Finite Group Databasebeta

← #11807839

Subgroups — #11807839

Order 1152.

1021 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2#10592928C211yesmaximal, characteristic, complemented
3C3×#5229C211yesmaximal, characteristic, complemented
4#10591316C211yesmaximal, characteristic
5#10591307C211yesmaximal, characteristic
6#10591305C211yesmaximal, characteristic
7#10591295C211yesmaximal, characteristic
8#10591294C211yesmaximal, characteristic
9#10591286C211yesmaximal, characteristic
10#10591270C211yesmaximal, characteristic, complemented
11#10591269C211yesmaximal, characteristic, complemented
12#10591268C211yesmaximal, characteristic, complemented
13#10591265C211yesmaximal, characteristic, complemented
14#10591201C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82750—31nomaximal
17#76617—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C3×#946C418yescomplemented
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×C22⋊Q8—31no—
55C2×#946D311yescharacteristic
56C3×#391—31no—
57#5229—31no—
58#5229—31no—
59#5229—61no—
60#5229D311yescharacteristic, complemented
61#5212—31no—
62#5211—31no—
63#4990—31no—
64#4984—31no—
65#4984—31no—
66#4980—31no—
67#4980—31no—
68#4980—31no—
69#4980—31no—
70#4976—31no—
71#4951—31no—
72#4951—31no—
73#4951—31no—
74#4951—31no—
75#4940—31no—
76#4933—31no—
77#4670—31no—
78#4669—31no—
79#4667—31no—
80#4664—31no—
81#4654—31no—
82#4653—31no—
83#4652—31no—
84#4647—31no—
85C23×C3×D3C2311yescharacteristic
86C2×C32×Q8—41no—
87C2×C32×Q8—41no—
88C2×C32×Q8C2×C414yes—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3C2×C414yes—
106C4⋊(C3⋊Dic3)—41no—
107C4×C3⋊Dic3—41no—
108C3×(C2×D3)⋊C4C2×C414yes—
109C3×(C2×D3)⋊C4C2×C414yes—
110C3×C4⋊Dic3—41no—
111C3×C4⋊Dic3C2×C414yes—
112C3×Dic3⋊C4C2×C414yes—
113C3×Dic3⋊C4C2×C414yes—
114C3×C4×Dic3—41no—
115Dic3⋊Dic3—41no—
116Dic3⋊Dic3—41no—
117Dic3⋊Dic3—41no—
118Dic3⋊Dic3—41no—
119(C2×D3)⋊Dic3—41no—
120(C2×D3)⋊Dic3—41no—
121(C2×D3)⋊Dic3—41no—
122(C2×D3)⋊Dic3—41no—
123Dic32—41no—
124Dic32—41no—
125#2378—91noSylow
126C22×C3×Q8—21no—
127C22×C3×Q8C2×D311yescharacteristic
128C22×C3×Q8C2×D311yescharacteristic
129C23×C3×C4—31no—
130C22×C4×D3C2×D311yescharacteristic
131C3×C22⋊Q8—38no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C42—31no—
139C2×#217—31no—
140C2×#217—31no—
141C2×#217—31no—
142C2×#217—31no—
143#946Dic318yescomplemented
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4C2×D311yescharacteristic
149C2×(C2×D3)⋊C4C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—61no—
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D311yescharacteristic
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4C2×D311yescharacteristic
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—61no—
172C2×C4×Dic3C2×D311yescharacteristic
173C3×#95—31no—
174C3×#95—31no—
175C3×#95—31no—
176C3×#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—61no—
198C3⋊#95—61no—
199C3⋊#95—61no—
200C3⋊#95—61no—
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3C22×C412yes—
213C32×Q8—44no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4C22×C412yes—
221C2×C32×C4C22×C412yes—
222C2×C32×C4C22×C412yes—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C2×C3×Dic3C22×C412yes—
256C3×C4×D3—44no—
257C2×C22⋊Q8—31no—
258#391—31no—
259#391—91no—
260#389—91no—
261#389—91no—
262#388—91no—
263#388—91no—
264#388—91no—
265#388—91no—
266#387—91no—
267#387—91no—
268#387—91no—
269#387—91no—
270#381—91no—
271#380—91no—
272C24×C3—31no—
273C23×D3C22×D311yescharacteristic
274C2×C3×Q8—24no—
275C2×C3×Q8—41no—
276C2×C3×Q8—41no—
277C2×C3×Q8—41no—
278C2×C3×Q8—41no—
279C2×C3×Q8—42no—
280C2×C3×Q8—42no—
281C2×C3×Q8C4×D314yes—
282C2×C3×Q8C2×Dic314yes—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—34no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—121no—
295C22×C3×C4—121no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C2×C4×D3—41no—
322C2×C4×D3—41no—
323C2×C4×D3C2×Dic314yes—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—121no—
328C3×C22⋊C4—34no—
329C3×C22⋊C4—34no—
330C3×C42—121no—
331#217—121no—
332#217—121no—
333#217—121no—
334#217—121no—
335(C2×D3)⋊C4—121no—
336(C2×D3)⋊C4—121no—
337(C2×D3)⋊C4—121no—
338(C2×D3)⋊C4—121no—
339(C2×D3)⋊C4C2×Dic314yes—
340(C2×D3)⋊C4C2×Dic314yes—
341C4⋊Dic3—41no—
342C4⋊Dic3—121no—
343C4⋊Dic3—121no—
344C4⋊Dic3—121no—
345C4⋊Dic3—121no—
346C4⋊Dic3—121no—
347C4⋊Dic3—121no—
348C4⋊Dic3—122no—
349C4⋊Dic3C2×Dic314yes—
350Dic3⋊C4—121no—
351Dic3⋊C4—121no—
352Dic3⋊C4—121no—
353Dic3⋊C4—121no—
354Dic3⋊C4C2×Dic314yes—
355Dic3⋊C4C2×Dic314yes—
356C4×Dic3—41no—
357C4×Dic3—121no—
358C4×Dic3—121no—
359C4×Dic3—121no—
360C4×Dic3—121no—
361C4×Dic3—121no—
362C4×Dic3—121no—
363C4×Dic3—122no—
364C22×C32C23×C411yescharacteristic
365C22×C32H(5,𝔽2)11yescharacteristic
366C22×C32H(5,𝔽2)11yescharacteristic
367C22×C32H(5,𝔽2)11yescharacteristic
368C22×C322−1+411yescharacteristic
369C22×C322−1+411yescharacteristic
370C22×C322−1+411yescharacteristic
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—41no—
375C2×C3×D3—41no—
376C2×C3×D3—41no—
377C2×C3×D3—41no—
378C32×C4—22no—
379C32×C4—22no—
380C32×C4—22no—
381C3⋊Dic3—41no—
382C3⋊Dic3—41no—
383C3⋊Dic3—41no—
384C3⋊Dic3—41no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C22×Q8D3211yescharacteristic
393C23×C4—31no—
394C22⋊Q8—38no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4—91no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C42—31no—
411C2×C42—91no—
412C2×C42—91no—
413C2×C42—91no—
414#95—31no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427#95—91no—
428C23×C3—21no—
429C23×C3—32no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—61no—
434C23×C3—61no—
435C23×C3—61no—
436C23×C3C23×D311yescharacteristic
437C23×C3C23×D311yescharacteristic
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3C22×Dic312yes—
445C3×Q8—44no—
446C3×Q8—44no—
447C3×Q8—48no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—124no—
491C2×C3×C4C2×C4×D312yes—
492C2×C3×C4C2×C4×D312yes—
493C2×C3×C4C2×C4×D312yes—
494C2×C3×C4C22×Dic312yes—
495C2×C3×C4C22×Dic312yes—
496C2×C3×C4C22×Dic312yes—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—62no—
516C2×Dic3—62no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3C22×Dic312yes—
552C2×Dic3C22×Dic312yes—
553C2×Dic3C22×Dic312yes—
554C4×D3—44no—
555C2×C32#51811yescharacteristic
556C2×C32#51911yescharacteristic
557C2×C32#52011yescharacteristic
558C2×C32#56211yescharacteristic
559C2×C32#56211yescharacteristic
560C2×C32#56311yescharacteristic
561C2×C32#56311yescharacteristic
562C3×D3—42no—
563C24—31no—
564C2×Q8—41no—
565C2×Q8—41no—
566C2×Q8D3×Dic314yes—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—34no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—121no—
580C22×C4—121no—
581C22×C4C2×D3211yescharacteristic
582C22×C4C2×D3211yescharacteristic
583C22×C4C2×D3211yescharacteristic
584C4⋊C4—34no—
585C4⋊C4—34no—
586C4⋊C4—34no—
587C4⋊C4—121no—
588C4⋊C4—361no—
589C4⋊C4—361no—
590C4⋊C4—361no—
591C4⋊C4—361no—
592C4⋊C4—361no—
593C22⋊C4—34no—
594C22⋊C4—34no—
595C22⋊C4—361no—
596C22⋊C4—361no—
597C22⋊C4—361no—
598C22⋊C4—361no—
599C42—121no—
600C42—361no—
601C42—361no—
602C42—361no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—62no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3C22×C4×D311yescharacteristic
618C22×C3#100411yescharacteristic
619C22×C3#100411yescharacteristic
620C22×C3#100411yescharacteristic
621C22×C3#100411yescharacteristic
622C22×C3#100711yescharacteristic
623C22×C3#100711yescharacteristic
624C22×C3#100711yescharacteristic
625C22×C3#100711yescharacteristic
626C22×C3#100911yescharacteristic
627C22×C3#100911yescharacteristic
628C22×C3#101011yescharacteristic
629C22×C3#101011yescharacteristic
630C22×C3C23×Dic311yescharacteristic
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C3×C4—24no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—62no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654Dic3—22no—
655Dic3—22no—
656Dic3—22no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—122no—
662Dic3—122no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—241no—
672Dic3—241no—
673C32#237811yescharacteristic, complemented, Sylow
674C23—32no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23C22×D3211yescharacteristic
682Q8—44no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—124no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4C2×D3×Dic312yes—
724C2×C4C2×D3×Dic312yes—
725C2×C4C2×D3×Dic312yes—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—122no—
734C2×C3#548611yescharacteristic
735C2×C3#557211yescharacteristic
736C2×C3#557411yescharacteristic
737C2×C3#564611yescharacteristic
738C2×C3#564611yescharacteristic
739C2×C3#564611yescharacteristic
740C2×C3#564711yescharacteristic
741C2×C3#564711yescharacteristic
742C2×C3#564711yescharacteristic
743C2×C3#568411yescharacteristic
744C2×C3#573511yescharacteristic
745C2×C3#579811yescharacteristic
746C2×C3#581211yescharacteristic
747C2×C3#582711yescharacteristic
748D3—42no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22#6431511yescharacteristic
757C22#6431511yescharacteristic
758C22#6431611yescharacteristic
759C22#6432011yescharacteristic
760C22C22×D3×Dic311yescharacteristic
761C22#6433011yescharacteristic
762C22#6433011yescharacteristic
763C4—22no—
764C4—22no—
765C4—22no—
766C4—62no—
767C4—62no—
768C4—62no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—361no—
774C4—361no—
775C4—361no—
776C4—361no—
777C3—21no—
778C3#7661711yescharacteristic, complemented
779C3#8275011yescharacteristic, complemented
780C2—122no—
781C2#1059534511yescharacteristic
782C2#1059534711yescharacteristic
783C2#1059539411yescharacteristic
784C2#1059541611yescharacteristic
785C2#1059541711yescharacteristic
786C2#1059541811yescharacteristic
787C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #10592928C2semidirect
3. C3×#5229C2semidirect
10. #10591270C2semidirect
11. #10591269C2semidirect
12. #10591268C2semidirect
13. #10591265C2semidirect
14. #10591201C2semidirect
15. #10591192C2semidirect
22. C3×#946C4semidirect
60. #5229D3semidirect
143. #946Dic3semidirect
673. C32#2378semidirect
778. C3#76617semidirect
779. C3#82750semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9462
#105929282
C3×#52292
#105913162
#105913072
#105913052
#105912952
#105912942
#105912862
#105912702
#105912692
#105912682
#105912652
#105912012
#105911922
#827503
#766173