Finite Group Databasebeta

← #11773442

Subgroups — #11773442

Order 1152.

1425 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#71568—31nomaximal
9#69420—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3750—22no—
18C2×#3750—22no—
19C2×#3750—22no—
20C2×C3×Dic3⋊C4—22no—
21C2×C3×Dic3⋊C4—22no—
22C2×C3×Dic3⋊C4—22no—
23C2×Dic3⋊Dic3—22no—
24C2×Dic3⋊Dic3—22no—
25C2×Dic3⋊Dic3—22no—
26C3×C3⋊#95—22no—
27#63579—22no—
28#63579—22no—
29#63579C414yescomplemented
30C22×C3×C4⋊C4—31no—
31C22×C4⋊Dic3—31no—
32C22×Dic3⋊C4—31no—
33C22×Dic3⋊C4—31no—
34C22×Dic3⋊C4—31no—
35C22×Dic3⋊C4—61no—
36C22×Dic3⋊C4D311yescharacteristic
37C2×C3×#95—31no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95D311yescharacteristic
45C24×C32C2311yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4D412yes—
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3—21no—
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3C2×C412yes—
64C22×C3⋊Dic3D412yes—
65C22×C3⋊Dic3D412yes—
66C22×C3⋊Dic3Q812yes—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—21no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3C2×C412yes—
88C22×C3×Dic3C2×C412yes—
89C22×C3×Dic3D412yes—
90C22×C3×Dic3D412yes—
91C22×C3×Dic3D412yes—
92C22×C3×Dic3Q812yes—
93C22×C3×Dic3Q812yes—
94C22×C3×Dic3Q812yes—
95#3750—28no—
96C3×Dic3⋊C4—28no—
97Dic3⋊Dic3—28no—
98#1444—91noSylow
99C23×C3×C4—21no—
100C23×C3×C4—31no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4—31no—
104C23×C3×C4C2×D311yescharacteristic
105C23×C3×C4C2×D311yescharacteristic
106C23×Dic3—31no—
107C23×Dic3—31no—
108C23×Dic3—31no—
109C23×Dic3—31no—
110C23×Dic3—61no—
111C23×Dic3—61no—
112C23×Dic3C2×D311yescharacteristic
113C23×Dic3C2×D311yescharacteristic
114C23×Dic3C2×D311yescharacteristic
115C23×Dic3C2×D311yescharacteristic
116C2×C3×C4⋊C4—62no—
117C2×C3×C4⋊C4—62no—
118C2×C3×C4⋊C4—62no—
119C2×C4⋊Dic3—62no—
120C2×C4⋊Dic3—62no—
121C2×C4⋊Dic3—62no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—62no—
126C2×Dic3⋊C4—62no—
127C2×Dic3⋊C4—62no—
128C2×Dic3⋊C4—62no—
129C2×Dic3⋊C4—62no—
130C2×Dic3⋊C4—62no—
131C2×Dic3⋊C4—64no—
132C2×Dic3⋊C4—64no—
133C2×Dic3⋊C4—64no—
134C2×Dic3⋊C4—62no—
135C2×Dic3⋊C4—62no—
136C2×Dic3⋊C4—62no—
137C3×#95—62no—
138C3⋊#95—22no—
139C3⋊#95—34no—
140C3⋊#95—34no—
141C3⋊#95—62no—
142C3⋊#95—62no—
143C3⋊#95—62no—
144C3⋊#95—62no—
145C23×C32C22×C411yescharacteristic
146C23×C32C2×D411yescharacteristic
147C23×C32C2×D411yescharacteristic
148C23×C32C2×D411yescharacteristic
149C23×C32C2×D411yescharacteristic
150C23×C32C2×D411yescharacteristic
151C23×C32C2×D411yescharacteristic
152C23×C32C2×Q811yescharacteristic
153C23×C32C2×Q811yescharacteristic
154C23×C32C2×Q811yescharacteristic
155C23×C32C2×Q811yescharacteristic
156C23×C32#4111yescharacteristic
157C23×C32#4111yescharacteristic
158C23×C32#4111yescharacteristic
159C23×C32#4111yescharacteristic
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—41no—
164C2×C32×C4—41no—
165C2×C32×C4—41no—
166C2×C32×C4—41no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—41no—
177C2×C3⋊Dic3—41no—
178C2×C3⋊Dic3—41no—
179C2×C3⋊Dic3—41no—
180C2×C3⋊Dic3C4⋊C414yescomplemented
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—41no—
200C2×C3×Dic3—41no—
201C2×C3×Dic3—41no—
202C2×C3×Dic3—41no—
203C2×C3×Dic3—41no—
204C2×C3×Dic3—41no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3—41no—
207C2×C3×Dic3C4⋊C414yescomplemented
208C2×C3×Dic3C4⋊C414yescomplemented
209C22×C4⋊C4—31no—
210C22×C4⋊C4—91no—
211C22×C4⋊C4—91no—
212C2×#95—31no—
213C2×#95—91no—
214C2×#95—91no—
215C2×#95—91no—
216C24×C3—21no—
217C24×C3C22×D311yescharacteristic
218C24×C3C22×D311yescharacteristic
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—32no—
235C22×C3×C4—32no—
236C22×C3×C4—32no—
237C22×C3×C4—32no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—41no—
243C22×C3×C4—41no—
244C22×C3×C4—41no—
245C22×C3×C4—41no—
246C22×C3×C4—61no—
247C22×C3×C4—61no—
248C22×C3×C4—61no—
249C22×C3×C4—61no—
250C22×C3×C4—61no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4—61no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4—61no—
257C22×C3×C4—61no—
258C22×C3×C4—61no—
259C22×C3×C4—61no—
260C22×C3×C4—61no—
261C22×C3×C4—61no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4—61no—
265C22×C3×C4—61no—
266C22×C3×C4D1212yes—
267C22×C3×C4#6712yes—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—32no—
289C22×Dic3—32no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—32no—
293C22×Dic3—32no—
294C22×Dic3—32no—
295C22×Dic3—32no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—62no—
299C22×Dic3—62no—
300C22×Dic3—62no—
301C22×Dic3—62no—
302C22×Dic3—62no—
303C22×Dic3—62no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—62no—
313C22×Dic3—62no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—121no—
327C22×Dic3—121no—
328C22×Dic3—121no—
329C22×Dic3—121no—
330C22×Dic3Dic612yes—
331C22×Dic3Dic612yes—
332C22×Dic3Dic612yes—
333C22×Dic3C4×D312yes—
334C22×Dic3C4×D312yes—
335C22×Dic3#6712yes—
336C22×Dic3#6712yes—
337C22×Dic3#6712yes—
338C3×C4⋊C4—68no—
339C4⋊Dic3—68no—
340Dic3⋊C4—28no—
341Dic3⋊C4—68no—
342Dic3⋊C4—616no—
343Dic3⋊C4—68no—
344Dic3⋊C4—68no—
345C22×C32C2×C4⋊C411yescharacteristic
346C22×C32C2×C4⋊C411yescharacteristic
347C22×C32C2×C4⋊C411yescharacteristic
348C22×C32C4×D411yescharacteristic
349C22×C32C4×D411yescharacteristic
350C22×C32C4×D411yescharacteristic
351C22×C32C4×Q811yescharacteristic
352C22×C32#12011yescharacteristic
353C22×C32#12011yescharacteristic
354C22×C32#12011yescharacteristic
355C22×C32#12111yescharacteristic
356C22×C32#12111yescharacteristic
357C22×C32#12111yescharacteristic
358C22×C32C22⋊Q811yescharacteristic
359C22×C32C22⋊Q811yescharacteristic
360C22×C32C22⋊Q811yescharacteristic
361C22×C32C22⋊Q811yescharacteristic
362C22×C32C22⋊Q811yescharacteristic
363C22×C32C22⋊Q811yescharacteristic
364C22×C32C22⋊Q811yescharacteristic
365C22×C32C22⋊Q811yescharacteristic
366C22×C32C22⋊Q811yescharacteristic
367C22×C32#12311yescharacteristic
368C22×C32#12311yescharacteristic
369C22×C32#12311yescharacteristic
370C22×C32#12511yescharacteristic
371C22×C32#12511yescharacteristic
372C22×C32#12511yescharacteristic
373C22×C32#12711yescharacteristic
374C22×C32C4⋊Q811yescharacteristic
375C22×C32C4⋊Q811yescharacteristic
376C22×C32C4⋊Q811yescharacteristic
377C22×C32C4⋊Q811yescharacteristic
378C22×C32C4⋊Q811yescharacteristic
379C22×C32C4⋊Q811yescharacteristic
380C32×C4—42no—
381C3⋊Dic3—24no—
382C3⋊Dic3—42no—
383C3×Dic3—24no—
384C3×Dic3—24no—
385C3×Dic3—42no—
386C3×Dic3—42no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—91no—
392C23×C4—91no—
393C23×C4D3211yescharacteristic
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—182no—
398C2×C4⋊C4—182no—
399C2×C4⋊C4—182no—
400C2×C4⋊C4—182no—
401C2×C4⋊C4—182no—
402C2×C4⋊C4—182no—
403#95—62no—
404#95—94no—
405#95—182no—
406#95—182no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3C2×Dic611yescharacteristic
423C23×C3C2×Dic611yescharacteristic
424C23×C3C2×Dic611yescharacteristic
425C23×C3C2×C4×D311yescharacteristic
426C23×C3C2×C4×D311yescharacteristic
427C23×C3C2×D1211yescharacteristic
428C23×C3#23511yescharacteristic
429C23×C3#23511yescharacteristic
430C23×C3#23511yescharacteristic
431C23×C3#23511yescharacteristic
432C23×C3D3×D411yescharacteristic
433C23×C3D3×D411yescharacteristic
434C23×C3D3×D411yescharacteristic
435C23×C3D3×D411yescharacteristic
436C23×C3D3×D411yescharacteristic
437C23×C3D3×D411yescharacteristic
438C23×C3D3×D411yescharacteristic
439C23×C3#23711yescharacteristic
440C23×C3#23711yescharacteristic
441C23×C3#23711yescharacteristic
442C23×C3D3×Q811yescharacteristic
443C23×C3D3×Q811yescharacteristic
444C23×C3D3×Q811yescharacteristic
445C23×C3D3×Q811yescharacteristic
446C23×C3D3×Q811yescharacteristic
447C23×C3#23911yescharacteristic
448C23×C3C2×#6711yescharacteristic
449C23×C3C2×#6711yescharacteristic
450C23×C3C2×#6711yescharacteristic
451C23×C3C2×#6711yescharacteristic
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—34no—
460C2×C3×C4—34no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—62no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—62no—
493C2×C3×C4—121no—
494C2×C3×C4—121no—
495C2×C3×C4—121no—
496C2×C3×C4—121no—
497C2×C3×C4—121no—
498C2×C3×C4—121no—
499C2×C3×C4—121no—
500C2×C3×C4—121no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—34no—
520C2×Dic3—34no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—64no—
530C2×Dic3—64no—
531C2×Dic3—64no—
532C2×Dic3—64no—
533C2×Dic3—64no—
534C2×Dic3—64no—
535C2×Dic3—64no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—62no—
548C2×Dic3—64no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—122no—
556C2×Dic3—122no—
557C2×Dic3—122no—
558C2×Dic3—122no—
559C2×Dic3—122no—
560C2×Dic3—122no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3Dic3⋊C414yescomplemented
570C2×Dic3Dic3⋊C414yescomplemented
571C2×C32#38411yescharacteristic
572C2×C32#38511yescharacteristic
573C2×C32#38511yescharacteristic
574C2×C32#38511yescharacteristic
575C2×C32#38911yescharacteristic
576C2×C32#38911yescharacteristic
577C2×C32#38911yescharacteristic
578C2×C32#39211yescharacteristic
579C2×C32#39511yescharacteristic
580C2×C32#39511yescharacteristic
581C2×C32#39511yescharacteristic
582C2×C32#39811yescharacteristic
583C2×C32#39811yescharacteristic
584C2×C32#39811yescharacteristic
585C2×C32#39911yescharacteristic
586C24C2×D3211yescharacteristic
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—92no—
622C22×C4—92no—
623C22×C4—92no—
624C22×C4—92no—
625C22×C4—181no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4—181no—
630C22×C4—181no—
631C22×C4—181no—
632C22×C4—181no—
633C22×C4—181no—
634C22×C4—181no—
635C22×C4#62612yes—
636C4⋊C4—68no—
637C4⋊C4—188no—
638C4⋊C4—188no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3C4×Dic611yescharacteristic
675C22×C3#86911yescharacteristic
676C22×C3#87011yescharacteristic
677C22×C3C4×D1211yescharacteristic
678C22×C3#87811yescharacteristic
679C22×C3#87811yescharacteristic
680C22×C3#87811yescharacteristic
681C22×C3#87811yescharacteristic
682C22×C3#67⋊C411yescharacteristic
683C22×C3#67⋊C411yescharacteristic
684C22×C3#88211yescharacteristic
685C22×C3#88211yescharacteristic
686C22×C3#88311yescharacteristic
687C22×C3#88311yescharacteristic
688C22×C3#88411yescharacteristic
689C22×C3#88411yescharacteristic
690C22×C3#88711yescharacteristic
691C22×C3#88811yescharacteristic
692C22×C3#88811yescharacteristic
693C22×C3#88811yescharacteristic
694C22×C3#88811yescharacteristic
695C22×C3#88811yescharacteristic
696C22×C3#88811yescharacteristic
697C22×C3#88811yescharacteristic
698C22×C3#88911yescharacteristic
699C22×C3#88911yescharacteristic
700C22×C3#88911yescharacteristic
701C22×C3#88911yescharacteristic
702C22×C3#89011yescharacteristic
703C22×C3D3×C4⋊C411yescharacteristic
704C22×C3D3×C4⋊C411yescharacteristic
705C22×C3D3×C4⋊C411yescharacteristic
706C22×C3D3×C4⋊C411yescharacteristic
707C22×C3#89311yescharacteristic
708C22×C3#89411yescharacteristic
709C22×C3#89411yescharacteristic
710C22×C3#89611yescharacteristic
711C22×C3#89611yescharacteristic
712C22×C3#89611yescharacteristic
713C22×C3#89611yescharacteristic
714C22×C3#89611yescharacteristic
715C22×C3#89611yescharacteristic
716C22×C3#89711yescharacteristic
717C22×C3#89711yescharacteristic
718C22×C3C2×Dic3⋊C411yescharacteristic
719C22×C3C2×Dic3⋊C411yescharacteristic
720C22×C3#92411yescharacteristic
721C22×C3#92411yescharacteristic
722C22×C3#92411yescharacteristic
723C22×C3C4×#6711yescharacteristic
724C22×C3C4×#6711yescharacteristic
725C22×C3#92911yescharacteristic
726C22×C3#93011yescharacteristic
727C22×C3#93511yescharacteristic
728C22×C3#93711yescharacteristic
729C22×C3#93711yescharacteristic
730C22×C3#93711yescharacteristic
731C22×C3#93811yescharacteristic
732C22×C3#93911yescharacteristic
733C22×C3#93911yescharacteristic
734C22×C3#94011yescharacteristic
735C22×C3#94011yescharacteristic
736C22×C3#94411yescharacteristic
737C22×C3#94411yescharacteristic
738C22×C3#94411yescharacteristic
739C22×C3#94411yescharacteristic
740C22×C3#94611yescharacteristic
741C22×C3#94611yescharacteristic
742C22×C3#94611yescharacteristic
743C22×C3#95311yescharacteristic
744C3×C4—44no—
745C3×C4—42no—
746C3×C4—42no—
747C3×C4—64no—
748C3×C4—64no—
749C3×C4—122no—
750C3×C4—122no—
751Dic3—24no—
752Dic3—24no—
753Dic3—42no—
754Dic3—42no—
755Dic3—68no—
756Dic3—64no—
757Dic3—64no—
758Dic3—124no—
759Dic3—122no—
760Dic3—122no—
761C32#144411yescharacteristic, complemented, Sylow
762C23D3×Dic611yescharacteristic
763C23D3×Dic611yescharacteristic
764C23D3×Dic611yescharacteristic
765C23#379511yescharacteristic
766C23#379611yescharacteristic
767C23#379711yescharacteristic
768C23#379811yescharacteristic
769C23C4×D3211yescharacteristic
770C23#380411yescharacteristic
771C23C2×#62611yescharacteristic
772C23D3×#6711yescharacteristic
773C23D3×#6711yescharacteristic
774C23D3×#6711yescharacteristic
775C23#381111yescharacteristic
776C23#381111yescharacteristic
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—34no—
781C2×C4—34no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—94no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4—121no—
811C2×C4—121no—
812C2×C4—121no—
813C2×C4—182no—
814C2×C4—182no—
815C2×C4—182no—
816C2×C4—182no—
817C2×C4—182no—
818C2×C4—182no—
819C2×C4—182no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—361no—
823C2×C4—361no—
824C2×C4—361no—
825C2×C4—361no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3#464711yescharacteristic
842C2×C3#464711yescharacteristic
843C2×C3#465611yescharacteristic
844C2×C3#465611yescharacteristic
845C2×C3#465711yescharacteristic
846C2×C3#465711yescharacteristic
847C2×C3#466811yescharacteristic
848C2×C3#466811yescharacteristic
849C2×C3#492811yescharacteristic
850C2×C3#494611yescharacteristic
851C2×C3#494911yescharacteristic
852C2×C3#496011yescharacteristic
853C2×C3#497211yescharacteristic
854C2×C3#497511yescharacteristic
855C2×C3#497511yescharacteristic
856C2×C3#497611yescharacteristic
857C2×C3#497611yescharacteristic
858C2×C3#497911yescharacteristic
859C2×C3#497911yescharacteristic
860C2×C3#497911yescharacteristic
861C2×C3#498111yescharacteristic
862C2×C3#498211yescharacteristic
863C2×C3#498211yescharacteristic
864C2×C3#498311yescharacteristic
865C2×C3#498911yescharacteristic
866C2×C3#498911yescharacteristic
867C2×C3#499311yescharacteristic
868C2×C3#521011yescharacteristic
869C2×C3#522311yescharacteristic
870C2×C3#523011yescharacteristic
871C22#6383711yescharacteristic
872C22#6383911yescharacteristic
873C22#6383911yescharacteristic
874C22#6383911yescharacteristic
875C22#6384011yescharacteristic
876C22#6384011yescharacteristic
877C22#6384611yescharacteristic
878C22#6384711yescharacteristic
879C22#6385111yescharacteristic
880C22#6385111yescharacteristic
881C22#6385311yescharacteristic
882C22#6385711yescharacteristic
883C22#6386511yescharacteristic
884C22#6386611yescharacteristic
885C22#6386711yescharacteristic
886C22#6387111yescharacteristic
887C22D3×Dic3⋊C411yescharacteristic
888C22D3×Dic3⋊C411yescharacteristic
889C22#6387911yescharacteristic
890C22#6388111yescharacteristic
891C22#6388311yescharacteristic
892C22#6388411yescharacteristic
893C22#6388711yescharacteristic
894C22#6388711yescharacteristic
895C22#6389611yescharacteristic
896C22#6389611yescharacteristic
897C22C4×#62611yescharacteristic
898C22#6390511yescharacteristic
899C22#6395811yescharacteristic
900C22#6397111yescharacteristic
901C22#6397711yescharacteristic
902C22#6397811yescharacteristic
903C22#6397911yescharacteristic
904C22#6398111yescharacteristic
905C22#6398311yescharacteristic
906C4—42no—
907C4—64no—
908C4—64no—
909C4—122no—
910C4—122no—
911C4—184no—
912C4—362no—
913C3—21no—
914C3#6942011yescharacteristic, complemented
915C3#7156811yescharacteristic, complemented
916C2#1059119511yescharacteristic
917C2#1059119811yescharacteristic
918C2#1059123411yescharacteristic
919C2#1059124411yescharacteristic
920C2#1059125611yescharacteristic
921C2#1059127811yescharacteristic
922C2#1059129011yescharacteristic
923C2#1059130311yescharacteristic
924C2#1059133011yescharacteristic
925C2#1059134011yescharacteristic
926C2#1059134211yescharacteristic
927C2#1059134611yescharacteristic
928C2#1059135411yescharacteristic
929C2#1059137211yescharacteristic
930C2#1059172411yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
29. #63579C4semidirect
180. C2×C3⋊Dic3C4⋊C4semidirect
207. C2×C3×Dic3C4⋊C4semidirect
208. C2×C3×Dic3C4⋊C4semidirect
569. C2×Dic3Dic3⋊C4semidirect
570. C2×Dic3Dic3⋊C4semidirect
761. C32#1444semidirect
914. C3#69420semidirect
915. C3#71568semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C22×C3×Dic3⋊C42
C22×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#715683
#694203