Finite Group Databasebeta

← #11806090

Subgroups — #11806090

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×#63455C211yesmaximal, characteristic, complemented
2C2×#63444C211yesmaximal, characteristic
3C2×C22⋊C4×D9C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D9C211yesmaximal, characteristic, complemented
5C2×C4×D36C211yesmaximal, characteristic, complemented
6C9×#388C211yesmaximal, characteristic, complemented
7#10588669C211yesmaximal, characteristic, complemented
8#10588637C211yesmaximal, characteristic, complemented
9#10588636C211yesmaximal, characteristic, complemented
10#10588631C211yesmaximal, characteristic, complemented
11C4×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
12#10588348C211yesmaximal, characteristic, complemented
13#10588346C211yesmaximal, characteristic, complemented
14#10588345C211yesmaximal, characteristic, complemented
15#10588345C211yesmaximal, characteristic, complemented
16#75836—31nomaximal
17C24×D9C2211yescharacteristic
18C22×#611C2211yescharacteristic
19C22×D36C2211yescharacteristic
20C22×D36C2211yescharacteristic
21C22×C4×D9C2211yescharacteristic
22C22×C4×D9C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic
24C22×C4×D9C2211yescharacteristic
25C22×C4×D9C2211yescharacteristic, complemented
26C2×C9×C4⋊C4C2211yescharacteristic, complemented
27C2×C9×C22⋊C4C2211yescharacteristic
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C9×C22⋊C4C2211yescharacteristic
30C2×C42×C9C2211yescharacteristic, complemented
31C2×#3676C2211yescharacteristic
32C2×#3676C2211yescharacteristic
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, complemented
40C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C2×C4⋊Dic9C2211yescharacteristic, complemented
43C2×Dic9⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic9C2211yescharacteristic, complemented
45C2×C4×Dic9C2211yescharacteristic, complemented
46#63455—24no—
47#63444C418yescomplemented
48C22⋊C4×D9—24no—
49C22⋊C4×D9—24no—
50C4×D36—24no—
51C9×#95C2211yescharacteristic, complemented
52C9×#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C9⋊#95C2211yescharacteristic, complemented
57C2×#893—31no—
58C2×#882—31no—
59C2×D3×C22⋊C4—31no—
60C2×D3×C22⋊C4—31no—
61C2×C4×D12—31no—
62C3×#388D311yescharacteristic
63#4989—31no—
64#4957—31no—
65#4956—31no—
66#4951—31no—
67C4×(C2×D3)⋊C4—31no—
68#4668—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×C9C2311yescharacteristic
84C22×C4×C9C2311yescharacteristic
85C22×C4×C9C2311yescharacteristic
86C22×C4×C9C2311yescharacteristic
87C22×C4×C9C2311yescharacteristic
88C22×C4×C9C2311yescharacteristic
89C2×#611—41no—
90C2×#611—41no—
91C2×#611C2×C414yescomplemented
92C22×Dic9C2311yescharacteristic
93C22×Dic9C2311yescharacteristic
94C22×Dic9C2311yescharacteristic
95C22×Dic9C2311yescharacteristic
96C22×Dic9C2311yescharacteristic
97C2×D36—22no—
98C2×D36—22no—
99C2×D36—22no—
100C2×D36—22no—
101C2×D36C2×C414yescomplemented
102C2×D36C2×C414yescomplemented
103C2×C4×D9—22no—
104C2×C4×D9—22no—
105C2×C4×D9—22no—
106C2×C4×D9—22no—
107C2×C4×D9—22no—
108C2×C4×D9—22no—
109C2×C4×D9—22no—
110C2×C4×D9—22no—
111C2×C4×D9—22no—
112C2×C4×D9—22no—
113C2×C4×D9—41no—
114C2×C4×D9—41no—
115C2×C4×D9—41no—
116C2×C4×D9—41no—
117C2×C4×D9—41no—
118C9×C4⋊C4—22no—
119C9×C22⋊C4—22no—
120C9×C22⋊C4—22no—
121C9×C22⋊C4C2×C414yescomplemented
122C42×C9—22no—
123#3676—22no—
124#3676—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—41no—
130(C2×D9)⋊C4C2×C414yescomplemented
131(C2×D9)⋊C4C2×C414yescomplemented
132(C2×D9)⋊C4D414yescomplemented
133(C2×D9)⋊C4D414yescomplemented
134C4⋊Dic9—22no—
135Dic9⋊C4—41no—
136C4×Dic9—22no—
137C4×Dic9—41no—
138#2358—91noSylow
139C24×D3—31no—
140C22×#67—31no—
141C22×D12—31no—
142C22×D12—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C22⋊C4C2×D311yescharacteristic
150C2×C3×C22⋊C4C2×D311yescharacteristic
151C2×C3×C22⋊C4C2×D311yescharacteristic
152C2×C3×C42C2×D311yescharacteristic
153C2×#217—31no—
154C2×#217—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×C4⋊Dic3—31no—
165C2×Dic3⋊C4—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168#893—64no—
169#882—38no—
170D3×C22⋊C4—64no—
171D3×C22⋊C4—64no—
172C4×D12—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×C9—21no—
184C23×C9—21no—
185C23×C9C22×C412yes—
186C23×C9C2411yescharacteristic
187C22×D9—21no—
188C22×D9—21no—
189C22×D9—21no—
190C22×D9—21no—
191C22×D9—21no—
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—28no—
202C22×D9—28no—
203C22×D9—44no—
204C22×D9—44no—
205C22×D9—44no—
206C22×D9—44no—
207C22×D9—44no—
208C22×D9C22×C412yes—
209C22×D9C22×C412yes—
210C22×D9C22×C412yes—
211C22×D9C2×D412yes—
212C22×D9C2×D412yes—
213C22×D9#4112yes—
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×C9C22×C412yes—
230C2×C4×C9C22×C412yes—
231C2×C4×C9C2×D412yes—
232C2×C4×C9C2×D412yes—
233#611—44no—
234C2×Dic9—21no—
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×Dic9C22×C412yes—
247C2×Dic9C2×D412yes—
248C2×Dic9C2×D412yes—
249D36—28no—
250D36—28no—
251C4×D9—44no—
252C4×D9—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#388D911yescharacteristic, complemented
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
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×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—34no—
289C2×#67—121no—
290C2×#67—121no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C2×D12—34no—
297C2×D12—34no—
298C2×D12—62no—
299C2×D12—62no—
300C2×D12—62no—
301C2×D12—62no—
302C2×C4×D3—62no—
303C2×C4×D3—62no—
304C2×C4×D3—62no—
305C2×C4×D3—62no—
306C2×C4×D3—62no—
307C2×C4×D3—62no—
308C2×C4×D3—62no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×C4×D3—121no—
313C2×C4×D3—121no—
314C2×C4×D3—121no—
315C2×C4×D3—121no—
316C2×C4×D3—121no—
317C3×C4⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4C4×D314yes—
321C3×C42—22no—
322#217—62no—
323#217—62no—
324(C2×D3)⋊C4—34no—
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—121no—
333C4⋊Dic3—62no—
334Dic3⋊C4—121no—
335C4×Dic3—62no—
336C4×Dic3—121no—
337C22×C9—22no—
338C22×C9—22no—
339C22×C9—22no—
340C22×C9—41no—
341C22×C9—41no—
342C22×C9—41no—
343C22×C9—41no—
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—22no—
364C2×D9—22no—
365C2×D9—22no—
366C2×D9—416no—
367C2×D9—41no—
368C2×D9—41no—
369C2×D9—41no—
370C2×D9—41no—
371C2×D9C4×D414yescomplemented
372C2×D9C4×D414yescomplemented
373C4×C9—22no—
374C4×C9—22no—
375C4×C9—22no—
376C4×C9—22no—
377C4×C9—41no—
378C4×C9—41no—
379Dic9—22no—
380Dic9—22no—
381Dic9—22no—
382Dic9—41no—
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×C4—91no—
393#120—98no—
394C4×D4—184no—
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—184no—
411C2×C22⋊C4—184no—
412C2×C22⋊C4C2×D911yescharacteristic
413C2×C22⋊C4C2×D911yescharacteristic
414C2×C22⋊C4C2×D911yescharacteristic
415C2×C42—91no—
416C2×C42—91no—
417C2×C42C2×D911yescharacteristic, complemented
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×C3—21no—
429C23×C3—21no—
430C23×C3C2×C4×D312yes—
431C23×C3C23×D311yescharacteristic
432C22×D3—32no—
433C22×D3—32no—
434C22×D3—32no—
435C22×D3—32no—
436C22×D3—32no—
437C22×D3—32no—
438C22×D3—32no—
439C22×D3—68no—
440C22×D3—68no—
441C22×D3—61no—
442C22×D3—61no—
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×C4C2×C4×D312yes—
475C2×C3×C4C2×C4×D312yes—
476C2×C3×C4D3×D412yes—
477C2×C3×C4D3×D412yes—
478#67—124no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—61no—
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—
494D12—68no—
495D12—68no—
496C4×D3—124no—
497C4×D3—124no—
498C4×D3—124no—
499C4×D3—124no—
500C4×D3—124no—
501C2×C9—42no—
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—24no—
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—91no—
533C22×C4—91no—
534C22×C4—91no—
535C22×C4—91no—
536C22×C4—91no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4—182no—
540C22×C4—182no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4—182no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—361no—
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—182no—
560C4⋊C4—361no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—94no—
564C22⋊C4—94no—
565C22⋊C4—94no—
566C22⋊C4—94no—
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—22no—
576C42—182no—
577C42—361no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3C22×C4×D311yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C22×C3C2×D3×D411yescharacteristic
588C22×C3D3×#4111yescharacteristic
589C22×C3D3×#4111yescharacteristic
590C22×C3#100911yescharacteristic
591C22×C3#100911yescharacteristic
592C2×D3—34no—
593C2×D3—34no—
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—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—
619C3×C4—41no—
620Dic3—62no—
621Dic3—62no—
622Dic3—62no—
623Dic3—121no—
624Dic3—121no—
625C9#235811yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—92no—
633C23—92no—
634C23—92no—
635C23—92no—
636C23—92no—
637C23—92no—
638C23—92no—
639C23—188no—
640C23—188no—
641C23—181no—
642C23—181no—
643C23—181no—
644C23—181no—
645C23—181no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23—181no—
653C23—181no—
654C23—181no—
655C23—364no—
656C23—364no—
657C23—364no—
658C23—364no—
659C23—364no—
660C23C2×C4×D912yes—
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—92no—
680C2×C4—92no—
681C2×C4—92no—
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—364no—
695C2×C4—364no—
696C2×C4—364no—
697C2×C4—364no—
698C2×C4—364no—
699C2×C4C2×C4×D912yes—
700C2×C4C2×C4×D912yes—
701C2×C4D4×D912yes—
702C2×C4D4×D912yes—
703C2×C3—42no—
704C2×C3#552111yescharacteristic
705C2×C3C4×D3×D411yescharacteristic
706C2×C3C4×D3×D411yescharacteristic
707C2×C3#560911yescharacteristic
708C2×C3#565411yescharacteristic
709C2×C3#567611yescharacteristic
710C2×C3#570511yescharacteristic
711D3—64no—
712D3—64no—
713D3—122no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—94no—
722C22—94no—
723C22—182no—
724C22—182no—
725C22—182no—
726C22—182no—
727C22—182no—
728C22—182no—
729C22—182no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22—182no—
734C22—182no—
735C22—182no—
736C22—182no—
737C22—182no—
738C22—3616no—
739C22—361no—
740C22—361no—
741C22—361no—
742C22—361no—
743C22C22×C4×D911yescharacteristic
744C22C2×D4×D911yescharacteristic
745C22C2×D4×D911yescharacteristic
746C22#41×D911yescharacteristic
747C22#41×D911yescharacteristic
748C22#6371511yescharacteristic
749C22#6371511yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—182no—
757C4—182no—
758C4—182no—
759C4—361no—
760C4—361no—
761C3#7583611yescharacteristic
762C2—42no—
763C2—184no—
764C2—184no—
765C2—362no—
766C2#1058962311yescharacteristic
767C2C4×D4×D911yescharacteristic
768C2C4×D4×D911yescharacteristic
769C2#1058971111yescharacteristic
770C2#1058975611yescharacteristic
771C2#1058977811yescharacteristic
772C2#1058980711yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#388C2
prime radicalC2×#63444C2
cosocleC23×C9C24
hypercenter#388D9
hypocenterC9#2358
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#63455C2semidirect
3. C2×C22⋊C4×D9C2semidirect
4. C2×C22⋊C4×D9C2semidirect
5. C2×C4×D36C2semidirect
6. C9×#388C2semidirect
7. #10588669C2semidirect
8. #10588637C2semidirect
9. #10588636C2semidirect
10. #10588631C2semidirect
11. C4×(C2×D9)⋊C4C2semidirect
12. #10588348C2semidirect
13. #10588346C2semidirect
14. #10588345C2semidirect
15. #10588345C2semidirect
25. C22×C4×D9C22semidirect
26. C2×C9×C4⋊C4C22semidirect
30. C2×C42×C9C22semidirect
39. C2×(C2×D9)⋊C4C22semidirect
40. C2×(C2×D9)⋊C4C22semidirect
41. C2×(C2×D9)⋊C4C22semidirect
42. C2×C4⋊Dic9C22semidirect
43. C2×Dic9⋊C4C22semidirect
44. C2×C4×Dic9C22semidirect
45. C2×C4×Dic9C22semidirect
47. #63444C4semidirect
51. C9×#95C22semidirect
52. C9×#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
56. C9⋊#95C22semidirect
79. C23×D9C2×C4semidirect
91. C2×#611C2×C4semidirect
101. C2×D36C2×C4semidirect
102. C2×D36C2×C4semidirect
121. C9×C22⋊C4C2×C4semidirect
130. (C2×D9)⋊C4C2×C4semidirect
131. (C2×D9)⋊C4C2×C4semidirect
132. (C2×D9)⋊C4D4semidirect
133. (C2×D9)⋊C4D4semidirect
263. #388D9semidirect
371. C2×D9C4×D4semidirect
372. C2×D9C4×D4semidirect
398. C2×C4⋊C4C2×D9semidirect
417. C2×C42C2×D9semidirect
422. #95C2×D9semidirect
423. #95C2×D9semidirect
574. C22⋊C4C4×D9semidirect
625. C9#2358semidirect

Maximal subgroups

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

subgroupindex
C2×#634552
C2×#634442
C2×C22⋊C4×D92
C2×C4×D362
C9×#3882
#105886692
#105886372
#105886362
#105886312
C4×(C2×D9)⋊C42
#105883482
#105883462
#105883452
#758363