Finite Group Databasebeta

← #11805780

Subgroups — #11805780

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
4#10591716C211yesmaximal, characteristic, complemented
5#10591713C211yesmaximal, characteristic
6#10591710C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic, complemented
8#10591305C211yesmaximal, characteristic, complemented
9#10591294C211yesmaximal, characteristic, complemented
10#10591286C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
12#10591223C211yesmaximal, characteristic, complemented
13#10591222C211yesmaximal, characteristic, complemented
14#10591201C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82336—31nomaximal
17#73462—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#67⋊C4C418yescomplemented
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×C4×D4—31no—
55C2×#67⋊C4D311yescharacteristic
56C3×C4×C22⋊C4—31no—
57#5220—31no—
58#5220—31no—
59#5213—31no—
60#5212—31no—
61#5211—31no—
62C4×#217—31no—
63C2×C3⋊#95—31no—
64C2×C3⋊#95—31no—
65#4980—31no—
66#4980—31no—
67#4958—31no—
68#4951—31no—
69#4951—31no—
70#4942—31no—
71Dic3×C22⋊C4—31no—
72Dic3×C22⋊C4—31no—
73Dic3×C22⋊C4—61no—
74Dic3×C22⋊C4D311yescharacteristic, complemented
75#4940—31no—
76C4×(C2×D3)⋊C4—31no—
77#4937—31no—
78#4933—31no—
79#4932—31no—
80#4932—31no—
81#4669—31no—
82#4664—31no—
83#4652—31no—
84#4651—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3—22no—
90C22×C3⋊Dic3—22no—
91C22×C3⋊Dic3—41no—
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C3×#67—22no—
97C2×C3×#67—22no—
98C2×C3×#67C2×C414yes—
99C22×C3×Dic3—22no—
100C22×C3×Dic3—22no—
101C22×C3×Dic3—41no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3C2×C414yes—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3C2×C414yescomplemented
115C32×C22⋊C4C2×C414yes—
116#3757—22no—
117C4×C3⋊Dic3—22no—
118C4×C3⋊Dic3—41no—
119C3×#217—22no—
120C3×(C2×D3)⋊C4C2×C414yescomplemented
121C3×Dic3⋊C4C2×C414yescomplemented
122C3×C4×Dic3—22no—
123C3×C4×Dic3—41no—
124C3×C4×Dic3C2×C414yescomplemented
125Dic3⋊Dic3—41no—
126Dic3⋊Dic3—41no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—41no—
130(C2×D3)⋊Dic3—41no—
131#2353—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×C3×C4—31no—
136C22×#67C2×D311yescharacteristic
137C23×Dic3—31no—
138C23×Dic3—31no—
139C23×Dic3—61no—
140C23×Dic3C2×D311yescharacteristic
141C23×Dic3C2×D311yescharacteristic
142C22×C4×D3C2×D311yescharacteristic
143C3×C4×D4—38no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4C2×D311yescharacteristic
149C2×C3×C22⋊C4C2×D311yescharacteristic
150C2×C3×C42—31no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—61no—
160C2×#217C2×D311yescharacteristic
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—61no—
176C2×C4×Dic3—61no—
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179C2×C4×Dic3C2×D311yescharacteristic
180#67⋊C4Dic318yescomplemented
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—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×C32C22×C412yes—
216C23×C32#4112yes—
217C23×C32#4112yes—
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×C4C22×C412yes—
231C2×C32×C4C22×C412yes—
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⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—44no—
244C2×C3⋊Dic3#4112yes—
245C3×#67—28no—
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×Dic3—44no—
264C2×C3×Dic3—44no—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3#4112yes—
269C3×C4×D3—44no—
270C2×C4×D4—31no—
271#388—91no—
272#388—91no—
273#387—91no—
274#387—91no—
275#386—91no—
276#386—91no—
277#383—91no—
278#381—91no—
279#380—91no—
280C4×C22⋊C4—31no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283#376—91no—
284C2×#95—91no—
285C24×C3—21no—
286C24×C3—31no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C23×D3C22×D311yescharacteristic
290C2×C3×D4—34no—
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—34no—
300C22×C3×C4—34no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—62no—
305C22×C3×C4—62no—
306C22×C3×C4—121no—
307C22×C3×C4—121no—
308C22×C3×C4—121no—
309C22×C3×C4—121no—
310C22×C3×C4—121no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—22no—
316C2×#67—22no—
317C2×#67C2×Dic314yes—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—41no—
329C22×Dic3—41no—
330C22×Dic3—41no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3—64no—
338C22×Dic3—62no—
339C22×Dic3—62no—
340C22×Dic3—122no—
341C22×Dic3—121no—
342C22×Dic3—121no—
343C22×Dic3—122no—
344C22×Dic3C2×Dic314yes—
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C2×C4×D3—41no—
353C2×C4×D3—41no—
354C2×C4×D3C2×Dic314yescomplemented
355C3×C4⋊C4—34no—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—34no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4C4×D314yes—
360C3×C22⋊C4C2×Dic314yes—
361C3×C42—34no—
362C3×C42—62no—
363C3×C42—121no—
364#217—22no—
365#217—62no—
366#217—64no—
367#217—62no—
368#217—62no—
369#217—62no—
370#217—121no—
371#217—121no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—121no—
376(C2×D3)⋊C4C2×Dic314yescomplemented
377C4⋊Dic3—121no—
378C4⋊Dic3—121no—
379Dic3⋊C4—121no—
380Dic3⋊C4—121no—
381Dic3⋊C4C2×Dic314yescomplemented
382C4×Dic3—22no—
383C4×Dic3—41no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—122no—
387C4×Dic3—121no—
388C4×Dic3—121no—
389C4×Dic3—122no—
390C4×Dic3C2×Dic314yescomplemented
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32#11714yes—
398C22×C32C23×C411yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32H(5,𝔽2)11yescharacteristic
404C22×C32H(5,𝔽2)11yescharacteristic
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—22no—
413C32×C4—22no—
414C3⋊Dic3—22no—
415C3⋊Dic3—41no—
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—91no—
430C4×D4—38no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—91no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4D3211yescharacteristic
442C2×C42—31no—
443C2×C42—31no—
444C2×C42—31no—
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—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
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—22no—
472C23×C3—22no—
473C23×C3—32no—
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×C3#23512yes—
486C23×C3#23512yes—
487C23×C3#23512yes—
488C23×C3#23512yes—
489C23×C3C22×Dic312yes—
490C23×C3C23×D311yescharacteristic
491C23×C3C23×D311yescharacteristic
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3C22×Dic312yes—
499C3×D4—68no—
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—21no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
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—61no—
534C2×C3×C4—61no—
535C2×C3×C4—124no—
536C2×C3×C4—124no—
537C2×C3×C4—124no—
538C2×C3×C4C2×C4×D312yes—
539C2×C3×C4C2×C4×D312yes—
540C2×C3×C4C22×Dic312yes—
541C2×C3×C4C22×Dic312yes—
542#67—28no—
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—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—32no—
561C2×Dic3—32no—
562C2×Dic3—44no—
563C2×Dic3—44no—
564C2×Dic3—62no—
565C2×Dic3—62no—
566C2×Dic3—62no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—62no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—124no—
599C2×Dic3—124no—
600C2×Dic3—128no—
601C2×Dic3#23712yes—
602C2×Dic3C22×Dic312yes—
603C2×Dic3C22×Dic312yes—
604C2×Dic3C22×Dic312yes—
605C4×D3—44no—
606C2×C32—24no—
607C2×C32C2×#11711yescharacteristic
608C2×C32C4×#4111yescharacteristic
609C2×C32#51811yescharacteristic
610C2×C32#55111yescharacteristic
611C2×C32#55111yescharacteristic
612C2×C32#55311yescharacteristic
613C2×C32#55311yescharacteristic
614C3×D3—42no—
615C24—31no—
616C24C2×D3211yescharacteristic
617C2×D4—34no—
618C2×D4—62no—
619C2×D4—62no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—34no—
625C22×C4—34no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—121no—
636C22×C4—121no—
637C22×C4—121no—
638C22×C4—121no—
639C22×C4—121no—
640C22×C4—182no—
641C22×C4—182no—
642C22×C4—361no—
643C22×C4C2×D3211yescharacteristic
644C22×C4C2×D3211yescharacteristic
645C4⋊C4—34no—
646C4⋊C4—361no—
647C4⋊C4—361no—
648C22⋊C4—34no—
649C22⋊C4—62no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—361no—
654C22⋊C4—361no—
655C22⋊C4D3×Dic314yes—
656C42—34no—
657C42—62no—
658C42—121no—
659C42—182no—
660C42—361no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—24no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3#87214yes—
695C22×C3#92614yes—
696C22×C3C22×C4×D311yescharacteristic
697C22×C3C2×#23511yescharacteristic
698C22×C3C2×#23511yescharacteristic
699C22×C3C2×#23511yescharacteristic
700C22×C3C2×#23511yescharacteristic
701C22×C3C2×#23711yescharacteristic
702C22×C3#100411yescharacteristic
703C22×C3#100411yescharacteristic
704C22×C3#100411yescharacteristic
705C22×C3D3×#4111yescharacteristic
706C22×C3D3×#4111yescharacteristic
707C22×C3D3×#4111yescharacteristic
708C22×C3#100911yescharacteristic
709C22×C3C23×Dic311yescharacteristic
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—62no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—62no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730Dic3—22no—
731Dic3—22no—
732Dic3—22no—
733Dic3—22no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—64no—
738Dic3—62no—
739Dic3—62no—
740Dic3—122no—
741Dic3—122no—
742Dic3—122no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749C32#235311yescharacteristic, complemented, Sylow
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—32no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23#379812yes—
762C23#379812yes—
763C23C2×D3×Dic312yes—
764C23C22×D3211yescharacteristic
765D4—68no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
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—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—92no—
792C2×C4—124no—
793C2×C4—124no—
794C2×C4—124no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—364no—
807C2×C4C2×D3×Dic312yes—
808C2×C4C2×D3×Dic312yes—
809C2×C3—24no—
810C2×C3—24no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—44no—
819C2×C3—122no—
820C2×C3C2×#87211yescharacteristic
821C2×C3#549511yescharacteristic
822C2×C3#552711yescharacteristic
823C2×C3C4×#23711yescharacteristic
824C2×C3#554011yescharacteristic
825C2×C3#554011yescharacteristic
826C2×C3#554011yescharacteristic
827C2×C3#554511yescharacteristic
828C2×C3#555611yescharacteristic
829C2×C3#555611yescharacteristic
830C2×C3#556511yescharacteristic
831C2×C3C2×#92611yescharacteristic
832C2×C3#579811yescharacteristic
833C2×C3Dic3×#4111yescharacteristic
834D3—42no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22#6385514yes—
849C22C2×#379811yescharacteristic
850C22C2×#379811yescharacteristic
851C22D3×#23711yescharacteristic
852C22#6431211yescharacteristic
853C22#6431311yescharacteristic
854C22#6431411yescharacteristic
855C22C22×D3×Dic311yescharacteristic
856C4—22no—
857C4—22no—
858C4—62no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—121no—
863C4—121no—
864C4—121no—
865C4—182no—
866C4—361no—
867C4—361no—
868C4—361no—
869C3—21no—
870C3#7346211yescharacteristic, complemented
871C3#8233611yescharacteristic, complemented
872C2—24no—
873C2—122no—
874C2#1059404011yescharacteristic
875C2#1059420911yescharacteristic
876C2#1059421811yescharacteristic
877C2#1059423111yescharacteristic
878C2C2×#6385511yescharacteristic
879C2Dic3×#23711yescharacteristic
880C2#1059521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C3⋊Dic3C2semidirect
3. C3×Dic3×C22⋊C4C2semidirect
4. #10591716C2semidirect
7. C2×#63579C2semidirect
8. #10591305C2semidirect
9. #10591294C2semidirect
10. #10591286C2semidirect
11. C4×(C2×D3)⋊Dic3C2semidirect
12. #10591223C2semidirect
13. #10591222C2semidirect
14. #10591201C2semidirect
15. #10591192C2semidirect
33. C3×#67⋊C4C4semidirect
74. Dic3×C22⋊C4D3semidirect
114. C2×C3×C4×D3C2×C4semidirect
120. C3×(C2×D3)⋊C4C2×C4semidirect
121. C3×Dic3⋊C4C2×C4semidirect
124. C3×C4×Dic3C2×C4semidirect
180. #67⋊C4Dic3semidirect
354. C2×C4×D3C2×Dic3semidirect
376. (C2×D3)⋊C4C2×Dic3semidirect
381. Dic3⋊C4C2×Dic3semidirect
390. C4×Dic3C2×Dic3semidirect
749. C32#2353semidirect
870. C3#73462semidirect
871. C3#82336semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C22⋊C4×C3⋊Dic32
C3×Dic3×C22⋊C42
#105917162
#105917132
#105917102
C2×#635792
#105913052
#105912942
#105912862
C4×(C2×D3)⋊Dic32
#105912232
#105912222
#105912012
#105911922
#823363
#734623