Finite Group Databasebeta

← #11805796

Subgroups — #11805796

Order 1152.

1285 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63881C211yesmaximal, characteristic
2#10592363C211yesmaximal, characteristic, complemented
3C3×#4666C211yesmaximal, characteristic, complemented
4C3×#4652C211yesmaximal, characteristic, complemented
5#10591382C211yesmaximal, characteristic
6#10591366C211yesmaximal, characteristic, complemented
7Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#10591364C211yesmaximal, characteristic
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591289C211yesmaximal, characteristic, complemented
11C4×#3722C211yesmaximal, characteristic, complemented
12#10591259C211yesmaximal, characteristic, complemented
13#10591248C211yesmaximal, characteristic, complemented
14#10591239C211yesmaximal, characteristic, complemented
15#10591201C211yesmaximal, characteristic, complemented
16#75306—31nomaximal
17#73462—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63881C418yescomplemented
40C32×#95C2211yescharacteristic
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×#893—31no—
55C2×#67⋊C4—31no—
56C3×#387—31no—
57C3×C4×C22⋊C4—31no—
58#5213—31no—
59C2×C3⋊#95—31no—
60#4990—31no—
61#4987—31no—
62#4980—31no—
63#4958—31no—
64#4942—31no—
65Dic3×C22⋊C4—31no—
66#4940—31no—
67C4×(C2×D3)⋊C4—31no—
68C4×(C2×D3)⋊C4—31no—
69C4×(C2×D3)⋊C4—31no—
70#4933—31no—
71#4932—31no—
72#4670—31no—
73#4669—31no—
74#4666D311yescharacteristic, complemented
75#4665—31no—
76#4665—31no—
77#4664—31no—
78#4664—31no—
79#4664—61no—
80D3×#95—31no—
81#4652D311yescharacteristic, complemented
82#4651—31no—
83#4651—31no—
84#4648—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
93C2×C4×C3⋊D3—41no—
94C2×C4×C3⋊D3—41no—
95C2×C4×C3⋊D3C2×C414yescomplemented
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—41no—
106C2×#626—22no—
107C2×#626—22no—
108C2×#626C2×C414yes—
109C2×D3×Dic3—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—41no—
112C2×D3×Dic3—41no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3C2×C414yes—
115#3752—41no—
116#3752—41no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4C2×C414yes—
119C3×Dic3⋊C4—41no—
120C3×Dic3⋊C4C2×C414yescomplemented
121C3×C4×Dic3—22no—
122C3×C4×Dic3—41no—
123C3×C4×Dic3—41no—
124Dic3⋊Dic3—41no—
125#3722—22no—
126#3722—22no—
127#3722C2×C414yescomplemented
128(C2×D3)⋊Dic3—22no—
129Dic32—22no—
130Dic32C2×C414yescomplemented
131#2353—91noSylow
132C23×C3×C4—31no—
133C22×#67—31no—
134C23×Dic3—31no—
135C23×Dic3—31no—
136C22×D12—31no—
137C22×C4×D3—31no—
138C22×C4×D3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3—61no—
142C22×C4×D3C2×D311yescharacteristic
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×C3×C42—31no—
150C2×#217—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—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—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×C4⋊Dic3—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#893—38no—
178#67⋊C4—38no—
179C3×#95—21no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95C2×D311yescharacteristic
185C3×#95C2×D311yescharacteristic
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—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⋊D3C22×C412yes—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
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×C4—21no—
233C2×C32×C4—21no—
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⋊Dic3C22×C412yes—
244C4×C3⋊D3—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×Dic3C22×C412yes—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3#4112yes—
265C2×C3×Dic3#4112yes—
266C3×C4×D3—44no—
267#626—28no—
268D3×Dic3—44no—
269D3×Dic3—44no—
270C2×C4×D4—91no—
271#388—91no—
272#388—91no—
273#387—31no—
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—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—61no—
289C23×D3C22×D311yescharacteristic
290C22×C3×C4—21no—
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—31no—
299C22×C3×C4—31no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4—121no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—34no—
310C2×#67—62no—
311C2×#67—62no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—34no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—62no—
323C22×Dic3—62no—
324C22×Dic3—121no—
325C22×Dic3—121no—
326C22×Dic3—121no—
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C2×D12—34no—
335C2×D12—62no—
336C2×D12—62no—
337C2×C4×D3—22no—
338C2×C4×D3—22no—
339C2×C4×D3—34no—
340C2×C4×D3—34no—
341C2×C4×D3—34no—
342C2×C4×D3—41no—
343C2×C4×D3—64no—
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×D3—121no—
351C2×C4×D3—121no—
352C2×C4×D3—121no—
353C2×C4×D3—122no—
354C2×C4×D3—122no—
355C3×C4⋊C4—34no—
356C3×C4⋊C4—121no—
357C3×C22⋊C4—34no—
358C3×C22⋊C4—62no—
359C3×C42—62no—
360C3×C42—121no—
361C3×C42—121no—
362#217—62no—
363(C2×D3)⋊C4—22no—
364(C2×D3)⋊C4—34no—
365(C2×D3)⋊C4—34no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—62no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4—121no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—122no—
376(C2×D3)⋊C4—122no—
377(C2×D3)⋊C4C4×D314yes—
378C4⋊Dic3—121no—
379Dic3⋊C4—41no—
380Dic3⋊C4—121no—
381Dic3⋊C4C4×D314yescomplemented
382C4×Dic3—22no—
383C4×Dic3—34no—
384C4×Dic3—34no—
385C4×Dic3—41no—
386C4×Dic3—41no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C22×C32C23×C411yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32H(5,𝔽2)11yescharacteristic
395C22×C32H(5,𝔽2)11yescharacteristic
396C2×C3⋊D3—22no—
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3#11714yes—
410C32×C4—22no—
411C32×C4—41no—
412C32×C4—41no—
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C22×D4—91no—
424C23×C4—31no—
425C23×C4—91no—
426C23×C4—91no—
427C23×C4—91no—
428C4×D4—98no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—91no—
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—31no—
443C2×C42—91no—
444C2×C42—91no—
445#95—31no—
446#95—31no—
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#95D3211yescharacteristic
459C23×C3—21no—
460C23×C3—32no—
461C23×C3—32no—
462C23×C3—32no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3C23×D311yescharacteristic
468C23×C3C23×D311yescharacteristic
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—32no—
474C22×D3—32no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3—62no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—121no—
492C22×D3—121no—
493C22×D3—121no—
494C22×D3C2×C4×D312yes—
495C22×D3#23512yes—
496C22×D3#23512yes—
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—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
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—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—124no—
544C2×C3×C4C2×C4×D312yes—
545C2×C3×C4C2×C4×D312yes—
546#67—68no—
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—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—62no—
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—61no—
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×Dic3—124no—
592C2×Dic3C2×C4×D312yes—
593C2×Dic3C2×C4×D312yes—
594C2×Dic3C2×C4×D312yes—
595C2×Dic3#23712yes—
596C2×Dic3#23912yes—
597D12—68no—
598C4×D3—44no—
599C4×D3—124no—
600C4×D3—124no—
601C4×D3—124no—
602C4×D3—128no—
603C4×D3—124no—
604C2×C32C2×#11711yescharacteristic
605C2×C32C4×#4111yescharacteristic
606C2×C32#51811yescharacteristic
607C2×C32#55111yescharacteristic
608C2×C32#55111yescharacteristic
609C2×C32#55311yescharacteristic
610C2×C32#55311yescharacteristic
611C3⋊D3—42no—
612C3×D3—24no—
613C24—31no—
614C24—91no—
615C2×D4—94no—
616C2×D4—182no—
617C2×D4—182no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—94no—
628C22×C4—91no—
629C22×C4—94no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—121no—
633C22×C4—182no—
634C22×C4—182no—
635C22×C4—361no—
636C22×C4—361no—
637C22×C4—361no—
638C22×C4—361no—
639C22×C4—361no—
640C22×C4C2×D3211yescharacteristic
641C22×C4C2×D3211yescharacteristic
642C22×C4C2×D3211yescharacteristic
643C4⋊C4—34no—
644C4⋊C4—121no—
645C4⋊C4—361no—
646C22⋊C4—34no—
647C22⋊C4—62no—
648C22⋊C4—94no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—361no—
653C22⋊C4—361no—
654C42—62no—
655C42—94no—
656C42—121no—
657C42—121no—
658C42—182no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—34no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—62no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—62no—
673C22×C3C22×C4×D311yescharacteristic
674C22×C3C22×C4×D311yescharacteristic
675C22×C3C2×#23511yescharacteristic
676C22×C3C2×#23511yescharacteristic
677C22×C3C2×#23711yescharacteristic
678C22×C3#100411yescharacteristic
679C22×C3#100411yescharacteristic
680C22×C3C2×#23911yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3D3×#4111yescharacteristic
684C22×C3D3×#4111yescharacteristic
685C22×C3#100911yescharacteristic
686C22×C3#100911yescharacteristic
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—64no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—122no—
703C2×D3—122no—
704C2×D3—122no—
705C2×D3—122no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3#87214yes—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—42no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—62no—
727C3×C4—81no—
728C3×C4—81no—
729C3×C4—121no—
730C3×C4—121no—
731Dic3—22no—
732Dic3—22no—
733Dic3—22no—
734Dic3—22no—
735Dic3—22no—
736Dic3—41no—
737Dic3—41no—
738Dic3—62no—
739Dic3—62no—
740Dic3—122no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—121no—
745Dic3—241no—
746Dic3—241no—
747C32#235311yescharacteristic, complemented, Sylow
748C23—32no—
749C23—32no—
750C23—32no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—92no—
756C23—181no—
757C23—181no—
758C23—181no—
759C23—181no—
760C23—181no—
761C23—181no—
762C23C22×D3211yescharacteristic
763D4—188no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
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—61no—
792C2×C4—61no—
793C2×C4—92no—
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—364no—
804C2×C4—364no—
805C2×C4—364no—
806C2×C4C4×D3212yes—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—64no—
815C2×C3C2×#87211yescharacteristic
816C2×C3#549511yescharacteristic
817C2×C3D3×#11711yescharacteristic
818C2×C3#552711yescharacteristic
819C2×C3C4×#23711yescharacteristic
820C2×C3#554011yescharacteristic
821C2×C3#554511yescharacteristic
822C2×C3#554511yescharacteristic
823C2×C3#556511yescharacteristic
824C2×C3C4×#23911yescharacteristic
825C2×C3#563711yescharacteristic
826C2×C3#566111yescharacteristic
827C2×C3#569511yescharacteristic
828C2×C3#570511yescharacteristic
829D3—24no—
830D3—124no—
831D3—122no—
832D3—122no—
833C22—34no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—62no—
839C22—62no—
840C22—182no—
841C22—182no—
842C22—182no—
843C22—361no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22C2×C4×D3211yescharacteristic
848C22D3×#23511yescharacteristic
849C22D3×#23511yescharacteristic
850C22D3×#23711yescharacteristic
851C22#6431411yescharacteristic
852C22#6431411yescharacteristic
853C22D3×#23911yescharacteristic
854C4—22no—
855C4—41no—
856C4—41no—
857C4—62no—
858C4—62no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—121no—
863C4—121no—
864C4—182no—
865C4—361no—
866C4—361no—
867C3—21no—
868C3#7346211yescharacteristic, complemented
869C3#7530611yescharacteristic, complemented
870C2—64no—
871C2—362no—
872C2D3×#87211yescharacteristic
873C2#1059409311yescharacteristic
874C2#1059419711yescharacteristic
875C2#1059425611yescharacteristic
876C2#1059436011yescharacteristic
877C2#1059441511yescharacteristic
878C2#1059464111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592363C2semidirect
3. C3×#4666C2semidirect
4. C3×#4652C2semidirect
6. #10591366C2semidirect
7. Dic3×(C2×D3)⋊C4C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591289C2semidirect
11. C4×#3722C2semidirect
12. #10591259C2semidirect
13. #10591248C2semidirect
14. #10591239C2semidirect
15. #10591201C2semidirect
39. #63881C4semidirect
74. #4666D3semidirect
81. #4652D3semidirect
95. C2×C4×C3⋊D3C2×C4semidirect
120. C3×Dic3⋊C4C2×C4semidirect
127. #3722C2×C4semidirect
130. Dic32C2×C4semidirect
381. Dic3⋊C4C4×D3semidirect
747. C32#2353semidirect
868. C3#73462semidirect
869. C3#75306semidirect

Maximal subgroups

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

subgroupindex
C2×#638812
#105923632
C3×#46662
C3×#46522
#105913822
#105913662
Dic3×(C2×D3)⋊C42
#105913642
D3×C3⋊#952
#105912892
C4×#37222
#105912592
#105912482
#105912392
#105912012
#753063
#734623