Finite Group Databasebeta

← #11802771

Subgroups — #11802771

Order 1152.

1439 conjugacy classes of subgroups.

The subgroup lattice has 967 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
2#10592650C211yesmaximal, characteristic, complemented
3C3×#4951C211yesmaximal, characteristic, complemented
4#10591706C211yesmaximal, characteristic
5#10591706C211yesmaximal, characteristic
6#10591702C211yesmaximal, characteristic, complemented
7#10591701C211yesmaximal, characteristic, complemented
8#10591316C211yesmaximal, characteristic, complemented
9#10591313C211yesmaximal, characteristic, complemented
10#10591307C211yesmaximal, characteristic, complemented
11#10591305C211yesmaximal, characteristic, complemented
12#10591295C211yesmaximal, characteristic, complemented
13#10591286C211yesmaximal, characteristic, complemented
14C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic, complemented
16#82093—31nomaximal
17#75825—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
25C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
32C2×C3×C4×Dic3C2211yescharacteristic, complemented
33C3×D3×C22⋊C4C418yescomplemented
34C2×Dic3⋊Dic3C2211yescharacteristic, complemented
35C2×Dic3⋊Dic3C2211yescharacteristic, complemented
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
44C2×Dic32C2211yescharacteristic, complemented
45C2×Dic32C2211yescharacteristic, complemented
46#63658C2211yescharacteristic, complemented
47#63658C2211yescharacteristic, complemented
48C3×C3⋊#95C2211yescharacteristic, complemented
49C3×C3⋊#95C2211yescharacteristic, complemented
50#63579C2211yescharacteristic, complemented
51#63579C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54C22×C3×C22⋊C4—31no—
55C2×D3×C22⋊C4D311yescharacteristic
56C3×#388—31no—
57#5247—31no—
58#5247—31no—
59#5212—31no—
60#5212—31no—
61C4×#217—31no—
62C4×#217—31no—
63#4990—31no—
64#4987—31no—
65#4955—31no—
66#4955—31no—
67#4951—31no—
68#4951—31no—
69#4951—31no—
70#4951—31no—
71#4951—31no—
72#4951—31no—
73#4951—31no—
74#4951—31no—
75#4951—61no—
76#4951D311yescharacteristic, complemented
77#4945—31no—
78#4944—31no—
79#4940—31no—
80C4×(C2×D3)⋊C4—31no—
81#4670—31no—
82#4669—31no—
83#4667—31no—
84#4666—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3—22no—
87C23×C3×D3—22no—
88C23×C3×D3—41no—
89C23×C3×D3—41no—
90C23×C3×D3—41no—
91C23×C3×D3—41no—
92C23×C3×D3C2×C414yes—
93C23×C3×D3C2311yescharacteristic
94C23×C3×D3C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×C4×D3—41no—
108C2×C3×C4×D3—41no—
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3C2×C414yes—
112C2×C3×C4×D3C2×C414yes—
113C32×C22⋊C4C2×C414yes—
114#3757—41no—
115#3757—41no—
116C4⋊(C3⋊Dic3)—41no—
117C4×C3⋊Dic3—41no—
118C3×#217—41no—
119C3×#217—41no—
120C3×#217C2×C414yes—
121C3×(C2×D3)⋊C4C2×C414yes—
122C3×(C2×D3)⋊C4C2×C414yes—
123C3×C4⋊Dic3—41no—
124C3×C4×Dic3—41no—
125Dic3⋊Dic3—41no—
126Dic3⋊Dic3—41no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3—41no—
132(C2×D3)⋊Dic3—41no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3—41no—
135Dic32—41no—
136Dic32—41no—
137#2312—91noSylow
138C25×C3—31no—
139C24×D3C2×D311yescharacteristic
140C23×C3×C4—31no—
141C23×C3×C4—31no—
142C22×C4×D3C2×D311yescharacteristic
143C22×C4×D3C2×D311yescharacteristic
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—38no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4C2×D311yescharacteristic
153C2×C3×C22⋊C4C2×D311yescharacteristic
154C2×C3×C42—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—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—61no—
168C2×#217—61no—
169C2×#217C2×D311yescharacteristic
170C2×#217C2×D311yescharacteristic
171C2×#217C2×D311yescharacteristic
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)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187C2×C4⋊Dic3C2×D311yescharacteristic, complemented
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—61no—
197C2×C4×Dic3C2×D311yescharacteristic, complemented
198D3×C22⋊C4Dic318yescomplemented
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—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—61no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic, complemented
216C3⋊#95C2×D311yescharacteristic, complemented
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32C22×C412yes—
224C23×C32C2411yescharacteristic
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—28no—
236C22×C3×D3—44no—
237C22×C3×D3—44no—
238C22×C3×D3—44no—
239C22×C3×D3—44no—
240C22×C3×D3—44no—
241C22×C3×D3—44no—
242C22×C3×D3C22×C412yes—
243C22×C3×D3C22×C412yes—
244C22×C3×D3#4112yes—
245C22×C3×D3#4112yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C22×C412yes—
251C2×C32×C4C22×C412yes—
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×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C22×C412yes—
281C2×C3×Dic3C22×C412yes—
282C3×C4×D3—44no—
283C3×C4×D3—44no—
284C22×C22⋊C4—31no—
285#388—31no—
286#388—91no—
287#388—91no—
288#388—91no—
289#388—91no—
290#388—91no—
291#388—91no—
292#388—91no—
293#380—91no—
294#380—91no—
295#379—91no—
296#379—91no—
297C4×C22⋊C4—91no—
298C4×C22⋊C4—91no—
299C24×C3—21no—
300C24×C3—31no—
301C24×C3—31no—
302C24×C3—34no—
303C24×C3—62no—
304C24×C3—62no—
305C24×C3—121no—
306C24×C3—121no—
307C24×C3—121no—
308C24×C3—121no—
309C24×C3C22×D311yescharacteristic
310C24×C3C22×D311yescharacteristic
311C23×D3—22no—
312C23×D3—22no—
313C23×D3—41no—
314C23×D3—41no—
315C23×D3—41no—
316C23×D3—41no—
317C23×D3C2×Dic314yes—
318C23×D3C22×D311yescharacteristic
319C23×D3C22×D311yescharacteristic
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—34no—
325C22×C3×C4—34no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—121no—
331C22×C3×C4—121no—
332C22×C3×C4—121no—
333C22×C3×C4—121no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C2×C4×D3—41no—
357C2×C4×D3—41no—
358C2×C4×D3—41no—
359C2×C4×D3—41no—
360C2×C4×D3C2×Dic314yes—
361C2×C4×D3C2×Dic314yes—
362C3×C4⋊C4—121no—
363C3×C22⋊C4—24no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—121no—
368C3×C22⋊C4—121no—
369C3×C22⋊C4C4×D314yes—
370C3×C22⋊C4C2×Dic314yes—
371C3×C42—121no—
372#217—41no—
373#217—41no—
374#217—62no—
375#217—62no—
376#217—62no—
377#217—62no—
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#217—122no—
387#217—122no—
388#217C2×Dic314yes—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—121no—
394(C2×D3)⋊C4—121no—
395(C2×D3)⋊C4—121no—
396(C2×D3)⋊C4—121no—
397(C2×D3)⋊C4C2×Dic314yes—
398(C2×D3)⋊C4C2×Dic314yes—
399C4⋊Dic3—41no—
400C4⋊Dic3—121no—
401C4⋊Dic3—121no—
402C4⋊Dic3—121no—
403C4⋊Dic3—121no—
404C4⋊Dic3—122no—
405Dic3⋊C4—121no—
406Dic3⋊C4—121no—
407C4×Dic3—41no—
408C4×Dic3—121no—
409C4×Dic3—121no—
410C4×Dic3—121no—
411C4×Dic3—121no—
412C4×Dic3—121no—
413C4×Dic3—121no—
414C4×Dic3—122no—
415C22×C32—22no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C23×C411yescharacteristic
423C22×C32C2×#4111yescharacteristic
424C22×C32C2×#4111yescharacteristic
425C22×C32H(5,𝔽2)11yescharacteristic
426C22×C32H(5,𝔽2)11yescharacteristic
427C22×C32H(5,𝔽2)11yescharacteristic
428C22×C32H(5,𝔽2)11yescharacteristic
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—416no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3#11714yes—
444C32×C4—22no—
445C32×C4—22no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C25—31no—
457C23×C4—31no—
458C23×C4—31no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—38no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
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×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4D3211yescharacteristic
480C2×C42—31no—
481C2×C42—91no—
482C2×C42—91no—
483C2×C42—91no—
484#95—31no—
485#95—31no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—22no—
506C23×C3—32no—
507C23×C3—32no—
508C23×C3—32no—
509C23×C3—32no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—68no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—124no—
528C23×C3—124no—
529C23×C3—124no—
530C23×C3—124no—
531C23×C3—124no—
532C23×C3—124no—
533C23×C3C2×C4×D312yes—
534C23×C3C22×Dic312yes—
535C23×C3C23×D311yescharacteristic
536C23×C3C23×D311yescharacteristic
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—28no—
548C22×D3—44no—
549C22×D3—44no—
550C22×D3—44no—
551C22×D3—44no—
552C22×D3—44no—
553C22×D3—44no—
554C22×D3#23512yes—
555C22×D3#23512yes—
556C22×D3C22×Dic312yes—
557C22×D3C22×Dic312yes—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
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—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—124no—
591C2×C3×C4—124no—
592C2×C3×C4C2×C4×D312yes—
593C2×C3×C4C2×C4×D312yes—
594C2×C3×C4C22×Dic312yes—
595C2×C3×C4C22×Dic312yes—
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—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
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—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—121no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3C22×Dic312yes—
649C2×Dic3C22×Dic312yes—
650C4×D3—44no—
651C4×D3—44no—
652C2×C32—42no—
653C2×C32C2×#11711yescharacteristic
654C2×C32#51811yescharacteristic
655C2×C32#51811yescharacteristic
656C2×C32#53811yescharacteristic
657C2×C32#53811yescharacteristic
658C2×C32#53811yescharacteristic
659C2×C32#53811yescharacteristic
660C3×D3—24no—
661C3×D3—42no—
662C24—31no—
663C24—31no—
664C24—34no—
665C24—62no—
666C24—62no—
667C24—121no—
668C24—121no—
669C24—121no—
670C24—121no—
671C24C2×D3211yescharacteristic
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—34no—
675C22×C4—34no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—121no—
685C22×C4—121no—
686C22×C4—121no—
687C22×C4—121no—
688C22×C4C2×D3211yescharacteristic
689C22×C4C2×D3211yescharacteristic
690C4⋊C4—121no—
691C4⋊C4—361no—
692C4⋊C4—361no—
693C4⋊C4—361no—
694C22⋊C4—34no—
695C22⋊C4—34no—
696C22⋊C4—34no—
697C22⋊C4—121no—
698C22⋊C4—121no—
699C22⋊C4—182no—
700C22⋊C4—182no—
701C22⋊C4—182no—
702C22⋊C4—182no—
703C22⋊C4—361no—
704C22⋊C4—361no—
705C22⋊C4—361no—
706C22⋊C4—361no—
707C22⋊C4—361no—
708C22⋊C4—361no—
709C22⋊C4D3×Dic314yes—
710C42—121no—
711C42—361no—
712C42—361no—
713C42—361no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—34no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—62no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—1216no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3C22×C4×D311yescharacteristic
758C22×C3C2×#23511yescharacteristic
759C22×C3C2×#23511yescharacteristic
760C22×C3#100411yescharacteristic
761C22×C3#100411yescharacteristic
762C22×C3#100411yescharacteristic
763C22×C3#100411yescharacteristic
764C22×C3#100411yescharacteristic
765C22×C3#100411yescharacteristic
766C22×C3D3×#4111yescharacteristic
767C22×C3D3×#4111yescharacteristic
768C22×C3#100911yescharacteristic
769C22×C3#100911yescharacteristic
770C22×C3C23×Dic311yescharacteristic
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—416no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3#92614yes—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—42no—
791C3×C4—42no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—121no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4—121no—
798Dic3—22no—
799Dic3—22no—
800Dic3—41no—
801Dic3—41no—
802Dic3—41no—
803Dic3—41no—
804Dic3—122no—
805Dic3—122no—
806Dic3—121no—
807Dic3—121no—
808Dic3—121no—
809Dic3—121no—
810Dic3—121no—
811Dic3—121no—
812Dic3—121no—
813Dic3—121no—
814Dic3—241no—
815Dic3—241no—
816C32#231211yescharacteristic, complemented, Sylow
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—32no—
824C23—32no—
825C23—32no—
826C23—32no—
827C23—68no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—124no—
839C23—124no—
840C23—124no—
841C23—124no—
842C23—124no—
843C23—124no—
844C23C2×D3×Dic312yes—
845C23C22×D3211yescharacteristic
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—181no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—181no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4C2×D3×Dic312yes—
883C2×C4C2×D3×Dic312yes—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—42no—
892C2×C3—42no—
893C2×C3—64no—
894C2×C3—82no—
895C2×C3—122no—
896C2×C3#549411yescharacteristic
897C2×C3#549411yescharacteristic
898C2×C3#549411yescharacteristic
899C2×C3#549411yescharacteristic
900C2×C3D3×#11711yescharacteristic
901C2×C3#554511yescharacteristic
902C2×C3#554511yescharacteristic
903C2×C3#561311yescharacteristic
904C2×C3#565711yescharacteristic
905C2×C3#567811yescharacteristic
906C2×C3#570411yescharacteristic
907C2×C3C2×#92611yescharacteristic
908C2×C3#579811yescharacteristic
909C2×C3#579811yescharacteristic
910D3—24no—
911D3—42no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—34no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—62no—
921C22—62no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—1216no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22D3×#23511yescharacteristic
935C22D3×#23511yescharacteristic
936C22#6431311yescharacteristic
937C22#6431311yescharacteristic
938C22#6431411yescharacteristic
939C22#6431411yescharacteristic
940C22C22×D3×Dic311yescharacteristic
941C4—22no—
942C4—22no—
943C4—62no—
944C4—62no—
945C4—121no—
946C4—121no—
947C4—121no—
948C4—121no—
949C4—361no—
950C4—361no—
951C4—361no—
952C4—361no—
953C3—21no—
954C3#7582511yescharacteristic, complemented
955C3#8209311yescharacteristic, complemented
956C2—42no—
957C2—64no—
958C2—122no—
959C2#1059419411yescharacteristic
960C2#1059419511yescharacteristic
961C2#1059419611yescharacteristic
962C2#1059419911yescharacteristic
963C2D3×#92611yescharacteristic
964C2#1059521511yescharacteristic
965C2#1059521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592650C2semidirect
3. C3×#4951C2semidirect
6. #10591702C2semidirect
7. #10591701C2semidirect
8. #10591316C2semidirect
9. #10591313C2semidirect
10. #10591307C2semidirect
11. #10591305C2semidirect
12. #10591295C2semidirect
13. #10591286C2semidirect
14. C4×(C2×D3)⋊Dic3C2semidirect
15. #10591237C2semidirect
24. C2×C4⋊(C3⋊Dic3)C22semidirect
25. C2×C4×C3⋊Dic3C22semidirect
31. C2×C3×C4⋊Dic3C22semidirect
32. C2×C3×C4×Dic3C22semidirect
33. C3×D3×C22⋊C4C4semidirect
34. C2×Dic3⋊Dic3C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
44. C2×Dic32C22semidirect
45. C2×Dic32C22semidirect
46. #63658C22semidirect
47. #63658C22semidirect
48. C3×C3⋊#95C22semidirect
49. C3×C3⋊#95C22semidirect
50. #63579C22semidirect
51. #63579C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
76. #4951D3semidirect
187. C2×C4⋊Dic3C2×D3semidirect
197. C2×C4×Dic3C2×D3semidirect
198. D3×C22⋊C4Dic3semidirect
215. C3⋊#95C2×D3semidirect
216. C3⋊#95C2×D3semidirect
816. C32#2312semidirect
954. C3#75825semidirect
955. C3#82093semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C22⋊C42
#105926502
C3×#49512
#105917062
#105917022
#105917012
#105913162
#105913132
#105913072
#105913052
#105912952
#105912862
C4×(C2×D3)⋊Dic32
#105912372
#820933
#758253