Finite Group Databasebeta

← #11807567

Subgroups — #11807567

Order 1152.

1199 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63961C211yesmaximal, characteristic
2#10592644C211yesmaximal, characteristic, complemented
3C3×#4957C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5#10591721C211yesmaximal, characteristic
6#10591703C211yesmaximal, characteristic, complemented
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591368C211yesmaximal, characteristic, complemented
9Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C4×#3724C211yesmaximal, characteristic, complemented
11#10591282C211yesmaximal, characteristic, complemented
12#10591280C211yesmaximal, characteristic, complemented
13#10591255C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#76308—31nomaximal
17#73478—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37#63961C418yescomplemented
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#935—31no—
55C2×#929—31no—
56C3×#390—31no—
57C3×C4×C22⋊C4—31no—
58#5220—31no—
59C4×#217—31no—
60#4978—31no—
61#4978—31no—
62#4957D311yescharacteristic
63#4956—31no—
64#4945—31no—
65#4945—31no—
66#4945—31no—
67#4945—31no—
68#4945—31no—
69#4945—61no—
70#4944—31no—
71Dic3×C22⋊C4—31no—
72Dic3×C22⋊C4—31no—
73Dic3×C22⋊C4—31no—
74Dic3×C22⋊C4D311yescharacteristic, complemented
75#4940—31no—
76C4×(C2×D3)⋊C4—31no—
77#4933—31no—
78C4×Dic3⋊C4—31no—
79C4×Dic3⋊C4—31no—
80C4×Dic3⋊C4—31no—
81#4669—31no—
82#4666—31no—
83#4652—31no—
84#4649—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C3×#67—41no—
94C2×C3×#67—41no—
95C2×C3×#67C2×C414yes—
96C22×C3×Dic3—41no—
97C22×C3×Dic3—41no—
98C22×C3×Dic3C2×C414yescomplemented
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×D3×Dic3—22no—
107C2×D3×Dic3—22no—
108C2×D3×Dic3—41no—
109C32×C22⋊C4—22no—
110#3757—22no—
111#3757C2×C414yescomplemented
112#3750—22no—
113C4×C3⋊Dic3—22no—
114C3×#217—22no—
115C3×#217—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×Dic3⋊C4—41no—
119C3×C4×Dic3—41no—
120C3×C4×Dic3—41no—
121C3×C4×Dic3—41no—
122#3724—22no—
123#3724C2×C414yescomplemented
124#3724C2×C414yescomplemented
125(C2×D3)⋊Dic3—41no—
126(C2×D3)⋊Dic3C2×C414yes—
127(C2×D3)⋊Dic3C2×C414yes—
128Dic32—22no—
129Dic32—41no—
130Dic32—41no—
131#2374—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—31no—
134C22×#67C2×D311yescharacteristic
135C23×Dic3—31no—
136C23×Dic3C2×D311yescharacteristic
137C22×C4×D3—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—61no—
157C2×#217—61no—
158C2×#217C2×D311yescharacteristic
159C2×#217C2×D311yescharacteristic
160#935—38no—
161#929—38no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×(C2×D3)⋊C4C2×D311yescharacteristic
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—61no—
176C2×Dic3⋊C4C2×D311yescharacteristic
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—61no—
186C2×C4×Dic3C2×D311yescharacteristic
187C2×C4×Dic3C2×D311yescharacteristic
188C2×C4×Dic3C2×D311yescharacteristic
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—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—61no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32C22×C412yes—
218C23×C32C2411yescharacteristic
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×D3C22×C412yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4#4112yes—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
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⋊Dic3C22×C412yes—
242C2×C3⋊Dic3C22×C412yes—
243C2×C3⋊Dic3#4112yes—
244C3×#67—44no—
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—44no—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3#4112yes—
266C2×C3×Dic3#4112yes—
267D3×Dic3—44no—
268C2×#123—91no—
269#390—31no—
270#388—91no—
271#388—91no—
272#388—91no—
273#388—91no—
274#387—91no—
275#387—91no—
276#386—91no—
277C4×C4⋊C4—91no—
278C4×C4⋊C4—91no—
279C4×C22⋊C4—31no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283C24×C3—21no—
284C24×C3—31no—
285C24×C3C22×D311yescharacteristic
286C24×C3C22×D311yescharacteristic
287C23×D3C22×D311yescharacteristic
288C2×C3×D4—34no—
289C2×C3×D4—121no—
290C2×C3×D4—121no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—34no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—121no—
302C22×C3×C4—121no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—41no—
308C2×#67—41no—
309C2×#67C4×D314yes—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—41no—
319C22×Dic3—41no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—62no—
325C22×Dic3—62no—
326C22×Dic3—121no—
327C22×Dic3C4×D314yescomplemented
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3—121no—
338C3×C4⋊C4—121no—
339C3×C22⋊C4—22no—
340C3×C22⋊C4—22no—
341C3×C22⋊C4—42no—
342C3×C22⋊C4—62no—
343C3×C22⋊C4—62no—
344C3×C22⋊C4—62no—
345C3×C22⋊C4—62no—
346C3×C42—121no—
347C3×C42—121no—
348C3×C42—121no—
349#217—22no—
350#217—22no—
351#217—34no—
352#217—34no—
353#217—34no—
354#217—34no—
355#217—64no—
356#217—62no—
357#217—62no—
358#217—122no—
359#217—121no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—34no—
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—121no—
365Dic3⋊C4—34no—
366Dic3⋊C4—34no—
367Dic3⋊C4—34no—
368Dic3⋊C4—34no—
369Dic3⋊C4—41no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—122no—
375C4×Dic3—41no—
376C4×Dic3—41no—
377C4×Dic3—41no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3—62no—
382C4×Dic3—122no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3—121no—
386C4×Dic3—121no—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32C23×C411yescharacteristic
395C22×C32C2×#4111yescharacteristic
396C22×C32C2×#4111yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32H(5,𝔽2)11yescharacteristic
400C22×C32H(5,𝔽2)11yescharacteristic
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C32×C4—22no—
409C32×C4—41no—
410C3⋊Dic3—22no—
411C3⋊Dic3—22no—
412C3⋊Dic3—22no—
413C3⋊Dic3—41no—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—31no—
422C23×C4—31no—
423C23×C4—91no—
424#123—98no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—91no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—91no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
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⋊C4D3211yescharacteristic
440C2×C42—31no—
441C2×C42—31no—
442C2×C42—31no—
443C2×C42—91no—
444C2×C42—91no—
445C2×C42—91no—
446C2×C42—91no—
447#95—31no—
448#95—31no—
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—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—22no—
471C23×C3—32no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3C2×C4×D312yes—
485C23×C3C2×C4×D312yes—
486C23×C3C23×D311yescharacteristic
487C23×C3C23×D311yescharacteristic
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3C2×C4×D312yes—
495C3×D4—124no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
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—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—124no—
534C2×C3×C4#23512yes—
535C2×C3×C4#23712yes—
536#67—44no—
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—21no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—44no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3—62no—
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—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—124no—
591C2×Dic3C2×C4×D312yes—
592C2×Dic3C2×C4×D312yes—
593C2×Dic3C2×C4×D312yes—
594C2×Dic3#23512yes—
595C2×Dic3#23712yes—
596C4×D3—124no—
597C2×C32—42no—
598C2×C32C4×#4111yescharacteristic
599C2×C32C4×#4111yescharacteristic
600C2×C32#51811yescharacteristic
601C2×C32#55111yescharacteristic
602C2×C32#55311yescharacteristic
603C2×C32#55311yescharacteristic
604C2×C32#55911yescharacteristic
605C3×D3—42no—
606C24—31no—
607C24C2×D3211yescharacteristic
608C2×D4—34no—
609C2×D4—121no—
610C2×D4—121no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—34no—
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—182no—
626C22×C4—182no—
627C22×C4—361no—
628C22×C4C2×D3211yescharacteristic
629C22×C4C2×D3211yescharacteristic
630C4⋊C4—94no—
631C4⋊C4—94no—
632C4⋊C4—121no—
633C4⋊C4—182no—
634C4⋊C4—182no—
635C22⋊C4—22no—
636C22⋊C4—62no—
637C22⋊C4—62no—
638C22⋊C4—62no—
639C22⋊C4—62no—
640C22⋊C4—94no—
641C22⋊C4—94no—
642C22⋊C4—94no—
643C22⋊C4—182no—
644C22⋊C4—361no—
645C42—121no—
646C42—121no—
647C42—121no—
648C42—182no—
649C42—182no—
650C42—361no—
651C42—361no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3C22×C4×D311yescharacteristic
688C22×C3C22×C4×D311yescharacteristic
689C22×C3C2×#23511yescharacteristic
690C22×C3C2×#23511yescharacteristic
691C22×C3C2×#23711yescharacteristic
692C22×C3C2×#23711yescharacteristic
693C22×C3#100411yescharacteristic
694C22×C3#100411yescharacteristic
695C22×C3#100411yescharacteristic
696C22×C3#100411yescharacteristic
697C22×C3D3×#4111yescharacteristic
698C22×C3D3×#4111yescharacteristic
699C22×C3D3×#4111yescharacteristic
700C22×C3D3×#4111yescharacteristic
701C2×D3—22no—
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—42no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—62no—
714C3×C4—62no—
715C3×C4—62no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—81no—
719C3×C4—121no—
720C3×C4—121no—
721Dic3—22no—
722Dic3—22no—
723Dic3—22no—
724Dic3—22no—
725Dic3—22no—
726Dic3—41no—
727Dic3—41no—
728Dic3—62no—
729Dic3—62no—
730Dic3—62no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—122no—
735Dic3—122no—
736Dic3—122no—
737Dic3—121no—
738Dic3—121no—
739Dic3—241no—
740C32#237411yescharacteristic, complemented, Sylow
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—32no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23C4×D3212yes—
755C23C22×D3211yescharacteristic
756D4—124no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—32no—
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—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—92no—
784C2×C4—92no—
785C2×C4—92no—
786C2×C4—124no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—364no—
797C2×C4#380412yes—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—42no—
806C2×C3—42no—
807C2×C3—82no—
808C2×C3—122no—
809C2×C3C4×#23511yescharacteristic
810C2×C3#548611yescharacteristic
811C2×C3#548611yescharacteristic
812C2×C3#552211yescharacteristic
813C2×C3C4×#23711yescharacteristic
814C2×C3C4×#23711yescharacteristic
815C2×C3#554011yescharacteristic
816C2×C3#555611yescharacteristic
817C2×C3#555811yescharacteristic
818C2×C3#555911yescharacteristic
819C2×C3#560111yescharacteristic
820C2×C3#560111yescharacteristic
821C2×C3#567911yescharacteristic
822C2×C3#571311yescharacteristic
823D3—42no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—62no—
832C22—62no—
833C22—62no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22C2×C4×D3211yescharacteristic
839C22D3×#23511yescharacteristic
840C22D3×#23711yescharacteristic
841C22#6431211yescharacteristic
842C22#6431311yescharacteristic
843C22#6431311yescharacteristic
844C22C2×#380411yescharacteristic
845C4—22no—
846C4—41no—
847C4—62no—
848C4—62no—
849C4—62no—
850C4—62no—
851C4—62no—
852C4—121no—
853C4—121no—
854C4—182no—
855C4—182no—
856C4—182no—
857C4—361no—
858C3—21no—
859C3#7347811yescharacteristic, complemented
860C3#7630811yescharacteristic, complemented
861C2—42no—
862C2—122no—
863C2#1059404811yescharacteristic
864C2#1059409611yescharacteristic
865C2#1059418111yescharacteristic
866C2#1059430011yescharacteristic
867C2C4×#380411yescharacteristic
868C2#1059519811yescharacteristic
869C2#1059520411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592644C2semidirect
4. C3×Dic3×C22⋊C4C2semidirect
6. #10591703C2semidirect
7. Dic3×#217C2semidirect
8. #10591368C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. C4×#3724C2semidirect
11. #10591282C2semidirect
12. #10591280C2semidirect
13. #10591255C2semidirect
14. #10591243C2semidirect
15. #10591193C2semidirect
37. #63961C4semidirect
74. Dic3×C22⋊C4D3semidirect
98. C22×C3×Dic3C2×C4semidirect
111. #3757C2×C4semidirect
123. #3724C2×C4semidirect
124. #3724C2×C4semidirect
327. C22×Dic3C4×D3semidirect
740. C32#2374semidirect
859. C3#73478semidirect
860. C3#76308semidirect

Maximal subgroups

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

subgroupindex
C2×#639612
#105926442
C3×#49572
C3×Dic3×C22⋊C42
#105917212
#105917032
Dic3×#2172
#105913682
Dic3×(C2×D3)⋊C42
C4×#37242
#105912822
#105912802
#105912552
#105912432
#105911932
#763083
#734783