Finite Group Databasebeta

← #11803270

Subgroups — #11803270

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×#63923C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4#10592638C211yesmaximal, characteristic, complemented
5C3×#4940C211yesmaximal, characteristic, complemented
6C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591383C211yesmaximal, characteristic, complemented
9#10591380C211yesmaximal, characteristic, complemented
10#10591379C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591316C211yesmaximal, characteristic, complemented
13#10591289C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591259C211yesmaximal, characteristic, complemented
16#75826—31nomaximal
17#73569—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic, complemented
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic, complemented
29C2×#3752C2211yescharacteristic, complemented
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic, complemented
47#63923C418yescomplemented
48D3×(C2×D3)⋊C4—24no—
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×C4×#67—31no—
57C22×(C2×D3)⋊C4—31no—
58C2×#893—31no—
59C2×#882—31no—
60C2×#882—31no—
61C2×D3×C22⋊C4—31no—
62C3×#388—31no—
63C3×C4×C22⋊C4—31no—
64#4990—31no—
65#4958—31no—
66#4957—31no—
67#4956—31no—
68#4955—31no—
69#4955—31no—
70#4951—31no—
71#4950—31no—
72#4940—31no—
73#4940D311yescharacteristic, complemented
74#4939—31no—
75#4939—31no—
76#4939—31no—
77#4939—61no—
78C4×(C2×D3)⋊C4D311yescharacteristic, complemented
79#4670—31no—
80#4670—31no—
81#4669—31no—
82#4668—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×D32—22no—
92C22×D32—22no—
93C22×D32—41no—
94C22×D32—41no—
95C22×D32—41no—
96C22×D32—41no—
97C22×D32C2×C414yescomplemented
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C2×C4⋊(C3⋊D3)—41no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2×C414yescomplemented
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×D3D414yescomplemented
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×D3×Dic3—22no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3—41no—
127C32×C42—41no—
128#3752—22no—
129#3752—22no—
130#3752—41no—
131#3752—41no—
132C4⋊(C3⋊Dic3)—41no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4C2×C414yescomplemented
137C3×(C2×D3)⋊C4C2×C414yescomplemented
138C3×Dic3⋊C4—22no—
139C3×C4×Dic3—41no—
140Dic3⋊Dic3—41no—
141#3722—22no—
142#3722—41no—
143#3722—41no—
144#3722C2×C414yescomplemented
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—41no—
148Dic32—22no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C23×C3×C4—31no—
153C22×#67—31no—
154C22×#67—31no—
155C23×Dic3—31no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3C2×D311yescharacteristic
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C42—21no—
172C2×C3×C42—31no—
173C2×C3×C42C2×D311yescharacteristic, complemented
174C2×C3×C42C2×D311yescharacteristic, complemented
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C4×#67—64no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
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—61no—
199C2×(C2×D3)⋊C4—61no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4—61no—
202C2×(C2×D3)⋊C4—64no—
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—61no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4C2×D311yescharacteristic, complemented
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3C2×D311yescharacteristic, complemented
217#893—64no—
218#882—38no—
219#882—38no—
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×C32C2411yescharacteristic
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3C22×C412yes—
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×D3C22×C412yes—
259C22×C3×D3C22×C412yes—
260C22×C3×D3C2×D412yes—
261C22×C3×D3#4112yes—
262C2×D32—28no—
263C2×D32—44no—
264C2×D32—44no—
265C2×D32—44no—
266C2×D32—44no—
267C2×D32—44no—
268C2×D32—44no—
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×C32×C4—21no—
276C2×C32×C4C22×C412yes—
277C2×C32×C4C2×D412yes—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C4⋊(C3⋊D3)—44no—
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—
304#626—28no—
305#626—44no—
306#624—44no—
307D3×Dic3—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—91no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—91no—
322C4×C22⋊C4—31no—
323C24×C3—31no—
324C24×C3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—34no—
330C23×D3—34no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—121no—
338C23×D3—121no—
339C23×D3—121no—
340C23×D3—121no—
341C23×D3—121no—
342C23×D3—121no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—34no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—121no—
358C22×C3×C4—121no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—121no—
370C2×#67—121no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—62no—
378C22×Dic3—121no—
379C22×Dic3—121no—
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C2×D12—34no—
387C2×D12—34no—
388C2×D12—34no—
389C2×D12—34no—
390C2×D12—64no—
391C2×D12—62no—
392C2×D12—62no—
393C2×D12—121no—
394C2×D12—121no—
395C2×D12—121no—
396C2×D12—121no—
397C2×D12—122no—
398C2×D12—122no—
399C2×D12—121no—
400C2×D12—121no—
401C2×C4×D3—41no—
402C2×C4×D3—41no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—121no—
407C2×C4×D3—121no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3D1214yescomplemented
413C3×C4⋊C4—62no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—121no—
419C3×C42—41no—
420C3×C42—41no—
421C3×C42—42no—
422C3×C42—121no—
423#217—62no—
424#217—62no—
425#217—121no—
426(C2×D3)⋊C4—22no—
427(C2×D3)⋊C4—22no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—41no—
431(C2×D3)⋊C4—62no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—122no—
440(C2×D3)⋊C4—122no—
441(C2×D3)⋊C4—121no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4—121no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—122no—
451(C2×D3)⋊C4—122no—
452(C2×D3)⋊C4C4×D314yescomplemented
453(C2×D3)⋊C4C4×D314yescomplemented
454C4⋊Dic3—121no—
455C4⋊Dic3—121no—
456C4⋊Dic3—121no—
457C4⋊Dic3—122no—
458Dic3⋊C4—22no—
459Dic3⋊C4—121no—
460C4×Dic3—41no—
461C4×Dic3—62no—
462C4×Dic3—62no—
463C22×C32C23×C411yescharacteristic
464C22×C32C22×D411yescharacteristic
465C22×C32C2×#4111yescharacteristic
466C22×C32H(5,𝔽2)11yescharacteristic
467C22×C32H(5,𝔽2)11yescharacteristic
468C22×C32H(5,𝔽2)11yescharacteristic
469C22×C32H(5,𝔽2)11yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
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—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3C4×D414yes—
498D32—416no—
499C32×C4—22no—
500C32×C4—22no—
501C32×C4—41no—
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—91no—
511C22×D4—91no—
512C22×D4—91no—
513C22×D4—91no—
514C23×C4—31no—
515C23×C4—91no—
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—91no—
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⋊C4—184no—
539C2×C42—31no—
540C2×C42—91no—
541C2×C42D3211yescharacteristic, complemented
542#95—31no—
543#95—31no—
544#95—31no—
545#95—31no—
546#95—91no—
547#95—91no—
548C23×C3—21no—
549C23×C3—32no—
550C23×C3—32no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3C23×D311yescharacteristic
564C23×C3C23×D311yescharacteristic
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—32no—
576C22×D3—32no—
577C22×D3—32no—
578C22×D3—32no—
579C22×D3—62no—
580C22×D3—62no—
581C22×D3—68no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—68no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—121no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—124no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—124no—
628C22×D3—124no—
629C22×D3—124no—
630C22×D3—124no—
631C22×D3C2×C4×D312yes—
632C22×D3C2×C4×D312yes—
633C22×D3C2×D1212yes—
634C22×D3#23512yes—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
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—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
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—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—124no—
677C2×C3×C4C2×C4×D312yes—
678C2×C3×C4C2×C4×D312yes—
679C2×C3×C4C2×D1212yes—
680C2×C3×C4D3×D412yes—
681#67—68no—
682#67—124no—
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—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—124no—
717C2×Dic3C2×C4×D312yes—
718C2×Dic3C2×C4×D312yes—
719C2×Dic3C2×D1212yes—
720D12—68no—
721D12—124no—
722D12—124no—
723D12—128no—
724D12—124no—
725C4×D3—44no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—124no—
729C2×C32C2×C4×D411yescharacteristic
730C2×C32#51811yescharacteristic
731C2×C32#51811yescharacteristic
732C2×C32#53411yescharacteristic
733C2×C32#53511yescharacteristic
734C2×C32#53811yescharacteristic
735C2×C32#53811yescharacteristic
736C3⋊D3—42no—
737C3⋊D3—42no—
738C3×D3—24no—
739C3×D3—42no—
740C24—31no—
741C24—31no—
742C24—94no—
743C24—91no—
744C24—91no—
745C24—182no—
746C24—182no—
747C24—361no—
748C24—361no—
749C24—361no—
750C24—361no—
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—91no—
768C22×C4—91no—
769C22×C4—121no—
770C22×C4—121no—
771C22×C4—182no—
772C22×C4—182no—
773C22×C4—361no—
774C22×C4—361no—
775C22×C4—361no—
776C22×C4—361no—
777C22×C4C2×D3211yescharacteristic
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—62no—
781C4⋊C4—361no—
782C4⋊C4—361no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—94no—
788C22⋊C4—121no—
789C22⋊C4—182no—
790C22⋊C4—182no—
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—41no—
800C42—121no—
801C42—182no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—34no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C22×C4×D311yescharacteristic
824C22×C3C22×C4×D311yescharacteristic
825C22×C3C22×D1211yescharacteristic
826C22×C3C2×#23511yescharacteristic
827C22×C3C2×D3×D411yescharacteristic
828C22×C3#100411yescharacteristic
829C22×C3#100411yescharacteristic
830C22×C3#100411yescharacteristic
831C22×C3D3×#4111yescharacteristic
832C22×C3#100911yescharacteristic
833C22×C3#100911yescharacteristic
834C22×C3#100911yescharacteristic
835C22×C3#100911yescharacteristic
836C22×C3#100911yescharacteristic
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—41no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—122no—
868C2×D3—1216no—
869C2×D3—1216no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—241no—
887C2×D3—241no—
888C2×D3—241no—
889C2×D3—241no—
890C2×D3—241no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3C4×D1214yes—
895C3×C4—24no—
896C3×C4—22no—
897C3×C4—22no—
898C3×C4—22no—
899C3×C4—22no—
900C3×C4—42no—
901C3×C4—42no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—62no—
905C3×C4—62no—
906C3×C4—62no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—121no—
910Dic3—22no—
911Dic3—22no—
912Dic3—22no—
913Dic3—41no—
914Dic3—41no—
915Dic3—41no—
916Dic3—121no—
917Dic3—121no—
918Dic3—121no—
919Dic3—121no—
920Dic3—241no—
921Dic3—241no—
922C32#232111yescharacteristic, complemented, Sylow
923C23—32no—
924C23—32no—
925C23—32no—
926C23—32no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—92no—
938C23—92no—
939C23—188no—
940C23—181no—
941C23—181no—
942C23—181no—
943C23—181no—
944C23—181no—
945C23—181no—
946C23—181no—
947C23—181no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—364no—
953C23—364no—
954C23—364no—
955C23—364no—
956C23—364no—
957C23—364no—
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—21no—
968C2×C4—21no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—32no—
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—61no—
986C2×C4—61no—
987C2×C4—124no—
988C2×C4—181no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—364no—
995C2×C4—364no—
996C2×C4C4×D3212yes—
997C2×C4D3×D1212yes—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—64no—
1006C2×C3—122no—
1007C2×C3C2×C4×D1211yescharacteristic
1008C2×C3#549311yescharacteristic
1009C2×C3#552111yescharacteristic
1010C2×C3#552511yescharacteristic
1011C2×C3C4×D3×D411yescharacteristic
1012C2×C3#554511yescharacteristic
1013C2×C3#554511yescharacteristic
1014C2×C3#554511yescharacteristic
1015C2×C3#556011yescharacteristic
1016C2×C3#556011yescharacteristic
1017C2×C3#560511yescharacteristic
1018C2×C3#565711yescharacteristic
1019C2×C3#567411yescharacteristic
1020C2×C3#570411yescharacteristic
1021D3—24no—
1022D3—42no—
1023D3—122no—
1024D3—122no—
1025D3—122no—
1026D3—122no—
1027D3—242no—
1028D3—242no—
1029C22—34no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—62no—
1038C22—62no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—182no—
1044C22—182no—
1045C22—182no—
1046C22—182no—
1047C22—182no—
1048C22—182no—
1049C22—3616no—
1050C22—361no—
1051C22—361no—
1052C22—361no—
1053C22—361no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22C2×C4×D3211yescharacteristic
1059C22C2×D3×D1211yescharacteristic
1060C22D3×#23511yescharacteristic
1061C22#6430711yescharacteristic
1062C22#6430811yescharacteristic
1063C22#6430811yescharacteristic
1064C22#6433011yescharacteristic
1065C4—22no—
1066C4—22no—
1067C4—41no—
1068C4—62no—
1069C4—62no—
1070C4—62no—
1071C4—121no—
1072C4—121no—
1073C4—121no—
1074C4—361no—
1075C4—361no—
1076C3—21no—
1077C3#7356911yescharacteristic, complemented
1078C3#7582611yescharacteristic, complemented
1079C2—64no—
1080C2—122no—
1081C2—362no—
1082C2—362no—
1083C2C4×D3×D1211yescharacteristic
1084C2#1059399411yescharacteristic
1085C2#1059400111yescharacteristic
1086C2#1059401311yescharacteristic
1087C2#1059505811yescharacteristic
1088C2#1059507211yescharacteristic
1089C2#1059508511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63923C2
hypercenterC2×C42D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×D3×(C2×D3)⋊C4C2semidirect
3. C2×#63904C2semidirect
4. #10592638C2semidirect
5. C3×#4940C2semidirect
6. C3×C4×(C2×D3)⋊C4C2semidirect
7. #10591399C2semidirect
8. #10591383C2semidirect
9. #10591380C2semidirect
10. #10591379C2semidirect
11. #10591364C2semidirect
12. #10591316C2semidirect
13. #10591289C2semidirect
14. #10591275C2semidirect
15. #10591259C2semidirect
23. C22×#624C22semidirect
25. C2×C32×C42C22semidirect
28. C2×#3752C22semidirect
29. C2×#3752C22semidirect
30. C2×C4⋊(C3⋊Dic3)C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
42. C2×#3722C22semidirect
46. C2×Dic32C22semidirect
47. #63923C4semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
73. #4940D3semidirect
78. C4×(C2×D3)⋊C4D3semidirect
97. C22×D32C2×C4semidirect
105. C2×C4⋊(C3⋊D3)C2×C4semidirect
114. C2×C3×C4×D3D4semidirect
120. C2×#626C2×C4semidirect
136. C3×(C2×D3)⋊C4C2×C4semidirect
137. C3×(C2×D3)⋊C4C2×C4semidirect
144. #3722C2×C4semidirect
173. C2×C3×C42C2×D3semidirect
174. C2×C3×C42C2×D3semidirect
213. 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
412. C2×C4×D3D12semidirect
452. (C2×D3)⋊C4C4×D3semidirect
453. (C2×D3)⋊C4C4×D3semidirect
541. C2×C42D32semidirect
922. C32#2321semidirect
1077. C3#73569semidirect
1078. C3#75826semidirect

Maximal subgroups

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

subgroupindex
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639042
#105926382
C3×#49402
C3×C4×(C2×D3)⋊C42
#105913992
#105913832
#105913802
#105913792
#105913642
#105913162
#105912892
#105912752
#105912592
#758263
#735693