Finite Group Databasebeta

← #11803935

Subgroups — #11803935

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63982C211yesmaximal, characteristic
2#10592641C211yesmaximal, characteristic
3C3×#4946C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic
5#10591718C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#10591332C211yesmaximal, characteristic, complemented
9#10591330C211yesmaximal, characteristic, complemented
10#10591251C211yesmaximal, characteristic, complemented
11#10591249C211yesmaximal, characteristic, complemented
12#10591235C211yesmaximal, characteristic, complemented
13#10591234C211yesmaximal, characteristic, complemented
14#10591193C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#74387—31nomaximal
17#73447—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32#63982C418yescomplemented
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#878—31no—
55C2×#878—31no—
56C3×#385—31no—
57C3×C4×C22⋊C4—31no—
58#5210—31no—
59C4×#217—31no—
60C2×C3⋊#95—31no—
61C2×C3⋊#95—31no—
62#4978—31no—
63#4976—31no—
64#4973—31no—
65#4972—31no—
66#4950—31no—
67#4946D311yescharacteristic
68#4942—31no—
69#4942—31no—
70#4942—61no—
71Dic3×C22⋊C4—31no—
72Dic3×C22⋊C4D311yescharacteristic
73#4933—31no—
74#4933—31no—
75#4929—31no—
76#4928—31no—
77#4655—31no—
78#4654—31no—
79#4653—31no—
80#4652—31no—
81#4652—31no—
82#4647—31no—
83#4646—31no—
84#4646—31no—
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3—41no—
89C22×C3⋊Dic3—41no—
90C22×C3⋊Dic3C2×C414yes—
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3—22no—
96C22×C3×Dic3—41no—
97C22×C3×Dic3—41no—
98C22×C3×Dic3—41no—
99C22×C3×Dic3—41no—
100C22×C3×Dic3Q814yescomplemented
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×#627—41no—
110C2×#627—41no—
111C2×#627C2×C414yescomplemented
112C32×C22⋊C4—22no—
113#3757—22no—
114#3750—41no—
115#3750—41no—
116C3×#217C2×C414yes—
117C3×#217C2×C414yes—
118C3×Dic3⋊C4—41no—
119C3×Dic3⋊C4—41no—
120C3×C4×Dic3—41no—
121C3×C4×Dic3—41no—
122#3724C2×C414yescomplemented
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125Dic3⋊Dic3C2×C414yescomplemented
126Dic3⋊Dic3C2×C414yescomplemented
127Dic32—41no—
128Dic32—41no—
129#2329—91noSylow
130C23×C3×C4—31no—
131C23×C3×C4—31no—
132C23×Dic3—31no—
133C23×Dic3—31no—
134C23×Dic3—61no—
135C23×Dic3C2×D311yescharacteristic
136C23×Dic3C2×D311yescharacteristic
137C22×Dic6—31no—
138C22×Dic6—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—61no—
151C2×#217C2×D311yescharacteristic
152C2×#217C2×D311yescharacteristic
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—61no—
168C2×Dic3⋊C4—61no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#878—38no—
178#878—38no—
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—31no—
202C3⋊#95—31no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32—21no—
213C23×C32C22×C412yes—
214C23×C32C2×Q812yes—
215C23×C32#4112yes—
216C23×C32C2411yescharacteristic
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
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—44no—
234C2×C3⋊Dic3C22×C412yes—
235C2×C3⋊Dic3C22×C412yes—
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×Dic3—21no—
254C2×C3×Dic3—44no—
255C2×C3×Dic3—44no—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3C22×C412yes—
258C2×C3×Dic3C22×C412yes—
259C2×C3×Dic3C22×C412yes—
260C2×C3×Dic3C2×Q812yes—
261C2×C3×Dic3C2×Q812yes—
262#627—44no—
263C2×C22⋊Q8—91no—
264#391—91no—
265#391—91no—
266#389—91no—
267#389—91no—
268#387—91no—
269#387—91no—
270#387—91no—
271#387—91no—
272#385—31no—
273#385—91no—
274#380—91no—
275C4×C22⋊C4—31no—
276C4×C22⋊C4—91no—
277C2×#95—91no—
278C24×C3—21no—
279C24×C3C22×D311yescharacteristic
280C24×C3C22×D311yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
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—62no—
293C22×C3×C4—121no—
294C22×C3×C4—121no—
295C22×C3×C4—121no—
296C22×C3×C4—121no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×Dic3—22no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—34no—
307C22×Dic3—34no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—41no—
313C22×Dic3—41no—
314C22×Dic3—41no—
315C22×Dic3—41no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—64no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322C22×Dic3—121no—
323C22×Dic3—121no—
324C22×Dic3—121no—
325C22×Dic3—122no—
326C22×Dic3—122no—
327C22×Dic3Dic614yescomplemented
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C2×Dic6—34no—
337C2×Dic6—34no—
338C2×Dic6—121no—
339C2×Dic6—121no—
340C2×Dic6—121no—
341C2×Dic6—121no—
342C3×C4⋊C4—121no—
343C3×C4⋊C4—121no—
344C3×C22⋊C4—22no—
345C3×C22⋊C4—22no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—42no—
349C3×C42—121no—
350C3×C42—121no—
351#217—62no—
352#217—62no—
353#217—122no—
354#217C4×D314yes—
355#217C4×D314yes—
356C4⋊Dic3—34no—
357C4⋊Dic3—34no—
358C4⋊Dic3—121no—
359C4⋊Dic3—121no—
360Dic3⋊C4—34no—
361Dic3⋊C4—34no—
362Dic3⋊C4—34no—
363Dic3⋊C4—34no—
364Dic3⋊C4—41no—
365Dic3⋊C4—41no—
366Dic3⋊C4—121no—
367Dic3⋊C4—121no—
368Dic3⋊C4—121no—
369Dic3⋊C4—121no—
370Dic3⋊C4—121no—
371Dic3⋊C4—121no—
372Dic3⋊C4—122no—
373Dic3⋊C4—122no—
374C4×Dic3—41no—
375C4×Dic3—41no—
376C4×Dic3—121no—
377C4×Dic3—121no—
378C4×Dic3—121no—
379C4×Dic3—121no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—22no—
386C22×C32C4×Q814yes—
387C22×C32C23×C411yescharacteristic
388C22×C32C22×Q811yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32H(5,𝔽2)11yescharacteristic
391C22×C32H(5,𝔽2)11yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C322−1+411yescharacteristic
394C32×C4—41no—
395C32×C4—41no—
396C3⋊Dic3—22no—
397C3⋊Dic3—22no—
398C3⋊Dic3—41no—
399C3⋊Dic3—41no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C22×Q8—91no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—91no—
412C22⋊Q8—98no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4D3211yescharacteristic
426C2×C42—31no—
427C2×C42—31no—
428C2×C42—91no—
429C2×C42—91no—
430#95—31no—
431#95—31no—
432#95—31no—
433#95—31no—
434#95—91no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3C2×Dic612yes—
461C23×C3C2×C4×D312yes—
462C23×C3C2×C4×D312yes—
463C23×C3#23512yes—
464C23×C3#23712yes—
465C23×C3D3×Q812yes—
466C23×C3C23×D311yescharacteristic
467C23×C3C23×D311yescharacteristic
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—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—124no—
511C2×C3×C4—124no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—32no—
534C2×Dic3—44no—
535C2×Dic3—44no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—124no—
569C2×Dic3—124no—
570C2×Dic3—128no—
571C2×Dic3C2×Dic612yes—
572C2×Dic3C2×Dic612yes—
573C2×Dic3C2×C4×D312yes—
574C2×Dic3C2×C4×D312yes—
575C2×Dic3C2×C4×D312yes—
576C2×Dic3C2×C4×D312yes—
577Dic6—124no—
578Dic6—124no—
579C2×C32—24no—
580C2×C32C2×C4×Q811yescharacteristic
581C2×C32#51811yescharacteristic
582C2×C32#52011yescharacteristic
583C2×C32#53811yescharacteristic
584C2×C32#53911yescharacteristic
585C2×C32#54311yescharacteristic
586C2×C32#54411yescharacteristic
587C24C2×D3211yescharacteristic
588C2×Q8—94no—
589C2×Q8—361no—
590C2×Q8—361no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—34no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—62no—
601C22×C4—91no—
602C22×C4—91no—
603C22×C4—94no—
604C22×C4—91no—
605C22×C4—91no—
606C22×C4—121no—
607C22×C4—121no—
608C22×C4—121no—
609C22×C4—121no—
610C22×C4—361no—
611C22×C4—361no—
612C22×C4C2×D3211yescharacteristic
613C22×C4C2×D3211yescharacteristic
614C4⋊C4—94no—
615C4⋊C4—94no—
616C4⋊C4—94no—
617C4⋊C4—121no—
618C4⋊C4—121no—
619C4⋊C4—361no—
620C4⋊C4—361no—
621C4⋊C4—361no—
622C4⋊C4—361no—
623C22⋊C4—22no—
624C22⋊C4—34no—
625C22⋊C4—34no—
626C22⋊C4—182no—
627C42—121no—
628C42—121no—
629C42—361no—
630C42—361no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—24no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3C4×Dic614yes—
658C22×C3#88714yes—
659C22×C3C22×Dic611yescharacteristic
660C22×C3C22×C4×D311yescharacteristic
661C22×C3C22×C4×D311yescharacteristic
662C22×C3C2×#23511yescharacteristic
663C22×C3C2×#23711yescharacteristic
664C22×C3#100411yescharacteristic
665C22×C3#100411yescharacteristic
666C22×C3#100411yescharacteristic
667C22×C3#100411yescharacteristic
668C22×C3C2×D3×Q811yescharacteristic
669C22×C3#100911yescharacteristic
670C22×C3#100911yescharacteristic
671C22×C3#101011yescharacteristic
672C22×C3#101011yescharacteristic
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—62no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—62no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687Dic3—22no—
688Dic3—22no—
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—22no—
693Dic3—41no—
694Dic3—41no—
695Dic3—64no—
696Dic3—62no—
697Dic3—62no—
698Dic3—62no—
699Dic3—62no—
700Dic3—122no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3—241no—
707C32#232911yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23D3×Dic612yes—
713C23C4×D3212yes—
714C23#380412yes—
715C23C22×D3211yescharacteristic
716Q8—364no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—92no—
748C2×C4—92no—
749C2×C4—124no—
750C2×C4—124no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—364no—
762C2×C3—24no—
763C2×C3—24no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—44no—
772C2×C3C2×C4×Dic611yescharacteristic
773C2×C3#548311yescharacteristic
774C2×C3C2×#88711yescharacteristic
775C2×C3#551911yescharacteristic
776C2×C3#554511yescharacteristic
777C2×C3#554511yescharacteristic
778C2×C3#554611yescharacteristic
779C2×C3#554611yescharacteristic
780C2×C3#556011yescharacteristic
781C2×C3#556411yescharacteristic
782C2×C3#559311yescharacteristic
783C2×C3#562311yescharacteristic
784C2×C3#563411yescharacteristic
785C2×C3#566511yescharacteristic
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22#6383714yes—
793C22C2×D3×Dic611yescharacteristic
794C22C2×C4×D3211yescharacteristic
795C22#6430911yescharacteristic
796C22#6431311yescharacteristic
797C22#6431411yescharacteristic
798C22#6431411yescharacteristic
799C22C2×#380411yescharacteristic
800C4—41no—
801C4—41no—
802C4—62no—
803C4—62no—
804C4—62no—
805C4—62no—
806C4—62no—
807C4—62no—
808C4—121no—
809C4—121no—
810C4—182no—
811C4—182no—
812C4—361no—
813C4—361no—
814C3—21no—
815C3#7344711yescharacteristic, complemented
816C3#7438711yescharacteristic, complemented
817C2—24no—
818C2#1059403511yescharacteristic
819C2#1059405111yescharacteristic
820C2#1059417011yescharacteristic
821C2#1059425611yescharacteristic
822C2C2×#6383711yescharacteristic
823C2#1059512311yescharacteristic
824C2#1059512711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2329
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591332C2semidirect
9. #10591330C2semidirect
10. #10591251C2semidirect
11. #10591249C2semidirect
12. #10591235C2semidirect
13. #10591234C2semidirect
14. #10591193C2semidirect
15. #10591191C2semidirect
32. #63982C4semidirect
100. C22×C3×Dic3Q8semidirect
111. C2×#627C2×C4semidirect
122. #3724C2×C4semidirect
125. Dic3⋊Dic3C2×C4semidirect
126. Dic3⋊Dic3C2×C4semidirect
327. C22×Dic3Dic6semidirect
707. C32#2329semidirect
815. C3#73447semidirect
816. C3#74387semidirect

Maximal subgroups

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

subgroupindex
C2×#639822
#105926412
C3×#49462
C3×Dic3×C22⋊C42
#105917182
Dic3×#2172
C2×#635792
#105913322
#105913302
#105912512
#105912492
#105912352
#105912342
#105911932
#105911912
#743873
#734473