Finite Group Databasebeta

← #11807762

Subgroups — #11807762

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic, complemented
3C3×#4980C211yesmaximal, characteristic, complemented
4#10591379C211yesmaximal, characteristic, complemented
5#10591377C211yesmaximal, characteristic, complemented
6#10591376C211yesmaximal, characteristic, complemented
7#10591376C211yesmaximal, characteristic, complemented
8#10591376C211yesmaximal, characteristic, complemented
9#10591376C211yesmaximal, characteristic, complemented
10#10591323C211yesmaximal, characteristic, complemented
11#10591318C211yesmaximal, characteristic, complemented
12#10591305C211yesmaximal, characteristic, complemented
13#10591295C211yesmaximal, characteristic, complemented
14#10591294C211yesmaximal, characteristic, complemented
15#10591286C211yesmaximal, characteristic, complemented
16#82639—31nomaximal
17#75313—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#895C418yescomplemented
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#121—31no—
55C2×#895D311yescharacteristic
56C3×#387—31no—
57#5221—31no—
58#5221—31no—
59#5220—31no—
60#5220—31no—
61#5220—31no—
62#5220—31no—
63#5212—31no—
64#5211—31no—
65#4989—31no—
66#4988—31no—
67#4980—31no—
68#4980—31no—
69#4980—61no—
70#4980D311yescharacteristic, complemented
71#4951—31no—
72#4951—31no—
73#4950—31no—
74#4950—31no—
75#4940—31no—
76#4939—31no—
77#4669—31no—
78#4668—31no—
79#4667—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—31no—
84#4664—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×D12—41no—
103C2×C3×D12—41no—
104C2×C3×D12—41no—
105C2×C3×D12—41no—
106C2×C3×D12C2×C414yes—
107C2×C3×D12C2×C414yescomplemented
108C2×C3×D12C2×C414yescomplemented
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3C2×C414yescomplemented
112C2×D3×Dic3—41no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3—41no—
115C2×D3×Dic3—41no—
116C2×D3×Dic3—41no—
117C2×D3×Dic3—41no—
118C32×C4⋊C4C2×C414yescomplemented
119C4⋊(C3⋊Dic3)—41no—
120C4×C3⋊Dic3—41no—
121C3×(C2×D3)⋊C4C2×C414yescomplemented
122C3×(C2×D3)⋊C4C2×C414yescomplemented
123C3×C4⋊Dic3—41no—
124C3×C4×Dic3—41no—
125Dic3⋊Dic3—41no—
126Dic3⋊Dic3—41no—
127(C2×D3)⋊Dic3—41no—
128(C2×D3)⋊Dic3—41no—
129(C2×D3)⋊Dic3—41no—
130(C2×D3)⋊Dic3—41no—
131(C2×D3)⋊Dic3—41no—
132(C2×D3)⋊Dic3—41no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3—41no—
135(C2×D3)⋊Dic3—41no—
136(C2×D3)⋊Dic3—41no—
137#2377—91noSylow
138C22×C3×D4—31no—
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C23×C3×C4—31no—
142C23×Dic3—31no—
143C23×Dic3—31no—
144C22×D12C2×D311yescharacteristic
145C22×D12C2×D311yescharacteristic
146C22×D12C2×D311yescharacteristic
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3C2×D311yescharacteristic
150C3×#121—38no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C2×D311yescharacteristic
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C42—31no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—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—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4C2×D311yescharacteristic
179C2×(C2×D3)⋊C4C2×D311yescharacteristic
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—61no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C2×C4×Dic3C2×D311yescharacteristic
192#895Dic318yescomplemented
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—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—61no—
210C3⋊#95—61no—
211C3⋊#95—61no—
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×D3—21no—
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×D3C22×C412yes—
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×C4C22×C412yes—
246C2×C32×C4C22×C412yes—
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⋊Dic3—21no—
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×Dic3—21no—
274C2×C3×Dic3C22×C412yes—
275C3×D12—44no—
276C3×D12—44no—
277C3×D12—44no—
278C3×C4×D3—44no—
279D3×Dic3—44no—
280D3×Dic3—44no—
281C2×#121—31no—
282#390—91no—
283#390—91no—
284#388—91no—
285#388—91no—
286#387—31no—
287#387—91no—
288#386—91no—
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—
298C24×C3—31no—
299C23×D3C22×D311yescharacteristic
300C23×D3C22×D311yescharacteristic
301C23×D3C22×D311yescharacteristic
302C2×C3×D4—34no—
303C2×C3×D4—34no—
304C2×C3×D4—34no—
305C2×C3×D4—121no—
306C2×C3×D4—121no—
307C2×C3×D4—121no—
308C2×C3×D4—121no—
309C2×C3×D4—121no—
310C2×C3×D4—121no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—34no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—121no—
321C22×C3×C4—121no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341C22×Dic3—121no—
342C22×Dic3—121no—
343C22×Dic3—121no—
344C22×Dic3—121no—
345C22×Dic3—121no—
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C2×D12—41no—
352C2×D12—41no—
353C2×D12—41no—
354C2×D12—41no—
355C2×D12—41no—
356C2×D12—41no—
357C2×D12C2×Dic314yes—
358C2×D12C2×Dic314yescomplemented
359C2×D12C2×Dic314yescomplemented
360C2×C4×D3—41no—
361C2×C4×D3—41no—
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×D3C2×Dic314yescomplemented
369C3×C4⋊C4—24no—
370C3×C4⋊C4—121no—
371C3×C4⋊C4C4×D314yescomplemented
372C3×C4⋊C4C2×Dic314yescomplemented
373C3×C22⋊C4—34no—
374C3×C22⋊C4—34no—
375C3×C42—121no—
376#217—121no—
377#217—121no—
378#217—121no—
379#217—121no—
380#217—121no—
381#217—121no—
382#217—121no—
383#217—121no—
384#217—121no—
385#217—121no—
386(C2×D3)⋊C4—121no—
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—121no—
394(C2×D3)⋊C4—121no—
395(C2×D3)⋊C4—121no—
396(C2×D3)⋊C4C2×Dic314yescomplemented
397(C2×D3)⋊C4C2×Dic314yescomplemented
398C4⋊Dic3—41no—
399C4⋊Dic3—121no—
400C4⋊Dic3—121no—
401C4⋊Dic3—121no—
402C4⋊Dic3—121no—
403C4⋊Dic3—122no—
404Dic3⋊C4—121no—
405Dic3⋊C4—121no—
406C4×Dic3—41no—
407C4×Dic3—121no—
408C4×Dic3—121no—
409C4×Dic3—122no—
410C22×C32C23×C411yescharacteristic
411C22×C32H(5,𝔽2)11yescharacteristic
412C22×C32H(5,𝔽2)11yescharacteristic
413C22×C32H(5,𝔽2)11yescharacteristic
414C22×C32H(5,𝔽2)11yescharacteristic
415C22×C32H(5,𝔽2)11yescharacteristic
416C22×C322−1+411yescharacteristic
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C32×C4—22no—
439C32×C4—22no—
440C32×C4—22no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3×Dic3—22no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—31no—
451C22×D4—31no—
452C22×D4—31no—
453C23×C4—31no—
454C23×C4—91no—
455C23×C4—91no—
456#121—38no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4D3211yescharacteristic
462C2×C22⋊C4—31no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
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×C42—31no—
475C2×C42—91no—
476#95—31no—
477#95—31no—
478#95—31no—
479#95—31no—
480#95—91no—
481#95—91no—
482#95—91no—
483#95—91no—
484#95—91no—
485#95—91no—
486C23×C3—21no—
487C23×C3—32no—
488C23×C3—32no—
489C23×C3—32no—
490C23×C3—61no—
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×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3C23×D311yescharacteristic
509C23×C3C23×D311yescharacteristic
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3C22×Dic312yes—
529C22×D3C22×Dic312yes—
530C22×D3C22×Dic312yes—
531C3×D4—124no—
532C3×D4—124no—
533C3×D4—124no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—32no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—124no—
571C2×C3×C4C2×C4×D312yes—
572C2×C3×C4C2×C4×D312yes—
573C2×C3×C4C2×C4×D312yes—
574C2×C3×C4C22×Dic312yes—
575C2×C3×C4C22×Dic312yes—
576C2×C3×C4C22×Dic312yes—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—62no—
592C2×Dic3—62no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3—121no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—124no—
628C2×Dic3—124no—
629C2×Dic3C22×Dic312yes—
630D12—44no—
631D12—44no—
632D12—44no—
633C4×D3—44no—
634C4×D3—124no—
635C4×D3—124no—
636C2×C32#51811yescharacteristic
637C2×C32#51811yescharacteristic
638C2×C32#52011yescharacteristic
639C2×C32#56011yescharacteristic
640C2×C32#56011yescharacteristic
641C2×C32#56211yescharacteristic
642C2×C32#56211yescharacteristic
643C3×D3—42no—
644C3×D3—42no—
645C3×D3—42no—
646C24—31no—
647C24—31no—
648C24—31no—
649C2×D4—34no—
650C2×D4—34no—
651C2×D4—34no—
652C2×D4—121no—
653C2×D4—121no—
654C2×D4—121no—
655C2×D4—121no—
656C2×D4—121no—
657C2×D4—121no—
658C22×C4—31no—
659C22×C4—34no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—91no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—91no—
668C22×C4—121no—
669C22×C4—121no—
670C22×C4—361no—
671C22×C4—361no—
672C22×C4—361no—
673C22×C4—361no—
674C22×C4—361no—
675C22×C4—361no—
676C22×C4C2×D3211yescharacteristic
677C22×C4C2×D3211yescharacteristic
678C22×C4C2×D3211yescharacteristic
679C4⋊C4—121no—
680C4⋊C4—361no—
681C4⋊C4—361no—
682C4⋊C4—361no—
683C4⋊C4D3×Dic314yescomplemented
684C22⋊C4—34no—
685C22⋊C4—34no—
686C22⋊C4—361no—
687C22⋊C4—361no—
688C22⋊C4—361no—
689C22⋊C4—361no—
690C22⋊C4—361no—
691C22⋊C4—361no—
692C22⋊C4—361no—
693C22⋊C4—361no—
694C22⋊C4—361no—
695C22⋊C4—361no—
696C42—121no—
697C42—361no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—62no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
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×C3—121no—
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
739C22×C3C23×Dic311yescharacteristic
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—42no—
770C3×C4—62no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4—121no—
775Dic3—22no—
776Dic3—41no—
777Dic3—41no—
778Dic3—41no—
779Dic3—41no—
780Dic3—122no—
781Dic3—122no—
782Dic3—121no—
783Dic3—121no—
784Dic3—121no—
785Dic3—121no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—241no—
791Dic3—241no—
792C32#237711yescharacteristic, complemented, Sylow
793C23—32no—
794C23—32no—
795C23—32no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23C22×D3211yescharacteristic
815D4—124no—
816D4—124no—
817D4—124no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—32no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—124no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—181no—
846C2×C4—181no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—364no—
853C2×C4—364no—
854C2×C4C2×D3×Dic312yes—
855C2×C4C2×D3×Dic312yes—
856C2×C4C2×D3×Dic312yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—122no—
865C2×C3—122no—
866C2×C3—122no—
867C2×C3#552111yescharacteristic
868C2×C3#554511yescharacteristic
869C2×C3#557411yescharacteristic
870C2×C3#562011yescharacteristic
871C2×C3#562011yescharacteristic
872C2×C3#562111yescharacteristic
873C2×C3#562111yescharacteristic
874C2×C3#564711yescharacteristic
875C2×C3#566611yescharacteristic
876C2×C3#570011yescharacteristic
877C2×C3#571111yescharacteristic
878C2×C3#579811yescharacteristic
879C2×C3#579811yescharacteristic
880C2×C3#582711yescharacteristic
881D3—42no—
882D3—42no—
883D3—42no—
884C22—62no—
885C22—62no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22#6430711yescharacteristic
906C22#6430711yescharacteristic
907C22#6431311yescharacteristic
908C22#6431411yescharacteristic
909C22#6431511yescharacteristic
910C22#6432011yescharacteristic
911C22C22×D3×Dic311yescharacteristic
912C4—22no—
913C4—22no—
914C4—22no—
915C4—62no—
916C4—121no—
917C4—121no—
918C4—121no—
919C4—121no—
920C4—361no—
921C4—361no—
922C4—361no—
923C4—361no—
924C3—21no—
925C3#7531311yescharacteristic, complemented
926C3#8263911yescharacteristic, complemented
927C2—122no—
928C2—122no—
929C2—122no—
930C2#1059449211yescharacteristic
931C2#1059449311yescharacteristic
932C2#1059466111yescharacteristic
933C2#1059466211yescharacteristic
934C2#1059498211yescharacteristic
935C2#1059521511yescharacteristic
936C2#1059539411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#895C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592679C2semidirect
3. C3×#4980C2semidirect
4. #10591379C2semidirect
5. #10591377C2semidirect
6. #10591376C2semidirect
7. #10591376C2semidirect
8. #10591376C2semidirect
9. #10591376C2semidirect
10. #10591323C2semidirect
11. #10591318C2semidirect
12. #10591305C2semidirect
13. #10591295C2semidirect
14. #10591294C2semidirect
15. #10591286C2semidirect
31. C3×#895C4semidirect
70. #4980D3semidirect
107. C2×C3×D12C2×C4semidirect
108. C2×C3×D12C2×C4semidirect
111. C2×C3×C4×D3C2×C4semidirect
118. C32×C4⋊C4C2×C4semidirect
121. C3×(C2×D3)⋊C4C2×C4semidirect
122. C3×(C2×D3)⋊C4C2×C4semidirect
192. #895Dic3semidirect
358. C2×D12C2×Dic3semidirect
359. C2×D12C2×Dic3semidirect
368. C2×C4×D3C2×Dic3semidirect
371. C3×C4⋊C4C4×D3semidirect
372. C3×C4⋊C4C2×Dic3semidirect
396. (C2×D3)⋊C4C2×Dic3semidirect
397. (C2×D3)⋊C4C2×Dic3semidirect
683. C4⋊C4D3×Dic3semidirect
792. C32#2377semidirect
925. C3#75313semidirect
926. C3#82639semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
#105926792
C3×#49802
#105913792
#105913772
#105913762
#105913232
#105913182
#105913052
#105912952
#105912942
#105912862
#826393
#753133