Finite Group Databasebeta

← #11806045

Subgroups — #11806045

Order 1152.

1215 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×#63904C211yesmaximal, characteristic
2#10592368C211yesmaximal, characteristic, complemented
3C3×#4664C211yesmaximal, characteristic, complemented
4C3×#4649C211yesmaximal, characteristic, complemented
5#10591384C211yesmaximal, characteristic
6#10591383C211yesmaximal, characteristic
7#10591371C211yesmaximal, characteristic, complemented
8#10591281C211yesmaximal, characteristic, complemented
9#10591279C211yesmaximal, characteristic, complemented
10C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
11#10591245C211yesmaximal, characteristic, complemented
12#10591243C211yesmaximal, characteristic, complemented
13#10591241C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#74061—31nomaximal
17#73646—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63904C418yescomplemented
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C4×#67—31no—
55C2×#893—31no—
56C3×#381—31no—
57C3×C4×C4⋊C4—31no—
58C4×#217—31no—
59#4988—31no—
60#4977—31no—
61Dic3×C4⋊C4—31no—
62#4957—31no—
63#4957—31no—
64#4944—31no—
65#4944—31no—
66#4940—31no—
67#4940—31no—
68#4939—31no—
69C4×(C2×D3)⋊C4—31no—
70C4×(C2×D3)⋊C4—31no—
71C4×Dic3⋊C4—31no—
72#4669—31no—
73#4669—31no—
74#4669—31no—
75#4669—31no—
76#4669—61no—
77#4666—31no—
78#4664—31no—
79#4664—31no—
80#4664D311yescharacteristic, complemented
81#4650—31no—
82#4649—31no—
83#4649—31no—
84#4649D311yescharacteristic, complemented
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×C4×D3—41no—
101C2×C3×C4×D3—41no—
102C2×C3×C4×D3C2×C414yes—
103C2×#626—22no—
104C2×#626—22no—
105C2×#626C2×C414yes—
106C2×#624—41no—
107C2×#624—41no—
108C2×#624C2×C414yes—
109#3752—22no—
110#3752—41no—
111#3752C2×C414yes—
112#3750—22no—
113C4×C3⋊Dic3—41no—
114C3×(C2×D3)⋊C4—41no—
115C3×(C2×D3)⋊C4—41no—
116C3×Dic3⋊C4—22no—
117C3×Dic3⋊C4C2×C414yes—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—41no—
120C3×C4×Dic3—41no—
121#3724—22no—
122Dic3⋊Dic3—22no—
123#3722—22no—
124#3722—41no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3C2×C414yes—
128Dic32—22no—
129Dic32—41no—
130Dic32C2×C414yes—
131#2357—91noSylow
132C23×C3×C4—31no—
133C22×#67—31no—
134C22×D12—31no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×C4×D3C2×D311yescharacteristic
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×#217—31no—
146C2×#217—31no—
147C2×#217—31no—
148C4×#67—38no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—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)⋊C4—61no—
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×(C2×D3)⋊C4C2×D311yescharacteristic
167C2×C4⋊Dic3—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—61no—
174C2×Dic3⋊C4C2×D311yescharacteristic
175C2×Dic3⋊C4C2×D311yescharacteristic
176C2×C4×Dic3—31no—
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—61no—
185C2×C4×Dic3C2×D311yescharacteristic
186C2×C4×Dic3C2×D311yescharacteristic
187C2×C4×Dic3C2×D311yescharacteristic
188#893—38no—
189C3×#95—21no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95C2×D311yescharacteristic
195C3×#95C2×D311yescharacteristic
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—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×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—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⋊Dic3C22×C412yes—
243C2×C3⋊Dic3#4112yes—
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×Dic3C22×C412yes—
260C2×C3×Dic3C22×C412yes—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3#4112yes—
263C2×C3×Dic3#4112yes—
264C2×C3×Dic3#4112yes—
265C3×C4×D3—44no—
266#626—28no—
267#624—44no—
268C2×C4×D4—91no—
269#390—91no—
270#390—91no—
271#388—91no—
272#388—91no—
273#388—91no—
274#388—91no—
275#382—91no—
276#381—31no—
277#381—91no—
278C4×C4⋊C4—31no—
279C4×C4⋊C4—91no—
280C4×C4⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283C24×C3—31no—
284C23×D3—31no—
285C23×D3—31no—
286C23×D3—61no—
287C23×D3C22×D311yescharacteristic
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—34no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—121no—
300C22×C3×C4—121no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—34no—
308C2×#67—62no—
309C2×#67—62no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C2×D12—34no—
327C2×D12—62no—
328C2×D12—62no—
329C2×C4×D3—34no—
330C2×C4×D3—34no—
331C2×C4×D3—41no—
332C2×C4×D3—41no—
333C2×C4×D3—121no—
334C2×C4×D3—121no—
335C2×C4×D3—121no—
336C2×C4×D3—121no—
337C2×C4×D3C4×D314yes—
338C3×C4⋊C4—34no—
339C3×C4⋊C4—62no—
340C3×C22⋊C4—121no—
341C3×C22⋊C4—121no—
342C3×C42—62no—
343C3×C42—121no—
344C3×C42—121no—
345#217—34no—
346#217—62no—
347#217—62no—
348(C2×D3)⋊C4—34no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—41no—
352(C2×D3)⋊C4—41no—
353(C2×D3)⋊C4—64no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—122no—
361(C2×D3)⋊C4—121no—
362(C2×D3)⋊C4—121no—
363(C2×D3)⋊C4—121no—
364(C2×D3)⋊C4—121no—
365(C2×D3)⋊C4—122no—
366C4⋊Dic3—62no—
367Dic3⋊C4—22no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—122no—
374Dic3⋊C4C4×D314yes—
375C4×Dic3—22no—
376C4×Dic3—34no—
377C4×Dic3—34no—
378C4×Dic3—41no—
379C4×Dic3—41no—
380C4×Dic3—62no—
381C4×Dic3—62no—
382C4×Dic3—121no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3—121no—
386C4×Dic3—122no—
387C22×C32C23×C411yescharacteristic
388C22×C32C2×#4111yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C32H(5,𝔽2)11yescharacteristic
394C2×C3⋊D3—22no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—41no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
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—
410C32×C4—41no—
411C3⋊Dic3—22no—
412C3⋊Dic3—22no—
413C3⋊Dic3—41no—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3#11714yes—
421C22×D4—91no—
422C23×C4—31no—
423C23×C4—91no—
424C4×D4—98no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—91no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—91no—
433C2×C22⋊C4—91no—
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—
445C2×C42—91no—
446C2×C42—91no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—31no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95D3211yescharacteristic
457C23×C3—21no—
458C23×C3—32no—
459C23×C3—61no—
460C23×C3—61no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3C23×D311yescharacteristic
466C23×C3C23×D311yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—32no—
474C22×D3—32no—
475C22×D3—62no—
476C22×D3—61no—
477C22×D3—61no—
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—121no—
489C22×D3—121no—
490C22×D3—121no—
491C22×D3—121no—
492C22×D3—121no—
493C22×D3—121no—
494C22×D3C2×C4×D312yes—
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—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—22no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
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—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—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—124no—
542C2×C3×C4C2×C4×D312yes—
543C2×C3×C4C2×C4×D312yes—
544#67—68no—
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—32no—
563C2×Dic3—32no—
564C2×Dic3—62no—
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—62no—
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×Dic3C2×C4×D312yes—
588C2×Dic3C2×C4×D312yes—
589C2×Dic3C2×C4×D312yes—
590C2×Dic3#23512yes—
591C2×Dic3#23512yes—
592C2×Dic3#23912yes—
593D12—68no—
594C4×D3—44no—
595C4×D3—124no—
596C4×D3—124no—
597C2×C32C2×#11711yescharacteristic
598C2×C32C4×#4111yescharacteristic
599C2×C32#51811yescharacteristic
600C2×C32#55311yescharacteristic
601C2×C32#55311yescharacteristic
602C2×C32#55911yescharacteristic
603C2×C32#55911yescharacteristic
604C3⋊D3—42no—
605C3×D3—42no—
606C24—31no—
607C24—91no—
608C2×D4—94no—
609C2×D4—182no—
610C2×D4—182no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—34no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—94no—
620C22×C4—91no—
621C22×C4—91no—
622C22×C4—91no—
623C22×C4—121no—
624C22×C4—121no—
625C22×C4—361no—
626C22×C4—361no—
627C22×C4C2×D3211yescharacteristic
628C22×C4C2×D3211yescharacteristic
629C22×C4C2×D3211yescharacteristic
630C4⋊C4—34no—
631C4⋊C4—62no—
632C4⋊C4—182no—
633C4⋊C4—182no—
634C4⋊C4—182no—
635C22⋊C4—94no—
636C22⋊C4—94no—
637C22⋊C4—121no—
638C22⋊C4—121no—
639C22⋊C4—182no—
640C22⋊C4—182no—
641C22⋊C4—182no—
642C22⋊C4—182no—
643C22⋊C4—361no—
644C22⋊C4—361no—
645C42—62no—
646C42—94no—
647C42—121no—
648C42—121no—
649C42—182no—
650C42—361no—
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—62no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C22×C4×D311yescharacteristic
667C22×C3C22×C4×D311yescharacteristic
668C22×C3C2×#23511yescharacteristic
669C22×C3C2×#23511yescharacteristic
670C22×C3#100411yescharacteristic
671C22×C3#100411yescharacteristic
672C22×C3#100411yescharacteristic
673C22×C3C2×#23911yescharacteristic
674C22×C3D3×#4111yescharacteristic
675C22×C3D3×#4111yescharacteristic
676C22×C3D3×#4111yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3#100911yescharacteristic
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—62no—
688C2×D3—62no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—122no—
694C2×D3—122no—
695C2×D3—122no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—241no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—34no—
711C3×C4—42no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—81no—
720C3×C4—81no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724Dic3—22no—
725Dic3—22no—
726Dic3—22no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—62no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—122no—
735Dic3—122no—
736Dic3—122no—
737Dic3—121no—
738Dic3—121no—
739Dic3#87214yes—
740C32#235711yescharacteristic, complemented, Sylow
741C23—32no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—92no—
749C23—181no—
750C23—181no—
751C23—181no—
752C23—181no—
753C23—181no—
754C23—181no—
755C23C22×D3211yescharacteristic
756D4—188no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
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—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—92no—
787C2×C4—92no—
788C2×C4—124no—
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×C4C4×D3212yes—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—122no—
806C2×C3C2×#87211yescharacteristic
807C2×C3#548611yescharacteristic
808C2×C3#551411yescharacteristic
809C2×C3D3×#11711yescharacteristic
810C2×C3#552211yescharacteristic
811C2×C3#553011yescharacteristic
812C2×C3#554511yescharacteristic
813C2×C3#555911yescharacteristic
814C2×C3C4×#23911yescharacteristic
815C2×C3#558511yescharacteristic
816C2×C3#566111yescharacteristic
817C2×C3#566111yescharacteristic
818C2×C3#566411yescharacteristic
819C2×C3#566411yescharacteristic
820D3—42no—
821D3—122no—
822D3—122no—
823D3—242no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—182no—
832C22—182no—
833C22—182no—
834C22—361no—
835C22—361no—
836C22—361no—
837C22—361no—
838C22C2×C4×D3211yescharacteristic
839C22D3×#23511yescharacteristic
840C22D3×#23511yescharacteristic
841C22#6431211yescharacteristic
842C22#6431311yescharacteristic
843C22#6431411yescharacteristic
844C22D3×#23911yescharacteristic
845C4—22no—
846C4—34no—
847C4—41no—
848C4—41no—
849C4—62no—
850C4—62no—
851C4—62no—
852C4—121no—
853C4—121no—
854C4—121no—
855C4—182no—
856C4—182no—
857C4—361no—
858C3—21no—
859C3#7364611yescharacteristic, complemented
860C3#7406111yescharacteristic, complemented
861C2—122no—
862C2—362no—
863C2D3×#87211yescharacteristic
864C2#1059420411yescharacteristic
865C2#1059420811yescharacteristic
866C2#1059425411yescharacteristic
867C2#1059436211yescharacteristic
868C2#1059454411yescharacteristic
869C2#1059454911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592368C2semidirect
3. C3×#4664C2semidirect
4. C3×#4649C2semidirect
7. #10591371C2semidirect
8. #10591281C2semidirect
9. #10591279C2semidirect
10. C4×(C2×D3)⋊Dic3C2semidirect
11. #10591245C2semidirect
12. #10591243C2semidirect
13. #10591241C2semidirect
14. #10591233C2semidirect
15. #10591202C2semidirect
43. #63904C4semidirect
80. #4664D3semidirect
84. #4649D3semidirect
740. C32#2357semidirect
859. C3#73646semidirect
860. C3#74061semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
#105923682
C3×#46642
C3×#46492
#105913842
#105913832
#105913712
#105912812
#105912792
C4×(C2×D3)⋊Dic32
#105912452
#105912432
#105912412
#105912332
#105912022
#740613
#736463