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3C2×C4×D312yes—
429C23×C3D3×D412yes—
430C23×C3#23912yes—
431C23×C3C23×D311yescharacteristic
432C22×D3—32no—
433C22×D3—32no—
434C22×D3—32no—
435C22×D3—32no—
436C22×D3—32no—
437C22×D3—68no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—61no—
441C22×D3—61no—
442C22×D3—68no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—61no—
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—
460C2×C3×C4—21no—
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—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—44no—
476C2×C3×C4C2×C4×D312yes—
477C2×C3×C4C2×C4×D312yes—
478C2×C3×C4D3×D412yes—
479#67—68no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—32no—
483C2×Dic3—32no—
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—124no—
496D12—68no—
497D12—124no—
498C4×D3—124no—
499C4×D3—124no—
500C4×D3—124no—
501C2×C9—24no—
502C2×C9C2×C4×D411yescharacteristic
503C2×C9C2×C4×D411yescharacteristic
504C2×C9#51811yescharacteristic
505C2×C9D4211yescharacteristic
506C2×C9#54611yescharacteristic
507C2×C9#54611yescharacteristic
508C2×C9#55111yescharacteristic
509D9—24no—
510D9—42no—
511D9—42no—
512C24—91no—
513C24—91no—
514C24—91no—
515C24—94no—
516C24—182no—
517C24—182no—
518C24—182no—
519C24—182no—
520C24—361no—
521C24—361no—
522C24C22×D911yescharacteristic
523C2×D4—94no—
524C2×D4—94no—
525C2×D4—94no—
526C2×D4—182no—
527C2×D4—182no—
528C2×D4—182no—
529C2×D4—182no—
530C2×D4—361no—
531C2×D4—361no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—91no—
536C22×C4—91no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—182no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4—182no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—182no—
548C22×C4—361no—
549C22×C4—361no—
550C22×C4—361no—
551C22×C4—361no—
552C22×C4C22×D911yescharacteristic
553C22×C4C22×D911yescharacteristic
554C22×C4C22×D911yescharacteristic
555C22×C4C22×D911yescharacteristic
556C22×C4C22×D911yescharacteristic
557C22×C4C22×D911yescharacteristic
558C4⋊C4—22no—
559C4⋊C4—41no—
560C4⋊C4—182no—
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⋊C4C4×D914yescomplemented
575C42—182no—
576C42—182no—
577C42—361no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3#89314yes—
585C22×C3C22×C4×D311yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C22×C3C2×D3×D411yescharacteristic
588C22×C3#100411yescharacteristic
589C22×C3C2×#23911yescharacteristic
590C22×C3D3×#4111yescharacteristic
591C22×C3#100911yescharacteristic
592C2×D3—34no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—62no—
604C2×D3—62no—
605C2×D3—1216no—
606C2×D3—121no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620Dic3—62no—
621Dic3—62no—
622Dic3—62no—
623Dic3—62no—
624Dic3—121no—
625C9#235811yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—92no—
631C23—92no—
632C23—92no—
633C23—92no—
634C23—92no—
635C23—188no—
636C23—181no—
637C23—181no—
638C23—181no—
639C23—181no—
640C23—181no—
641C23—181no—
642C23—181no—
643C23—181no—
644C23—181no—
645C23—181no—
646C23—188no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23—181no—
653C23—364no—
654C23—364no—
655C23—364no—
656C23—364no—
657C23—364no—
658C23C2×C4×D912yes—
659C23D4×D912yes—
660C23#370112yes—
661C23C23×D911yescharacteristic
662D4—188no—
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—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—44no—
681C2×C4—92no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—92no—
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×C4—364no—
700C2×C4C2×C4×D912yes—
701C2×C4C2×C4×D912yes—
702C2×C4D4×D912yes—
703C2×C3—24no—
704C2×C3C2×#89311yescharacteristic
705C2×C3C4×D3×D411yescharacteristic
706C2×C3#554511yescharacteristic
707C2×C3#559011yescharacteristic
708C2×C3#563011yescharacteristic
709C2×C3#563711yescharacteristic
710C2×C3#565411yescharacteristic
711D3—64no—
712D3—122no—
713D3—122no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—94no—
721C22—182no—
722C22—182no—
723C22—182no—
724C22—182no—
725C22—182no—
726C22—182no—
727C22—182no—
728C22—182no—
729C22—182no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22—3616no—
734C22—361no—
735C22—361no—
736C22—361no—
737C22—361no—
738C22—361no—
739C22—361no—
740C22—361no—
741C22—361no—
742C22#6345514yescomplemented
743C22C22×C4×D911yescharacteristic
744C22C2×D4×D911yescharacteristic
745C22C2×D4×D911yescharacteristic
746C22#6371011yescharacteristic
747C22C2×#370111yescharacteristic
748C22#41×D911yescharacteristic
749C22#6371511yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—182no—
757C4—182no—
758C4—182no—
759C4—182no—
760C4—361no—
761C3#7459611yescharacteristic
762C2—24no—
763C2—184no—
764C2—362no—
765C2—362no—
766C2C2×#6345511yescharacteristic
767C2C4×D4×D911yescharacteristic
768C2#1058964711yescharacteristic
769C2#1058969211yescharacteristic
770C2#1058973211yescharacteristic
771C2#1058973911yescharacteristic
772C2#1058975611yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#385C2
prime radicalC2×#63444C2
cosocleC23×C9C24
hypercenter#385D9
hypocenterC9#2358
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×C4×#611C2semidirect
2. C22×(C2×D9)⋊C4C2semidirect
3. C2×#63455C2semidirect
5. C2×C22⋊C4×D9C2semidirect
6. C9×#385C2semidirect
7. #10588670C2semidirect
8. #10588669C2semidirect
9. #10588668C2semidirect
10. #10588638C2semidirect
11. C22⋊C4×Dic9C2semidirect
12. #10588349C2semidirect
13. #10588346C2semidirect
14. #10588345C2semidirect
15. #10588345C2semidirect
25. C22×C4×D9C22semidirect
26. C2×C9×C4⋊C4C22semidirect
27. C2×C9×C4⋊C4C22semidirect
41. C2×(C2×D9)⋊C4C22semidirect
42. C2×(C2×D9)⋊C4C22semidirect
43. C2×(C2×D9)⋊C4C22semidirect
44. C2×Dic9⋊C4C22semidirect
45. C2×C4×Dic9C22semidirect
46. C2×C4×Dic9C22semidirect
47. C2×C4×Dic9C22semidirect
49. #63444C4semidirect
51. C9×#95C22semidirect
52. C9×#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
56. C9⋊#95C22semidirect
79. C23×D9C2×C4semidirect
94. C2×#611C2×C4semidirect
107. C2×D36C2×C4semidirect
108. C2×D36C2×C4semidirect
121. C9×C22⋊C4C2×C4semidirect
122. #3676D4semidirect
131. (C2×D9)⋊C4C2×C4semidirect
132. (C2×D9)⋊C4C2×C4semidirect
133. (C2×D9)⋊C4D4semidirect
268. #385D9semidirect
343. C22×C9C4×D4semidirect
372. C2×D9C4×D4semidirect
397. C2×C4⋊C4C2×D9semidirect
398. C2×C4⋊C4C2×D9semidirect
422. #95C2×D9semidirect
423. #95C2×D9semidirect
574. C22⋊C4C4×D9semidirect
625. C9#2358semidirect
742. C22#63455semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6112
C22×(C2×D9)⋊C42
C2×#634552
C2×#634442
C2×C22⋊C4×D92
C9×#3852
#105886702
#105886692
#105886682
#105886382
C22⋊C4×Dic92
#105883492
#105883462
#105883452
#745963