Finite Group Databasebeta

← #11803913

Subgroups — #11803913

Order 1152.

1185 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×#63895C211yesmaximal, characteristic
2#10592365C211yesmaximal, characteristic
3C3×#4655C211yesmaximal, characteristic, complemented
4C3×#4654C211yesmaximal, characteristic, complemented
5#10591396C211yesmaximal, characteristic, complemented
6#10591378C211yesmaximal, characteristic
7#10591375C211yesmaximal, characteristic
8#10591370C211yesmaximal, characteristic
9#10591367C211yesmaximal, characteristic
10#10591357C211yesmaximal, characteristic, complemented
11#10591334C211yesmaximal, characteristic, complemented
12#10591327C211yesmaximal, characteristic, complemented
13C4×#3722C211yesmaximal, characteristic
14#10591192C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#75300—31nomaximal
17#75299—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39#63895C418yescomplemented
40C32×#95C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
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×#897—31no—
55C2×#896—31no—
56C3×#387—31no—
57C3×#387—31no—
58#4989—31no—
59#4987—31no—
60#4984—31no—
61#4980—31no—
62#4978—31no—
63#4972—31no—
64C4×(C2×D3)⋊C4—31no—
65C4×(C2×D3)⋊C4—31no—
66#4929—31no—
67#4928—31no—
68#4668—31no—
69#4668—31no—
70#4668—31no—
71#4667—31no—
72#4666—31no—
73#4666—31no—
74#4666—61no—
75D3×#95—31no—
76D3×#95—31no—
77#4655D311yescharacteristic, complemented
78#4654D311yescharacteristic, complemented
79#4653—31no—
80#4652—31no—
81#4647—31no—
82#4646—31no—
83#4646—31no—
84#4646—31no—
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C2×C4×C3⋊D3—41no—
93C2×C4×C3⋊D3—41no—
94C2×C4×C3⋊D3Q814yescomplemented
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×#627—41no—
104C2×#627—41no—
105C2×#627C2×C414yescomplemented
106C2×#624—22no—
107C2×#624—41no—
108C2×#624—41no—
109C2×#624—41no—
110C2×#624—41no—
111C2×#624C2×C414yes—
112#3752—22no—
113#3752C2×C414yes—
114C4×C3⋊Dic3—41no—
115C4×C3⋊Dic3—41no—
116C3×C4⋊Dic3—41no—
117C3×C4⋊Dic3C2×C414yescomplemented
118C3×Dic3⋊C4—41no—
119C3×Dic3⋊C4C2×C414yescomplemented
120C3×C4×Dic3—41no—
121C3×C4×Dic3—41no—
122#3724—41no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125Dic3⋊Dic3—41no—
126Dic3⋊Dic3C2×C414yescomplemented
127#3722—22no—
128#3722C2×C414yes—
129#2329—91noSylow
130C22×C4×D3—31no—
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C22×C4×D3—31no—
134C22×C4×D3—31no—
135C22×C4×D3—31no—
136C22×C4×D3—61no—
137C22×Dic6—31no—
138C22×Dic6—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—61no—
154C2×(C2×D3)⋊C4—61no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3C2×D311yescharacteristic
160C2×C4⋊Dic3C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#897—38no—
178#896—38no—
179C3×#95—21no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95C2×D311yescharacteristic
187C3×#95C2×D311yescharacteristic
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—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C23×C32C2411yescharacteristic
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3C22×C412yes—
215C22×C3⋊D3C2×Q812yes—
216C22×C3⋊D3#4112yes—
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×C32×C4—21no—
224C2×C32×C4C22×C412yes—
225C2×C32×C4C2×Q812yes—
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⋊Dic3C22×C412yes—
234C2×C3⋊Dic3C2×Q812yes—
235C4×C3⋊D3—44no—
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—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3C22×C412yes—
258C2×C3×Dic3C22×C412yes—
259C2×C3×Dic3C22×C412yes—
260#627—44no—
261#624—44no—
262#624—44no—
263C2×C22⋊Q8—91no—
264#391—91no—
265#391—91no—
266#389—91no—
267#389—91no—
268#387—31no—
269#387—31no—
270#387—91no—
271#387—91no—
272#385—91no—
273#385—91no—
274#380—91no—
275C4×C22⋊C4—91no—
276C4×C22⋊C4—91no—
277C2×#95—91no—
278C23×D3—31no—
279C23×D3—31no—
280C23×D3—61no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C2×C4×D3—34no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—34no—
319C2×C4×D3—64no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×C4×D3—121no—
323C2×C4×D3—121no—
324C2×C4×D3—121no—
325C2×C4×D3—121no—
326C2×C4×D3—121no—
327C2×C4×D3—121no—
328C2×C4×D3—121no—
329C2×C4×D3—121no—
330C2×C4×D3—121no—
331C2×C4×D3—121no—
332C2×C4×D3—121no—
333C2×C4×D3—121no—
334C2×C4×D3—122no—
335C2×C4×D3—122no—
336C2×Dic6—34no—
337C2×Dic6—34no—
338C2×Dic6—121no—
339C2×Dic6—121no—
340C2×Dic6—121no—
341C2×Dic6—121no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—34no—
344C3×C4⋊C4—121no—
345C3×C4⋊C4—121no—
346C3×C42—121no—
347C3×C42—121no—
348(C2×D3)⋊C4—34no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—64no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—64no—
358C4⋊Dic3—34no—
359C4⋊Dic3—41no—
360C4⋊Dic3—121no—
361C4⋊Dic3—121no—
362C4⋊Dic3—121no—
363C4⋊Dic3C4×D314yescomplemented
364Dic3⋊C4—34no—
365Dic3⋊C4—41no—
366Dic3⋊C4—121no—
367Dic3⋊C4—121no—
368Dic3⋊C4—121no—
369Dic3⋊C4—121no—
370Dic3⋊C4—121no—
371Dic3⋊C4C4×D314yescomplemented
372C4×Dic3—41no—
373C4×Dic3—41no—
374C4×Dic3—121no—
375C4×Dic3—121no—
376C4×Dic3—121no—
377C4×Dic3—121no—
378C4×Dic3—122no—
379C4×Dic3—122no—
380C22×C32C23×C411yescharacteristic
381C22×C32C22×Q811yescharacteristic
382C22×C32C2×#4111yescharacteristic
383C22×C32H(5,𝔽2)11yescharacteristic
384C22×C32H(5,𝔽2)11yescharacteristic
385C22×C32H(5,𝔽2)11yescharacteristic
386C22×C322−1+411yescharacteristic
387C2×C3⋊D3—22no—
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3C4×Q814yes—
394C32×C4—22no—
395C32×C4—22no—
396C32×C4—41no—
397C3⋊Dic3—22no—
398C3⋊Dic3—22no—
399C3⋊Dic3—41no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C22×Q8—91no—
409C23×C4—91no—
410C23×C4—91no—
411C23×C4—91no—
412C22⋊Q8—98no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4—91no—
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—31no—
435#95—31no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95D3211yescharacteristic
444C23×C3—21no—
445C23×C3C23×D311yescharacteristic
446C23×C3C23×D311yescharacteristic
447C22×D3—32no—
448C22×D3—32no—
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—32no—
452C22×D3—32no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—121no—
465C22×D3—121no—
466C22×D3—121no—
467C22×D3—121no—
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—22no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
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—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4C2×C4×D312yes—
516C2×C3×C4C2×C4×D312yes—
517C2×C3×C4D3×Q812yes—
518C2×C3×C4D3×Q812yes—
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—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—62no—
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—62no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3C2×C4×D312yes—
567C2×Dic3C2×C4×D312yes—
568C2×Dic3C2×C4×D312yes—
569C2×Dic3C2×C4×D312yes—
570C4×D3—124no—
571C4×D3—124no—
572C4×D3—124no—
573C4×D3—124no—
574C4×D3—124no—
575C4×D3—124no—
576C4×D3—128no—
577Dic6—124no—
578Dic6—124no—
579C2×C32C2×C4×Q811yescharacteristic
580C2×C32#51811yescharacteristic
581C2×C32#52011yescharacteristic
582C2×C32#53811yescharacteristic
583C2×C32#53911yescharacteristic
584C2×C32#54311yescharacteristic
585C2×C32#54411yescharacteristic
586C3⋊D3—24no—
587C24—91no—
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—31no—
598C22×C4—31no—
599C22×C4—94no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—94no—
603C22×C4—91no—
604C22×C4—182no—
605C22×C4—361no—
606C22×C4—361no—
607C22×C4—361no—
608C22×C4—361no—
609C22×C4—361no—
610C22×C4—361no—
611C22×C4C2×D3211yescharacteristic
612C22×C4C2×D3211yescharacteristic
613C22×C4C2×D3211yescharacteristic
614C4⋊C4—34no—
615C4⋊C4—34no—
616C4⋊C4—94no—
617C4⋊C4—121no—
618C4⋊C4—121no—
619C4⋊C4—361no—
620C4⋊C4—361no—
621C4⋊C4—361no—
622C4⋊C4—361no—
623C22⋊C4—94no—
624C22⋊C4—94no—
625C22⋊C4—182no—
626C22⋊C4—182no—
627C42—121no—
628C42—121no—
629C42—361no—
630C42—361no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3C22×C4×D311yescharacteristic
639C22×C3C22×C4×D311yescharacteristic
640C22×C3#100411yescharacteristic
641C22×C3#100411yescharacteristic
642C22×C3C2×D3×Q811yescharacteristic
643C22×C3C2×D3×Q811yescharacteristic
644C22×C3D3×#4111yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3#100911yescharacteristic
647C22×C3#100911yescharacteristic
648C22×C3#100911yescharacteristic
649C22×C3#100911yescharacteristic
650C22×C3#101011yescharacteristic
651C22×C3#101011yescharacteristic
652C2×D3—34no—
653C2×D3—34no—
654C2×D3—64no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—122no—
668C2×D3—122no—
669C2×D3—122no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—122no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—62no—
683C3×C4—62no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690Dic3—22no—
691Dic3—22no—
692Dic3—22no—
693Dic3—22no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—64no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—62no—
703Dic3—122no—
704Dic3—122no—
705Dic3—121no—
706Dic3—121no—
707C32#232911yescharacteristic, complemented, Sylow
708C23—92no—
709C23—92no—
710C23—92no—
711C23—181no—
712C23—181no—
713C23—181no—
714C23—181no—
715C23C22×D3211yescharacteristic
716Q8—364no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—61no—
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—61no—
748C2×C4—92no—
749C2×C4—92no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—364no—
758C2×C4—364no—
759C2×C4—364no—
760C2×C4#379712yes—
761C2×C4C4×D3212yes—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3#552111yescharacteristic
770C2×C3#552311yescharacteristic
771C2×C3#554511yescharacteristic
772C2×C3#554611yescharacteristic
773C2×C3C4×D3×Q811yescharacteristic
774C2×C3C4×D3×Q811yescharacteristic
775C2×C3#563411yescharacteristic
776C2×C3#563411yescharacteristic
777C2×C3#565711yescharacteristic
778C2×C3#566011yescharacteristic
779C2×C3#568911yescharacteristic
780C2×C3#568911yescharacteristic
781C2×C3#570411yescharacteristic
782C2×C3#570711yescharacteristic
783D3—64no—
784D3—64no—
785D3—124no—
786C22—94no—
787C22—182no—
788C22—182no—
789C22—182no—
790C22—182no—
791C22—182no—
792C22—182no—
793C22C2×#379711yescharacteristic
794C22C2×C4×D3211yescharacteristic
795C22#6430611yescharacteristic
796C22#6430911yescharacteristic
797C22#6431411yescharacteristic
798C22#6431411yescharacteristic
799C22#6432011yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—62no—
804C4—62no—
805C4—62no—
806C4—62no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4—121no—
811C4—182no—
812C4—182no—
813C4—361no—
814C3—21no—
815C3#7529911yescharacteristic, complemented
816C3#7530011yescharacteristic, complemented
817C2—184no—
818C2C4×#379711yescharacteristic
819C2#1059404911yescharacteristic
820C2#1059418011yescharacteristic
821C2#1059422711yescharacteristic
822C2#1059450811yescharacteristic
823C2#1059460411yescharacteristic
824C2#1059465711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2329
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4655C2semidirect
4. C3×#4654C2semidirect
5. #10591396C2semidirect
10. #10591357C2semidirect
11. #10591334C2semidirect
12. #10591327C2semidirect
14. #10591192C2semidirect
15. #10591191C2semidirect
39. #63895C4semidirect
77. #4655D3semidirect
78. #4654D3semidirect
94. C2×C4×C3⋊D3Q8semidirect
105. C2×#627C2×C4semidirect
117. C3×C4⋊Dic3C2×C4semidirect
119. C3×Dic3⋊C4C2×C4semidirect
126. Dic3⋊Dic3C2×C4semidirect
363. C4⋊Dic3C4×D3semidirect
371. Dic3⋊C4C4×D3semidirect
707. C32#2329semidirect
815. C3#75299semidirect
816. C3#75300semidirect

Maximal subgroups

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

subgroupindex
C2×#638952
#105923652
C3×#46552
C3×#46542
#105913962
#105913782
#105913752
#105913702
#105913672
#105913572
#105913342
#105913272
C4×#37222
#105911922
#105911912
#753003
#752993