Finite Group Databasebeta

← #11810345

Subgroups — #11810345

Order 1152.

1695 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#883C211yesmaximal, characteristic, complemented
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#63976C211yesmaximal, characteristic
4C2×C4×#625C211yesmaximal, characteristic, complemented
5#10592650C211yesmaximal, characteristic, complemented
6#10591708C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591694C211yesmaximal, characteristic, complemented
9#10591394C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591381C211yesmaximal, characteristic, complemented
12#10591324C211yesmaximal, characteristic, complemented
13#10591313C211yesmaximal, characteristic, complemented
14#10591283C211yesmaximal, characteristic, complemented
15#10591277C211yesmaximal, characteristic, complemented
16#82896—31nomaximal
17#82128—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic, complemented
23C22×#625C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C3×#883—24no—
38C3×D3×C22⋊C4—24no—
39#63976—24no—
40C2×#3724C2211yescharacteristic, complemented
41C2×#3724C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50C4×#625—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#123—31no—
58C22×C3×C22⋊C4—31no—
59C2×#953—31no—
60C2×#937—31no—
61C2×C4×#67—31no—
62C2×C4×#67—31no—
63C2×#883D311yescharacteristic, complemented
64C2×D3×C22⋊C4D311yescharacteristic, complemented
65#5247—31no—
66#5222—31no—
67#5213—31no—
68#5213—31no—
69#5212—31no—
70#5210—31no—
71#4993—31no—
72#4990—31no—
73#4989—31no—
74#4987—31no—
75#4961—31no—
76#4961—31no—
77#4959—31no—
78#4956—31no—
79#4956—31no—
80#4955—31no—
81#4952—31no—
82#4952—31no—
83#4951—31no—
84#4951—31no—
85#4951—61no—
86#4949—31no—
87#4945—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—41no—
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—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—41no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3—41no—
122C2×#625—22no—
123C2×#625—22no—
124C2×#625—22no—
125C2×#625—22no—
126C2×#625—41no—
127C2×#625D414yes—
128C32×C22⋊C4D414yescomplemented
129#3757—22no—
130#3757—41no—
131C4⋊(C3⋊Dic3)—41no—
132C4×C3⋊Dic3—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×C4⋊Dic3—22no—
139C3×Dic3⋊C4—22no—
140#3724—22no—
141#3724—41no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149(C2×D3)⋊Dic3—41no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C23×C3×C4—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67C2×D311yescharacteristic
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D311yescharacteristic
164C22×C4×D3C2×D311yescharacteristic, complemented
165C3×#123—64no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—21no—
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×C3×C22⋊C4—64no—
175C2×C3×C22⋊C4C2×D311yescharacteristic
176C2×C3×C22⋊C4C2×D311yescharacteristic
177#953—64no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—61no—
191C2×#217—61no—
192C2×#217C2×D311yescharacteristic
193C2×#217C2×D311yescharacteristic
194#937—64no—
195C4×#67—64no—
196C4×#67—64no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—61no—
211C2×C4⋊Dic3C2×D311yescharacteristic, complemented
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4C2×D311yescharacteristic, complemented
217C2×C4×Dic3—31no—
218C2×C4×Dic3—31no—
219C2×C4×Dic3—61no—
220#883—24no—
221D3×C22⋊C4—24no—
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—31no—
233C3⋊#95—31no—
234C3⋊#95—61no—
235C3⋊#95—61no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32C2×D412yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—28no—
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×D3—21no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3C2×D412yes—
268C22×C3×D3C2×D412yes—
269C22×C3×D3#4112yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4C2×D412yes—
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—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D412yes—
290C3×#67—44no—
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×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C3×C4×D3—44no—
307C3×C4×D3—44no—
308C3×C4×D3—44no—
309#625—28no—
310#625—44no—
311C2×#123—31no—
312C2×#120—91no—
313C2×C4×D4—91no—
314C22×C22⋊C4—31no—
315#399—91no—
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—21no—
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—41no—
345C23×D3—41no—
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—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—62no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—62no—
365C22×C3×C4—121no—
366C22×C3×C4—121no—
367C22×C3×C4—121no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—22no—
373C2×#67—22no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—41no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—62no—
384C2×#67—62no—
385C2×#67—121no—
386C2×#67—121no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—22no—
409C2×C4×D3—22no—
410C2×C4×D3—41no—
411C2×C4×D3—41no—
412C2×C4×D3—41no—
413C3×C4⋊C4—62no—
414C3×C4⋊C4—62no—
415C3×C22⋊C4—24no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4#6714yescomplemented
422C3×C22⋊C4#6714yescomplemented
423#217—22no—
424#217—22no—
425#217—62no—
426#217—62no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—122no—
434#217—121no—
435#217—121no—
436#217—121no—
437#217—121no—
438#217—122no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—22no—
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—121no—
449(C2×D3)⋊C4—121no—
450C4⋊Dic3—22no—
451C4⋊Dic3—121no—
452C4⋊Dic3—121no—
453C4⋊Dic3—122no—
454Dic3⋊C4—22no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4—121no—
458Dic3⋊C4—121no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—122no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C22×C32C22×D411yescharacteristic
471C22×C32C2×#4111yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
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—22no—
488C2×C3×D3—416no—
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—41no—
496C2×C3×D3—41no—
497C2×C3×D3#12314yescomplemented
498C32×C4—22no—
499C32×C4—22no—
500C3⋊Dic3—22no—
501C3⋊Dic3—41no—
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C25—31no—
510C22×D4—31no—
511C22×D4—91no—
512C22×D4—91no—
513C23×C4—31no—
514C23×C4—31no—
515C23×C4—31no—
516#123—64no—
517#120—184no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—64no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4D3211yescharacteristic
541C2×C42—91no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—68no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3—124no—
595C23×C3—124no—
596C23×C3C2×#6712yes—
597C23×C3C2×#6712yes—
598C23×C3C23×D311yescharacteristic
599C23×C3C23×D311yescharacteristic
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—28no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3—44no—
620C22×D3—44no—
621C22×D3—44no—
622C22×D3—44no—
623C22×D3#23512yes—
624C22×D3#23512yes—
625C22×D3D3×D412yes—
626C22×D3D3×D412yes—
627C22×D3#23712yes—
628C3×D4—124no—
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—22no—
638C2×C3×C4—22no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—124no—
659C2×C3×C4—124no—
660C2×C3×C4—124no—
661C2×C3×C4C2×#6712yes—
662C2×C3×C4C2×#6712yes—
663C2×C3×C4C2×#6712yes—
664C2×C3×C4C2×#6712yes—
665#67—44no—
666#67—68no—
667#67—68no—
668#67—124no—
669#67—124no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
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—32no—
686C2×Dic3—32no—
687C2×Dic3—62no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—62no—
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—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C4×D3—44no—
722C4×D3—44no—
723C4×D3—44no—
724C2×C32—42no—
725C2×C32C2×#12311yescharacteristic
726C2×C32#52511yescharacteristic
727C2×C32#53811yescharacteristic
728C2×C32D4211yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#54611yescharacteristic
731C2×C32#55111yescharacteristic
732C3×D3—24no—
733C3×D3—42no—
734C3×D3—42no—
735C24—31no—
736C24—31no—
737C24—31no—
738C24—62no—
739C24—62no—
740C24—62no—
741C24—62no—
742C24—62no—
743C24—121no—
744C24—121no—
745C24C2×D3211yescharacteristic
746C2×D4—62no—
747C2×D4—62no—
748C2×D4—94no—
749C2×D4—121no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—182no—
753C2×D4—182no—
754C2×D4—361no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—62no—
765C22×C4—62no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—121no—
771C22×C4—121no—
772C22×C4—121no—
773C22×C4C2×D3211yescharacteristic
774C22×C4C2×D3211yescharacteristic
775C4⋊C4—62no—
776C4⋊C4—62no—
777C4⋊C4—182no—
778C4⋊C4—361no—
779C4⋊C4—361no—
780C22⋊C4—62no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—182no—
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—
795C22⋊C4#62514yescomplemented
796C42—182no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—34no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—1216no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3C2×#23511yescharacteristic
848C22×C3C2×#23511yescharacteristic
849C22×C3C2×D3×D411yescharacteristic
850C22×C3C2×D3×D411yescharacteristic
851C22×C3C2×#23711yescharacteristic
852C22×C3#100411yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3D3×#4111yescharacteristic
856C22×C3D3×#4111yescharacteristic
857C22×C3D3×#4111yescharacteristic
858C22×C3#100911yescharacteristic
859C22×C3C22×#6711yescharacteristic
860C22×C3C22×#6711yescharacteristic
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—416no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3#88314yescomplemented
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—121no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4—121no—
893C3×C4—121no—
894Dic3—41no—
895Dic3—41no—
896Dic3—41no—
897Dic3—41no—
898Dic3—41no—
899Dic3—62no—
900Dic3—62no—
901Dic3—122no—
902Dic3—122no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—241no—
910Dic3—241no—
911C32#241811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—32no—
923C23—68no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—124no—
941C23—124no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23—124no—
946C23C2×#62512yes—
947C23C22×D3211yescharacteristic
948D4—124no—
949D4—188no—
950D4—364no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
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—92no—
971C2×C4—124no—
972C2×C4—124no—
973C2×C4—124no—
974C2×C4—181no—
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—181no—
985C2×C4C2×#62512yes—
986C2×C4C2×#62512yes—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—42no—
995C2×C3—42no—
996C2×C3—64no—
997C2×C3—82no—
998C2×C3—122no—
999C2×C3—122no—
1000C2×C3C2×#88311yescharacteristic
1001C2×C3#549011yescharacteristic
1002C2×C3#549411yescharacteristic
1003C2×C3#549511yescharacteristic
1004C2×C3D3×#12311yescharacteristic
1005C2×C3#565411yescharacteristic
1006C2×C3#565711yescharacteristic
1007C2×C3#565911yescharacteristic
1008C2×C3#579111yescharacteristic
1009C2×C3D4×#6711yescharacteristic
1010C2×C3D4×#6711yescharacteristic
1011C2×C3#580611yescharacteristic
1012C2×C3#582811yescharacteristic
1013C2×C3#582911yescharacteristic
1014D3—24no—
1015D3—42no—
1016D3—42no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—34no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—1216no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22D3×#23511yescharacteristic
1047C22D3×#23511yescharacteristic
1048C22D32×D411yescharacteristic
1049C22D3×#23711yescharacteristic
1050C22#6431311yescharacteristic
1051C22#6431411yescharacteristic
1052C22C22×#62511yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—121no—
1056C4—121no—
1057C4—121no—
1058C4—121no—
1059C4—121no—
1060C4—182no—
1061C4—361no—
1062C4—361no—
1063C4—361no—
1064C3—21no—
1065C3#8212811yescharacteristic, complemented
1066C3#8289611yescharacteristic, complemented
1067C2—42no—
1068C2—64no—
1069C2—122no—
1070C2—122no—
1071C2#1059419311yescharacteristic
1072C2#1059419411yescharacteristic
1073C2D3×#88311yescharacteristic
1074C2#1059427211yescharacteristic
1075C2#1059502211yescharacteristic
1076C2D4×#62511yescharacteristic
1077C2#1059524411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63976C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#883C2semidirect
2. C2×C3×D3×C22⋊C4C2semidirect
4. C2×C4×#625C2semidirect
5. #10592650C2semidirect
6. #10591708C2semidirect
7. #10591706C2semidirect
8. #10591694C2semidirect
9. #10591394C2semidirect
10. #10591381C2semidirect
11. #10591381C2semidirect
12. #10591324C2semidirect
13. #10591313C2semidirect
14. #10591283C2semidirect
15. #10591277C2semidirect
22. C22×C3×C4×D3C22semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
40. C2×#3724C22semidirect
41. C2×#3724C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
63. C2×#883D3semidirect
64. C2×D3×C22⋊C4D3semidirect
128. C32×C22⋊C4D4semidirect
164. C22×C4×D3C2×D3semidirect
207. C2×(C2×D3)⋊C4C2×D3semidirect
211. C2×C4⋊Dic3C2×D3semidirect
216. C2×Dic3⋊C4C2×D3semidirect
421. C3×C22⋊C4#67semidirect
422. C3×C22⋊C4#67semidirect
497. C2×C3×D3#123semidirect
795. C22⋊C4#625semidirect
882. C2×D3#883semidirect
911. C32#2418semidirect
1065. C3#82128semidirect
1066. C3#82896semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8832
C2×C3×D3×C22⋊C42
C2×#639762
C2×C4×#6252
#105926502
#105917082
#105917062
#105916942
#105913942
#105913812
#105913242
#105913132
#105912832
#105912772
#828963
#821283