Finite Group Databasebeta

← #11802427

Subgroups — #11802427

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#879C211yesmaximal, characteristic
2C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
3C3×#4951C211yesmaximal, characteristic
4#10591705C211yesmaximal, characteristic
5#10591705C211yesmaximal, characteristic
6#10591702C211yesmaximal, characteristic
7#10591701C211yesmaximal, characteristic
8#10591274C211yesmaximal, characteristic, complemented
9#10591270C211yesmaximal, characteristic, complemented
10#10591262C211yesmaximal, characteristic, complemented
11#10591241C211yesmaximal, characteristic, complemented
12#10591241C211yesmaximal, characteristic, complemented
13C4×Dic32C211yesmaximal, characteristic, complemented
14#10591223C211yesmaximal, characteristic, complemented
15#10591201C211yesmaximal, characteristic, complemented
16Dic3×#126—31nomaximal
17#75455—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#879C418yescomplemented
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#126—31no—
55C2×#879D311yescharacteristic
56C3×#388—31no—
57#4980—31no—
58#4980—31no—
59#4980—31no—
60#4978—31no—
61Dic3×C4⋊C4—31no—
62Dic3×C4⋊C4—31no—
63Dic3×C4⋊C4—31no—
64Dic3×C4⋊C4—31no—
65#4951—31no—
66#4951—31no—
67#4951D311yescharacteristic
68#4945—31no—
69#4944—31no—
70Dic3×C22⋊C4—31no—
71Dic3×C22⋊C4—31no—
72Dic3×C22⋊C4—31no—
73Dic3×C22⋊C4—31no—
74Dic3×C22⋊C4—31no—
75Dic3×C22⋊C4—31no—
76Dic3×C22⋊C4—61no—
77#4937—31no—
78#4933—31no—
79C42×Dic3—31no—
80C42×Dic3—31no—
81#4654—31no—
82#4651—31no—
83#4649—31no—
84#4649—31no—
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3—22no—
89C22×C3⋊Dic3—22no—
90C22×C3⋊Dic3—22no—
91C22×C3⋊Dic3C2311yescharacteristic
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
103C32×C22⋊C4C2×C414yes—
104#3757—22no—
105C4×C3⋊Dic3—22no—
106C4×C3⋊Dic3—22no—
107C3×#217—22no—
108C3×#217—22no—
109C3×#217C2×C414yes—
110C3×#217C2×C414yes—
111C3×C4⋊Dic3—22no—
112C3×C4⋊Dic3C2×C414yescomplemented
113C3×Dic3⋊C4C2×C414yescomplemented
114C3×Dic3⋊C4C2×C414yescomplemented
115C3×C4×Dic3—22no—
116C3×C4×Dic3C2×C414yescomplemented
117Dic3⋊Dic3—22no—
118Dic3⋊Dic3—22no—
119Dic32—22no—
120Dic32—22no—
121Dic32—22no—
122Dic32—22no—
123Dic32—22no—
124Dic32—22no—
125C4×#126—91noSylow
126C23×Dic3—31no—
127C23×Dic3—31no—
128C23×Dic3—61no—
129C3×#126—38no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4C2×D311yescharacteristic
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—61no—
146C2×#217C2×D311yescharacteristic
147C2×#217C2×D311yescharacteristic
148C2×#217C2×D311yescharacteristic
149C2×#217C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3C2×D311yescharacteristic
153C2×C4⋊Dic3C2×D311yescharacteristic
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4C2×D311yescharacteristic
157C2×Dic3⋊C4C2×D311yescharacteristic
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
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—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3—61no—
176C2×C4×Dic3C2×D311yescharacteristic
177C2×C4×Dic3C2×D311yescharacteristic
178#879Dic318yescomplemented
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—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—61no—
202C3⋊#95—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32C22×C412yes—
212C23×C32C2411yescharacteristic
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4C22×C412yes—
218C2×C32×C4C22×C412yes—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—44no—
228C2×C3⋊Dic3#4112yes—
229C2×C3⋊Dic3#4112yes—
230C2×C3⋊Dic3#4112yes—
231C2×C3⋊Dic3#4112yes—
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×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3#4112yes—
255C2×C3×Dic3#4112yes—
256C2×#126—31no—
257#388—31no—
258#388—91no—
259#388—91no—
260#387—91no—
261#387—91no—
262#387—91no—
263#383—91no—
264C4×C4⋊C4—91no—
265C4×C4⋊C4—91no—
266C4×C4⋊C4—91no—
267C4×C22⋊C4—91no—
268C4×C22⋊C4—91no—
269C4×C22⋊C4—91no—
270C43—91no—
271C24×C3—21no—
272C24×C3C22×D311yescharacteristic
273C24×C3C22×D311yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—62no—
301C22×Dic3—62no—
302C22×Dic3—62no—
303C22×Dic3—62no—
304C22×Dic3—62no—
305C22×Dic3—62no—
306C22×Dic3—64no—
307C22×Dic3—122no—
308C22×Dic3—122no—
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C3×C4⋊C4—34no—
318C3×C4⋊C4—34no—
319C3×C4⋊C4—34no—
320C3×C4⋊C4—62no—
321C3×C22⋊C4—24no—
322C3×C22⋊C4—34no—
323C3×C22⋊C4—34no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—62no—
326C3×C22⋊C4C4×D314yes—
327C3×C22⋊C4C2×Dic314yes—
328C3×C42—34no—
329C3×C42—62no—
330#217—22no—
331#217—22no—
332#217—62no—
333#217—62no—
334#217—64no—
335#217C2×Dic314yes—
336#217C2×Dic314yes—
337C4⋊Dic3—22no—
338C4⋊Dic3—62no—
339C4⋊Dic3—62no—
340C4⋊Dic3C2×Dic314yescomplemented
341Dic3⋊C4—62no—
342Dic3⋊C4—62no—
343Dic3⋊C4C2×Dic314yescomplemented
344Dic3⋊C4C2×Dic314yescomplemented
345C4×Dic3—22no—
346C4×Dic3—62no—
347C4×Dic3—62no—
348C4×Dic3—62no—
349C4×Dic3—62no—
350C4×Dic3—62no—
351C4×Dic3—62no—
352C4×Dic3—62no—
353C4×Dic3—62no—
354C4×Dic3—62no—
355C4×Dic3—62no—
356C4×Dic3—62no—
357C4×Dic3—62no—
358C4×Dic3—62no—
359C4×Dic3—62no—
360C4×Dic3—62no—
361C4×Dic3—62no—
362C4×Dic3—122no—
363C4×Dic3—122no—
364C4×Dic3C2×Dic314yescomplemented
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—41no—
369C22×C32—41no—
370C22×C32—41no—
371C22×C32—41no—
372C22×C32C23×C411yescharacteristic
373C22×C32C2×#4111yescharacteristic
374C22×C32C2×#4111yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C22×C32C2×#4111yescharacteristic
378C22×C32C2×#4111yescharacteristic
379C32×C4—22no—
380C32×C4—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—41no—
383C3⋊Dic3—41no—
384C3⋊Dic3#12614yescomplemented
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—22no—
390C3×Dic3—22no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C23×C4—91no—
394#126—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×C22⋊C4—31no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4D3211yescharacteristic
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—91no—
410C2×C42—91no—
411C2×C42—91no—
412C2×C42—91no—
413C2×C42—91no—
414C2×C42—91no—
415C2×C42—91no—
416C2×C42—91no—
417#95—31no—
418#95—31no—
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—
428#95—91no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—22no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3C2×C4×D312yes—
450C23×C3C22×Dic312yes—
451C23×C3C23×D311yescharacteristic
452C23×C3C23×D311yescharacteristic
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—22no—
462C2×C3×C4—22no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
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—61no—
491C2×C3×C4C2×C4×D312yes—
492C2×C3×C4C2×C4×D312yes—
493C2×C3×C4C22×Dic312yes—
494C2×C3×C4C22×Dic312yes—
495C2×Dic3—21no—
496C2×Dic3—21no—
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—32no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—62no—
530C2×Dic3—62no—
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—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—124no—
550C2×Dic3—124no—
551C2×Dic3—128no—
552C2×Dic3#23712yes—
553C2×Dic3#23712yes—
554C2×Dic3C22×Dic312yes—
555C2×Dic3C22×Dic312yes—
556C2×Dic3C22×Dic312yes—
557C2×Dic3C22×Dic312yes—
558C2×C32—42no—
559C2×C32C4×#4111yescharacteristic
560C2×C32C4×#4111yescharacteristic
561C2×C32C4×#4111yescharacteristic
562C2×C32C2×#12611yescharacteristic
563C2×C32#52911yescharacteristic
564C2×C32#52911yescharacteristic
565C2×C32#52911yescharacteristic
566C24C2×D3211yescharacteristic
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
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—182no—
580C22×C4—182no—
581C22×C4—182no—
582C22×C4C2×D3211yescharacteristic
583C22×C4C2×D3211yescharacteristic
584C4⋊C4—34no—
585C4⋊C4—34no—
586C4⋊C4—34no—
587C4⋊C4—62no—
588C4⋊C4—182no—
589C4⋊C4—182no—
590C22⋊C4—34no—
591C22⋊C4—34no—
592C22⋊C4—62no—
593C22⋊C4—62no—
594C22⋊C4—182no—
595C22⋊C4D3×Dic314yes—
596C42—34no—
597C42—62no—
598C42—182no—
599C42—182no—
600C42—182no—
601C42—182no—
602C42—182no—
603C42—182no—
604C42—182no—
605C42—182no—
606C22×C3—24no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3C22×C4×D311yescharacteristic
635C22×C3C2×#23711yescharacteristic
636C22×C3C2×#23711yescharacteristic
637C22×C3D3×#4111yescharacteristic
638C22×C3D3×#4111yescharacteristic
639C22×C3D3×#4111yescharacteristic
640C22×C3D3×#4111yescharacteristic
641C22×C3D3×#4111yescharacteristic
642C22×C3D3×#4111yescharacteristic
643C22×C3D3×#4111yescharacteristic
644C22×C3D3×#4111yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C22×C3C23×Dic311yescharacteristic
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—62no—
657C3×C4—62no—
658C3×C4—62no—
659C3×C4—62no—
660C3×C4—121no—
661C3×C4—121no—
662Dic3—22no—
663Dic3—22no—
664Dic3—22no—
665Dic3—22no—
666Dic3—22no—
667Dic3—22no—
668Dic3—34no—
669Dic3—34no—
670Dic3—41no—
671Dic3—41no—
672Dic3—64no—
673Dic3—62no—
674Dic3—62no—
675Dic3—122no—
676Dic3—122no—
677Dic3—122no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682C32C4×#12611yescharacteristic, complemented, Sylow
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23C2×D3×Dic312yes—
690C23C22×D3211yescharacteristic
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—32no—
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—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—92no—
720C2×C4—92no—
721C2×C4—92no—
722C2×C4—92no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—364no—
732C2×C4C2×D3×Dic312yes—
733C2×C4C2×D3×Dic312yes—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—44no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3#552211yescharacteristic
745C2×C3C4×#23711yescharacteristic
746C2×C3C4×#23711yescharacteristic
747C2×C3#560011yescharacteristic
748C2×C3#564911yescharacteristic
749C2×C3#568011yescharacteristic
750C2×C3D3×#12611yescharacteristic
751C2×C3D3×#12611yescharacteristic
752C2×C3#570611yescharacteristic
753C2×C3#570611yescharacteristic
754C2×C3#570611yescharacteristic
755C2×C3Dic3×#4111yescharacteristic
756C2×C3Dic3×#4111yescharacteristic
757C2×C3Dic3×#4111yescharacteristic
758C22—22no—
759C22—22no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22#6430611yescharacteristic
766C22#6430611yescharacteristic
767C22D3×#23711yescharacteristic
768C22D3×#23711yescharacteristic
769C22#6431211yescharacteristic
770C22#6431211yescharacteristic
771C22C22×D3×Dic311yescharacteristic
772C4—22no—
773C4—22no—
774C4—62no—
775C4—62no—
776C4—62no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—94no—
781C4—121no—
782C4—121no—
783C4—182no—
784C4—361no—
785C4—361no—
786C3—21no—
787C3#7545511yescharacteristic, complemented
788C3Dic3×#12611yescharacteristic, complemented
789C2—42no—
790C2#1059411211yescharacteristic
791C2#1059413011yescharacteristic
792C2#1059413711yescharacteristic
793C2#1059415411yescharacteristic
794C2#1059495811yescharacteristic
795C2Dic3×#23711yescharacteristic
796C2Dic3×#23711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591274C2semidirect
9. #10591270C2semidirect
10. #10591262C2semidirect
11. #10591241C2semidirect
12. #10591241C2semidirect
13. C4×Dic32C2semidirect
14. #10591223C2semidirect
15. #10591201C2semidirect
33. C3×#879C4semidirect
112. C3×C4⋊Dic3C2×C4semidirect
113. C3×Dic3⋊C4C2×C4semidirect
114. C3×Dic3⋊C4C2×C4semidirect
116. C3×C4×Dic3C2×C4semidirect
178. #879Dic3semidirect
340. C4⋊Dic3C2×Dic3semidirect
343. Dic3⋊C4C2×Dic3semidirect
344. Dic3⋊C4C2×Dic3semidirect
364. C4×Dic3C2×Dic3semidirect
384. C3⋊Dic3#126semidirect
682. C32C4×#126semidirect
787. C3#75455semidirect
788. C3Dic3×#126semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8792
C22⋊C4×C3⋊Dic32
C3×#49512
#105917052
#105917022
#105917012
#105912742
#105912702
#105912622
#105912412
C4×Dic322
#105912232
#105912012
Dic3×#1263
#754553