Finite Group Databasebeta

← #11810322

Subgroups — #11810322

Order 1152.

1719 conjugacy classes of subgroups.

The subgroup lattice has 1094 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
4C2×#63897C211yesmaximal, characteristic, complemented
5#10592690C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591366C211yesmaximal, characteristic, complemented
10#10591364C211yesmaximal, characteristic, complemented
11#10591312C211yesmaximal, characteristic, complemented
12#10591285C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591259C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#78101—31nomaximal
17#74603—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic, complemented
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic, complemented
29C2×#3752C2211yescharacteristic, complemented
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, 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#63923—24no—
48D3×(C2×D3)⋊C4—24no—
49#63904—24no—
50#63897—24no—
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C4×#67—31no—
58C22×(C2×D3)⋊C4—31no—
59C2×#894—31no—
60C2×#894—31no—
61C2×#893—31no—
62C2×#882—31no—
63C2×#882—31no—
64C2×D3×C22⋊C4—31no—
65C3×#399—31no—
66C3×#385—31no—
67#4993D311yescharacteristic, complemented
68#4992—31no—
69#4991—31no—
70#4991—31no—
71#4991—61no—
72#4990—31no—
73#4989D311yescharacteristic, complemented
74#4987—31no—
75#4961—31no—
76#4958—31no—
77#4956—31no—
78#4955—31no—
79#4955—31no—
80#4944—31no—
81#4942—31no—
82#4675—31no—
83#4672—31no—
84#4670—31no—
85#4669—31no—
86#4665—31no—
87#4665—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×D32—22no—
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—41no—
98C22×D32—41no—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—22no—
106C2×C4⋊(C3⋊D3)—41no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—41no—
121C2×#626D414yes—
122C2×#624—22no—
123C2×#624—22no—
124C2×#624—41no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C4⋊C4—41no—
129#3752—22no—
130#3752—22no—
131#3752—41no—
132#3752—41no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—41no—
138C3×Dic3⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141Dic3⋊Dic3—41no—
142#3722—22no—
143#3722—22no—
144#3722—22no—
145#3722D414yescomplemented
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149Dic32—22no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C23×C3×C4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C23×Dic3—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×D12—61no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3C2×D311yescharacteristic
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
171C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C4×#67—64no—
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—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4—61no—
202C2×(C2×D3)⋊C4—61no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—64no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×C4⋊Dic3—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4C2×D311yescharacteristic, complemented
213C2×Dic3⋊C4C2×D311yescharacteristic, complemented
214C2×Dic3⋊C4C2×D311yescharacteristic, complemented
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217#894—64no—
218#894—64no—
219#893—64no—
220#882—64no—
221#882—64no—
222D3×C22⋊C4—64no—
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⋊#95—31no—
232C3⋊#95—61no—
233C3⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C23×C32C2411yescharacteristic
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⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3C2×D412yes—
250C22×C3⋊D3C2×D412yes—
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—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3C2×D412yes—
262C22×C3×D3#4112yes—
263C22×C3×D3#4112yes—
264C22×C3×D3#4112yes—
265C2×D32—28no—
266C2×D32—44no—
267C2×D32—44no—
268C2×D32—44no—
269C2×D32—44no—
270C2×D32—44no—
271C2×D32—44no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C4⋊(C3⋊D3)—44no—
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×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D412yes—
304C2×C3×Dic3C2×D412yes—
305C2×C3×Dic3C2×D412yes—
306C3×C4×D3—44no—
307#626—28no—
308#626—44no—
309#624—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—91no—
314C22×C22⋊C4—91no—
315#399—31no—
316#397—91no—
317#394—91no—
318#394—91no—
319#388—91no—
320#388—91no—
321#386—91no—
322#386—91no—
323#385—31no—
324#380—91no—
325#379—91no—
326C24×C3—31no—
327C24×C3—31no—
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—61no—
333C23×D3—61no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—121no—
345C23×D3—121no—
346C23×D3—121no—
347C23×D3—121no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—62no—
360C22×C3×C4—62no—
361C22×C3×C4—121no—
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C2×#67—34no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—121no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—62no—
381C22×Dic3—62no—
382C22×Dic3—121no—
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C2×D12—34no—
390C2×D12—62no—
391C2×D12—62no—
392C2×D12—62no—
393C2×D12—62no—
394C2×D12—62no—
395C2×D12—62no—
396C2×D12—62no—
397C2×D12—62no—
398C2×D12—122no—
399C2×D12—122no—
400C2×D12—121no—
401C2×D12—121no—
402C2×D12—122no—
403C2×D12—121no—
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—41no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—121no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C3×C4⋊C4—41no—
417C3×C4⋊C4—41no—
418C3×C4⋊C4—42no—
419C3×C4⋊C4—62no—
420C3×C4⋊C4—62no—
421C3×C4⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—121no—
427#217—62no—
428#217—62no—
429#217—62no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—22no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—41no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
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—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—122no—
451(C2×D3)⋊C4—122no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4—121no—
454(C2×D3)⋊C4—121no—
455(C2×D3)⋊C4—121no—
456(C2×D3)⋊C4—122no—
457(C2×D3)⋊C4—122no—
458C4⋊Dic3—121no—
459Dic3⋊C4—22no—
460Dic3⋊C4—22no—
461Dic3⋊C4—22no—
462Dic3⋊C4—121no—
463C4×Dic3—62no—
464C4×Dic3—62no—
465C22×C32C22×D411yescharacteristic
466C22×C32C22×D411yescharacteristic
467C22×C32C2×#4111yescharacteristic
468C22×C32C2×#4111yescharacteristic
469C22×C32C2×#4111yescharacteristic
470C22×C32H(5,𝔽2)11yescharacteristic
471C22×C32H(5,𝔽2)11yescharacteristic
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—22no—
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—41no—
485C2×C3⋊D3—41no—
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—22no—
494C2×C3×D3—22no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3#12314yescomplemented
500D32—416no—
501C32×C4—41no—
502C32×C4—41no—
503C32×C4—41no—
504C3⋊Dic3—41no—
505C3⋊Dic3—41no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C25—91no—
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—91no—
516C23×C4—31no—
517C23×C4—91no—
518C23×C4—91no—
519#123—184no—
520#120—184no—
521C4×D4—184no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4D3211yescharacteristic, complemented
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
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—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—184no—
544C2×C42—91no—
545#95—31no—
546#95—31no—
547#95—31no—
548#95—91no—
549#95—91no—
550#95—91no—
551C23×C3—21no—
552C23×C3—32no—
553C23×C3—32no—
554C23×C3—32no—
555C23×C3—32no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3C23×D311yescharacteristic
567C23×C3C23×D311yescharacteristic
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—32no—
579C22×D3—32no—
580C22×D3—32no—
581C22×D3—32no—
582C22×D3—62no—
583C22×D3—62no—
584C22×D3—68no—
585C22×D3—68no—
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—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
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—121no—
620C22×D3—121no—
621C22×D3—121no—
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×D3—124no—
632C22×D3—124no—
633C22×D3—124no—
634C22×D3#23512yes—
635C22×D3D3×D412yes—
636C22×D3#23912yes—
637C22×D3#23912yes—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
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—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
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—61no—
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—124no—
684#67—68no—
685#67—124no—
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—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
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—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—124no—
720C2×Dic3D3×D412yes—
721C2×Dic3D3×D412yes—
722C2×Dic3D3×D412yes—
723D12—68no—
724D12—124no—
725D12—124no—
726D12—128no—
727D12—124no—
728C4×D3—44no—
729C4×D3—124no—
730C4×D3—124no—
731C4×D3—124no—
732C2×C32C2×#12311yescharacteristic
733C2×C32#52511yescharacteristic
734C2×C32#53811yescharacteristic
735C2×C32D4211yescharacteristic
736C2×C32#54611yescharacteristic
737C2×C32#54611yescharacteristic
738C2×C32#55111yescharacteristic
739C3⋊D3—42no—
740C3⋊D3—42no—
741C3×D3—24no—
742C3×D3—42no—
743C24—31no—
744C24—31no—
745C24—91no—
746C24—91no—
747C24—182no—
748C24—182no—
749C24—182no—
750C24—182no—
751C24—182no—
752C24—361no—
753C24—361no—
754C2×D4—94no—
755C2×D4—182no—
756C2×D4—182no—
757C2×D4—182no—
758C2×D4—182no—
759C2×D4—182no—
760C2×D4—182no—
761C2×D4—361no—
762C2×D4—361no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—62no—
770C22×C4—62no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—121no—
774C22×C4—182no—
775C22×C4—182no—
776C22×C4—182no—
777C22×C4—182no—
778C22×C4—361no—
779C22×C4—361no—
780C22×C4C2×D3211yescharacteristic
781C22×C4C2×D3211yescharacteristic
782C22×C4C2×D3211yescharacteristic
783C4⋊C4—41no—
784C4⋊C4—62no—
785C4⋊C4—62no—
786C4⋊C4—62no—
787C4⋊C4—361no—
788C22⋊C4—62no—
789C22⋊C4—62no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—94no—
793C22⋊C4—121no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—182no—
798C22⋊C4—182no—
799C22⋊C4—182no—
800C22⋊C4—182no—
801C22⋊C4—182no—
802C22⋊C4—361no—
803C22⋊C4—361no—
804C42—182no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—34no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—121no—
826C22×C3C2×#23511yescharacteristic
827C22×C3C2×D3×D411yescharacteristic
828C22×C3C2×D3×D411yescharacteristic
829C22×C3C2×D3×D411yescharacteristic
830C22×C3C2×D3×D411yescharacteristic
831C22×C3#100411yescharacteristic
832C22×C3#100411yescharacteristic
833C22×C3C2×#23911yescharacteristic
834C22×C3C2×#23911yescharacteristic
835C22×C3D3×#4111yescharacteristic
836C22×C3D3×#4111yescharacteristic
837C22×C3D3×#4111yescharacteristic
838C22×C3#100911yescharacteristic
839C22×C3#100911yescharacteristic
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
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—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—122no—
868C2×D3—122no—
869C2×D3—122no—
870C2×D3—122no—
871C2×D3—1216no—
872C2×D3—1216no—
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—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—241no—
890C2×D3—241no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3—241no—
895C2×D3—241no—
896C2×D3—241no—
897C2×D3#89414yescomplemented
898C3×C4—42no—
899C3×C4—42no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—41no—
905C3×C4—41no—
906C3×C4—62no—
907C3×C4—62no—
908C3×C4—62no—
909C3×C4—81no—
910C3×C4—121no—
911C3×C4—121no—
912C3×C4—121no—
913Dic3—22no—
914Dic3—22no—
915Dic3—22no—
916Dic3—41no—
917Dic3—41no—
918Dic3—41no—
919Dic3—121no—
920Dic3—121no—
921Dic3—121no—
922Dic3—121no—
923Dic3—241no—
924Dic3—241no—
925C32#241811yescharacteristic, complemented, Sylow
926C23—32no—
927C23—32no—
928C23—32no—
929C23—32no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—92no—
941C23—92no—
942C23—188no—
943C23—181no—
944C23—181no—
945C23—181no—
946C23—181no—
947C23—181no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—364no—
956C23—364no—
957C23—364no—
958C23—364no—
959C23—364no—
960C23—364no—
961C23C22×D3211yescharacteristic
962D4—188no—
963D4—364no—
964D4—364no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—32no—
975C2×C4—32no—
976C2×C4—32no—
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—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—124no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—364no—
1000C2×C4—364no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—64no—
1009C2×C3—122no—
1010C2×C3C2×#89411yescharacteristic
1011C2×C3#554711yescharacteristic
1012C2×C3#556011yescharacteristic
1013C2×C3#559011yescharacteristic
1014C2×C3#562711yescharacteristic
1015C2×C3#563011yescharacteristic
1016C2×C3#563011yescharacteristic
1017C2×C3#563711yescharacteristic
1018C2×C3#563711yescharacteristic
1019C2×C3D3×#12311yescharacteristic
1020C2×C3#565411yescharacteristic
1021C2×C3#565411yescharacteristic
1022C2×C3#565711yescharacteristic
1023C2×C3#571711yescharacteristic
1024D3—24no—
1025D3—42no—
1026D3—122no—
1027D3—122no—
1028D3—122no—
1029D3—122no—
1030D3—242no—
1031D3—242no—
1032C22—34no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22—182no—
1047C22—182no—
1048C22—182no—
1049C22—182no—
1050C22—182no—
1051C22—182no—
1052C22—3616no—
1053C22—361no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22—361no—
1059C22—361no—
1060C22—361no—
1061C22D3×#23511yescharacteristic
1062C22#6430811yescharacteristic
1063C22D32×D411yescharacteristic
1064C22D32×D411yescharacteristic
1065C22D3×#23911yescharacteristic
1066C22D3×#23911yescharacteristic
1067C22#6433011yescharacteristic
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—62no—
1072C4—62no—
1073C4—62no—
1074C4—121no—
1075C4—121no—
1076C4—121no—
1077C4—361no—
1078C4—361no—
1079C3—21no—
1080C3#7460311yescharacteristic, complemented
1081C3#7810111yescharacteristic, complemented
1082C2—64no—
1083C2—122no—
1084C2—362no—
1085C2—362no—
1086C2D3×#89411yescharacteristic
1087C2#1059462011yescharacteristic
1088C2#1059462011yescharacteristic
1089C2#1059462311yescharacteristic
1090C2#1059508511yescharacteristic
1091C2#1059529511yescharacteristic
1092C2#1059543611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63923C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×(C2×D3)⋊C4C2semidirect
3. C2×#63904C2semidirect
4. C2×#63897C2semidirect
5. #10592690C2semidirect
6. C3×#4993C2semidirect
7. C3×#4989C2semidirect
8. #10591399C2semidirect
9. #10591366C2semidirect
10. #10591364C2semidirect
11. #10591312C2semidirect
12. #10591285C2semidirect
13. #10591275C2semidirect
14. #10591259C2semidirect
15. #10591204C2semidirect
23. C22×#624C22semidirect
25. C2×C32×C4⋊C4C22semidirect
28. C2×#3752C22semidirect
29. C2×#3752C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
42. C2×#3722C22semidirect
46. C2×Dic32C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
67. #4993D3semidirect
73. #4989D3semidirect
145. #3722D4semidirect
170. C2×C3×C4⋊C4C2×D3semidirect
171. C2×C3×C4⋊C4C2×D3semidirect
212. C2×Dic3⋊C4C2×D3semidirect
213. C2×Dic3⋊C4C2×D3semidirect
214. C2×Dic3⋊C4C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
499. C2×C3×D3#123semidirect
526. C2×C4⋊C4D32semidirect
897. C2×D3#894semidirect
925. C32#2418semidirect
1080. C3#74603semidirect
1081. C3#78101semidirect

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
C2×#638972
#105926902
C3×#49932
C3×#49892
#105913992
#105913662
#105913642
#105913122
#105912852
#105912752
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