Finite Group Databasebeta

← #11810337

Subgroups — #11810337

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×#63977C211yesmaximal, characteristic
2C2×#63975C211yesmaximal, characteristic, complemented
3C2×D3×#217C211yesmaximal, characteristic, complemented
4C2×#63880C211yesmaximal, characteristic, complemented
5#10592660C211yesmaximal, characteristic, complemented
6C3×#4955C211yesmaximal, characteristic, complemented
7C3×#4945C211yesmaximal, characteristic, complemented
8#10591717C211yesmaximal, characteristic, complemented
9#10591379C211yesmaximal, characteristic, complemented
10#10591366C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591317C211yesmaximal, characteristic, complemented
13#10591305C211yesmaximal, characteristic, complemented
14#10591291C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#75844—31nomaximal
17#73826—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic, complemented
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×#3752C2211yescharacteristic, complemented
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39#63977—24no—
40#63975—24no—
41D3×#217—24no—
42C2×Dic3⋊Dic3C2211yescharacteristic, complemented
43C2×Dic3⋊Dic3C2211yescharacteristic, complemented
44C2×Dic3⋊Dic3C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50#63880—24no—
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#953—31no—
58C22×#217—31no—
59C2×#883—31no—
60C2×#883—31no—
61C2×#882—31no—
62C2×#67⋊C4—31no—
63C2×D3×C22⋊C4—31no—
64C2×C4×D12—31no—
65C3×#388—31no—
66C3×#379—31no—
67#4991—31no—
68#4987—31no—
69#4961—31no—
70#4961—31no—
71#4961—61no—
72#4959—31no—
73#4958—31no—
74#4956—31no—
75#4955D311yescharacteristic, complemented
76#4953—31no—
77#4952—31no—
78#4951—31no—
79#4950—31no—
80#4949—31no—
81#4945D311yescharacteristic, complemented
82#4942—31no—
83#4940—31no—
84#4677—31no—
85#4668—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×#626—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—41no—
118C2×#626D414yes—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—41no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—41no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—41no—
129#3757—22no—
130#3752—22no—
131#3752—41no—
132C4⋊(C3⋊Dic3)—41no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217D414yescomplemented
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—41no—
140C3×Dic3⋊C4—41no—
141C3×C4×Dic3—22no—
142Dic3⋊Dic3—22no—
143Dic3⋊Dic3—22no—
144Dic3⋊Dic3—22no—
145#3722—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—22no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—61no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C22×D12—31no—
161C22×D12—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
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—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4C2×D311yescharacteristic
176C2×C3×C22⋊C4C2×D311yescharacteristic
177C2×C3×C42—31no—
178#953—64no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—61no—
186C2×#217—64no—
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189C2×#217C2×D311yescharacteristic
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4—61no—
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—61no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4C2×D311yescharacteristic, complemented
216C2×C4×Dic3C2×D311yescharacteristic, complemented
217#883—64no—
218#883—64no—
219#882—64no—
220#67⋊C4—64no—
221D3×C22⋊C4—64no—
222C4×D12—64no—
223C3×#95—31no—
224C3×#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—61no—
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—
306#626—28no—
307#626—44no—
308#624—44no—
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—91no—
318#394—91no—
319#388—31no—
320#388—91no—
321#386—91no—
322#386—91no—
323#385—91no—
324#380—91no—
325#379—31no—
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×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C2×#67—34no—
363C2×#67—62no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—122no—
372C2×#67—122no—
373C2×#67—121no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—122no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—62no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3—121no—
391C22×Dic3—121no—
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—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—121no—
413C2×C4×D3—121no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C3×C4⋊C4—121no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—41no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—42no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—121no—
427C3×C42—62no—
428#217—22no—
429#217—22no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—62no—
435#217—62no—
436#217—122no—
437#217D1214yescomplemented
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—41no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—122no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4—122no—
454C4⋊Dic3—62no—
455C4⋊Dic3—62no—
456C4⋊Dic3—62no—
457C4⋊Dic3—121no—
458C4⋊Dic3—121no—
459C4⋊Dic3—122no—
460Dic3⋊C4—41no—
461Dic3⋊C4—62no—
462Dic3⋊C4—62no—
463Dic3⋊C4—62no—
464C4×Dic3—22no—
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—91no—
517C23×C4—91no—
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—31no—
533C2×C22⋊C4—31no—
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—184no—
543C2×C22⋊C4D3211yescharacteristic
544C2×C42—31no—
545#95—31no—
546#95—31no—
547#95—91no—
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×C3C2×D1212yes—
593C23×C3D3×D412yes—
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×D3D3×D412yes—
636C22×D3#23712yes—
637C22×D3#23712yes—
638C2×C3×C4—22no—
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—21no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
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—
674#67—68no—
675#67—124no—
676#67—124no—
677#67—124no—
678#67—128no—
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—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—62no—
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—61no—
712C2×Dic3—61no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C2×Dic3—124no—
722C2×Dic3—124no—
723C2×Dic3C2×D1212yes—
724C2×Dic3C2×D1212yes—
725C2×Dic3D3×D412yes—
726D12—68no—
727D12—124no—
728C4×D3—124no—
729C4×D3—124no—
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—91no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—182no—
773C22×C4—182no—
774C22×C4—182no—
775C22×C4—182no—
776C22×C4—182no—
777C22×C4—182no—
778C22×C4—361no—
779C22×C4—361no—
780C22×C4—361no—
781C22×C4C2×D3211yescharacteristic
782C22×C4C2×D3211yescharacteristic
783C4⋊C4—121no—
784C4⋊C4—182no—
785C4⋊C4—182no—
786C4⋊C4—182no—
787C4⋊C4—361no—
788C22⋊C4—34no—
789C22⋊C4—41no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—62no—
794C22⋊C4—62no—
795C22⋊C4—121no—
796C22⋊C4—182no—
797C22⋊C4—182no—
798C22⋊C4—182no—
799C22⋊C4—182no—
800C22⋊C4—182no—
801C22⋊C4—182no—
802C22⋊C4—182no—
803C22⋊C4—361no—
804C42—62no—
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×C3C22×D1211yescharacteristic
849C22×C3C2×#23511yescharacteristic
850C22×C3C2×D3×D411yescharacteristic
851C22×C3C2×D3×D411yescharacteristic
852C22×C3C2×D3×D411yescharacteristic
853C22×C3C2×#23711yescharacteristic
854C22×C3C2×#23711yescharacteristic
855C22×C3#100411yescharacteristic
856C22×C3#100411yescharacteristic
857C22×C3#100411yescharacteristic
858C22×C3D3×#4111yescharacteristic
859C22×C3D3×#4111yescharacteristic
860C22×C3D3×#4111yescharacteristic
861C22×C3#100911yescharacteristic
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—42no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—62no—
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—121no—
918Dic3—121no—
919Dic3—121no—
920Dic3—121no—
921Dic3—121no—
922Dic3—121no—
923Dic3—241no—
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×D1212yes—
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—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—364no—
999C2×C4—364no—
1000C2×C4—364no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—64no—
1011C2×C3—82no—
1012C2×C3—122no—
1013C2×C3C2×#88311yescharacteristic
1014C2×C3#549011yescharacteristic
1015C2×C3#549511yescharacteristic
1016C2×C3#552411yescharacteristic
1017C2×C3D4×D1211yescharacteristic
1018C2×C3#555411yescharacteristic
1019C2×C3#558611yescharacteristic
1020C2×C3#559011yescharacteristic
1021C2×C3#559111yescharacteristic
1022C2×C3#559311yescharacteristic
1023C2×C3#561211yescharacteristic
1024C2×C3D3×#12311yescharacteristic
1025C2×C3#567811yescharacteristic
1026C2×C3#570511yescharacteristic
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—
1061C22C2×D3×D1211yescharacteristic
1062C22D3×#23511yescharacteristic
1063C22D32×D411yescharacteristic
1064C22D3×#23711yescharacteristic
1065C22D3×#23711yescharacteristic
1066C22#6431411yescharacteristic
1067C22#6433011yescharacteristic
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#7382611yescharacteristic, complemented
1081C3#7584411yescharacteristic, complemented
1082C2—42no—
1083C2—64no—
1084C2—122no—
1085C2—362no—
1086C2#1059407811yescharacteristic
1087C2#1059409411yescharacteristic
1088C2D3×#88311yescharacteristic
1089C2#1059427711yescharacteristic
1090C2#1059507311yescharacteristic
1091C2#1059518411yescharacteristic
1092C2#1059529411yescharacteristic
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
2. C2×#63975C2semidirect
3. C2×D3×#217C2semidirect
4. C2×#63880C2semidirect
5. #10592660C2semidirect
6. C3×#4955C2semidirect
7. C3×#4945C2semidirect
8. #10591717C2semidirect
9. #10591379C2semidirect
10. #10591366C2semidirect
11. #10591364C2semidirect
12. #10591317C2semidirect
13. #10591305C2semidirect
14. #10591291C2semidirect
15. #10591275C2semidirect
22. C22×#624C22semidirect
27. C2×#3752C22semidirect
28. C2×#3752C22semidirect
29. C2×C4⋊(C3⋊Dic3)C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
45. C2×#3722C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
75. #4955D3semidirect
81. #4945D3semidirect
135. C3×#217D4semidirect
215. C2×Dic3⋊C4C2×D3semidirect
216. C2×C4×Dic3C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
437. #217D12semidirect
500. C2×C3×D3#123semidirect
897. C2×D3#883semidirect
925. C32#2418semidirect
1080. C3#73826semidirect
1081. C3#75844semidirect

Maximal subgroups

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

subgroupindex
C2×#639772
C2×#639752
C2×D3×#2172
C2×#638802
#105926602
C3×#49552
C3×#49452
#105917172
#105913792
#105913662
#105913642
#105913172
#105913052
#105912912
#105912752
#758443
#738263