Finite Group Databasebeta

← #11803278

Subgroups — #11803278

Order 1152.

1745 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#63977C211yesmaximal, characteristic
3C2×#63904C211yesmaximal, characteristic, complemented
4#10592656C211yesmaximal, characteristic, complemented
5C3×#4945C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591283C211yesmaximal, characteristic, complemented
12#10591281C211yesmaximal, characteristic, complemented
13#10591278C211yesmaximal, characteristic, complemented
14C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#82096—31nomaximal
17#75826—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×#3752C2211yescharacteristic, complemented
29C2×#3750C2211yescharacteristic, complemented
30C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38C3×D3×C22⋊C4—24no—
39#63977C418yescomplemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×Dic32C2211yescharacteristic, complemented
49#63904—24no—
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C22×C3×C22⋊C4—31no—
57C2×#953—31no—
58C2×C4×#67—31no—
59C2×#893—31no—
60C2×#882—31no—
61C2×D3×C22⋊C4D311yescharacteristic, complemented
62C3×#388—31no—
63#5247—31no—
64#5213—31no—
65#5210—31no—
66C4×#217—31no—
67#4990—31no—
68#4957—31no—
69#4957—31no—
70#4957—31no—
71#4957—61no—
72#4956—31no—
73#4956—31no—
74#4956—31no—
75#4955—31no—
76#4951—31no—
77#4945—31no—
78#4945D311yescharacteristic, complemented
79#4944—31no—
80#4944—31no—
81#4939—31no—
82C4×(C2×D3)⋊C4—31no—
83#4669—31no—
84#4668—31no—
85#4665—31no—
86#4665—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—41no—
92C23×C3×D3—41no—
93C23×C3×D3—41no—
94C23×C3×D3—41no—
95C23×C3×D3C2×C414yescomplemented
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—41no—
101C2×#638—41no—
102C2×#638C2×C414yescomplemented
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
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—22no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3—41no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3D414yescomplemented
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—41no—
121C2×#626—41no—
122C2×#626C2×C414yes—
123C2×#626C2×C414yescomplemented
124C2×#624—22no—
125C2×#624—41no—
126C2×#624—41no—
127C32×C22⋊C4—22no—
128#3757—41no—
129#3752—22no—
130#3752—41no—
131#3750—41no—
132C4×C3⋊Dic3—41no—
133C3×#217—22no—
134C3×#217—41no—
135C3×#217C2×C414yescomplemented
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×Dic3⋊C4—22no—
139C3×C4×Dic3—41no—
140Dic3⋊Dic3—41no—
141#3722—41no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—41no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3C2×C414yescomplemented
147(C2×D3)⋊Dic3C2×C414yescomplemented
148Dic32—22no—
149#2321—91noSylow
150C25×C3—31no—
151C24×D3C2×D311yescharacteristic
152C23×C3×C4—31no—
153C23×C3×C4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—61no—
159C22×D12—31no—
160C22×D12—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3C2×D311yescharacteristic
164C22×C4×D3C2×D311yescharacteristic
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—64no—
173C2×C3×C22⋊C4C2×D311yescharacteristic
174C2×C3×C22⋊C4C2×D311yescharacteristic
175C2×C3×C42—31no—
176#953—38no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—61no—
186C2×#217C2×D311yescharacteristic
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189C4×#67—64no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—61no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×C4⋊Dic3—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—61no—
211C2×Dic3⋊C4C2×D311yescharacteristic, complemented
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—61no—
217C2×C4×Dic3C2×D311yescharacteristic, complemented
218#893—64no—
219#882—38no—
220D3×C22⋊C4—24no—
221C3×#95—31no—
222C3×#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95C2×D311yescharacteristic, complemented
232C3⋊#95C2×D311yescharacteristic, complemented
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3C22×C412yes—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—28no—
259C22×C3×D3—44no—
260C22×C3×D3—44no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3C22×C412yes—
266C22×C3×D3C22×C412yes—
267C22×C3×D3C2×D412yes—
268C22×C3×D3#4112yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4C2×D412yes—
275#638—44no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3C22×C412yes—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C22×C412yes—
301C2×C3×Dic3C22×C412yes—
302C2×C3×Dic3C2×D412yes—
303C3×C4×D3—44no—
304C3×C4×D3—44no—
305#626—28no—
306#626—44no—
307#624—44no—
308C2×#120—91no—
309C2×C4×D4—91no—
310C22×C22⋊C4—31no—
311#390—91no—
312#390—91no—
313#388—31no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—91no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—91no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—34no—
327C24×C3—62no—
328C24×C3—62no—
329C24×C3—121no—
330C24×C3—121no—
331C24×C3—121no—
332C24×C3—121no—
333C24×C3C22×D311yescharacteristic
334C24×C3C22×D311yescharacteristic
335C23×D3—22no—
336C23×D3—22no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—41no—
340C23×D3—41no—
341C23×D3—41no—
342C23×D3—41no—
343C23×D3—61no—
344C23×D3C4×D314yescomplemented
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—34no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—62no—
357C22×C3×C4—121no—
358C22×C3×C4—121no—
359C22×C3×C4—121no—
360C22×C3×C4—121no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—34no—
369C2×#67—64no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—121no—
373C2×#67—121no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—121no—
378C2×#67—122no—
379C2×#67—122no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C2×D12—34no—
396C2×D12—34no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—121no—
400C2×D12—121no—
401C2×C4×D3—22no—
402C2×C4×D3—41no—
403C2×C4×D3—41no—
404C2×C4×D3—41no—
405C2×C4×D3—41no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3#6714yescomplemented
413C3×C4⋊C4—62no—
414C3×C22⋊C4—22no—
415C3×C22⋊C4—22no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—42no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—121no—
422C3×C42—121no—
423#217—22no—
424#217—34no—
425#217—34no—
426#217—41no—
427#217—62no—
428#217—62no—
429#217—121no—
430#217—121no—
431#217—121no—
432#217—121no—
433#217—122no—
434#217C4×D314yescomplemented
435(C2×D3)⋊C4—22no—
436(C2×D3)⋊C4—22no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—122no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—122no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451C4⋊Dic3—121no—
452Dic3⋊C4—22no—
453Dic3⋊C4—121no—
454Dic3⋊C4—121no—
455Dic3⋊C4—121no—
456Dic3⋊C4—122no—
457C4×Dic3—41no—
458C4×Dic3—62no—
459C4×Dic3—62no—
460C4×Dic3—121no—
461C4×Dic3—121no—
462C4×Dic3—122no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32C23×C411yescharacteristic
471C22×C32C22×D411yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—416no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3C4×D414yes—
499C32×C4—22no—
500C32×C4—41no—
501C3⋊Dic3—22no—
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C25—31no—
511C22×D4—91no—
512C22×D4—91no—
513C22×D4—91no—
514C23×C4—31no—
515C23×C4—31no—
516C23×C4—91no—
517#120—98no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—64no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4D3211yescharacteristic
539C2×C42—31no—
540C2×C42—91no—
541C2×C42—91no—
542#95—31no—
543#95—31no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—68no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—124no—
584C23×C3—124no—
585C23×C3—124no—
586C23×C3—124no—
587C23×C3—124no—
588C23×C3—124no—
589C23×C3C2×C4×D312yes—
590C23×C3C2×C4×D312yes—
591C23×C3C23×D311yescharacteristic
592C23×C3C23×D311yescharacteristic
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—28no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—44no—
607C22×D3—44no—
608C22×D3—44no—
609C22×D3—44no—
610C22×D3—44no—
611C22×D3—44no—
612C22×D3—62no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3C2×C4×D312yes—
632C22×D3C2×C4×D312yes—
633C22×D3#23512yes—
634C22×D3C2×#6712yes—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—22no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—124no—
670C2×C3×C4—124no—
671C2×C3×C4D3×D412yes—
672C2×C3×C4C2×#6712yes—
673#67—68no—
674#67—124no—
675#67—124no—
676#67—124no—
677#67—128no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—62no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3C2×C4×D312yes—
721C2×Dic3C2×C4×D312yes—
722C2×Dic3C2×#6712yes—
723D12—68no—
724D12—124no—
725C4×D3—44no—
726C4×D3—44no—
727C4×D3—124no—
728C4×D3—124no—
729C2×C32—42no—
730C2×C32C2×C4×D411yescharacteristic
731C2×C32#51811yescharacteristic
732C2×C32#51811yescharacteristic
733C2×C32#53411yescharacteristic
734C2×C32#53511yescharacteristic
735C2×C32#53811yescharacteristic
736C2×C32#53811yescharacteristic
737C3⋊D3—42no—
738C3×D3—24no—
739C3×D3—42no—
740C24—31no—
741C24—31no—
742C24—34no—
743C24—62no—
744C24—62no—
745C24—91no—
746C24—121no—
747C24—121no—
748C24—121no—
749C24—121no—
750C24C2×D3211yescharacteristic
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—361no—
757C2×D4—361no—
758C2×D4—361no—
759C2×D4—361no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—34no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—62no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—121no—
772C22×C4—121no—
773C22×C4—121no—
774C22×C4—121no—
775C22×C4—182no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—62no—
781C4⋊C4—361no—
782C4⋊C4—361no—
783C22⋊C4—22no—
784C22⋊C4—34no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—121no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—361no—
795C22⋊C4—361no—
796C22⋊C4—361no—
797C22⋊C4—361no—
798C22⋊C4—361no—
799C42—121no—
800C42—182no—
801C42—361no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—34no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—1216no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3C22×C4×D311yescharacteristic
846C22×C3C22×C4×D311yescharacteristic
847C22×C3C2×#23511yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C22×C3#100411yescharacteristic
850C22×C3#100411yescharacteristic
851C22×C3#100411yescharacteristic
852C22×C3#100411yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3D3×#4111yescharacteristic
855C22×C3#100911yescharacteristic
856C22×C3#100911yescharacteristic
857C22×C3#100911yescharacteristic
858C22×C3C22×#6711yescharacteristic
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—416no—
869C2×D3—41no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—122no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—241no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3C4×#6714yes—
895C3×C4—22no—
896C3×C4—22no—
897C3×C4—42no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—62no—
901C3×C4—62no—
902C3×C4—62no—
903C3×C4—81no—
904C3×C4—121no—
905C3×C4—121no—
906C3×C4—121no—
907Dic3—22no—
908Dic3—22no—
909Dic3—22no—
910Dic3—41no—
911Dic3—41no—
912Dic3—41no—
913Dic3—64no—
914Dic3—62no—
915Dic3—62no—
916Dic3—122no—
917Dic3—121no—
918Dic3—121no—
919Dic3—121no—
920Dic3—121no—
921Dic3—241no—
922C32#232111yescharacteristic, complemented, Sylow
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—32no—
930C23—32no—
931C23—32no—
932C23—32no—
933C23—68no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—92no—
945C23—124no—
946C23—124no—
947C23—124no—
948C23—124no—
949C23—124no—
950C23—124no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23C4×D3212yes—
958C23C22×D3211yescharacteristic
959D4—188no—
960D4—364no—
961D4—364no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—92no—
986C2×C4—124no—
987C2×C4—124no—
988C2×C4—181no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—364no—
997C2×C4D3×#6712yes—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—42no—
1006C2×C3—42no—
1007C2×C3—64no—
1008C2×C3—82no—
1009C2×C3—122no—
1010C2×C3#548611yescharacteristic
1011C2×C3#548611yescharacteristic
1012C2×C3#549411yescharacteristic
1013C2×C3#549411yescharacteristic
1014C2×C3#552111yescharacteristic
1015C2×C3C4×D3×D411yescharacteristic
1016C2×C3#554511yescharacteristic
1017C2×C3#560511yescharacteristic
1018C2×C3#565711yescharacteristic
1019C2×C3#567411yescharacteristic
1020C2×C3#570411yescharacteristic
1021C2×C3C2×C4×#6711yescharacteristic
1022C2×C3#580411yescharacteristic
1023C2×C3#580511yescharacteristic
1024D3—24no—
1025D3—42no—
1026D3—122no—
1027D3—122no—
1028D3—242no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—34no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—1216no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22—121no—
1051C22—182no—
1052C22—182no—
1053C22—182no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22C2×C4×D3211yescharacteristic
1059C22D3×#23511yescharacteristic
1060C22#6431311yescharacteristic
1061C22#6431411yescharacteristic
1062C22#6431411yescharacteristic
1063C22#6431411yescharacteristic
1064C22C2×D3×#6711yescharacteristic
1065C4—22no—
1066C4—41no—
1067C4—62no—
1068C4—62no—
1069C4—62no—
1070C4—121no—
1071C4—121no—
1072C4—121no—
1073C4—182no—
1074C4—361no—
1075C4—361no—
1076C3—21no—
1077C3#7582611yescharacteristic, complemented
1078C3#8209611yescharacteristic, complemented
1079C2—42no—
1080C2—64no—
1081C2—122no—
1082C2—362no—
1083C2#1059418211yescharacteristic
1084C2#1059419411yescharacteristic
1085C2#1059419911yescharacteristic
1086C2#1059425411yescharacteristic
1087C2C4×D3×#6711yescharacteristic
1088C2#1059523511yescharacteristic
1089C2#1059530211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C22⋊C4C2semidirect
3. C2×#63904C2semidirect
4. #10592656C2semidirect
5. C3×#4945C2semidirect
6. #10591722C2semidirect
7. #10591706C2semidirect
8. #10591701C2semidirect
9. #10591383C2semidirect
10. #10591382C2semidirect
11. #10591283C2semidirect
12. #10591281C2semidirect
13. #10591278C2semidirect
14. C4×(C2×D3)⋊Dic3C2semidirect
15. #10591275C2semidirect
24. C22×#624C22semidirect
27. C2×#3752C22semidirect
28. C2×#3752C22semidirect
29. C2×#3750C22semidirect
30. C2×C4×C3⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
39. #63977C4semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×#3722C22semidirect
48. C2×Dic32C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
61. C2×D3×C22⋊C4D3semidirect
78. #4945D3semidirect
95. C23×C3×D3C2×C4semidirect
102. C2×#638C2×C4semidirect
117. C2×C3×C4×D3D4semidirect
123. C2×#626C2×C4semidirect
135. C3×#217C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
147. (C2×D3)⋊Dic3C2×C4semidirect
211. C2×Dic3⋊C4C2×D3semidirect
217. C2×C4×Dic3C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
344. C23×D3C4×D3semidirect
412. C2×C4×D3#67semidirect
434. #217C4×D3semidirect
922. C32#2321semidirect
1077. C3#75826semidirect
1078. C3#82096semidirect

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
C2×#639772
C2×#639042
#105926562
C3×#49452
#105917222
#105917062
#105917012
#105913832
#105913822
#105912832
#105912812
#105912782
C4×(C2×D3)⋊Dic32
#105912752
#820963
#758263