Finite Group Databasebeta

← #11810334

Subgroups — #11810334

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×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#63977C211yesmaximal, characteristic
3C2×#63975C211yesmaximal, characteristic, complemented
4C2×#63904C211yesmaximal, characteristic, complemented
5#10592658C211yesmaximal, characteristic, complemented
6C3×#4952C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591312C211yesmaximal, characteristic, complemented
11#10591303C211yesmaximal, characteristic, complemented
12#10591295C211yesmaximal, characteristic, complemented
13#10591284C211yesmaximal, characteristic, complemented
14#10591278C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#82128—31nomaximal
17#77669—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×#3752C2211yescharacteristic, complemented
29C2×#3750C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C3×D3×C22⋊C4—24no—
37#63977—24no—
38#63975—24no—
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic, complemented
50#63904—24no—
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C22×C3×C22⋊C4—31no—
58C2×#953—31no—
59C2×C4×#67—31no—
60C2×#893—31no—
61C2×#883—31no—
62C2×#883—31no—
63C2×#882—31no—
64C2×D3×C22⋊C4D311yescharacteristic, complemented
65C3×#397—31no—
66#5247—31no—
67#5213—31no—
68#5212—31no—
69#5210—31no—
70#4993—31no—
71#4961—31no—
72#4959—31no—
73#4959—31no—
74#4959—61no—
75#4956—31no—
76#4955—31no—
77#4952D311yescharacteristic, complemented
78#4951—31no—
79#4949—31no—
80#4945—31no—
81#4944—31no—
82#4672—31no—
83#4670—31no—
84#4668—31no—
85#4667—31no—
86#4665—31no—
87#4665—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—22no—
102C2×#638—22no—
103C2×#638—41no—
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
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—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—41no—
118C2×C3×C4×D3—41no—
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626—41no—
124C2×#626D414yes—
125C2×#624—22no—
126C2×#624—22no—
127C2×#624—41no—
128C32×C22⋊C4—22no—
129#3757—41no—
130#3752—22no—
131#3752—41no—
132#3750—41no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217D414yescomplemented
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×Dic3⋊C4—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—41no—
142#3722—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—
149Dic32—22no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C23×C3×C4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—61no—
160C22×D12—31no—
161C22×D12—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3C2×D311yescharacteristic
165C22×C4×D3C2×D311yescharacteristic
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—21no—
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—64no—
174C2×C3×C22⋊C4C2×D311yescharacteristic
175C2×C3×C22⋊C4C2×D311yescharacteristic
176#953—64no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—61no—
186C2×#217C2×D311yescharacteristic
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189C4×#67—64no—
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—31no—
202C2×(C2×D3)⋊C4—61no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—61no—
215C2×Dic3⋊C4C2×D311yescharacteristic, complemented
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218#893—64no—
219#883—64no—
220#883—64no—
221#882—64no—
222D3×C22⋊C4—24no—
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×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—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3C2×D412yes—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—28no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
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×C4—21no—
277C2×C32×C4—21no—
278#638—44no—
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×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—
307C3×C4×D3—44no—
308#626—28no—
309#626—44no—
310#624—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—91no—
314C22×C22⋊C4—31no—
315#399—91no—
316#397—31no—
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—62no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—121no—
335C24×C3—121no—
336C24×C3C22×D311yescharacteristic
337C24×C3C22×D311yescharacteristic
338C23×D3—22no—
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—41no—
346C23×D3—41no—
347C23×D3—61no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—62no—
359C22×C3×C4—62no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—121no—
363C22×C3×C4—121no—
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—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—122no—
378C2×#67—122no—
379C2×#67—121no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67—122no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C2×D12—34no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—121no—
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—62no—
413C2×C4×D3—62no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C3×C4⋊C4—62no—
417C3×C22⋊C4—22no—
418C3×C22⋊C4—22no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—42no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425#217—22no—
426#217—22no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—121no—
433#217—121no—
434#217—121no—
435#217—122no—
436#217#6714yescomplemented
437(C2×D3)⋊C4—22no—
438(C2×D3)⋊C4—22no—
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—121no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—122no—
452(C2×D3)⋊C4—121no—
453C4⋊Dic3—62no—
454C4⋊Dic3—62no—
455C4⋊Dic3—121no—
456Dic3⋊C4—22no—
457Dic3⋊C4—62no—
458Dic3⋊C4—62no—
459Dic3⋊C4—121no—
460Dic3⋊C4—121no—
461Dic3⋊C4—121no—
462Dic3⋊C4—122no—
463C4×Dic3—62no—
464C4×Dic3—62no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32C22×D411yescharacteristic
473C22×C32C22×D411yescharacteristic
474C22×C32C2×#4111yescharacteristic
475C22×C32C2×#4111yescharacteristic
476C22×C32C2×#4111yescharacteristic
477C22×C32H(5,𝔽2)11yescharacteristic
478C22×C32H(5,𝔽2)11yescharacteristic
479C2×C3⋊D3—22no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
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—416no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3#12314yescomplemented
501C32×C4—41no—
502C32×C4—41no—
503C3⋊Dic3—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—31no—
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—91no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—91no—
519#123—184no—
520#120—184no—
521C4×D4—184no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—64no—
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⋊C4D3211yescharacteristic
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—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—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—22no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—32no—
568C23×C3—32no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—68no—
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—124no—
587C23×C3—124no—
588C23×C3—124no—
589C23×C3—124no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3D3×D412yes—
593C23×C3C2×#6712yes—
594C23×C3C23×D311yescharacteristic
595C23×C3C23×D311yescharacteristic
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—28no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—32no—
608C22×D3—32no—
609C22×D3—44no—
610C22×D3—44no—
611C22×D3—44no—
612C22×D3—44no—
613C22×D3—44no—
614C22×D3—44no—
615C22×D3—62no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3#23512yes—
635C22×D3#23512yes—
636C22×D3D3×D412yes—
637C22×D3#23712yes—
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—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
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—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—124no—
675C2×C3×C4—124no—
676#67—68no—
677#67—124no—
678#67—124no—
679#67—124no—
680#67—128no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—62no—
697C2×Dic3—62no—
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—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3D3×D412yes—
724C2×Dic3C2×#6712yes—
725C2×Dic3C2×#6712yes—
726D12—68no—
727D12—124no—
728C4×D3—44no—
729C4×D3—44no—
730C4×D3—124no—
731C4×D3—124no—
732C2×C32—42no—
733C2×C32C2×#12311yescharacteristic
734C2×C32#52511yescharacteristic
735C2×C32#53811yescharacteristic
736C2×C32D4211yescharacteristic
737C2×C32#54611yescharacteristic
738C2×C32#54611yescharacteristic
739C2×C32#55111yescharacteristic
740C3⋊D3—42no—
741C3×D3—24no—
742C3×D3—42no—
743C24—31no—
744C24—31no—
745C24—62no—
746C24—62no—
747C24—62no—
748C24—62no—
749C24—62no—
750C24—91no—
751C24—121no—
752C24—121no—
753C24C2×D3211yescharacteristic
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—62no—
772C22×C4—62no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—121no—
777C22×C4—121no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—361no—
781C22×C4C2×D3211yescharacteristic
782C22×C4C2×D3211yescharacteristic
783C4⋊C4—62no—
784C4⋊C4—182no—
785C4⋊C4—182no—
786C4⋊C4—361no—
787C4⋊C4—361no—
788C22⋊C4—22no—
789C22⋊C4—34no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—62no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—182no—
798C22⋊C4—182no—
799C22⋊C4—182no—
800C22⋊C4—182no—
801C22⋊C4—361no—
802C22⋊C4—361no—
803C22⋊C4—361no—
804C42—182no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—34no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—81no—
842C22×C3—81no—
843C22×C3—1216no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—121no—
848C22×C3C2×#23511yescharacteristic
849C22×C3C2×#23511yescharacteristic
850C22×C3C2×D3×D411yescharacteristic
851C22×C3C2×D3×D411yescharacteristic
852C22×C3C2×D3×D411yescharacteristic
853C22×C3C2×#23711yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3#100411yescharacteristic
856C22×C3D3×#4111yescharacteristic
857C22×C3D3×#4111yescharacteristic
858C22×C3D3×#4111yescharacteristic
859C22×C3#100911yescharacteristic
860C22×C3#100911yescharacteristic
861C22×C3C22×#6711yescharacteristic
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—416no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—241no—
894C2×D3—241no—
895C2×D3—241no—
896C2×D3—241no—
897C2×D3#88314yescomplemented
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—81no—
906C3×C4—81no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—121no—
910Dic3—22no—
911Dic3—22no—
912Dic3—22no—
913Dic3—41no—
914Dic3—41no—
915Dic3—41no—
916Dic3—122no—
917Dic3—122no—
918Dic3—121no—
919Dic3—121no—
920Dic3—121no—
921Dic3—121no—
922Dic3—121no—
923Dic3—121no—
924Dic3—241no—
925C32#241811yescharacteristic, complemented, Sylow
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—32no—
933C23—32no—
934C23—32no—
935C23—32no—
936C23—68no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—92no—
948C23—124no—
949C23—124no—
950C23—124no—
951C23—124no—
952C23—124no—
953C23—124no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—181no—
958C23—181no—
959C23—181no—
960C23D3×#6712yes—
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—32no—
972C2×C4—32no—
973C2×C4—32no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—124no—
990C2×C4—124no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—181no—
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—42no—
1009C2×C3—42no—
1010C2×C3—64no—
1011C2×C3—82no—
1012C2×C3—122no—
1013C2×C3C2×#88311yescharacteristic
1014C2×C3#549011yescharacteristic
1015C2×C3#549411yescharacteristic
1016C2×C3#549511yescharacteristic
1017C2×C3#560911yescharacteristic
1018C2×C3D3×#12311yescharacteristic
1019C2×C3#565411yescharacteristic
1020C2×C3#565611yescharacteristic
1021C2×C3#567611yescharacteristic
1022C2×C3#570411yescharacteristic
1023C2×C3#570511yescharacteristic
1024C2×C3#579111yescharacteristic
1025C2×C3D4×#6711yescharacteristic
1026C2×C3#580611yescharacteristic
1027D3—24no—
1028D3—42no—
1029D3—122no—
1030D3—122no—
1031D3—242no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—34no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—1216no—
1050C22—121no—
1051C22—121no—
1052C22—121no—
1053C22—121no—
1054C22—182no—
1055C22—182no—
1056C22—182no—
1057C22—361no—
1058C22—361no—
1059C22—361no—
1060C22—361no—
1061C22D3×#23511yescharacteristic
1062C22D3×#23511yescharacteristic
1063C22D32×D411yescharacteristic
1064C22D3×#23711yescharacteristic
1065C22#6431411yescharacteristic
1066C22#6431411yescharacteristic
1067C22C2×D3×#6711yescharacteristic
1068C4—41no—
1069C4—41no—
1070C4—62no—
1071C4—62no—
1072C4—62no—
1073C4—121no—
1074C4—121no—
1075C4—121no—
1076C4—361no—
1077C4—361no—
1078C4—361no—
1079C3—21no—
1080C3#7766911yescharacteristic, complemented
1081C3#8212811yescharacteristic, complemented
1082C2—42no—
1083C2—64no—
1084C2—122no—
1085C2—362no—
1086C2#1059409411yescharacteristic
1087C2#1059419911yescharacteristic
1088C2D3×#88311yescharacteristic
1089C2#1059428011yescharacteristic
1090C2#1059489611yescharacteristic
1091C2#1059514811yescharacteristic
1092C2#1059529111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63977C2
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×D3×C22⋊C4C2semidirect
3. C2×#63975C2semidirect
4. C2×#63904C2semidirect
5. #10592658C2semidirect
6. C3×#4952C2semidirect
7. #10591706C2semidirect
8. #10591701C2semidirect
9. #10591382C2semidirect
10. #10591312C2semidirect
11. #10591303C2semidirect
12. #10591295C2semidirect
13. #10591284C2semidirect
14. #10591278C2semidirect
15. #10591275C2semidirect
24. C22×#624C22semidirect
27. C2×#3752C22semidirect
28. C2×#3752C22semidirect
29. C2×#3750C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
42. C2×#3722C22semidirect
49. C2×Dic32C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
64. C2×D3×C22⋊C4D3semidirect
77. #4952D3semidirect
135. C3×#217D4semidirect
215. C2×Dic3⋊C4C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
436. #217#67semidirect
500. C2×C3×D3#123semidirect
897. C2×D3#883semidirect
925. C32#2418semidirect
1080. C3#77669semidirect
1081. C3#82128semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C22⋊C42
C2×#639772
C2×#639752
C2×#639042
#105926582
C3×#49522
#105917062
#105917012
#105913822
#105913122
#105913032
#105912952
#105912842
#105912782
#105912752
#821283
#776693