Finite Group Databasebeta

← #11810325

Subgroups — #11810325

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic
3C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#63850C211yesmaximal, characteristic, complemented
5#10592691C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591390C211yesmaximal, characteristic, complemented
9#10591381C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591366C211yesmaximal, characteristic, complemented
12#10591291C211yesmaximal, characteristic, complemented
13#10591279C211yesmaximal, characteristic, complemented
14#10591277C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#82404—31nomaximal
17#78101—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×#626C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C3×#893—24no—
38C2×#3724C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48#63922—24no—
49D3×(C2×D3)⋊C4—24no—
50#63850—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×C4×D4—31no—
58C2×#937—31no—
59C2×#929—31no—
60C22×(C2×D3)⋊C4—31no—
61C2×#894—31no—
62C2×#893D311yescharacteristic, complemented
63C2×#882—31no—
64C2×D3×C22⋊C4—31no—
65C3×#399—31no—
66#5220—31no—
67#5213—31no—
68#5210—31no—
69#4993D311yescharacteristic, complemented
70#4992—31no—
71#4992—31no—
72#4992—61no—
73#4991—31no—
74#4989—31no—
75#4987—31no—
76#4961—31no—
77#4959—31no—
78#4959—31no—
79#4956—31no—
80#4955—31no—
81#4955—31no—
82#4944—31no—
83#4942—31no—
84#4940—31no—
85#4940—31no—
86#4670—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
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×D12—22no—
111C2×C3×D12—22no—
112C2×C3×D12D414yes—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—41no—
118C2×C3×C4×D3—41no—
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—41no—
122C2×#625—22no—
123C2×#625—22no—
124C2×#625—41no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C4⋊C4—22no—
129#3752—22no—
130#3752—22no—
131#3752—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—41no—
137C3×Dic3⋊C4—22no—
138C3×Dic3⋊C4—41no—
139C3×C4×Dic3—22no—
140#3724—22no—
141Dic3⋊Dic3—41no—
142#3722—41no—
143#3722D414yescomplemented
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—41no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C23×Dic3—31no—
160C22×D12—31no—
161C22×D12C2×D311yescharacteristic
162C22×C4×D3—31no—
163C22×C4×D3C2×D311yescharacteristic
164C22×C4×D3C2×D311yescharacteristic, complemented
165C3×C4×D4—64no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
170C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C42—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183#937—64no—
184#929—64no—
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—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, complemented
210C2×C4⋊Dic3—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4C2×D311yescharacteristic, complemented
215C2×Dic3⋊C4C2×D311yescharacteristic, complemented
216C2×C4×Dic3C2×D311yescharacteristic, complemented
217#894—64no—
218#893—24no—
219#882—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⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—61no—
233C3⋊#95—61no—
234C3⋊#95—61no—
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⋊D3C2×D412yes—
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—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×D3C2×D412yes—
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×C4C2×D412yes—
281C2×C3⋊Dic3—21no—
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×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—
305C3×D12—28no—
306C3×C4×D3—44no—
307C3×C4×D3—44no—
308#626—44no—
309#625—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—31no—
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—91no—
324#380—91no—
325#379—91no—
326C24×C3—31no—
327C24×C3—31no—
328C24×C3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—61no—
332C23×D3—62no—
333C23×D3—62no—
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—121no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3—121no—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×D4—34no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—121no—
365C22×C3×C4—121no—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—121no—
379C2×#67—121no—
380C2×#67—121no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—62no—
391C22×Dic3—62no—
392C22×Dic3—121no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C2×D12—22no—
399C2×D12—22no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—121no—
403C2×D12#6714yes—
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—41no—
409C2×C4×D3—41no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—121no—
413C3×C4⋊C4—22no—
414C3×C4⋊C4—22no—
415C3×C4⋊C4—42no—
416C3×C4⋊C4—62no—
417C3×C4⋊C4—121no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—121no—
423C3×C42—62no—
424#217—62no—
425#217—62no—
426#217—62no—
427#217—62no—
428#217—62no—
429#217—121no—
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—122no—
449(C2×D3)⋊C4—122no—
450(C2×D3)⋊C4—122no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4—121no—
454C4⋊Dic3—121no—
455Dic3⋊C4—22no—
456Dic3⋊C4—41no—
457Dic3⋊C4—62no—
458Dic3⋊C4—62no—
459Dic3⋊C4—121no—
460C4×Dic3—22no—
461C22×C32C22×D411yescharacteristic
462C22×C32C22×D411yescharacteristic
463C22×C32C2×#4111yescharacteristic
464C22×C32C2×#4111yescharacteristic
465C22×C32C2×#4111yescharacteristic
466C22×C32H(5,𝔽2)11yescharacteristic
467C22×C32H(5,𝔽2)11yescharacteristic
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
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—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3#12314yescomplemented
496D32—416no—
497C32×C4—22no—
498C32×C4—41no—
499C32×C4—41no—
500C3⋊Dic3—41no—
501C3⋊Dic3—41no—
502C3⋊Dic3—41no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C25—91no—
509C22×D4—31no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—31no—
513C23×C4—31no—
514C23×C4—91no—
515#123—184no—
516#120—184no—
517C4×D4—64no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4D3211yescharacteristic, complemented
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
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—91no—
539C2×C22⋊C4—184no—
540C2×C42—31no—
541#95—31no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547C23×C3—21no—
548C23×C3—32no—
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×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3C23×D311yescharacteristic
570C23×C3C23×D311yescharacteristic
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—62no—
590C22×D3—68no—
591C22×D3—68no—
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—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—124no—
611C22×D3—124no—
612C22×D3—124no—
613C22×D3—124no—
614C22×D3—124no—
615C22×D3—124no—
616C22×D3—124no—
617C22×D3—124no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—124no—
622C22×D3#23512yes—
623C22×D3#23512yes—
624C22×D3#23912yes—
625C22×D3C2×#6712yes—
626C22×D3C2×#6712yes—
627C3×D4—68no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
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—22no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
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—124no—
669C2×C3×C4—124no—
670C2×C3×C4D3×D412yes—
671C2×C3×C4C2×#6712yes—
672#67—124no—
673#67—124no—
674#67—124no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
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—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
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—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—124no—
716C2×Dic3D3×D412yes—
717C2×Dic3D3×D412yes—
718D12—28no—
719D12—124no—
720C4×D3—44no—
721C4×D3—44no—
722C4×D3—124no—
723C2×C32C2×#12311yescharacteristic
724C2×C32#52511yescharacteristic
725C2×C32#53811yescharacteristic
726C2×C32D4211yescharacteristic
727C2×C32#54611yescharacteristic
728C2×C32#54611yescharacteristic
729C2×C32#55111yescharacteristic
730C3⋊D3—42no—
731C3×D3—24no—
732C3×D3—42no—
733C3×D3—42no—
734C24—31no—
735C24—31no—
736C24—31no—
737C24—91no—
738C24—182no—
739C24—182no—
740C24—182no—
741C24—182no—
742C24—182no—
743C24—361no—
744C24—361no—
745C2×D4—34no—
746C2×D4—62no—
747C2×D4—62no—
748C2×D4—182no—
749C2×D4—182no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—361no—
753C2×D4—361no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—62no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—91no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—121no—
767C22×C4—121no—
768C22×C4—182no—
769C22×C4—182no—
770C22×C4—361no—
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3211yescharacteristic
773C22×C4C2×D3211yescharacteristic
774C4⋊C4—22no—
775C4⋊C4—62no—
776C4⋊C4—121no—
777C4⋊C4—182no—
778C4⋊C4—361no—
779C22⋊C4—62no—
780C22⋊C4—62no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—94no—
784C22⋊C4—121no—
785C22⋊C4—182no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—361no—
794C22⋊C4—361no—
795C42—62no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—34no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3C2×#23511yescharacteristic
825C22×C3C2×#23511yescharacteristic
826C22×C3C2×D3×D411yescharacteristic
827C22×C3C2×D3×D411yescharacteristic
828C22×C3C2×D3×D411yescharacteristic
829C22×C3#100411yescharacteristic
830C22×C3#100411yescharacteristic
831C22×C3C2×#23911yescharacteristic
832C22×C3D3×#4111yescharacteristic
833C22×C3D3×#4111yescharacteristic
834C22×C3D3×#4111yescharacteristic
835C22×C3#100911yescharacteristic
836C22×C3#100911yescharacteristic
837C22×C3C22×#6711yescharacteristic
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—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—122no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—1216no—
868C2×D3—1216no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—241no—
878C2×D3—241no—
879C2×D3—241no—
880C2×D3—241no—
881C2×D3#92914yescomplemented
882C3×C4—22no—
883C3×C4—22no—
884C3×C4—42no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—62no—
890C3×C4—62no—
891C3×C4—81no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4—121no—
896Dic3—22no—
897Dic3—22no—
898Dic3—41no—
899Dic3—41no—
900Dic3—41no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—121no—
907Dic3—241no—
908Dic3—241no—
909Dic3—241no—
910C32#241811yescharacteristic, complemented, Sylow
911C23—32no—
912C23—32no—
913C23—32no—
914C23—32no—
915C23—32no—
916C23—61no—
917C23—61no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—92no—
933C23—188no—
934C23—181no—
935C23—181no—
936C23—181no—
937C23—181no—
938C23—181no—
939C23—181no—
940C23—364no—
941C23—364no—
942C23—364no—
943C23—364no—
944C23—364no—
945C23—364no—
946C23C22×D3211yescharacteristic
947D4—68no—
948D4—364no—
949D4—364no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—124no—
974C2×C4—124no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—181no—
984C2×C4—364no—
985C2×C4D3×#6712yes—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—64no—
994C2×C3—122no—
995C2×C3—122no—
996C2×C3#554711yescharacteristic
997C2×C3#555011yescharacteristic
998C2×C3#555611yescharacteristic
999C2×C3#556011yescharacteristic
1000C2×C3#562711yescharacteristic
1001C2×C3#563011yescharacteristic
1002C2×C3#563711yescharacteristic
1003C2×C3D3×#12311yescharacteristic
1004C2×C3#565411yescharacteristic
1005C2×C3#565711yescharacteristic
1006C2×C3#571711yescharacteristic
1007C2×C3C2×#92911yescharacteristic
1008C2×C3D4×#6711yescharacteristic
1009C2×C3#582911yescharacteristic
1010D3—24no—
1011D3—42no—
1012D3—42no—
1013D3—122no—
1014D3—122no—
1015D3—242no—
1016C22—34no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—182no—
1038C22—182no—
1039C22—182no—
1040C22—3616no—
1041C22—361no—
1042C22—361no—
1043C22—361no—
1044C22—361no—
1045C22D3×#23511yescharacteristic
1046C22D3×#23511yescharacteristic
1047C22D32×D411yescharacteristic
1048C22#6431311yescharacteristic
1049C22D3×#23911yescharacteristic
1050C22#6432011yescharacteristic
1051C22C2×D3×#6711yescharacteristic
1052C4—22no—
1053C4—41no—
1054C4—41no—
1055C4—62no—
1056C4—62no—
1057C4—121no—
1058C4—121no—
1059C4—121no—
1060C4—361no—
1061C4—361no—
1062C4—361no—
1063C3—21no—
1064C3#7810111yescharacteristic, complemented
1065C3#8240411yescharacteristic, complemented
1066C2—64no—
1067C2—122no—
1068C2—122no—
1069C2—362no—
1070C2#1059461911yescharacteristic
1071C2#1059462311yescharacteristic
1072C2#1059463911yescharacteristic
1073C2#1059464211yescharacteristic
1074C2D3×#92911yescharacteristic
1075C2#1059529311yescharacteristic
1076C2#1059542711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63922C2
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
1. C2×C3×#893C2semidirect
3. C2×D3×(C2×D3)⋊C4C2semidirect
4. C2×#63850C2semidirect
5. #10592691C2semidirect
6. C3×#4993C2semidirect
7. #10591399C2semidirect
8. #10591390C2semidirect
9. #10591381C2semidirect
10. #10591376C2semidirect
11. #10591366C2semidirect
12. #10591291C2semidirect
13. #10591279C2semidirect
14. #10591277C2semidirect
15. #10591194C2semidirect
21. C22×C3×C4×D3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
38. C2×#3724C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
62. C2×#893D3semidirect
69. #4993D3semidirect
143. #3722D4semidirect
164. C22×C4×D3C2×D3semidirect
169. C2×C3×C4⋊C4C2×D3semidirect
170. C2×C3×C4⋊C4C2×D3semidirect
209. C2×(C2×D3)⋊C4C2×D3semidirect
214. C2×Dic3⋊C4C2×D3semidirect
215. C2×Dic3⋊C4C2×D3semidirect
216. C2×C4×Dic3C2×D3semidirect
235. C3⋊#95C2×D3semidirect
495. C2×C3×D3#123semidirect
522. C2×C4⋊C4D32semidirect
881. C2×D3#929semidirect
910. C32#2418semidirect
1064. C3#78101semidirect
1065. C3#82404semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#638502
#105926912
C3×#49932
#105913992
#105913902
#105913812
#105913762
#105913662
#105912912
#105912792
#105912772
#105911942
#824043
#781013