Finite Group Databasebeta

← #11810328

Subgroups — #11810328

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×#63922C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#63890C211yesmaximal, characteristic, complemented
4C2×#63879C211yesmaximal, characteristic, complemented
5#10592374C211yesmaximal, characteristic, complemented
6C3×#4672C211yesmaximal, characteristic, complemented
7C3×#4668C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591376C211yesmaximal, characteristic, complemented
10#10591366C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591307C211yesmaximal, characteristic, complemented
13#10591303C211yesmaximal, characteristic, complemented
14#10591291C211yesmaximal, characteristic, complemented
15#10591258C211yesmaximal, characteristic, complemented
16#77112—31nomaximal
17#74603—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
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×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63922—24no—
48D3×(C2×D3)⋊C4—24no—
49#63890—24no—
50#63879—24no—
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#937—31no—
58C2×C4×#67—31no—
59C22×(C2×D3)⋊C4—31no—
60C2×#894—31no—
61C2×#886—31no—
62C2×#882—31no—
63C2×#67⋊C4—31no—
64C2×D3×C22⋊C4—31no—
65C3×#394—31no—
66C3×#385—31no—
67#5220—31no—
68#4993—31no—
69#4991—31no—
70#4990—31no—
71#4990—31no—
72#4987—31no—
73#4959—31no—
74#4958—31no—
75#4956—31no—
76#4955—31no—
77#4955—31no—
78#4951—31no—
79#4949—31no—
80#4942—31no—
81#4675—31no—
82#4675—31no—
83#4675—61no—
84#4672D311yescharacteristic, complemented
85#4669—31no—
86#4668D311yescharacteristic, complemented
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×D12—41no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—41no—
119C2×#625—22no—
120C2×#625—22no—
121C2×#625D414yes—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—41no—
127C2×D3×Dic3—41no—
128#3752—22no—
129#3752—22no—
130#3752—22no—
131#3750—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—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×C4⋊Dic3—22no—
139C3×Dic3⋊C4—41no—
140C3×Dic3⋊C4—41no—
141Dic3⋊Dic3—22no—
142#3722—41no—
143#3722D414yescomplemented
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—41no—
148(C2×D3)⋊Dic3—41no—
149Dic32—22no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C22×D12—31no—
161C22×D12C2×D311yescharacteristic
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3C2×D311yescharacteristic
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179#937—64no—
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—61no—
197C2×(C2×D3)⋊C4—61no—
198C2×(C2×D3)⋊C4—61no—
199C2×(C2×D3)⋊C4—64no—
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
205C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3C2×D311yescharacteristic, complemented
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—61no—
212C2×Dic3⋊C4C2×D311yescharacteristic, complemented
213C2×Dic3⋊C4C2×D311yescharacteristic, complemented
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216#894—64no—
217#886—64no—
218#882—64no—
219#67⋊C4—64no—
220D3×C22⋊C4—64no—
221C3×#95—21no—
222C3×#95—31no—
223C3×#95C2×D311yescharacteristic, complemented
224C3×#95C2×D311yescharacteristic, complemented
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
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×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—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D412yes—
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—44no—
306C3×C4×D3—44no—
307#626—44no—
308#625—28no—
309D3×Dic3—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—91no—
314C22×C22⋊C4—91no—
315#399—91no—
316#397—91no—
317#394—31no—
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—
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—62no—
350C2×C3×D4—62no—
351C2×C3×D4—121no—
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—121no—
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—121no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3—62no—
391C22×Dic3—121no—
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—41no—
401C2×D12—62no—
402C2×D12—62no—
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—121no—
412C2×C4×D3—121no—
413C3×C4⋊C4—62no—
414C3×C4⋊C4—121no—
415C3×C4⋊C4—121no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—62no—
422#217—62no—
423#217—62no—
424#217—62no—
425#217—121no—
426#217—121no—
427(C2×D3)⋊C4—22no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
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—122no—
445(C2×D3)⋊C4—122no—
446(C2×D3)⋊C4—122no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451C4⋊Dic3—22no—
452C4⋊Dic3—62no—
453Dic3⋊C4—41no—
454Dic3⋊C4—41no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4—62no—
458Dic3⋊C4—122no—
459C4×Dic3—62no—
460C4×Dic3—62no—
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—41no—
498C32×C4—41no—
499C32×C4—41no—
500C3⋊Dic3—22no—
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—91no—
514C23×C4—91no—
515#123—184no—
516#120—184no—
517C4×D4—184no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
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—91no—
541#95—31no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95D3211yescharacteristic, complemented
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×D3D3×D412yes—
624C22×D3D3×D412yes—
625C22×D3#23712yes—
626C22×D3#23912yes—
627C3×D4—124no—
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—21no—
645C2×C3×C4—21no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
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—41no—
656C2×C3×C4—41no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—124no—
671#67—68no—
672#67—68no—
673#67—124no—
674C2×Dic3—21no—
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—32no—
688C2×Dic3—32no—
689C2×Dic3—62no—
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—124no—
715C2×Dic3—124no—
716C2×Dic3D3×D412yes—
717C2×Dic3D3×D412yes—
718D12—44no—
719D12—124no—
720C4×D3—44no—
721C4×D3—124no—
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—62no—
746C2×D4—62no—
747C2×D4—94no—
748C2×D4—121no—
749C2×D4—182no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—182no—
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—91no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—121no—
765C22×C4—182no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4—182no—
769C22×C4—361no—
770C22×C4—361no—
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3211yescharacteristic
773C22×C4C2×D3211yescharacteristic
774C4⋊C4—62no—
775C4⋊C4—121no—
776C4⋊C4—121no—
777C4⋊C4—182no—
778C4⋊C4—182no—
779C22⋊C4—62no—
780C22⋊C4—62no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—94no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—361no—
793C22⋊C4—361no—
794C22⋊C4—361no—
795C42—182no—
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×D3×D411yescharacteristic
826C22×C3C2×D3×D411yescharacteristic
827C22×C3C2×D3×D411yescharacteristic
828C22×C3C2×D3×D411yescharacteristic
829C22×C3C2×#23711yescharacteristic
830C22×C3#100411yescharacteristic
831C22×C3#100411yescharacteristic
832C22×C3C2×#23911yescharacteristic
833C22×C3D3×#4111yescharacteristic
834C22×C3D3×#4111yescharacteristic
835C22×C3D3×#4111yescharacteristic
836C22×C3#100911yescharacteristic
837C22×C3#100911yescharacteristic
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#89414yescomplemented
882C3×C4—41no—
883C3×C4—41no—
884C3×C4—41no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—62no—
889C3×C4—62no—
890C3×C4—81no—
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—62no—
902Dic3—62no—
903Dic3—122no—
904Dic3—121no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
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—124no—
948D4—188no—
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—21no—
959C2×C4—32no—
960C2×C4—32no—
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—61no—
974C2×C4—92no—
975C2×C4—124no—
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×C4—364no—
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×C3C2×#89411yescharacteristic
997C2×C3#554711yescharacteristic
998C2×C3#556011yescharacteristic
999C2×C3#559011yescharacteristic
1000C2×C3#559111yescharacteristic
1001C2×C3#560611yescharacteristic
1002C2×C3#560911yescharacteristic
1003C2×C3#561011yescharacteristic
1004C2×C3#563011yescharacteristic
1005C2×C3#563711yescharacteristic
1006C2×C3D3×#12311yescharacteristic
1007C2×C3#565411yescharacteristic
1008C2×C3#565811yescharacteristic
1009C2×C3#567811yescharacteristic
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
1046C22#6430711yescharacteristic
1047C22#6430711yescharacteristic
1048C22D32×D411yescharacteristic
1049C22D32×D411yescharacteristic
1050C22D3×#23711yescharacteristic
1051C22D3×#23911yescharacteristic
1052C4—41no—
1053C4—41no—
1054C4—41no—
1055C4—62no—
1056C4—62no—
1057C4—121no—
1058C4—121no—
1059C4—121no—
1060C4—182no—
1061C4—361no—
1062C4—361no—
1063C3—21no—
1064C3#7460311yescharacteristic, complemented
1065C3#7711211yescharacteristic, complemented
1066C2—64no—
1067C2—122no—
1068C2—122no—
1069C2—362no—
1070C2#1059401211yescharacteristic
1071C2#1059427411yescharacteristic
1072C2#1059427511yescharacteristic
1073C2#1059428611yescharacteristic
1074C2D3×#89411yescharacteristic
1075C2#1059462211yescharacteristic
1076C2#1059464711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC2×#63922C2
hypercenter#95D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×D3×(C2×D3)⋊C4C2semidirect
3. C2×#63890C2semidirect
4. C2×#63879C2semidirect
5. #10592374C2semidirect
6. C3×#4672C2semidirect
7. C3×#4668C2semidirect
8. #10591399C2semidirect
9. #10591376C2semidirect
10. #10591366C2semidirect
11. #10591363C2semidirect
12. #10591307C2semidirect
13. #10591303C2semidirect
14. #10591291C2semidirect
15. #10591258C2semidirect
24. C22×D3×Dic3C22semidirect
28. C2×#3750C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×Dic32C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
84. #4672D3semidirect
86. #4668D3semidirect
143. #3722D4semidirect
204. C2×(C2×D3)⋊C4C2×D3semidirect
205. C2×(C2×D3)⋊C4C2×D3semidirect
207. C2×C4⋊Dic3C2×D3semidirect
212. C2×Dic3⋊C4C2×D3semidirect
213. C2×Dic3⋊C4C2×D3semidirect
223. C3×#95C2×D3semidirect
224. C3×#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
495. C2×C3×D3#123semidirect
546. #95D32semidirect
881. C2×D3#894semidirect
910. C32#2418semidirect
1064. C3#74603semidirect
1065. C3#77112semidirect

Maximal subgroups

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

subgroupindex
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#638902
C2×#638792
#105923742
C3×#46722
C3×#46682
#105913992
#105913762
#105913662
#105913632
#105913072
#105913032
#105912912
#105912582
#771123
#746033