Finite Group Databasebeta

← #11810343

Subgroups — #11810343

Order 1152.

1771 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic, complemented
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#63977C211yesmaximal, characteristic
4C2×C4×#626C211yesmaximal, characteristic, complemented
5C3×#4951C211yesmaximal, characteristic, complemented
6#10591717C211yesmaximal, characteristic, complemented
7#10591712C211yesmaximal, characteristic, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591392C211yesmaximal, characteristic, complemented
10#10591387C211yesmaximal, characteristic, complemented
11#10591382C211yesmaximal, characteristic, complemented
12#10591317C211yesmaximal, characteristic, complemented
13#10591313C211yesmaximal, characteristic, complemented
14#10591280C211yesmaximal, characteristic, complemented
15#10591278C211yesmaximal, characteristic, complemented
16#82128—31nomaximal
17#75844—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic, complemented
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C2×#3750C2211yescharacteristic, complemented
30#64092—24no—
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38C3×D3×C22⋊C4—24no—
39#63977—24no—
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic, complemented
43C2×#3722C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C4×#626—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C22×C3×C22⋊C4—31no—
58C2×#953—31no—
59C2×C4×#67—31no—
60C2×#883—31no—
61C2×#883—31no—
62C2×#883—61no—
63C2×#882—31no—
64C2×D3×C22⋊C4D311yescharacteristic, complemented
65C2×C4×D12—31no—
66C3×#388—31no—
67#5247—31no—
68#5213—31no—
69#5212—31no—
70#5210—31no—
71#4991—31no—
72#4987—31no—
73#4961—31no—
74#4961—31no—
75#4959—31no—
76#4956—31no—
77#4955—31no—
78#4953—31no—
79#4952—31no—
80#4951D311yescharacteristic, complemented
81#4949—31no—
82#4945—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
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—41no—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3—41no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#626—41no—
127C2×#626D414yes—
128C32×C22⋊C4D414yescomplemented
129#3757—22no—
130#3752—22no—
131C4⋊(C3⋊Dic3)—22no—
132#3750—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—41no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×C4⋊Dic3—41no—
139C3×C4×Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—41no—
142#3722—22no—
143#3722—41no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—41no—
150#2418—91noSylow
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×D3—61no—
165C22×C4×D3C2×D311yescharacteristic
166C22×C4×D3C2×D311yescharacteristic
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
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—31no—
186C2×#217—31no—
187C2×#217—61no—
188C2×#217C2×D311yescharacteristic
189C2×#217C2×D311yescharacteristic
190C2×#217C2×D311yescharacteristic
191C4×#67—64no—
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—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—61no—
212C2×C4⋊Dic3C2×D311yescharacteristic, complemented
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—61no—
218C2×C4×Dic3C2×D311yescharacteristic, complemented
219#883—68no—
220#883—64no—
221#883—64no—
222#882—64no—
223D3×C22⋊C4—24no—
224C4×D12—64no—
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—31no—
235C3⋊#95C2×D311yescharacteristic, complemented
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2×D412yes—
244C23×C32C2411yescharacteristic
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⋊D3C2×D412yes—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—28no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3—44no—
269C22×C3×D3C2×D412yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C22×C3×D3#4112yes—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2×D412yes—
278C2×C32×C4C2×D412yes—
279#638—44no—
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—
289C4×C3⋊D3—44no—
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×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D412yes—
308C3×C4×D3—44no—
309C3×C4×D3—44no—
310#626—28no—
311#626—44no—
312C2×#123—91no—
313C2×#120—91no—
314C2×C4×D4—91no—
315C22×C22⋊C4—31no—
316#399—91no—
317#397—91no—
318#394—91no—
319#394—91no—
320#388—31no—
321#388—91no—
322#386—91no—
323#386—91no—
324#385—91no—
325#380—91no—
326#379—91no—
327C24×C3—21no—
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—31no—
345C23×D3—31no—
346C23×D3—41no—
347C23×D3—41no—
348C23×D3—61no—
349C23×D3C22×D311yescharacteristic
350C23×D3C22×D311yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—31no—
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—121no—
364C22×C3×C4—121no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—34no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—64no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—122no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67—121no—
383C2×#67—122no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×D12—34no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—121no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—22no—
409C2×C4×D3—41no—
410C2×C4×D3—41no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—64no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—122no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—122no—
420C3×C4⋊C4—121no—
421C3×C22⋊C4—24no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—121no—
427C3×C22⋊C4D1214yescomplemented
428C3×C22⋊C4#6714yescomplemented
429C3×C42—62no—
430#217—22no—
431#217—22no—
432#217—41no—
433#217—62no—
434#217—62no—
435#217—62no—
436#217—62no—
437#217—64no—
438#217—62no—
439#217—62no—
440#217—62no—
441#217—121no—
442(C2×D3)⋊C4—22no—
443(C2×D3)⋊C4—22no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—64no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—121no—
455(C2×D3)⋊C4—121no—
456(C2×D3)⋊C4—121no—
457C4⋊Dic3—41no—
458C4⋊Dic3—62no—
459C4⋊Dic3—64no—
460C4⋊Dic3—62no—
461C4⋊Dic3—62no—
462C4⋊Dic3—121no—
463Dic3⋊C4—64no—
464Dic3⋊C4—62no—
465Dic3⋊C4—62no—
466Dic3⋊C4—62no—
467Dic3⋊C4—121no—
468C4×Dic3—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32C22×D411yescharacteristic
477C22×C32C22×D411yescharacteristic
478C22×C32C2×#4111yescharacteristic
479C22×C32C2×#4111yescharacteristic
480C22×C32C2×#4111yescharacteristic
481C22×C32H(5,𝔽2)11yescharacteristic
482C22×C32H(5,𝔽2)11yescharacteristic
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—41no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—416no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3#12314yescomplemented
505C32×C4—22no—
506C32×C4—22no—
507C3⋊Dic3—41no—
508C3⋊Dic3—41no—
509C3⋊Dic3—41no—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C25—31no—
517C22×D4—91no—
518C22×D4—91no—
519C22×D4—91no—
520C23×C4—31no—
521C23×C4—31no—
522C23×C4—91no—
523#123—184no—
524#120—184no—
525C4×D4—184no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—64no—
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⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4D3211yescharacteristic
548C2×C42—31no—
549#95—31no—
550#95—31no—
551#95—91no—
552#95—91no—
553#95—91no—
554#95—91no—
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—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—22no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—68no—
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×D1212yes—
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—32no—
612C22×D3—32no—
613C22×D3—44no—
614C22×D3—44no—
615C22×D3—44no—
616C22×D3—44no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—121no—
635C22×D3—121no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3#23512yes—
639C22×D3#23512yes—
640C22×D3D3×D412yes—
641C22×D3#23712yes—
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—22no—
651C2×C3×C4—22no—
652C2×C3×C4—32no—
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—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—124no—
675C2×C3×C4—124no—
676C2×C3×C4C2×D1212yes—
677C2×C3×C4C2×D1212yes—
678C2×C3×C4C2×#6712yes—
679C2×C3×C4C2×#6712yes—
680#67—68no—
681#67—124no—
682#67—124no—
683#67—124no—
684#67—128no—
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—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3—62no—
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—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×Dic3D3×D412yes—
730D12—68no—
731D12—124no—
732C4×D3—44no—
733C4×D3—44no—
734C4×D3—124no—
735C4×D3—124no—
736C4×D3—128no—
737C2×C32—42no—
738C2×C32C2×#12311yescharacteristic
739C2×C32#52511yescharacteristic
740C2×C32#53811yescharacteristic
741C2×C32D4211yescharacteristic
742C2×C32#54611yescharacteristic
743C2×C32#54611yescharacteristic
744C2×C32#55111yescharacteristic
745C3⋊D3—42no—
746C3×D3—24no—
747C3×D3—42no—
748C24—31no—
749C24—31no—
750C24—62no—
751C24—62no—
752C24—62no—
753C24—62no—
754C24—62no—
755C24—91no—
756C24—121no—
757C24—121no—
758C24C2×D3211yescharacteristic
759C2×D4—94no—
760C2×D4—182no—
761C2×D4—182no—
762C2×D4—182no—
763C2×D4—182no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—361no—
767C2×D4—361no—
768C22×C4—31no—
769C22×C4—31no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—62no—
775C22×C4—62no—
776C22×C4—62no—
777C22×C4—62no—
778C22×C4—91no—
779C22×C4—91no—
780C22×C4—91no—
781C22×C4—121no—
782C22×C4—121no—
783C22×C4—182no—
784C22×C4—182no—
785C22×C4—361no—
786C22×C4C2×D3211yescharacteristic
787C22×C4C2×D3211yescharacteristic
788C4⋊C4—121no—
789C4⋊C4—182no—
790C4⋊C4—182no—
791C4⋊C4—182no—
792C4⋊C4—361no—
793C22⋊C4—62no—
794C22⋊C4—62no—
795C22⋊C4—62no—
796C22⋊C4—62no—
797C22⋊C4—121no—
798C22⋊C4—182no—
799C22⋊C4—182no—
800C22⋊C4—182no—
801C22⋊C4—182no—
802C22⋊C4—182no—
803C22⋊C4—182no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—361no—
807C22⋊C4—361no—
808C22⋊C4#62614yescomplemented
809C42—62no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—34no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—1216no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3C22×D1211yescharacteristic
854C22×C3C2×#23511yescharacteristic
855C22×C3C2×#23511yescharacteristic
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C22×C3C2×#23711yescharacteristic
859C22×C3#100411yescharacteristic
860C22×C3#100411yescharacteristic
861C22×C3#100411yescharacteristic
862C22×C3D3×#4111yescharacteristic
863C22×C3D3×#4111yescharacteristic
864C22×C3D3×#4111yescharacteristic
865C22×C3#100911yescharacteristic
866C22×C3C22×#6711yescharacteristic
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—416no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—64no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—122no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—121no—
895C2×D3—121no—
896C2×D3—121no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—121no—
901C2×D3—121no—
902C2×D3#88314yescomplemented
903C3×C4—22no—
904C3×C4—22no—
905C3×C4—22no—
906C3×C4—22no—
907C3×C4—42no—
908C3×C4—42no—
909C3×C4—62no—
910C3×C4—121no—
911C3×C4—121no—
912C3×C4—121no—
913C3×C4—121no—
914C3×C4—121no—
915Dic3—22no—
916Dic3—41no—
917Dic3—41no—
918Dic3—41no—
919Dic3—41no—
920Dic3—41no—
921Dic3—122no—
922Dic3—122no—
923Dic3—122no—
924Dic3—121no—
925Dic3—121no—
926Dic3—121no—
927Dic3—121no—
928Dic3—121no—
929Dic3—121no—
930C32#241811yescharacteristic, complemented, Sylow
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—32no—
938C23—32no—
939C23—32no—
940C23—32no—
941C23—68no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—92no—
953C23—124no—
954C23—124no—
955C23—124no—
956C23—124no—
957C23—124no—
958C23—124no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23—181no—
963C23—181no—
964C23—181no—
965C23C2×#62612yes—
966C23C22×D3211yescharacteristic
967D4—188no—
968D4—364no—
969D4—364no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—32no—
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—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—124no—
993C2×C4—124no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—364no—
1004C2×C4C2×#62612yes—
1005C2×C4C2×#62612yes—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—42no—
1014C2×C3—42no—
1015C2×C3—64no—
1016C2×C3—82no—
1017C2×C3—122no—
1018C2×C3C2×#88311yescharacteristic
1019C2×C3#549011yescharacteristic
1020C2×C3#549411yescharacteristic
1021C2×C3#549511yescharacteristic
1022C2×C3#552411yescharacteristic
1023C2×C3D4×D1211yescharacteristic
1024C2×C3#555411yescharacteristic
1025C2×C3#561211yescharacteristic
1026C2×C3D3×#12311yescharacteristic
1027C2×C3#567811yescharacteristic
1028C2×C3#570511yescharacteristic
1029C2×C3#579111yescharacteristic
1030C2×C3D4×#6711yescharacteristic
1031C2×C3#580611yescharacteristic
1032D3—24no—
1033D3—42no—
1034D3—124no—
1035D3—122no—
1036D3—122no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—34no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—1216no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—121no—
1059C22—182no—
1060C22—182no—
1061C22—182no—
1062C22—361no—
1063C22—361no—
1064C22—361no—
1065C22—361no—
1066C22D3×#23511yescharacteristic
1067C22D3×#23511yescharacteristic
1068C22D32×D411yescharacteristic
1069C22D3×#23711yescharacteristic
1070C22#6431311yescharacteristic
1071C22#6431411yescharacteristic
1072C22C22×#62611yescharacteristic
1073C4—22no—
1074C4—22no—
1075C4—62no—
1076C4—121no—
1077C4—121no—
1078C4—121no—
1079C4—121no—
1080C4—121no—
1081C4—361no—
1082C4—361no—
1083C4—361no—
1084C3—21no—
1085C3#7584411yescharacteristic, complemented
1086C3#8212811yescharacteristic, complemented
1087C2—42no—
1088C2—64no—
1089C2—122no—
1090C2—362no—
1091C2#1059409311yescharacteristic
1092C2#1059419611yescharacteristic
1093C2D3×#88311yescharacteristic
1094C2#1059427811yescharacteristic
1095C2#1059502311yescharacteristic
1096C2D4×#62611yescharacteristic
1097C2#1059524611yescharacteristic
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×#64092C2semidirect
2. C2×C3×D3×C22⋊C4C2semidirect
4. C2×C4×#626C2semidirect
5. C3×#4951C2semidirect
6. #10591717C2semidirect
7. #10591712C2semidirect
8. #10591706C2semidirect
9. #10591392C2semidirect
10. #10591387C2semidirect
11. #10591382C2semidirect
12. #10591317C2semidirect
13. #10591313C2semidirect
14. #10591280C2semidirect
15. #10591278C2semidirect
20. C22×C4×C3⋊D3C22semidirect
27. C2×#3752C22semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×#3750C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×C4×Dic3C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
42. C2×#3722C22semidirect
43. C2×#3722C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
64. C2×D3×C22⋊C4D3semidirect
80. #4951D3semidirect
128. C32×C22⋊C4D4semidirect
212. C2×C4⋊Dic3C2×D3semidirect
218. C2×C4×Dic3C2×D3semidirect
235. C3⋊#95C2×D3semidirect
236. C3⋊#95C2×D3semidirect
427. C3×C22⋊C4D12semidirect
428. C3×C22⋊C4#67semidirect
504. C2×C3×D3#123semidirect
808. C22⋊C4#626semidirect
902. C2×D3#883semidirect
930. C32#2418semidirect
1085. C3#75844semidirect
1086. C3#82128semidirect

Maximal subgroups

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

subgroupindex
C2×#640922
C2×C3×D3×C22⋊C42
C2×#639772
C2×C4×#6262
C3×#49512
#105917172
#105917122
#105917062
#105913922
#105913872
#105913822
#105913172
#105913132
#105912802
#105912782
#821283
#758443