Finite Group Databasebeta

← #11803880

Subgroups — #11803880

Order 1152.

1623 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63979C211yesmaximal, characteristic
2C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4#10592657C211yesmaximal, characteristic, complemented
5C3×#4957C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7#10591722C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591363C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591245C211yesmaximal, characteristic, complemented
15#10591239C211yesmaximal, characteristic, complemented
16#76298—31nomaximal
17#74667—31nomaximal
18C22×#638C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38#63979C418yescomplemented
39#67⋊Dic3—24no—
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63904—24no—
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#940—31no—
57C2×#940—31no—
58C2×D4×Dic3—31no—
59C2×C4×#67—31no—
60C2×#893—31no—
61C2×#67⋊C4—31no—
62C3×#390—31no—
63C3×#386—31no—
64#5220—31no—
65#5213—31no—
66#4977—31no—
67#4958—31no—
68#4958—31no—
69#4958—31no—
70#4958—31no—
71#4958—31no—
72#4958—61no—
73#4957—31no—
74#4957D311yescharacteristic, complemented
75#4956—31no—
76#4956—31no—
77#4956—31no—
78#4956—31no—
79#4956—31no—
80#4956D311yescharacteristic, complemented
81#4939—31no—
82#4932—31no—
83#4665—31no—
84#4665—31no—
85#4650—31no—
86#4648—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—41no—
94C2×#638—41no—
95C2×#638C2×C414yescomplemented
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—41no—
98C22×C3⋊Dic3—41no—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C2×C3×#67C2×C414yescomplemented
107C2×C3×#67C2×C414yescomplemented
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—41no—
120C2×#626—41no—
121C2×#626C2×C414yescomplemented
122C2×#626C2×C414yescomplemented
123C2×#625—41no—
124C2×#625—41no—
125C2×#625C2×C414yescomplemented
126C2×#624—22no—
127C2×#624—41no—
128C2×#624—41no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—41no—
131C2×D3×Dic3—41no—
132C32×C22⋊C4—41no—
133#3752—22no—
134#3752—41no—
135C3×#217—22no—
136C3×#217—41no—
137C3×(C2×D3)⋊C4—41no—
138C3×(C2×D3)⋊C4—41no—
139C3×(C2×D3)⋊C4—41no—
140C3×Dic3⋊C4—22no—
141C3×C4×Dic3—22no—
142Dic3⋊Dic3—22no—
143#3722—41no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—41no—
147Dic32C2×C414yescomplemented
148Dic32D414yescomplemented
149#2328—91noSylow
150C22×C3×D4—31no—
151C22×C3×D4—31no—
152C23×C3×C4—31no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—61no—
160C22×#67C2×D311yescharacteristic
161C22×#67C2×D311yescharacteristic
162C23×Dic3—31no—
163C23×Dic3—31no—
164C23×Dic3—31no—
165C23×Dic3—61no—
166C22×D12—31no—
167C22×D12—31no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3C2×D311yescharacteristic
172C2×C3×C4⋊C4—31no—
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4C2×D311yescharacteristic
180C2×C3×C22⋊C4C2×D311yescharacteristic
181C2×C3×C42—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217C2×D311yescharacteristic
186C2×#217C2×D311yescharacteristic
187#940—38no—
188#940—38no—
189D4×Dic3—64no—
190C4×#67—64no—
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×C4⋊Dic3—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4C2×D311yescharacteristic
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3C2×D311yescharacteristic
213#893—64no—
214#67⋊C4—64no—
215C3×#95—31no—
216C3×#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—61no—
230C3⋊#95—61no—
231C3⋊#95C2×D311yescharacteristic
232C3⋊#95C2×D311yescharacteristic
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3C22×C412yes—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C22×C412yes—
261C22×C3×D3C22×C412yes—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268#638—44no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—44no—
277C2×C3⋊Dic3C22×C412yes—
278C2×C3⋊Dic3C2×D412yes—
279C3×#67—28no—
280C3×#67—44no—
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×Dic3C22×C412yes—
295C2×C3×Dic3C22×C412yes—
296C2×C3×Dic3C2×D412yes—
297C2×C3×Dic3C2×D412yes—
298C2×C3×Dic3#4112yes—
299C3×C4×D3—44no—
300#626—28no—
301#626—44no—
302#625—44no—
303#624—44no—
304D3×Dic3—44no—
305C2×#127—91no—
306C2×C4×D4—91no—
307C2×C4×D4—91no—
308#390—31no—
309#390—91no—
310#386—31no—
311#386—91no—
312#386—91no—
313#386—91no—
314#386—91no—
315#386—91no—
316#386—91no—
317#386—91no—
318#382—91no—
319#376—91no—
320C24×C3—21no—
321C24×C3—31no—
322C24×C3—31no—
323C24×C3C22×D311yescharacteristic
324C24×C3C22×D311yescharacteristic
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—61no—
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D311yescharacteristic
330C2×C3×D4—34no—
331C2×C3×D4—34no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
334C2×C3×D4—121no—
335C2×C3×D4—121no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—62no—
345C22×C3×C4—121no—
346C22×C3×C4—121no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—22no—
352C2×#67—22no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—41no—
360C2×#67—41no—
361C2×#67—64no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—121no—
365C2×#67—121no—
366C2×#67—121no—
367C2×#67—121no—
368C2×#67—121no—
369C2×#67—121no—
370C2×#67—121no—
371C2×#67—121no—
372C2×#67—121no—
373C2×#67—121no—
374C2×#67—122no—
375C2×#67—122no—
376C2×#67C4×D314yescomplemented
377C2×#67C4×D314yescomplemented
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3—122no—
391C22×Dic3—121no—
392C22×Dic3—121no—
393C22×Dic3—121no—
394C22×Dic3—121no—
395C22×Dic3—121no—
396C22×Dic3—121no—
397C22×Dic3—122no—
398C22×Dic3—122no—
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C2×D12—34no—
406C2×D12—34no—
407C2×D12—62no—
408C2×D12—62no—
409C2×D12—121no—
410C2×D12—121no—
411C2×C4×D3—22no—
412C2×C4×D3—41no—
413C2×C4×D3—41no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—121no—
423C3×C4⋊C4—62no—
424C3×C22⋊C4—41no—
425C3×C22⋊C4—41no—
426C3×C22⋊C4—42no—
427C3×C22⋊C4—62no—
428C3×C22⋊C4—121no—
429C3×C22⋊C4—121no—
430C3×C22⋊C4—121no—
431C3×C22⋊C4—121no—
432C3×C42—62no—
433#217—22no—
434#217—41no—
435#217—62no—
436#217—62no—
437#217—121no—
438(C2×D3)⋊C4—41no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—41no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—122no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—122no—
451(C2×D3)⋊C4—121no—
452C4⋊Dic3—62no—
453Dic3⋊C4—22no—
454Dic3⋊C4—62no—
455C4×Dic3—22no—
456C4×Dic3—34no—
457C4×Dic3—34no—
458C4×Dic3—34no—
459C4×Dic3—34no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32C23×C411yescharacteristic
468C22×C32C22×D411yescharacteristic
469C22×C32C2×#4111yescharacteristic
470C22×C32H(5,𝔽2)11yescharacteristic
471C22×C32H(5,𝔽2)11yescharacteristic
472C22×C32H(5,𝔽2)11yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C32×C4—41no—
496C32×C4—41no—
497C3⋊Dic3—22no—
498C3⋊Dic3—22no—
499C3⋊Dic3—41no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3C4×D414yes—
506C22×D4—31no—
507C22×D4—31no—
508C22×D4—91no—
509C22×D4—91no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—31no—
513C23×C4—91no—
514C23×C4—91no—
515C23×C4—91no—
516#127—98no—
517C4×D4—184no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4D3211yescharacteristic
533C2×C42—31no—
534C2×C42—91no—
535C2×C42—91no—
536#95—31no—
537#95—31no—
538#95—91no—
539#95—91no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95—91no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—21no—
547C23×C3—21no—
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—22no—
560C23×C3—32no—
561C23×C3—32no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3C2×C4×D312yes—
579C23×C3C2×C4×D312yes—
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—62no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3C2×C4×D312yes—
616C22×D3C2×C4×D312yes—
617C3×D4—68no—
618C3×D4—124no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—61no—
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—124no—
656#67—28no—
657#67—44no—
658#67—68no—
659#67—124no—
660#67—124no—
661#67—124no—
662#67—124no—
663#67—124no—
664#67—128no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
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—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
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—121no—
700C2×Dic3—121no—
701C2×Dic3—121no—
702C2×Dic3—121no—
703C2×Dic3—121no—
704C2×Dic3—121no—
705C2×Dic3—124no—
706C2×Dic3—124no—
707C2×Dic3—124no—
708C2×Dic3—128no—
709C2×Dic3C2×C4×D312yes—
710C2×Dic3C2×C4×D312yes—
711C2×Dic3D3×D412yes—
712C2×Dic3D3×D412yes—
713C2×Dic3#23712yes—
714D12—68no—
715D12—124no—
716C4×D3—44no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—124no—
720C2×C32—42no—
721C2×C32C2×C4×D411yescharacteristic
722C2×C32#51811yescharacteristic
723C2×C32#51811yescharacteristic
724C2×C32#53511yescharacteristic
725C2×C32#53511yescharacteristic
726C2×C32#54011yescharacteristic
727C2×C32#54011yescharacteristic
728C3⋊D3—42no—
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24—91no—
734C24C2×D3211yescharacteristic
735C2×D4—34no—
736C2×D4—34no—
737C2×D4—62no—
738C2×D4—62no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—121no—
744C2×D4—121no—
745C2×D4—182no—
746C2×D4—182no—
747C2×D4—361no—
748C2×D4—361no—
749C2×D4—361no—
750C2×D4—361no—
751C2×D4—361no—
752C2×D4—361no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—62no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—121no—
764C22×C4—121no—
765C22×C4—182no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4—361no—
769C22×C4—361no—
770C22×C4—361no—
771C22×C4—361no—
772C22×C4—361no—
773C22×C4—361no—
774C22×C4C2×D3211yescharacteristic
775C22×C4C2×D3211yescharacteristic
776C4⋊C4—62no—
777C4⋊C4—182no—
778C22⋊C4—41no—
779C22⋊C4—62no—
780C22⋊C4—121no—
781C22⋊C4—121no—
782C22⋊C4—121no—
783C22⋊C4—121no—
784C22⋊C4—182no—
785C22⋊C4—182no—
786C22⋊C4—182no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C22⋊C4—361no—
790C42—62no—
791C42—94no—
792C42—94no—
793C22×C3—24no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3C22×C4×D311yescharacteristic
836C22×C3C22×C4×D311yescharacteristic
837C22×C3C2×D3×D411yescharacteristic
838C22×C3C2×D3×D411yescharacteristic
839C22×C3C2×#23711yescharacteristic
840C22×C3#100411yescharacteristic
841C22×C3#100411yescharacteristic
842C22×C3#100411yescharacteristic
843C22×C3#100411yescharacteristic
844C22×C3#100411yescharacteristic
845C22×C3D3×#4111yescharacteristic
846C22×C3#100911yescharacteristic
847C22×C3#100911yescharacteristic
848C22×C3#100911yescharacteristic
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—122no—
870C2×D3—122no—
871C2×D3—122no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—241no—
881C2×D3—241no—
882C2×D3—241no—
883C2×D3—241no—
884C3×C4—34no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—62no—
890C3×C4—62no—
891C3×C4—81no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4—121no—
896Dic3—22no—
897Dic3—22no—
898Dic3—41no—
899Dic3—41no—
900Dic3—41no—
901Dic3—62no—
902Dic3—62no—
903Dic3—62no—
904Dic3—62no—
905Dic3—122no—
906Dic3—122no—
907Dic3—122no—
908Dic3—121no—
909Dic3—121no—
910Dic3#67⋊C414yes—
911C32#232811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—32no—
919C23—32no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—92no—
933C23—181no—
934C23—181no—
935C23—181no—
936C23—181no—
937C23—181no—
938C23—181no—
939C23C4×D3212yes—
940C23C22×D3211yescharacteristic
941D4—68no—
942D4—124no—
943D4—188no—
944D4—364no—
945D4—364no—
946D4—364no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
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—61no—
971C2×C4—92no—
972C2×C4—92no—
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—364no—
982C2×C4—364no—
983C2×C4—364no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—44no—
992C2×C3—42no—
993C2×C3—42no—
994C2×C3—122no—
995C2×C3—122no—
996C2×C3C2×#67⋊C411yescharacteristic
997C2×C3#548611yescharacteristic
998C2×C3C4×D3×D411yescharacteristic
999C2×C3#554511yescharacteristic
1000C2×C3#554511yescharacteristic
1001C2×C3#554511yescharacteristic
1002C2×C3#559211yescharacteristic
1003C2×C3#560711yescharacteristic
1004C2×C3#561511yescharacteristic
1005C2×C3#561911yescharacteristic
1006C2×C3#561911yescharacteristic
1007C2×C3#566311yescharacteristic
1008C2×C3#567411yescharacteristic
1009C2×C3#571511yescharacteristic
1010D3—42no—
1011D3—42no—
1012D3—122no—
1013D3—122no—
1014D3—242no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—121no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—182no—
1037C22—182no—
1038C22—182no—
1039C22—361no—
1040C22—361no—
1041C22—361no—
1042C22—361no—
1043C22C2×C4×D3211yescharacteristic
1044C22#6430811yescharacteristic
1045C22D32×D411yescharacteristic
1046C22D3×#23711yescharacteristic
1047C22#6431311yescharacteristic
1048C22#6431411yescharacteristic
1049C22#6433011yescharacteristic
1050C4—34no—
1051C4—41no—
1052C4—41no—
1053C4—62no—
1054C4—62no—
1055C4—121no—
1056C4—121no—
1057C4—121no—
1058C4—182no—
1059C4—182no—
1060C4—361no—
1061C3—21no—
1062C3#7466711yescharacteristic, complemented
1063C3#7629811yescharacteristic, complemented
1064C2—42no—
1065C2—122no—
1066C2—122no—
1067C2—362no—
1068C2#1059422011yescharacteristic
1069C2D3×#67⋊C411yescharacteristic
1070C2#1059425411yescharacteristic
1071C2#1059428711yescharacteristic
1072C2#1059505811yescharacteristic
1073C2#1059525011yescharacteristic
1074C2#1059528611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#67⋊Dic3C2semidirect
3. C2×#63904C2semidirect
4. #10592657C2semidirect
5. C3×#4957C2semidirect
6. C3×#4956C2semidirect
7. #10591722C2semidirect
8. #10591713C2semidirect
9. #10591383C2semidirect
10. #10591381C2semidirect
11. #10591364C2semidirect
12. #10591363C2semidirect
13. #10591275C2semidirect
14. #10591245C2semidirect
15. #10591239C2semidirect
38. #63979C4semidirect
74. #4957D3semidirect
80. #4956D3semidirect
95. C2×#638C2×C4semidirect
106. C2×C3×#67C2×C4semidirect
107. C2×C3×#67C2×C4semidirect
121. C2×#626C2×C4semidirect
122. C2×#626C2×C4semidirect
125. C2×#625C2×C4semidirect
147. Dic32C2×C4semidirect
148. Dic32D4semidirect
376. C2×#67C4×D3semidirect
377. C2×#67C4×D3semidirect
911. C32#2328semidirect
1062. C3#74667semidirect
1063. C3#76298semidirect

Maximal subgroups

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

subgroupindex
C2×#639792
C2×#67⋊Dic32
C2×#639042
#105926572
C3×#49572
C3×#49562
#105917222
#105917132
#105913832
#105913812
#105913642
#105913632
#105912752
#105912452
#105912392
#762983
#746673