Finite Group Databasebeta

← #11803274

Subgroups — #11803274

Order 1152.

1869 conjugacy classes of subgroups.

The subgroup lattice has 1113 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63981C211yesmaximal, characteristic
2C2×#63974C211yesmaximal, characteristic, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4#10592654C211yesmaximal, characteristic, complemented
5C3×#4956C211yesmaximal, characteristic, complemented
6C3×#4944C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591375C211yesmaximal, characteristic, complemented
12#10591275C211yesmaximal, characteristic, complemented
13#10591259C211yesmaximal, characteristic, complemented
14#10591258C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#75826—31nomaximal
17#74876—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic, complemented
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37#63981C418yescomplemented
38#63974—24no—
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×Dic32C2211yescharacteristic, complemented
48C2×Dic32C2211yescharacteristic, complemented
49#63904—24no—
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#937—31no—
57C2×C4×#67—31no—
58C2×#893—31no—
59C2×#882—31no—
60C2×D3×C22⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#388—31no—
63C3×#386—31no—
64#5221—31no—
65#5213—31no—
66#4990—31no—
67#4957—31no—
68#4957—31no—
69#4956—31no—
70#4956D311yescharacteristic, complemented
71#4955—31no—
72#4955—31no—
73#4955—61no—
74#4951—31no—
75#4944—31no—
76#4944D311yescharacteristic, complemented
77#4939—31no—
78C4×(C2×D3)⋊C4—31no—
79#4670—31no—
80#4669—31no—
81#4669—31no—
82#4668—31no—
83#4668—31no—
84#4666—31no—
85#4665—31no—
86#4665—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3—22no—
89C23×C3⋊D3—22no—
90C23×C3⋊D3—41no—
91C23×C3⋊D3—41no—
92C23×C3⋊D3—41no—
93C23×C3⋊D3—41no—
94C23×C3⋊D3C2×C414yescomplemented
95C23×C3⋊D3C2311yescharacteristic
96C23×C3⋊D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—41no—
103C2×C3×#67—41no—
104C2×C3×#67C2×C414yescomplemented
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×#626—22no—
116C2×#626—22no—
117C2×#626—41no—
118C2×#626—41no—
119C2×#626C2×C414yes—
120C2×#626C2×C414yescomplemented
121C2×#624—22no—
122C2×#624—41no—
123C2×#624—41no—
124C2×#624—41no—
125C2×#624—41no—
126C2×#624D414yescomplemented
127C32×C22⋊C4—41no—
128#3757—41no—
129#3752—22no—
130#3752—22no—
131#3752—41no—
132#3752—41no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217C2×C414yescomplemented
136C3×(C2×D3)⋊C4—41no—
137C3×Dic3⋊C4—22no—
138C3×C4×Dic3—41no—
139Dic3⋊Dic3—41no—
140Dic3⋊Dic3—41no—
141#3722—22no—
142#3722—22no—
143#3722C2×C414yescomplemented
144#3722C2×C414yescomplemented
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—41no—
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C24×D3—61no—
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67C2×D311yescharacteristic
158C22×D12—31no—
159C22×D12—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3C2×D311yescharacteristic, complemented
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⋊C4C2×D311yescharacteristic
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C42—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—61no—
179C2×#217C2×D311yescharacteristic
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182#937—38no—
183C4×#67—64no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
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)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4C2×D311yescharacteristic, complemented
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3C2×D311yescharacteristic, complemented
217#893—64no—
218#882—38no—
219D3×C22⋊C4—64no—
220D3×C22⋊C4—64no—
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⋊#95C2×D311yescharacteristic, complemented
230C3⋊#95C2×D311yescharacteristic, complemented
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⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—28no—
252C22×C3⋊D3—44no—
253C22×C3⋊D3—44no—
254C22×C3⋊D3—44no—
255C22×C3⋊D3—44no—
256C22×C3⋊D3—44no—
257C22×C3⋊D3—44no—
258C22×C3⋊D3C22×C412yes—
259C22×C3⋊D3C22×C412yes—
260C22×C3⋊D3C2×D412yes—
261C22×C3⋊D3#4112yes—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3C22×C412yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C3×#67—44no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
299C2×C3×Dic3C22×C412yes—
300C2×C3×Dic3C22×C412yes—
301C2×C3×Dic3C2×D412yes—
302C2×C3×Dic3C2×D412yes—
303C3×C4×D3—44no—
304#626—28no—
305#626—44no—
306#624—44no—
307#624—44no—
308C2×#120—91no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—91no—
312#390—91no—
313#388—31no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—31no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—91no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—34no—
332C23×D3—34no—
333C23×D3—61no—
334C23×D3—61no—
335C23×D3—64no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—122no—
341C23×D3—122no—
342C23×D3—121no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3—121no—
346C23×D3—121no—
347C23×D3—121no—
348C23×D3—121no—
349C23×D3—121no—
350C23×D3—122no—
351C23×D3—122no—
352C23×D3—122no—
353C23×D3—122no—
354C23×D3C22×D311yescharacteristic
355C2×C3×D4—34no—
356C2×C3×D4—121no—
357C2×C3×D4—121no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—62no—
368C22×C3×C4—121no—
369C22×C3×C4—121no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—41no—
377C2×#67—41no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67C4×D314yescomplemented
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C2×D12—34no—
397C2×D12—34no—
398C2×D12—62no—
399C2×D12—62no—
400C2×D12—121no—
401C2×D12—121no—
402C2×C4×D3—22no—
403C2×C4×D3—34no—
404C2×C4×D3—34no—
405C2×C4×D3—41no—
406C2×C4×D3—41no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C2×C4×D3—121no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C3×C4⋊C4—62no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—41no—
421C3×C22⋊C4—42no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—121no—
425C3×C42—121no—
426#217—22no—
427#217—22no—
428#217—62no—
429#217—121no—
430#217—121no—
431#217—121no—
432#217—122no—
433#217C4×D314yescomplemented
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—41no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—122no—
449(C2×D3)⋊C4—122no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4—121no—
454(C2×D3)⋊C4—121no—
455(C2×D3)⋊C4—122no—
456(C2×D3)⋊C4—122no—
457C4⋊Dic3—121no—
458C4⋊Dic3—121no—
459Dic3⋊C4—22no—
460Dic3⋊C4—121no—
461Dic3⋊C4—121no—
462C4×Dic3—41no—
463C4×Dic3—62no—
464C4×Dic3—62no—
465C4×Dic3—121no—
466C4×Dic3—121no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32C23×C411yescharacteristic
475C22×C32C22×D411yescharacteristic
476C22×C32C2×#4111yescharacteristic
477C22×C32H(5,𝔽2)11yescharacteristic
478C22×C32H(5,𝔽2)11yescharacteristic
479C22×C32H(5,𝔽2)11yescharacteristic
480C22×C32H(5,𝔽2)11yescharacteristic
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—22no—
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—416no—
491C2×C3⋊D3—41no—
492C2×C3⋊D3—41no—
493C2×C3⋊D3—41no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3C4×D414yes—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C32×C4—41no—
504C32×C4—41no—
505C3⋊Dic3—41no—
506C3⋊Dic3—41no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C25—91no—
515C22×D4—31no—
516C22×D4—91no—
517C22×D4—91no—
518C23×C4—31no—
519C23×C4—91no—
520C23×C4—91no—
521#120—98no—
522C4×D4—184no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
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⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—184no—
542C2×C22⋊C4D3211yescharacteristic
543C2×C42—31no—
544C2×C42—91no—
545C2×C42—91no—
546#95—31no—
547#95—31no—
548#95—31no—
549#95—31no—
550#95—91no—
551#95—91no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—22no—
568C23×C3—32no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3C2×C4×D312yes—
580C23×C3C2×C4×D312yes—
581C23×C3C23×D311yescharacteristic
582C23×C3C23×D311yescharacteristic
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—32no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—68no—
602C22×D3—68no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—62no—
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—128no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3—124no—
635C22×D3—124no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—128no—
639C22×D3—124no—
640C22×D3—124no—
641C22×D3—124no—
642C22×D3—124no—
643C22×D3—124no—
644C22×D3—124no—
645C22×D3—124no—
646C22×D3—124no—
647C22×D3—128no—
648C22×D3—128no—
649C22×D3—128no—
650C22×D3—128no—
651C22×D3—128no—
652C22×D3C2×C4×D312yes—
653C3×D4—124no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—124no—
694#67—44no—
695#67—68no—
696#67—124no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×Dic3—121no—
730C2×Dic3—121no—
731C2×Dic3C2×C4×D312yes—
732C2×Dic3C2×C4×D312yes—
733C2×Dic3C2×C4×D312yes—
734C2×Dic3D3×D412yes—
735C2×Dic3D3×D412yes—
736D12—68no—
737D12—124no—
738C4×D3—44no—
739C4×D3—124no—
740C4×D3—124no—
741C4×D3—124no—
742C4×D3—124no—
743C2×C32—42no—
744C2×C32C2×C4×D411yescharacteristic
745C2×C32#51811yescharacteristic
746C2×C32#51811yescharacteristic
747C2×C32#53411yescharacteristic
748C2×C32#53511yescharacteristic
749C2×C32#53811yescharacteristic
750C2×C32#53811yescharacteristic
751C3⋊D3—24no—
752C3⋊D3—42no—
753C3×D3—42no—
754C24—31no—
755C24—91no—
756C24—91no—
757C24—94no—
758C24—182no—
759C24—182no—
760C24—361no—
761C24—361no—
762C24—361no—
763C24—361no—
764C24C2×D3211yescharacteristic
765C2×D4—34no—
766C2×D4—94no—
767C2×D4—94no—
768C2×D4—121no—
769C2×D4—121no—
770C2×D4—182no—
771C2×D4—182no—
772C2×D4—361no—
773C2×D4—361no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—31no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—62no—
782C22×C4—94no—
783C22×C4—91no—
784C22×C4—91no—
785C22×C4—121no—
786C22×C4—121no—
787C22×C4—182no—
788C22×C4—361no—
789C22×C4—361no—
790C22×C4—361no—
791C22×C4—361no—
792C22×C4C2×D3211yescharacteristic
793C22×C4C2×D3211yescharacteristic
794C4⋊C4—62no—
795C4⋊C4—361no—
796C4⋊C4—361no—
797C22⋊C4—34no—
798C22⋊C4—41no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—94no—
802C22⋊C4—94no—
803C22⋊C4—121no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—182no—
809C22⋊C4—361no—
810C22⋊C4—361no—
811C22⋊C4—361no—
812C22⋊C4—361no—
813C42—121no—
814C42—182no—
815C42—361no—
816C22×C3—24no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—121no—
848C22×C3—121no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3C22×C4×D311yescharacteristic
852C22×C3C22×C4×D311yescharacteristic
853C22×C3C2×D3×D411yescharacteristic
854C22×C3C2×D3×D411yescharacteristic
855C22×C3#100411yescharacteristic
856C22×C3#100411yescharacteristic
857C22×C3#100411yescharacteristic
858C22×C3#100411yescharacteristic
859C22×C3D3×#4111yescharacteristic
860C22×C3D3×#4111yescharacteristic
861C22×C3#100911yescharacteristic
862C22×C3#100911yescharacteristic
863C22×C3#100911yescharacteristic
864C22×C3#100911yescharacteristic
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—34no—
869C2×D3—34no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—64no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—64no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—122no—
898C2×D3—122no—
899C2×D3—122no—
900C2×D3—122no—
901C2×D3—122no—
902C2×D3—1216no—
903C2×D3—1216no—
904C2×D3—122no—
905C2×D3—122no—
906C2×D3—122no—
907C2×D3—122no—
908C2×D3—1232no—
909C2×D3—121no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C2×D3—121no—
914C2×D3—121no—
915C2×D3—121no—
916C2×D3—121no—
917C3×C4—41no—
918C3×C4—41no—
919C3×C4—41no—
920C3×C4—41no—
921C3×C4—62no—
922C3×C4—62no—
923C3×C4—62no—
924C3×C4—62no—
925C3×C4—62no—
926C3×C4—81no—
927C3×C4—81no—
928C3×C4—121no—
929C3×C4—121no—
930Dic3—22no—
931Dic3—22no—
932Dic3—22no—
933Dic3—22no—
934Dic3—22no—
935Dic3—41no—
936Dic3—41no—
937Dic3—121no—
938Dic3—121no—
939Dic3—121no—
940Dic3—121no—
941Dic3—241no—
942Dic3—241no—
943C32#232111yescharacteristic, complemented, Sylow
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—32no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—92no—
958C23—92no—
959C23—92no—
960C23—92no—
961C23—188no—
962C23—181no—
963C23—181no—
964C23—181no—
965C23—181no—
966C23—181no—
967C23—181no—
968C23—181no—
969C23—181no—
970C23—181no—
971C23—181no—
972C23—364no—
973C23—364no—
974C23—364no—
975C23—364no—
976C23—364no—
977C23—364no—
978C23C4×D3212yes—
979C23C22×D3211yescharacteristic
980D4—124no—
981D4—188no—
982D4—364no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—32no—
990C2×C4—32no—
991C2×C4—32no—
992C2×C4—32no—
993C2×C4—32no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—124no—
1011C2×C4—181no—
1012C2×C4—181no—
1013C2×C4—181no—
1014C2×C4—181no—
1015C2×C4—181no—
1016C2×C4—181no—
1017C2×C4—364no—
1018C2×C4—364no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—44no—
1027C2×C3—42no—
1028C2×C3—42no—
1029C2×C3—122no—
1030C2×C3#548611yescharacteristic
1031C2×C3#552111yescharacteristic
1032C2×C3C4×D3×D411yescharacteristic
1033C2×C3C4×D3×D411yescharacteristic
1034C2×C3#554511yescharacteristic
1035C2×C3#554511yescharacteristic
1036C2×C3#558911yescharacteristic
1037C2×C3#560511yescharacteristic
1038C2×C3#560711yescharacteristic
1039C2×C3#561311yescharacteristic
1040C2×C3#565711yescharacteristic
1041C2×C3#565711yescharacteristic
1042C2×C3#567411yescharacteristic
1043C2×C3#570411yescharacteristic
1044D3—42no—
1045D3—64no—
1046D3—64no—
1047D3—124no—
1048D3—124no—
1049D3—122no—
1050D3—122no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—94no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—121no—
1066C22—182no—
1067C22—182no—
1068C22—182no—
1069C22—182no—
1070C22—182no—
1071C22—182no—
1072C22—182no—
1073C22—182no—
1074C22—182no—
1075C22—3616no—
1076C22—361no—
1077C22—361no—
1078C22—361no—
1079C22—361no—
1080C22C2×C4×D3211yescharacteristic
1081C22#6430811yescharacteristic
1082C22D32×D411yescharacteristic
1083C22#6431211yescharacteristic
1084C22#6431411yescharacteristic
1085C22#6431411yescharacteristic
1086C22#6433011yescharacteristic
1087C4—41no—
1088C4—41no—
1089C4—62no—
1090C4—62no—
1091C4—62no—
1092C4—62no—
1093C4—62no—
1094C4—121no—
1095C4—121no—
1096C4—361no—
1097C4—361no—
1098C3—21no—
1099C3#7487611yescharacteristic, complemented
1100C3#7582611yescharacteristic, complemented
1101C2—42no—
1102C2—122no—
1103C2—184no—
1104C2—362no—
1105C2#1059418211yescharacteristic
1106C2#1059423211yescharacteristic
1107C2#1059425511yescharacteristic
1108C2#1059428711yescharacteristic
1109C2#1059505811yescharacteristic
1110C2#1059525511yescharacteristic
1111C2#1059528111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
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
2. C2×#63974C2semidirect
3. C2×#63904C2semidirect
4. #10592654C2semidirect
5. C3×#4956C2semidirect
6. C3×#4944C2semidirect
7. #10591707C2semidirect
8. #10591701C2semidirect
9. #10591383C2semidirect
10. #10591382C2semidirect
11. #10591375C2semidirect
12. #10591275C2semidirect
13. #10591259C2semidirect
14. #10591258C2semidirect
15. #10591233C2semidirect
20. C22×C3×C4×D3C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
37. #63981C4semidirect
39. C2×Dic3⋊Dic3C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×Dic32C22semidirect
48. C2×Dic32C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
70. #4956D3semidirect
76. #4944D3semidirect
94. C23×C3⋊D3C2×C4semidirect
104. C2×C3×#67C2×C4semidirect
120. C2×#626C2×C4semidirect
126. C2×#624D4semidirect
135. C3×#217C2×C4semidirect
143. #3722C2×C4semidirect
144. #3722C2×C4semidirect
164. C22×C4×D3C2×D3semidirect
206. C2×(C2×D3)⋊C4C2×D3semidirect
211. C2×Dic3⋊C4C2×D3semidirect
216. C2×C4×Dic3C2×D3semidirect
229. C3⋊#95C2×D3semidirect
230. C3⋊#95C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
382. C2×#67C4×D3semidirect
433. #217C4×D3semidirect
943. C32#2321semidirect
1099. C3#74876semidirect
1100. C3#75826semidirect

Maximal subgroups

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

subgroupindex
C2×#639812
C2×#639742
C2×#639042
#105926542
C3×#49562
C3×#49442
#105917072
#105917012
#105913832
#105913822
#105913752
#105912752
#105912592
#105912582
#105912332
#758263
#748763