Finite Group Databasebeta

← #11773312

Subgroups — #11773312

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3757C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic
3C22×C3×#217C211yesmaximal, characteristic
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63579C211yesmaximal, characteristic, complemented
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#71547—31nomaximal
9#71546—31nomaximal
10C25×C32C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3757—22no—
18C2×#3757—22no—
19C2×#3757—22no—
20C2×C3×#217—22no—
21C2×C3×#217—22no—
22C2×C3×#217—22no—
23C2×C3×#217—22no—
24C2×C3×#217—22no—
25C2×C3×#217C414yescomplemented
26C2×Dic3⋊Dic3—22no—
27C2×Dic3⋊Dic3—22no—
28C2×Dic3⋊Dic3—22no—
29#63579—22no—
30#63579—22no—
31#63579—22no—
32C22×C3×C22⋊C4—31no—
33C22×C3×C22⋊C4—31no—
34C22×#217—31no—
35C22×#217—31no—
36C22×#217—61no—
37C22×#217D311yescharacteristic
38C22×#217D311yescharacteristic
39C22×C4⋊Dic3—31no—
40C22×Dic3⋊C4—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—31no—
46C2×C3⋊#95—31no—
47C24×C32—21no—
48C24×C32—21no—
49C24×C32—21no—
50C24×C32—21no—
51C24×C32—21no—
52C24×C32—21no—
53C24×C32—21no—
54C24×C32—21no—
55C24×C32—21no—
56C24×C32—21no—
57C24×C32—21no—
58C24×C32—21no—
59C24×C32C2×C412yes—
60C24×C32D412yes—
61C24×C32Q812yes—
62C24×C32C2311yescharacteristic
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⋊Dic3D412yes—
76C22×C3⋊Dic3D412yes—
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×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3C2×C412yes—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103C22×C3×Dic3D412yes—
104C22×C3×Dic3D412yes—
105#3757—28no—
106C3×#217—28no—
107C3×#217—28no—
108Dic3⋊Dic3—28no—
109#1439—91noSylow
110C25×C3—21no—
111C25×C3C2×D311yescharacteristic
112C25×C3C2×D311yescharacteristic
113C23×C3×C4—31no—
114C23×C3×C4—31no—
115C23×C3×C4—31no—
116C23×C3×C4—31no—
117C23×Dic3—31no—
118C23×Dic3—31no—
119C23×Dic3—31no—
120C23×Dic3—31no—
121C23×Dic3—61no—
122C23×Dic3—61no—
123C23×Dic3C2×D311yescharacteristic
124C23×Dic3C2×D311yescharacteristic
125C23×Dic3C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C2×C3×C22⋊C4—34no—
128C2×C3×C22⋊C4—62no—
129C2×C3×C22⋊C4—62no—
130C2×C3×C22⋊C4—62no—
131C2×C3×C22⋊C4—62no—
132C2×C3×C22⋊C4—62no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—62no—
139C2×#217—62no—
140C2×#217—62no—
141C2×#217—62no—
142C2×#217—64no—
143C2×#217—64no—
144C2×#217—64no—
145C2×#217—62no—
146C2×#217—62no—
147C2×#217Dic314yescomplemented
148C2×C4⋊Dic3—62no—
149C2×C4⋊Dic3—62no—
150C2×C4⋊Dic3—62no—
151C2×Dic3⋊C4—62no—
152C2×Dic3⋊C4—62no—
153C2×Dic3⋊C4—62no—
154C3⋊#95—62no—
155C3⋊#95—62no—
156C3⋊#95—62no—
157C3⋊#95—62no—
158C3⋊#95—62no—
159C3⋊#95—62no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32—22no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—41no—
179C23×C32—41no—
180C23×C32—41no—
181C23×C32—41no—
182C23×C32—41no—
183C23×C32—41no—
184C23×C32—41no—
185C23×C32—41no—
186C23×C32—41no—
187C23×C32—41no—
188C23×C32—41no—
189C23×C32—41no—
190C23×C32—41no—
191C23×C32—41no—
192C23×C32—41no—
193C23×C32—41no—
194C23×C32C4⋊C414yescomplemented
195C23×C32C22×C411yescharacteristic
196C23×C32C2×D411yescharacteristic
197C23×C32C2×D411yescharacteristic
198C23×C32C2×D411yescharacteristic
199C23×C32C2×D411yescharacteristic
200C23×C32C2×D411yescharacteristic
201C23×C32C2×D411yescharacteristic
202C23×C32C2×D411yescharacteristic
203C23×C32C2×Q811yescharacteristic
204C23×C32#4111yescharacteristic
205C23×C32#4111yescharacteristic
206C23×C32#4111yescharacteristic
207C23×C32#4111yescharacteristic
208C23×C32#4111yescharacteristic
209C23×C32#4111yescharacteristic
210C2×C3⋊Dic3—22no—
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3—22no—
213C2×C3⋊Dic3—22no—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—41no—
217C2×C3⋊Dic3—41no—
218C2×C3⋊Dic3—41no—
219C2×C3⋊Dic3—41no—
220C2×C3⋊Dic3—41no—
221C2×C3⋊Dic3—41no—
222C2×C3⋊Dic3—41no—
223C2×C3⋊Dic3—41no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—41no—
240C2×C3×Dic3—41no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C2×C3×Dic3—41no—
244C2×C3×Dic3—41no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—41no—
248C2×C3×Dic3—41no—
249C2×C3×Dic3—41no—
250C2×C3×Dic3—41no—
251C2×C3×Dic3C22⋊C414yescomplemented
252C22×C4⋊C4—91no—
253C22×C22⋊C4—31no—
254C22×C22⋊C4—31no—
255C22×C22⋊C4—91no—
256C2×#95—91no—
257C2×#95—91no—
258C2×#95—91no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—22no—
262C24×C3—22no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3—21no—
268C24×C3—21no—
269C24×C3—21no—
270C24×C3—21no—
271C24×C3—21no—
272C24×C3—21no—
273C24×C3—21no—
274C24×C3—21no—
275C24×C3—21no—
276C24×C3—21no—
277C24×C3—21no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3—21no—
281C24×C3—21no—
282C24×C3—21no—
283C24×C3—21no—
284C24×C3—21no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3—22no—
288C24×C3—22no—
289C24×C3—22no—
290C24×C3—21no—
291C24×C3—41no—
292C24×C3—41no—
293C24×C3—41no—
294C24×C3—41no—
295C24×C3—41no—
296C24×C3—41no—
297C24×C3—41no—
298C24×C3—41no—
299C24×C3Dic612yes—
300C24×C3Dic612yes—
301C24×C3C4×D312yes—
302C24×C3D1212yes—
303C24×C3C2×Dic312yes—
304C24×C3#6712yes—
305C24×C3C22×D311yescharacteristic
306C24×C3C22×D311yescharacteristic
307C22×C3×C4—32no—
308C22×C3×C4—32no—
309C22×C3×C4—32no—
310C22×C3×C4—32no—
311C22×C3×C4—32no—
312C22×C3×C4—32no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—32no—
358C22×Dic3—32no—
359C22×Dic3—32no—
360C22×Dic3—32no—
361C22×Dic3—62no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—121no—
392C22×Dic3—121no—
393C22×Dic3—121no—
394C22×Dic3—121no—
395C22×Dic3—121no—
396C22×Dic3—121no—
397C22×Dic3—121no—
398C22×Dic3—121no—
399C22×Dic3C2×Dic312yes—
400C22×Dic3C2×Dic312yes—
401C22×Dic3#6712yes—
402C22×Dic3#6712yes—
403C22×Dic3#6712yes—
404C22×Dic3#6712yes—
405C3×C22⋊C4—68no—
406C3×C22⋊C4—68no—
407#217—28no—
408#217—28no—
409#217—616no—
410#217—68no—
411#217—68no—
412C4⋊Dic3—68no—
413Dic3⋊C4—68no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—42no—
418C22×C32—42no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32—42no—
426C22×C32—42no—
427C22×C32—42no—
428C22×C32—42no—
429C22×C32C2×C22⋊C411yescharacteristic
430C22×C32C2×C4⋊C411yescharacteristic
431C22×C32#11711yescharacteristic
432C22×C32C4×D411yescharacteristic
433C22×C32C4×D411yescharacteristic
434C22×C32C4×D411yescharacteristic
435C22×C32C4×D411yescharacteristic
436C22×C32#12011yescharacteristic
437C22×C32#12011yescharacteristic
438C22×C32#12011yescharacteristic
439C22×C32#12111yescharacteristic
440C22×C32#12111yescharacteristic
441C22×C32#12111yescharacteristic
442C22×C32#12111yescharacteristic
443C22×C32#12111yescharacteristic
444C22×C32#12111yescharacteristic
445C22×C32#12111yescharacteristic
446C22×C32#12111yescharacteristic
447C22×C32C22⋊Q811yescharacteristic
448C22×C32C22⋊Q811yescharacteristic
449C22×C32C22⋊Q811yescharacteristic
450C22×C32C22⋊Q811yescharacteristic
451C22×C32C22⋊Q811yescharacteristic
452C22×C32C22⋊Q811yescharacteristic
453C22×C32#12311yescharacteristic
454C22×C32#12311yescharacteristic
455C22×C32#12311yescharacteristic
456C22×C32#12311yescharacteristic
457C22×C32#12311yescharacteristic
458C22×C32#12411yescharacteristic
459C22×C32#12411yescharacteristic
460C22×C32#12411yescharacteristic
461C22×C32#12611yescharacteristic
462C22×C32#12611yescharacteristic
463C22×C32#12711yescharacteristic
464C3⋊Dic3—42no—
465C3⋊Dic3—42no—
466C3×Dic3—24no—
467C3×Dic3—42no—
468C3×Dic3—42no—
469C3×Dic3—42no—
470C25D3211yescharacteristic
471C23×C4—31no—
472C23×C4—31no—
473C23×C4—31no—
474C23×C4—31no—
475C23×C4—91no—
476C23×C4—91no—
477C2×C4⋊C4—182no—
478C2×C4⋊C4—182no—
479C2×C4⋊C4—182no—
480C2×C22⋊C4—34no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—182no—
487C2×C22⋊C4—182no—
488C2×C22⋊C4—182no—
489#95—182no—
490#95—182no—
491#95—182no—
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—24no—
495C23×C3—24no—
496C23×C3—24no—
497C23×C3—24no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—24no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—42no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3—42no—
558C23×C3—42no—
559C23×C3—42no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—42no—
566C23×C3—42no—
567C23×C3—42no—
568C23×C3—42no—
569C23×C3—42no—
570C23×C3—42no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3Dic3⋊C414yescomplemented
611C23×C3C4⋊Dic314yescomplemented
612C23×C3C2×Dic611yescharacteristic
613C23×C3C2×Dic611yescharacteristic
614C23×C3C2×C4×D311yescharacteristic
615C23×C3C2×D1211yescharacteristic
616C23×C3#23511yescharacteristic
617C23×C3#23511yescharacteristic
618C23×C3#23511yescharacteristic
619C23×C3#23511yescharacteristic
620C23×C3D3×D411yescharacteristic
621C23×C3D3×D411yescharacteristic
622C23×C3D3×D411yescharacteristic
623C23×C3D3×D411yescharacteristic
624C23×C3D3×D411yescharacteristic
625C23×C3D3×D411yescharacteristic
626C23×C3D3×D411yescharacteristic
627C23×C3D3×D411yescharacteristic
628C23×C3#23711yescharacteristic
629C23×C3#23711yescharacteristic
630C23×C3#23711yescharacteristic
631C23×C3#23711yescharacteristic
632C23×C3#23711yescharacteristic
633C23×C3#23711yescharacteristic
634C23×C3#23711yescharacteristic
635C23×C3#23711yescharacteristic
636C23×C3C22×Dic311yescharacteristic
637C23×C3C2×#6711yescharacteristic
638C23×C3C2×#6711yescharacteristic
639C23×C3C2×#6711yescharacteristic
640C23×C3C2×#6711yescharacteristic
641C23×C3C2×#6711yescharacteristic
642C2×C3×C4—34no—
643C2×C3×C4—62no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—62no—
647C2×C3×C4—62no—
648C2×C3×C4—62no—
649C2×C3×C4—62no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—121no—
659C2×C3×C4—121no—
660C2×C3×C4—121no—
661C2×C3×C4—121no—
662C2×C3×C4—121no—
663C2×C3×C4—121no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4—121no—
669C2×C3×C4—121no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—41no—
686C2×Dic3—41no—
687C2×Dic3—41no—
688C2×Dic3—41no—
689C2×Dic3—41no—
690C2×Dic3—41no—
691C2×Dic3—41no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—64no—
698C2×Dic3—64no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—62no—
708C2×Dic3—62no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—122no—
712C2×Dic3—122no—
713C2×Dic3—122no—
714C2×Dic3—122no—
715C2×Dic3—122no—
716C2×Dic3—122no—
717C2×Dic3—122no—
718C2×Dic3—122no—
719C2×Dic3—122no—
720C2×Dic3—122no—
721C2×Dic3—122no—
722C2×Dic3—122no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×Dic3—121no—
730C2×Dic3—121no—
731C2×Dic3—121no—
732C2×Dic3—121no—
733C2×Dic3—121no—
734C2×Dic3—121no—
735C2×Dic3—121no—
736C2×Dic3—121no—
737C2×Dic3—121no—
738C2×Dic3—121no—
739C2×Dic3#21714yescomplemented
740C2×C32—44no—
741C2×C32#38011yescharacteristic
742C2×C32#38511yescharacteristic
743C2×C32#38511yescharacteristic
744C2×C32#38611yescharacteristic
745C2×C32#38811yescharacteristic
746C2×C32#38811yescharacteristic
747C2×C32#39011yescharacteristic
748C2×C32#39211yescharacteristic
749C2×C32#39311yescharacteristic
750C2×C32#39411yescharacteristic
751C2×C32#39411yescharacteristic
752C2×C32#39611yescharacteristic
753C2×C32#39611yescharacteristic
754C2×C32#39711yescharacteristic
755C2×C32#39911yescharacteristic
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24D3×Dic312yes—
769C24#62612yes—
770C24#62712yes—
771C24C2×D3211yescharacteristic
772C22×C4—32no—
773C22×C4—32no—
774C22×C4—32no—
775C22×C4—32no—
776C22×C4—32no—
777C22×C4—32no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—92no—
801C22×C4—92no—
802C22×C4—181no—
803C22×C4—181no—
804C22×C4—181no—
805C22×C4—181no—
806C22×C4—181no—
807C22×C4—181no—
808C22×C4—181no—
809C22×C4—181no—
810C22×C4—181no—
811C22×C4—181no—
812C22×C4—181no—
813C22×C4—181no—
814C4⋊C4—188no—
815C22⋊C4—68no—
816C22⋊C4—68no—
817C22⋊C4—188no—
818C22×C3—28no—
819C22×C3—24no—
820C22×C3—24no—
821C22×C3—24no—
822C22×C3—24no—
823C22×C3—24no—
824C22×C3—24no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—44no—
861C22×C3—44no—
862C22×C3—44no—
863C22×C3—44no—
864C22×C3—44no—
865C22×C3—44no—
866C22×C3—44no—
867C22×C3—44no—
868C22×C3—44no—
869C22×C3—44no—
870C22×C3—44no—
871C22×C3—44no—
872C22×C3—44no—
873C22×C3—44no—
874C22×C3—42no—
875C22×C3—42no—
876C22×C3—42no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—42no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—42no—
889C22×C3—42no—
890C22×C3—42no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3#87711yescharacteristic
899C22×C3#87811yescharacteristic
900C22×C3#87811yescharacteristic
901C22×C3#87811yescharacteristic
902C22×C3#87811yescharacteristic
903C22×C3#87811yescharacteristic
904C22×C3#87811yescharacteristic
905C22×C3#87811yescharacteristic
906C22×C3#87811yescharacteristic
907C22×C3#87911yescharacteristic
908C22×C3#87911yescharacteristic
909C22×C3#87911yescharacteristic
910C22×C3#87911yescharacteristic
911C22×C3D3×C22⋊C411yescharacteristic
912C22×C3#67⋊C411yescharacteristic
913C22×C3#67⋊C411yescharacteristic
914C22×C3#88211yescharacteristic
915C22×C3#88211yescharacteristic
916C22×C3#88311yescharacteristic
917C22×C3#88311yescharacteristic
918C22×C3#88311yescharacteristic
919C22×C3#88311yescharacteristic
920C22×C3#88411yescharacteristic
921C22×C3#88411yescharacteristic
922C22×C3#88411yescharacteristic
923C22×C3#88411yescharacteristic
924C22×C3#88511yescharacteristic
925C22×C3#88511yescharacteristic
926C22×C3#88511yescharacteristic
927C22×C3#88511yescharacteristic
928C22×C3#88611yescharacteristic
929C22×C3#88611yescharacteristic
930C22×C3C2×Dic3⋊C411yescharacteristic
931C22×C3#92411yescharacteristic
932C22×C3#92411yescharacteristic
933C22×C3#92411yescharacteristic
934C22×C3#92411yescharacteristic
935C22×C3C2×C4⋊Dic311yescharacteristic
936C22×C3#92611yescharacteristic
937C22×C3C4×#6711yescharacteristic
938C22×C3C4×#6711yescharacteristic
939C22×C3#92911yescharacteristic
940C22×C3#93011yescharacteristic
941C22×C3#93011yescharacteristic
942C22×C3D4×Dic311yescharacteristic
943C22×C3D4×Dic311yescharacteristic
944C22×C3D4×Dic311yescharacteristic
945C22×C3D4×Dic311yescharacteristic
946C22×C3#93511yescharacteristic
947C22×C3#93511yescharacteristic
948C22×C3#93511yescharacteristic
949C22×C3#93611yescharacteristic
950C22×C3#93611yescharacteristic
951C22×C3#93711yescharacteristic
952C22×C3#93711yescharacteristic
953C22×C3#93711yescharacteristic
954C22×C3#93811yescharacteristic
955C22×C3#93811yescharacteristic
956C22×C3#93811yescharacteristic
957C22×C3#93811yescharacteristic
958C22×C3#93911yescharacteristic
959C22×C3#93911yescharacteristic
960C22×C3#93911yescharacteristic
961C22×C3#93911yescharacteristic
962C22×C3#93911yescharacteristic
963C22×C3#93911yescharacteristic
964C22×C3#94011yescharacteristic
965C22×C3#94011yescharacteristic
966C22×C3C2×#21711yescharacteristic
967C22×C3#95311yescharacteristic
968C3×C4—64no—
969C3×C4—122no—
970C3×C4—122no—
971C3×C4—122no—
972Dic3—24no—
973Dic3—42no—
974Dic3—42no—
975Dic3—42no—
976Dic3—124no—
977Dic3—124no—
978Dic3—122no—
979Dic3—122no—
980Dic3—122no—
981Dic3—122no—
982C32#143911yescharacteristic, complemented, Sylow
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23Dic3⋊Dic314yescomplemented
1018C23C2×D3×Dic311yescharacteristic
1019C23#380411yescharacteristic
1020C23#380411yescharacteristic
1021C23#380411yescharacteristic
1022C23#380411yescharacteristic
1023C23#380511yescharacteristic
1024C23#380511yescharacteristic
1025C23C2×#62611yescharacteristic
1026C23C2×#62711yescharacteristic
1027C23D3×#6711yescharacteristic
1028C23D3×#6711yescharacteristic
1029C23D3×#6711yescharacteristic
1030C23D3×#6711yescharacteristic
1031C23#381111yescharacteristic
1032C23#381111yescharacteristic
1033C2×C4—34no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—182no—
1062C2×C4—182no—
1063C2×C4—182no—
1064C2×C4—182no—
1065C2×C4—182no—
1066C2×C4—182no—
1067C2×C4—361no—
1068C2×C4—361no—
1069C2×C4—361no—
1070C2×C4—361no—
1071C2×C4—361no—
1072C2×C4—361no—
1073C2×C4—361no—
1074C2×C4—361no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—21no—
1090C2×C3—48no—
1091C2×C3—44no—
1092C2×C3—44no—
1093C2×C3#494211yescharacteristic
1094C2×C3#494411yescharacteristic
1095C2×C3#494511yescharacteristic
1096C2×C3#494611yescharacteristic
1097C2×C3#494711yescharacteristic
1098C2×C3#494711yescharacteristic
1099C2×C3#494811yescharacteristic
1100C2×C3#494811yescharacteristic
1101C2×C3#494811yescharacteristic
1102C2×C3#494811yescharacteristic
1103C2×C3#494911yescharacteristic
1104C2×C3#494911yescharacteristic
1105C2×C3#495011yescharacteristic
1106C2×C3#495011yescharacteristic
1107C2×C3#495111yescharacteristic
1108C2×C3#495111yescharacteristic
1109C2×C3#495211yescharacteristic
1110C2×C3#495311yescharacteristic
1111C2×C3#495611yescharacteristic
1112C2×C3#495711yescharacteristic
1113C2×C3#495911yescharacteristic
1114C2×C3#496011yescharacteristic
1115C2×C3#496111yescharacteristic
1116C2×C3#496111yescharacteristic
1117C2×C3#521011yescharacteristic
1118C2×C3#521211yescharacteristic
1119C2×C3#522011yescharacteristic
1120C2×C3#522111yescharacteristic
1121C2×C3#522211yescharacteristic
1122C2×C3#522311yescharacteristic
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22#6395311yescharacteristic
1139C22#6395511yescharacteristic
1140C22#6395611yescharacteristic
1141C22#6395611yescharacteristic
1142C22#6395811yescharacteristic
1143C22#6395811yescharacteristic
1144C22#6395911yescharacteristic
1145C22#6395911yescharacteristic
1146C22#6396211yescharacteristic
1147C22#6396411yescharacteristic
1148C22#6396411yescharacteristic
1149C22#6396411yescharacteristic
1150C22#6396411yescharacteristic
1151C22C2×Dic3⋊Dic311yescharacteristic
1152C22#6396611yescharacteristic
1153C22D3×#21711yescharacteristic
1154C22#6396911yescharacteristic
1155C22#6396911yescharacteristic
1156C22#6397011yescharacteristic
1157C22#6397011yescharacteristic
1158C22#6397111yescharacteristic
1159C22#6397111yescharacteristic
1160C22Dic3×#6711yescharacteristic
1161C22Dic3×#6711yescharacteristic
1162C22#67⋊Dic311yescharacteristic
1163C22#67⋊Dic311yescharacteristic
1164C22#6397511yescharacteristic
1165C22#6397711yescharacteristic
1166C22#6397811yescharacteristic
1167C22#6397811yescharacteristic
1168C22#6397911yescharacteristic
1169C22#6398111yescharacteristic
1170C22#6398211yescharacteristic
1171C22#6398211yescharacteristic
1172C22#6398311yescharacteristic
1173C4—64no—
1174C4—122no—
1175C4—122no—
1176C4—122no—
1177C4—362no—
1178C4—362no—
1179C3—21no—
1180C3#7154611yescharacteristic, complemented
1181C3#7154711yescharacteristic, complemented
1182C2—44no—
1183C2#1059169111yescharacteristic
1184C2#1059169111yescharacteristic
1185C2#1059169211yescharacteristic
1186C2#1059170111yescharacteristic
1187C2#1059170211yescharacteristic
1188C2#1059170711yescharacteristic
1189C2#1059170911yescharacteristic
1190C2#1059171211yescharacteristic
1191C2#1059171511yescharacteristic
1192C2#1059171611yescharacteristic
1193C2#1059171711yescharacteristic
1194C2#1059171811yescharacteristic
1195C2#1059171911yescharacteristic
1196C2#1059172111yescharacteristic
1197C2#1059172411yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
Fitting, prime radicalC25×C32C22
socle, cosocleC24×C32C23
hypercenterC25D32
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊Dic3C2semidirect
5. C2×#63579C2semidirect
6. C2×#63579C2semidirect
7. C2×#63579C2semidirect
25. C2×C3×#217C4semidirect
147. C2×#217Dic3semidirect
194. C23×C32C4⋊C4semidirect
251. C2×C3×Dic3C22⋊C4semidirect
610. C23×C3Dic3⋊C4semidirect
611. C23×C3C4⋊Dic3semidirect
739. C2×Dic3#217semidirect
982. C32#1439semidirect
1017. C23Dic3⋊Dic3semidirect
1180. C3#71546semidirect
1181. C3#71547semidirect

Maximal subgroups

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

subgroupindex
C22×#37572
C22×C3×#2172
C22×Dic3⋊Dic32
C2×#635792
#715473
#715463