Finite Group Databasebeta

← #11807772

Subgroups — #11807772

Order 1152.

1247 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63886C211yesmaximal, characteristic
2#10592368C211yesmaximal, characteristic, complemented
3C3×#4665C211yesmaximal, characteristic, complemented
4C3×#4655C211yesmaximal, characteristic, complemented
5#10591383C211yesmaximal, characteristic, complemented
6#10591382C211yesmaximal, characteristic, complemented
7#10591378C211yesmaximal, characteristic, complemented
8#10591369C211yesmaximal, characteristic, complemented
9#10591362C211yesmaximal, characteristic, complemented
10#10591323C211yesmaximal, characteristic, complemented
11#10591279C211yesmaximal, characteristic, complemented
12#10591278C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#75313—31nomaximal
17#74683—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43#63886C418yescomplemented
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#939—31no—
55C2×#895—31no—
56C3×#387—31no—
57C3×#386—31no—
58#5221—31no—
59#5213—31no—
60#5210—31no—
61#4989—31no—
62#4988—31no—
63#4980—31no—
64#4957—31no—
65#4956—31no—
66#4956—31no—
67#4944—31no—
68#4943—31no—
69#4942—31no—
70#4940—31no—
71#4939—31no—
72#4669—31no—
73#4669—31no—
74#4669—61no—
75#4668—31no—
76#4668—31no—
77#4667—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665D311yescharacteristic, complemented
82#4664—31no—
83#4655D311yescharacteristic, complemented
84#4652—31no—
85C23×C3⋊D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
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
100C2×C3×D12—41no—
101C2×C3×D12—41no—
102C2×C3×D12C2×C414yescomplemented
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3—41no—
106C2×#626—41no—
107C2×#626—41no—
108C2×#626—41no—
109C2×#626—41no—
110C2×#626C2×C414yes—
111C2×#626C2×C414yescomplemented
112C2×#624—41no—
113C2×#624—41no—
114C2×#624—41no—
115C2×D3×Dic3—41no—
116C2×D3×Dic3—41no—
117C2×D3×Dic3C2×C414yescomplemented
118#3752—41no—
119#3752—41no—
120#3752C2×C414yescomplemented
121#3750—41no—
122C4×C3⋊Dic3—41no—
123C3×(C2×D3)⋊C4—41no—
124C3×(C2×D3)⋊C4—41no—
125C3×(C2×D3)⋊C4—41no—
126C3×C4⋊Dic3—41no—
127C3×Dic3⋊C4C2×C414yescomplemented
128C3×C4×Dic3—41no—
129#3724—41no—
130Dic3⋊Dic3—41no—
131#3722—41no—
132(C2×D3)⋊Dic3—41no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3—41no—
135(C2×D3)⋊Dic3—41no—
136(C2×D3)⋊Dic3C2×C414yescomplemented
137#2377—91noSylow
138C22×C3×D4—31no—
139C23×C3×C4—31no—
140C22×#67—31no—
141C22×#67—31no—
142C23×Dic3—31no—
143C22×D12—31no—
144C22×D12—31no—
145C22×D12C2×D311yescharacteristic
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3C2×D311yescharacteristic
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C42—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—31no—
161#939—38no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—61no—
176C2×(C2×D3)⋊C4—61no—
177C2×(C2×D3)⋊C4—61no—
178C2×(C2×D3)⋊C4C2×D311yescharacteristic
179C2×(C2×D3)⋊C4C2×D311yescharacteristic
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3C2×D311yescharacteristic
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—61no—
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—61no—
193C2×C4×Dic3C2×D311yescharacteristic
194#895—38no—
195C3×#95—21no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95C2×D311yescharacteristic
201C3×#95C2×D311yescharacteristic
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—61no—
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C23×C32C2411yescharacteristic
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3C22×C412yes—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C22×C412yes—
238C22×C3×D3C22×C412yes—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C22×C412yes—
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×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C22×C412yes—
274C2×C3×Dic3C22×C412yes—
275C3×D12—44no—
276C3×C4×D3—44no—
277#626—44no—
278#626—44no—
279#624—44no—
280D3×Dic3—44no—
281C2×#121—91no—
282#390—91no—
283#390—91no—
284#388—91no—
285#388—91no—
286#387—31no—
287#387—91no—
288#386—31no—
289#386—91no—
290#386—91no—
291#386—91no—
292#385—91no—
293#385—91no—
294#381—91no—
295#380—91no—
296C24×C3—31no—
297C24×C3—31no—
298C23×D3—31no—
299C23×D3—31no—
300C23×D3—61no—
301C23×D3C22×D311yescharacteristic
302C23×D3C22×D311yescharacteristic
303C2×C3×D4—34no—
304C2×C3×D4—121no—
305C2×C3×D4—121no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—121no—
316C22×C3×C4—121no—
317C22×C3×C4—121no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C2×#67—34no—
325C2×#67—34no—
326C2×#67—121no—
327C2×#67—121no—
328C2×#67—121no—
329C2×#67—121no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—34no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341C22×Dic3—121no—
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C2×D12—34no—
349C2×D12—34no—
350C2×D12—41no—
351C2×D12—41no—
352C2×D12—121no—
353C2×D12—121no—
354C2×D12—121no—
355C2×D12—121no—
356C2×D12C4×D314yescomplemented
357C2×C4×D3—34no—
358C2×C4×D3—41no—
359C2×C4×D3—41no—
360C2×C4×D3—41no—
361C2×C4×D3—121no—
362C2×C4×D3—121no—
363C2×C4×D3—121no—
364C2×C4×D3—121no—
365C2×C4×D3—121no—
366C2×C4×D3—121no—
367C2×C4×D3—121no—
368C2×C4×D3—121no—
369C3×C4⋊C4—34no—
370C3×C4⋊C4—121no—
371C3×C22⋊C4—121no—
372C3×C22⋊C4—121no—
373C3×C22⋊C4—121no—
374C3×C42—121no—
375#217—34no—
376#217—121no—
377#217—121no—
378#217—121no—
379#217—121no—
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—34no—
383(C2×D3)⋊C4—41no—
384(C2×D3)⋊C4—41no—
385(C2×D3)⋊C4—41no—
386(C2×D3)⋊C4—64no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4—121no—
390(C2×D3)⋊C4—121no—
391(C2×D3)⋊C4—121no—
392(C2×D3)⋊C4—121no—
393(C2×D3)⋊C4—122no—
394(C2×D3)⋊C4—122no—
395(C2×D3)⋊C4—121no—
396(C2×D3)⋊C4—121no—
397(C2×D3)⋊C4—121no—
398(C2×D3)⋊C4—121no—
399C4⋊Dic3—41no—
400C4⋊Dic3—121no—
401Dic3⋊C4—121no—
402Dic3⋊C4—121no—
403Dic3⋊C4—121no—
404Dic3⋊C4—121no—
405Dic3⋊C4—121no—
406Dic3⋊C4—122no—
407Dic3⋊C4C4×D314yescomplemented
408C4×Dic3—41no—
409C4×Dic3—121no—
410C4×Dic3—121no—
411C4×Dic3—122no—
412C22×C32C23×C411yescharacteristic
413C22×C32H(5,𝔽2)11yescharacteristic
414C22×C32H(5,𝔽2)11yescharacteristic
415C22×C32H(5,𝔽2)11yescharacteristic
416C22×C32H(5,𝔽2)11yescharacteristic
417C22×C32H(5,𝔽2)11yescharacteristic
418C22×C322−1+411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—22no—
441C32×C4—41no—
442C32×C4—41no—
443C3⋊Dic3—22no—
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C22×D4—31no—
453C22×D4—91no—
454C22×D4—91no—
455C23×C4—31no—
456C23×C4—91no—
457C23×C4—91no—
458#121—98no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—31no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4—91no—
469C2×C22⋊C4—91no—
470C2×C22⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C42—31no—
477C2×C42—91no—
478#95—31no—
479#95—31no—
480#95—31no—
481#95—31no—
482#95—91no—
483#95—91no—
484#95—91no—
485#95—91no—
486#95—91no—
487#95D3211yescharacteristic
488C23×C3—21no—
489C23×C3—32no—
490C23×C3—32no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3C23×D311yescharacteristic
504C23×C3C23×D311yescharacteristic
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—32no—
518C22×D3—32no—
519C22×D3—62no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—121no—
533C22×D3—121no—
534C22×D3—121no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—121no—
538C22×D3C2×C4×D312yes—
539C22×D3C2×C4×D312yes—
540C3×D4—124no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—22no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—124no—
585C2×C3×C4C2×C4×D312yes—
586C2×C3×C4C2×C4×D312yes—
587#67—124no—
588#67—124no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—32no—
606C2×Dic3—32no—
607C2×Dic3—62no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—62no—
613C2×Dic3—62no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3—121no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—121no—
632C2×Dic3—124no—
633C2×Dic3C2×C4×D312yes—
634C2×Dic3C2×C4×D312yes—
635D12—44no—
636D12—124no—
637D12—124no—
638C4×D3—44no—
639C4×D3—124no—
640C4×D3—124no—
641C4×D3—124no—
642C2×C32#51811yescharacteristic
643C2×C32#51811yescharacteristic
644C2×C32#52011yescharacteristic
645C2×C32#56011yescharacteristic
646C2×C32#56011yescharacteristic
647C2×C32#56211yescharacteristic
648C2×C32#56211yescharacteristic
649C3⋊D3—42no—
650C3×D3—42no—
651C3×D3—42no—
652C24—31no—
653C24—31no—
654C24—91no—
655C2×D4—34no—
656C2×D4—94no—
657C2×D4—94no—
658C2×D4—121no—
659C2×D4—121no—
660C2×D4—361no—
661C2×D4—361no—
662C2×D4—361no—
663C2×D4—361no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—94no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—121no—
675C22×C4—121no—
676C22×C4—121no—
677C22×C4—361no—
678C22×C4—361no—
679C22×C4—361no—
680C22×C4—361no—
681C22×C4—361no—
682C22×C4C2×D3211yescharacteristic
683C22×C4C2×D3211yescharacteristic
684C22×C4C2×D3211yescharacteristic
685C4⋊C4—34no—
686C4⋊C4—121no—
687C4⋊C4—361no—
688C4⋊C4—361no—
689C4⋊C4—361no—
690C22⋊C4—94no—
691C22⋊C4—94no—
692C22⋊C4—121no—
693C22⋊C4—121no—
694C22⋊C4—121no—
695C22⋊C4—361no—
696C22⋊C4—361no—
697C22⋊C4—361no—
698C22⋊C4—361no—
699C22⋊C4—361no—
700C22⋊C4—361no—
701C22⋊C4—361no—
702C42—121no—
703C42—361no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3C22×C4×D311yescharacteristic
726C22×C3C22×C4×D311yescharacteristic
727C22×C3#100411yescharacteristic
728C22×C3#100411yescharacteristic
729C22×C3#100411yescharacteristic
730C22×C3#100411yescharacteristic
731C22×C3#100411yescharacteristic
732C22×C3#100711yescharacteristic
733C22×C3#100911yescharacteristic
734C22×C3#100911yescharacteristic
735C22×C3#100911yescharacteristic
736C22×C3#100911yescharacteristic
737C22×C3#100911yescharacteristic
738C22×C3#101011yescharacteristic
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—241no—
774C3×C4—22no—
775C3×C4—22no—
776C3×C4—42no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—41no—
781C3×C4—62no—
782C3×C4—62no—
783C3×C4—81no—
784C3×C4—81no—
785C3×C4—121no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4—121no—
789Dic3—22no—
790Dic3—22no—
791Dic3—41no—
792Dic3—41no—
793Dic3—41no—
794Dic3—41no—
795Dic3—62no—
796Dic3—62no—
797Dic3—122no—
798Dic3—122no—
799Dic3—122no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804C32#237711yescharacteristic, complemented, Sylow
805C23—32no—
806C23—32no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—92no—
820C23—181no—
821C23—181no—
822C23—181no—
823C23—181no—
824C23—181no—
825C23—181no—
826C23C22×D3211yescharacteristic
827D4—124no—
828D4—364no—
829D4—364no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—92no—
857C2×C4—124no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—364no—
867C2×C4—364no—
868C2×C4C4×D3212yes—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—122no—
877C2×C3—122no—
878C2×C3#548611yescharacteristic
879C2×C3#552111yescharacteristic
880C2×C3#554511yescharacteristic
881C2×C3#554511yescharacteristic
882C2×C3#554611yescharacteristic
883C2×C3#557411yescharacteristic
884C2×C3#559511yescharacteristic
885C2×C3#562011yescharacteristic
886C2×C3#562111yescharacteristic
887C2×C3#564711yescharacteristic
888C2×C3#566611yescharacteristic
889C2×C3#566711yescharacteristic
890C2×C3#570011yescharacteristic
891C2×C3#571111yescharacteristic
892D3—42no—
893D3—42no—
894D3—122no—
895D3—122no—
896D3—242no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—182no—
912C22—182no—
913C22—182no—
914C22—361no—
915C22—361no—
916C22—361no—
917C22—361no—
918C22#6429711yescharacteristic
919C22C2×C4×D3211yescharacteristic
920C22#6430711yescharacteristic
921C22#6431311yescharacteristic
922C22#6431411yescharacteristic
923C22#6431411yescharacteristic
924C22#6432011yescharacteristic
925C4—22no—
926C4—41no—
927C4—41no—
928C4—62no—
929C4—62no—
930C4—121no—
931C4—121no—
932C4—121no—
933C4—121no—
934C4—182no—
935C4—361no—
936C4—361no—
937C3—21no—
938C3#7468311yescharacteristic, complemented
939C3#7531311yescharacteristic, complemented
940C2—122no—
941C2—122no—
942C2—362no—
943C2#1059388911yescharacteristic
944C2#1059417411yescharacteristic
945C2#1059423611yescharacteristic
946C2#1059425411yescharacteristic
947C2#1059450011yescharacteristic
948C2#1059460411yescharacteristic
949C2#1059466211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63886C2
hypercenter#95D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592368C2semidirect
3. C3×#4665C2semidirect
4. C3×#4655C2semidirect
5. #10591383C2semidirect
6. #10591382C2semidirect
7. #10591378C2semidirect
8. #10591369C2semidirect
9. #10591362C2semidirect
10. #10591323C2semidirect
11. #10591279C2semidirect
12. #10591278C2semidirect
13. #10591275C2semidirect
14. #10591275C2semidirect
15. #10591192C2semidirect
43. #63886C4semidirect
81. #4665D3semidirect
83. #4655D3semidirect
102. C2×C3×D12C2×C4semidirect
111. C2×#626C2×C4semidirect
117. C2×D3×Dic3C2×C4semidirect
120. #3752C2×C4semidirect
127. C3×Dic3⋊C4C2×C4semidirect
136. (C2×D3)⋊Dic3C2×C4semidirect
356. C2×D12C4×D3semidirect
407. Dic3⋊C4C4×D3semidirect
804. C32#2377semidirect
938. C3#74683semidirect
939. C3#75313semidirect

Maximal subgroups

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

subgroupindex
C2×#638862
#105923682
C3×#46652
C3×#46552
#105913832
#105913822
#105913782
#105913692
#105913622
#105913232
#105912792
#105912782
#105912752
#105911922
#753133
#746833