Finite Group Databasebeta

← #11803092

Subgroups — #11803092

Order 1152.

1213 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic, complemented
3C3×#4980C211yesmaximal, characteristic, complemented
4#10591379C211yesmaximal, characteristic, complemented
5#10591377C211yesmaximal, characteristic, complemented
6#10591376C211yesmaximal, characteristic
7#10591376C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic, complemented
9#10591313C211yesmaximal, characteristic, complemented
10#10591305C211yesmaximal, characteristic, complemented
11#10591294C211yesmaximal, characteristic, complemented
12#10591286C211yesmaximal, characteristic, complemented
13C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
14#10591223C211yesmaximal, characteristic, complemented
15#10591206C211yesmaximal, characteristic, complemented
16#82324—31nomaximal
17#74945—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#893C418yescomplemented
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
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
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×C3×C4×D4—31no—
55C2×#893D311yescharacteristic
56C3×#387—31no—
57#5220—31no—
58#5220—31no—
59#5212—31no—
60#5211—31no—
61C4×#217—31no—
62C2×C3⋊#95—31no—
63#4989—31no—
64#4987—31no—
65#4980—31no—
66#4980—31no—
67#4980—61no—
68#4980D311yescharacteristic, complemented
69#4951—31no—
70#4951—31no—
71#4950—31no—
72#4950—31no—
73#4940—31no—
74C4×(C2×D3)⋊C4—31no—
75#4937—31no—
76#4936—31no—
77#4669—31no—
78#4668—31no—
79#4665—31no—
80#4665—31no—
81#4664—31no—
82D3×#95—31no—
83#4651—31no—
84#4650—31no—
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
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—22no—
101C2×C3×D12—22no—
102C2×C3×D12C2×C414yes—
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3—41no—
106C2×C3×C4×D3—41no—
107C2×C3×C4×D3C2×C414yes—
108C2×C3×C4×D3C2×C414yescomplemented
109C2×D3×Dic3—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—41no—
112C2×D3×Dic3—41no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3—41no—
115C32×C4⋊C4C2×C414yescomplemented
116C4⋊(C3⋊Dic3)—41no—
117C4×C3⋊Dic3—41no—
118C3×(C2×D3)⋊C4C2×C414yes—
119C3×(C2×D3)⋊C4C2×C414yescomplemented
120C3×C4⋊Dic3—41no—
121C3×C4×Dic3—41no—
122C3×C4×Dic3C2×C414yescomplemented
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—41no—
128(C2×D3)⋊Dic3—41no—
129(C2×D3)⋊Dic3—41no—
130(C2×D3)⋊Dic3—41no—
131#2318—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×Dic3—31no—
136C23×Dic3—31no—
137C22×D12C2×D311yescharacteristic
138C22×C4×D3—31no—
139C22×C4×D3—31no—
140C22×C4×D3C2×D311yescharacteristic
141C22×C4×D3C2×D311yescharacteristic
142C3×C4×D4—38no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4C2×D311yescharacteristic
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—61no—
170C2×C4⋊Dic3C2×D311yescharacteristic
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—61no—
176C2×C4×Dic3C2×D311yescharacteristic
177C2×C4×Dic3C2×D311yescharacteristic
178#893Dic318yescomplemented
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⋊#95—61no—
206C3⋊#95—61no—
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32C2411yescharacteristic
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3C22×C412yes—
223C22×C3×D3C22×C412yes—
224C22×C3×D3#4112yes—
225C22×C3×D3#4112yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4C22×C412yes—
233C2×C32×C4C22×C412yes—
234C2×C32×C4C22×C412yes—
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×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×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C3×D12—28no—
266C3×C4×D3—44no—
267C3×C4×D3—44no—
268D3×Dic3—44no—
269D3×Dic3—44no—
270C2×C4×D4—31no—
271#388—91no—
272#388—91no—
273#387—31no—
274#387—91no—
275#386—91no—
276#386—91no—
277#385—91no—
278#385—91no—
279#383—91no—
280#382—91no—
281#381—91no—
282#380—91no—
283C4×C22⋊C4—91no—
284C2×#95—91no—
285C24×C3—31no—
286C24×C3—31no—
287C23×D3C22×D311yescharacteristic
288C23×D3C22×D311yescharacteristic
289C2×C3×D4—34no—
290C2×C3×D4—62no—
291C2×C3×D4—62no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—34no—
298C22×C3×C4—34no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—121no—
304C22×C3×C4—121no—
305C22×C3×C4—121no—
306C22×C3×C4—121no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—62no—
326C22×Dic3—62no—
327C22×Dic3—121no—
328C22×Dic3—121no—
329C22×Dic3—121no—
330C22×Dic3—121no—
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C2×D12—22no—
338C2×D12—22no—
339C2×D12C2×Dic314yes—
340C2×C4×D3—41no—
341C2×C4×D3—41no—
342C2×C4×D3—41no—
343C2×C4×D3—41no—
344C2×C4×D3—62no—
345C2×C4×D3—62no—
346C2×C4×D3—121no—
347C2×C4×D3—121no—
348C2×C4×D3—121no—
349C2×C4×D3—121no—
350C2×C4×D3C2×Dic314yes—
351C2×C4×D3C2×Dic314yescomplemented
352C3×C4⋊C4—24no—
353C3×C4⋊C4—121no—
354C3×C4⋊C4C4×D314yescomplemented
355C3×C4⋊C4C2×Dic314yescomplemented
356C3×C22⋊C4—34no—
357C3×C22⋊C4—34no—
358C3×C42—34no—
359C3×C42—121no—
360#217—62no—
361#217—62no—
362#217—121no—
363#217—121no—
364#217—121no—
365#217—121no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4—121no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4C2×Dic314yes—
373(C2×D3)⋊C4C2×Dic314yescomplemented
374C4⋊Dic3—41no—
375C4⋊Dic3—121no—
376C4⋊Dic3—121no—
377C4⋊Dic3—121no—
378C4⋊Dic3—121no—
379C4⋊Dic3—122no—
380Dic3⋊C4—121no—
381Dic3⋊C4—121no—
382C4×Dic3—41no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3—122no—
386C4×Dic3C2×Dic314yescomplemented
387C22×C32C23×C411yescharacteristic
388C22×C32C2×#4111yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32H(5,𝔽2)11yescharacteristic
391C22×C32H(5,𝔽2)11yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C322−1+411yescharacteristic
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3#11714yes—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—22no—
411C3⋊Dic3—41no—
412C3⋊Dic3—41no—
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—91no—
425C23×C4—91no—
426C4×D4—38no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—91no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4D3211yescharacteristic
432C2×C22⋊C4—31no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—91no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—91no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440C2×C42—31no—
441C2×C42—31no—
442C2×C42—91no—
443#95—31no—
444#95—31no—
445#95—31no—
446#95—31no—
447#95—91no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457C23×C3—21no—
458C23×C3—32no—
459C23×C3—32no—
460C23×C3—32no—
461C23×C3—32no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3C23×D311yescharacteristic
473C23×C3C23×D311yescharacteristic
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3#23512yes—
485C22×D3#23512yes—
486C22×D3C22×Dic312yes—
487C22×D3C22×Dic312yes—
488C3×D4—68no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—124no—
529C2×C3×C4—124no—
530C2×C3×C4C2×C4×D312yes—
531C2×C3×C4C2×C4×D312yes—
532C2×C3×C4C2×C4×D312yes—
533C2×C3×C4C22×Dic312yes—
534C2×C3×C4C22×Dic312yes—
535C2×C3×C4C22×Dic312yes—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—121no—
579C2×Dic3—121no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—124no—
589C2×Dic3—124no—
590C2×Dic3C22×Dic312yes—
591C2×Dic3C22×Dic312yes—
592D12—28no—
593C4×D3—44no—
594C4×D3—44no—
595C4×D3—124no—
596C4×D3—124no—
597C2×C32C2×#11711yescharacteristic
598C2×C32#51811yescharacteristic
599C2×C32#52011yescharacteristic
600C2×C32#53811yescharacteristic
601C2×C32#53811yescharacteristic
602C2×C32#53911yescharacteristic
603C2×C32#53911yescharacteristic
604C3×D3—24no—
605C3×D3—42no—
606C24—31no—
607C24—31no—
608C2×D4—34no—
609C2×D4—62no—
610C2×D4—62no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—34no—
614C22×C4—34no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—91no—
620C22×C4—91no—
621C22×C4—91no—
622C22×C4—91no—
623C22×C4—121no—
624C22×C4—121no—
625C22×C4—121no—
626C22×C4—121no—
627C22×C4—182no—
628C22×C4—182no—
629C22×C4—361no—
630C22×C4—361no—
631C22×C4—361no—
632C22×C4—361no—
633C22×C4C2×D3211yescharacteristic
634C22×C4C2×D3211yescharacteristic
635C22×C4C2×D3211yescharacteristic
636C4⋊C4—121no—
637C4⋊C4—361no—
638C4⋊C4—361no—
639C4⋊C4—361no—
640C4⋊C4D3×Dic314yescomplemented
641C22⋊C4—34no—
642C22⋊C4—34no—
643C22⋊C4—182no—
644C22⋊C4—182no—
645C22⋊C4—361no—
646C22⋊C4—361no—
647C22⋊C4—361no—
648C22⋊C4—361no—
649C42—34no—
650C42—121no—
651C42—361no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—34no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—62no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C22×C4×D311yescharacteristic
674C22×C3C2×#23511yescharacteristic
675C22×C3C2×#23511yescharacteristic
676C22×C3#100411yescharacteristic
677C22×C3#100411yescharacteristic
678C22×C3#100411yescharacteristic
679C22×C3#100711yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3#100911yescharacteristic
683C22×C3#100911yescharacteristic
684C22×C3#100911yescharacteristic
685C22×C3#101011yescharacteristic
686C22×C3C23×Dic311yescharacteristic
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3#92614yes—
701C3×C4—22no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—22no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—42no—
710C3×C4—62no—
711C3×C4—62no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716Dic3—22no—
717Dic3—22no—
718Dic3—41no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722Dic3—122no—
723Dic3—122no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—241no—
733Dic3—241no—
734C32#231811yescharacteristic, complemented, Sylow
735C23—32no—
736C23—32no—
737C23—32no—
738C23—32no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23C22×D3211yescharacteristic
750D4—68no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—124no—
776C2×C4—124no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—364no—
790C2×C4—364no—
791C2×C4C2×D3×Dic312yes—
792C2×C4C2×D3×Dic312yes—
793C2×C4C2×D3×Dic312yes—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—64no—
802C2×C3—122no—
803C2×C3D3×#11711yescharacteristic
804C2×C3#554511yescharacteristic
805C2×C3#556011yescharacteristic
806C2×C3#556011yescharacteristic
807C2×C3#556411yescharacteristic
808C2×C3#556411yescharacteristic
809C2×C3#557411yescharacteristic
810C2×C3#563811yescharacteristic
811C2×C3#565711yescharacteristic
812C2×C3#569211yescharacteristic
813C2×C3#570411yescharacteristic
814C2×C3C2×#92611yescharacteristic
815C2×C3#579811yescharacteristic
816C2×C3#582711yescharacteristic
817D3—24no—
818D3—42no—
819C22—34no—
820C22—62no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—62no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22D3×#23511yescharacteristic
834C22D3×#23511yescharacteristic
835C22#6431311yescharacteristic
836C22#6431411yescharacteristic
837C22#6431511yescharacteristic
838C22#6432011yescharacteristic
839C22C22×D3×Dic311yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—62no—
844C4—62no—
845C4—121no—
846C4—121no—
847C4—121no—
848C4—121no—
849C4—361no—
850C4—361no—
851C4—361no—
852C4—361no—
853C3—21no—
854C3#7494511yescharacteristic, complemented
855C3#8232411yescharacteristic, complemented
856C2—64no—
857C2—122no—
858C2#1059440611yescharacteristic
859C2#1059440711yescharacteristic
860C2#1059463811yescharacteristic
861C2#1059463911yescharacteristic
862C2D3×#92611yescharacteristic
863C2#1059521511yescharacteristic
864C2#1059539411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2318
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
8. D3×C3⋊#95C2semidirect
9. #10591313C2semidirect
10. #10591305C2semidirect
11. #10591294C2semidirect
12. #10591286C2semidirect
13. C4×(C2×D3)⋊Dic3C2semidirect
14. #10591223C2semidirect
15. #10591206C2semidirect
31. C3×#893C4semidirect
68. #4980D3semidirect
108. C2×C3×C4×D3C2×C4semidirect
115. C32×C4⋊C4C2×C4semidirect
119. C3×(C2×D3)⋊C4C2×C4semidirect
122. C3×C4×Dic3C2×C4semidirect
178. #893Dic3semidirect
351. C2×C4×D3C2×Dic3semidirect
354. C3×C4⋊C4C4×D3semidirect
355. C3×C4⋊C4C2×Dic3semidirect
373. (C2×D3)⋊C4C2×Dic3semidirect
386. C4×Dic3C2×Dic3semidirect
640. C4⋊C4D3×Dic3semidirect
734. C32#2318semidirect
854. C3#74945semidirect
855. C3#82324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
#105926792
C3×#49802
#105913792
#105913772
#105913762
D3×C3⋊#952
#105913132
#105913052
#105912942
#105912862
C4×(C2×D3)⋊Dic32
#105912232
#105912062
#823243
#749453