Finite Group Databasebeta

← #11773402

Subgroups — #11773402

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C2×C3×C3⋊#95C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C211yesmaximal, characteristic
5C2×#63579C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#69414—31nomaximal
9#69413—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—
20C3×C3⋊#95—22no—
21C3×C3⋊#95—22no—
22#63579—22no—
23#63579—22no—
24#63579—22no—
25#63579C414yescomplemented
26C22×Dic3⋊C4—31no—
27C22×Dic3⋊C4—31no—
28C22×Dic3⋊C4—61no—
29C2×C3×#95—31no—
30C2×C3×#95—31no—
31C2×C3⋊#95—31no—
32C2×C3⋊#95—31no—
33C2×C3⋊#95—31no—
34C2×C3⋊#95—31no—
35C2×C3⋊#95—31no—
36C2×C3⋊#95—31no—
37C2×C3⋊#95—31no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95D311yescharacteristic
40C2×C3⋊#95D311yescharacteristic
41C24×C32C2311yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4D412yes—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—21no—
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⋊Dic3C2×C412yes—
60C22×C3⋊Dic3D412yes—
61C22×C3⋊Dic3D412yes—
62C22×C3⋊Dic3Q812yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
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×Dic3Q812yes—
91#3750—28no—
92#1442—91noSylow
93C23×C3×C4—21no—
94C23×C3×C4—31no—
95C23×C3×C4—31no—
96C23×C3×C4—31no—
97C23×C3×C4—31no—
98C23×C3×C4C2×D311yescharacteristic
99C23×C3×C4C2×D311yescharacteristic
100C23×Dic3—31no—
101C23×Dic3—31no—
102C23×Dic3—31no—
103C23×Dic3—31no—
104C23×Dic3—61no—
105C23×Dic3—61no—
106C23×Dic3C2×D311yescharacteristic
107C23×Dic3C2×D311yescharacteristic
108C23×Dic3C2×D311yescharacteristic
109C23×Dic3C2×D311yescharacteristic
110C2×Dic3⋊C4—62no—
111C2×Dic3⋊C4—62no—
112C2×Dic3⋊C4—62no—
113C2×Dic3⋊C4—62no—
114C2×Dic3⋊C4—64no—
115C2×Dic3⋊C4—64no—
116C2×Dic3⋊C4—64no—
117C2×Dic3⋊C4—62no—
118C2×Dic3⋊C4—62no—
119C3×#95—62no—
120C3×#95—62no—
121C3⋊#95—22no—
122C3⋊#95—22no—
123C3⋊#95—34no—
124C3⋊#95—34no—
125C3⋊#95—62no—
126C3⋊#95—62no—
127C3⋊#95—62no—
128C3⋊#95—62no—
129C3⋊#95—62no—
130C3⋊#95—62no—
131C23×C32C22×C411yescharacteristic
132C23×C32C2×D411yescharacteristic
133C23×C32C2×D411yescharacteristic
134C23×C32C2×D411yescharacteristic
135C23×C32C2×D411yescharacteristic
136C23×C32C2×Q811yescharacteristic
137C23×C32C2×Q811yescharacteristic
138C23×C32#4111yescharacteristic
139C23×C32#4111yescharacteristic
140C23×C32#4111yescharacteristic
141C23×C32#4111yescharacteristic
142C23×C32#4111yescharacteristic
143C23×C32#4111yescharacteristic
144C23×C32#4111yescharacteristic
145C23×C32#4111yescharacteristic
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—41no—
150C2×C32×C4—41no—
151C2×C32×C4—41no—
152C2×C32×C4—41no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3—41no—
164C2×C3⋊Dic3—41no—
165C2×C3⋊Dic3—41no—
166C2×C3⋊Dic3C4⋊C414yes—
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—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—41no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3—41no—
183C2×C3×Dic3—41no—
184C2×C3×Dic3—41no—
185C2×C3×Dic3—41no—
186C2×C3×Dic3—41no—
187C2×C3×Dic3—41no—
188C2×C3×Dic3—41no—
189C2×C3×Dic3—41no—
190C2×C3×Dic3—41no—
191C2×C3×Dic3—41no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3—41no—
195C22×C4⋊C4—91no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—91no—
199C2×#95—91no—
200C2×#95—91no—
201C2×#95—91no—
202C24×C3—21no—
203C24×C3C22×D311yescharacteristic
204C24×C3C22×D311yescharacteristic
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—41no—
225C22×C3×C4—41no—
226C22×C3×C4—41no—
227C22×C3×C4—41no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4—61no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4—61no—
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×C4D1212yes—
253C22×C3×C4#6712yes—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
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—32no—
279C22×Dic3—32no—
280C22×Dic3—32no—
281C22×Dic3—32no—
282C22×Dic3—32no—
283C22×Dic3—32no—
284C22×Dic3—32no—
285C22×Dic3—32no—
286C22×Dic3—62no—
287C22×Dic3—62no—
288C22×Dic3—62no—
289C22×Dic3—62no—
290C22×Dic3—62no—
291C22×Dic3—62no—
292C22×Dic3—62no—
293C22×Dic3—62no—
294C22×Dic3—61no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
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—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—121no—
317C22×Dic3—121no—
318C22×Dic3—121no—
319C22×Dic3—121no—
320C22×Dic3Dic612yes—
321C22×Dic3C4×D312yes—
322C22×Dic3C4×D312yes—
323C22×Dic3#6712yes—
324Dic3⋊C4—616no—
325Dic3⋊C4—68no—
326Dic3⋊C4—68no—
327C22×C32C2×C4⋊C411yescharacteristic
328C22×C32#11711yescharacteristic
329C22×C32#11711yescharacteristic
330C22×C32C4×D411yescharacteristic
331C22×C32C4×D411yescharacteristic
332C22×C32C4×D411yescharacteristic
333C22×C32C4×Q811yescharacteristic
334C22×C32#12011yescharacteristic
335C22×C32#12111yescharacteristic
336C22×C32#12111yescharacteristic
337C22×C32#12111yescharacteristic
338C22×C32C22⋊Q811yescharacteristic
339C22×C32C22⋊Q811yescharacteristic
340C22×C32C22⋊Q811yescharacteristic
341C22×C32C22⋊Q811yescharacteristic
342C22×C32C22⋊Q811yescharacteristic
343C22×C32#12311yescharacteristic
344C22×C32#12311yescharacteristic
345C22×C32#12311yescharacteristic
346C22×C32#12311yescharacteristic
347C22×C32#12311yescharacteristic
348C22×C32#12411yescharacteristic
349C22×C32#12411yescharacteristic
350C22×C32#12411yescharacteristic
351C22×C32#12411yescharacteristic
352C22×C32#12511yescharacteristic
353C22×C32#12511yescharacteristic
354C22×C32#12511yescharacteristic
355C22×C32#12511yescharacteristic
356C22×C32#12511yescharacteristic
357C22×C32#12611yescharacteristic
358C22×C32#12611yescharacteristic
359C22×C32#12611yescharacteristic
360C22×C32#12611yescharacteristic
361C22×C32C4⋊Q811yescharacteristic
362C32×C4—42no—
363C3⋊Dic3—24no—
364C3⋊Dic3—42no—
365C3×Dic3—42no—
366C3×Dic3—42no—
367C3×Dic3—42no—
368C3×Dic3—42no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—91no—
374C23×C4—91no—
375C23×C4D3211yescharacteristic
376C2×C4⋊C4—182no—
377C2×C4⋊C4—182no—
378C2×C4⋊C4—182no—
379#95—62no—
380#95—62no—
381#95—94no—
382#95—182no—
383#95—182no—
384#95—182no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3C2×Dic611yescharacteristic
401C23×C3C2×C4×D311yescharacteristic
402C23×C3C2×C4×D311yescharacteristic
403C23×C3C2×D1211yescharacteristic
404C23×C3#23511yescharacteristic
405C23×C3#23511yescharacteristic
406C23×C3#23511yescharacteristic
407C23×C3#23511yescharacteristic
408C23×C3#23511yescharacteristic
409C23×C3#23511yescharacteristic
410C23×C3#23511yescharacteristic
411C23×C3#23511yescharacteristic
412C23×C3D3×D411yescharacteristic
413C23×C3D3×D411yescharacteristic
414C23×C3D3×D411yescharacteristic
415C23×C3D3×D411yescharacteristic
416C23×C3D3×D411yescharacteristic
417C23×C3#23711yescharacteristic
418C23×C3#23711yescharacteristic
419C23×C3#23711yescharacteristic
420C23×C3#23711yescharacteristic
421C23×C3#23711yescharacteristic
422C23×C3#23711yescharacteristic
423C23×C3#23711yescharacteristic
424C23×C3D3×Q811yescharacteristic
425C23×C3D3×Q811yescharacteristic
426C23×C3D3×Q811yescharacteristic
427C23×C3#23911yescharacteristic
428C23×C3C2×#6711yescharacteristic
429C23×C3C2×#6711yescharacteristic
430C2×C3×C4—24no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—121no—
464C2×C3×C4—121no—
465C2×C3×C4—121no—
466C2×C3×C4—121no—
467C2×C3×C4—121no—
468C2×C3×C4—121no—
469C2×C3×C4—121no—
470C2×C3×C4—121no—
471C2×C3×C4—121no—
472C2×C3×C4—121no—
473C2×C3×C4—121no—
474C2×C3×C4—121no—
475C2×C3×C4—121no—
476C2×C3×C4—121no—
477C2×C3×C4—121no—
478C2×C3×C4—121no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—34no—
492C2×Dic3—34no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—64no—
510C2×Dic3—64no—
511C2×Dic3—64no—
512C2×Dic3—64no—
513C2×Dic3—64no—
514C2×Dic3—64no—
515C2×Dic3—64no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—64no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—122no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×C32#38211yescharacteristic
550C2×C32#38511yescharacteristic
551C2×C32#38711yescharacteristic
552C2×C32#38711yescharacteristic
553C2×C32#38811yescharacteristic
554C2×C32#38811yescharacteristic
555C2×C32#38911yescharacteristic
556C2×C32#39311yescharacteristic
557C2×C32#39411yescharacteristic
558C2×C32#39711yescharacteristic
559C2×C32#39811yescharacteristic
560C2×C32#39811yescharacteristic
561C2×C32#40011yescharacteristic
562C2×C32#40011yescharacteristic
563C2×C32#40011yescharacteristic
564C24C2×D3211yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—92no—
600C22×C4—92no—
601C22×C4—92no—
602C22×C4—92no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4#62612yes—
614C4⋊C4—188no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
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×C3C4×Dic611yescharacteristic
651C22×C3#87011yescharacteristic
652C22×C3#87211yescharacteristic
653C22×C3#87211yescharacteristic
654C22×C3C4×D1211yescharacteristic
655C22×C3#87511yescharacteristic
656C22×C3#87611yescharacteristic
657C22×C3#87611yescharacteristic
658C22×C3#87711yescharacteristic
659C22×C3#87711yescharacteristic
660C22×C3#87811yescharacteristic
661C22×C3#87811yescharacteristic
662C22×C3#87911yescharacteristic
663C22×C3#87911yescharacteristic
664C22×C3#87911yescharacteristic
665C22×C3#87911yescharacteristic
666C22×C3#67⋊C411yescharacteristic
667C22×C3#67⋊C411yescharacteristic
668C22×C3#88211yescharacteristic
669C22×C3#88311yescharacteristic
670C22×C3#88311yescharacteristic
671C22×C3#88311yescharacteristic
672C22×C3#88311yescharacteristic
673C22×C3#88411yescharacteristic
674C22×C3#88411yescharacteristic
675C22×C3#88511yescharacteristic
676C22×C3#88511yescharacteristic
677C22×C3#88511yescharacteristic
678C22×C3#88511yescharacteristic
679C22×C3#88511yescharacteristic
680C22×C3#88511yescharacteristic
681C22×C3#88611yescharacteristic
682C22×C3#88711yescharacteristic
683C22×C3#88811yescharacteristic
684C22×C3#88911yescharacteristic
685C22×C3#88911yescharacteristic
686C22×C3#88911yescharacteristic
687C22×C3#88911yescharacteristic
688C22×C3#88911yescharacteristic
689C22×C3#88911yescharacteristic
690C22×C3#88911yescharacteristic
691C22×C3#88911yescharacteristic
692C22×C3#89011yescharacteristic
693C22×C3D3×C4⋊C411yescharacteristic
694C22×C3D3×C4⋊C411yescharacteristic
695C22×C3#89311yescharacteristic
696C22×C3#89411yescharacteristic
697C22×C3#89411yescharacteristic
698C22×C3#89611yescharacteristic
699C22×C3#89611yescharacteristic
700C22×C3#89611yescharacteristic
701C22×C3#89611yescharacteristic
702C22×C3#89711yescharacteristic
703C22×C3#89711yescharacteristic
704C22×C3#89811yescharacteristic
705C22×C3#89811yescharacteristic
706C22×C3#92411yescharacteristic
707C22×C3C4×#6711yescharacteristic
708C22×C3C4×#6711yescharacteristic
709C22×C3#92911yescharacteristic
710C22×C3#92911yescharacteristic
711C22×C3#93011yescharacteristic
712C22×C3#93511yescharacteristic
713C22×C3#93611yescharacteristic
714C22×C3#93711yescharacteristic
715C22×C3#93811yescharacteristic
716C22×C3#93911yescharacteristic
717C22×C3#93911yescharacteristic
718C22×C3#94411yescharacteristic
719C22×C3#94611yescharacteristic
720C3×C4—44no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—122no—
724C3×C4—122no—
725C3×C4—122no—
726C3×C4—122no—
727Dic3—42no—
728Dic3—42no—
729Dic3—42no—
730Dic3—42no—
731Dic3—68no—
732Dic3—64no—
733Dic3—64no—
734Dic3—124no—
735Dic3—122no—
736Dic3—122no—
737C32#144211yescharacteristic, complemented, Sylow
738C23D3×Dic611yescharacteristic
739C23#379511yescharacteristic
740C23#379511yescharacteristic
741C23#379511yescharacteristic
742C23#379611yescharacteristic
743C23#379711yescharacteristic
744C23#379811yescharacteristic
745C23C4×D3211yescharacteristic
746C23#380411yescharacteristic
747C23#380411yescharacteristic
748C23#380411yescharacteristic
749C23C2×#62611yescharacteristic
750C23D3×#6711yescharacteristic
751C23#381111yescharacteristic
752C23#381111yescharacteristic
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—94no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—182no—
790C2×C4—182no—
791C2×C4—182no—
792C2×C4—182no—
793C2×C4—182no—
794C2×C4—182no—
795C2×C4—182no—
796C2×C4—182no—
797C2×C4—182no—
798C2×C4—361no—
799C2×C4—361no—
800C2×C4—361no—
801C2×C4—361no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3#464711yescharacteristic
818C2×C3#465011yescharacteristic
819C2×C3#465011yescharacteristic
820C2×C3#465211yescharacteristic
821C2×C3#465311yescharacteristic
822C2×C3#465411yescharacteristic
823C2×C3#465711yescharacteristic
824C2×C3#465811yescharacteristic
825C2×C3#465811yescharacteristic
826C2×C3#465811yescharacteristic
827C2×C3#465911yescharacteristic
828C2×C3#466011yescharacteristic
829C2×C3#466811yescharacteristic
830C2×C3#466911yescharacteristic
831C2×C3#467311yescharacteristic
832C2×C3#467511yescharacteristic
833C2×C3#493311yescharacteristic
834C2×C3#494011yescharacteristic
835C2×C3#494411yescharacteristic
836C2×C3#494511yescharacteristic
837C2×C3#494711yescharacteristic
838C2×C3#495211yescharacteristic
839C2×C3#495911yescharacteristic
840C2×C3#496111yescharacteristic
841C2×C3#497611yescharacteristic
842C2×C3#498111yescharacteristic
843C2×C3#498211yescharacteristic
844C2×C3#498311yescharacteristic
845C2×C3#498511yescharacteristic
846C2×C3#498911yescharacteristic
847C22#6383711yescharacteristic
848C22#6383911yescharacteristic
849C22#6384611yescharacteristic
850C22#6384711yescharacteristic
851C22#6384711yescharacteristic
852C22#6384711yescharacteristic
853C22#6385311yescharacteristic
854C22#6385711yescharacteristic
855C22#6385811yescharacteristic
856C22#6385811yescharacteristic
857C22#6385911yescharacteristic
858C22#6385911yescharacteristic
859C22#6386011yescharacteristic
860C22#6386511yescharacteristic
861C22#6386711yescharacteristic
862C22#6387111yescharacteristic
863C22#6387711yescharacteristic
864C22#6387711yescharacteristic
865C22#6387911yescharacteristic
866C22#6388111yescharacteristic
867C22#6388311yescharacteristic
868C22#6388411yescharacteristic
869C22#6389611yescharacteristic
870C22#6389611yescharacteristic
871C22C4×#62611yescharacteristic
872C22#6390511yescharacteristic
873C22#6391311yescharacteristic
874C22#6391311yescharacteristic
875C22#6395311yescharacteristic
876C22#6395811yescharacteristic
877C22#6396611yescharacteristic
878C22#6397111yescharacteristic
879C22#6397511yescharacteristic
880C22#6397811yescharacteristic
881C22#6398111yescharacteristic
882C4—42no—
883C4—122no—
884C4—122no—
885C4—122no—
886C4—122no—
887C4—184no—
888C4—362no—
889C3—21no—
890C3#6941311yescharacteristic, complemented
891C3#6941411yescharacteristic, complemented
892C2#1059119811yescharacteristic
893C2#1059121011yescharacteristic
894C2#1059121711yescharacteristic
895C2#1059122711yescharacteristic
896C2#1059124711yescharacteristic
897C2#1059125111yescharacteristic
898C2#1059125611yescharacteristic
899C2#1059128011yescharacteristic
900C2#1059128111yescharacteristic
901C2#1059129011yescharacteristic
902C2#1059129811yescharacteristic
903C2#1059132211yescharacteristic
904C2#1059133211yescharacteristic
905C2#1059134211yescharacteristic
906C2#1059171211yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1442
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
25. #63579C4semidirect
737. C32#1442semidirect
890. C3#69413semidirect
891. C3#69414semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×C3⋊#952
C2×#635792
#694143
#694133