Finite Group Databasebeta

← #10723607

Subgroups — #10723607

Order 768.

1390 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#387C211yesmaximal, characteristic
2C2×#4984C211yesmaximal, characteristic
3C2×#4972C211yesmaximal, characteristic
4C2×#4980C211yesmaximal, characteristic
5C2×#4928C211yesmaximal, characteristic
6#71568C211yesmaximal, characteristic
7#71536C211yesmaximal, characteristic
8#69420C211yesmaximal, characteristic
9#69411C211yesmaximal, characteristic
10#69411C211yesmaximal, characteristic
11#69411C211yesmaximal, characteristic
12#69411C211yesmaximal, characteristic
13#69406C211yesmaximal, characteristic
14Dic3⋊#95C211yesmaximal, characteristic
15Dic3⋊#95C211yesmaximal, characteristic
16#14441—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C3×#387—24no—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53#4984C418yescomplemented
54#4980—24no—
55#4972—24no—
56#4928—24no—
57C2×#389—31no—
58C2×#389—31no—
59C2×#389—31no—
60C2×#387—31no—
61C2×#387D311yescharacteristic
62#1444—31no—
63#1444—31no—
64#1441—31no—
65#1441—31no—
66#1441—31no—
67#1441—31no—
68#1436—31no—
69#1436—31no—
70C4⋊#95—31no—
71C4⋊#95—31no—
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—41no—
90C2×C3×C4⋊C4C2×C414yes—
91C2×C3×C4⋊C4D414yes—
92C2×C3×C4⋊C4Q814yes—
93C2×C3×C42—22no—
94C2×C3×C42—22no—
95C2×C3×C42—41no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—41no—
103C2×C4⋊Dic3—41no—
104C2×C4⋊Dic3—41no—
105C2×C4⋊Dic3C2×C414yes—
106C2×C4⋊Dic3C2×C414yes—
107C2×C4⋊Dic3C2×C414yes—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—22no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—41no—
113C2×Dic3⋊C4—41no—
114C2×Dic3⋊C4—41no—
115C2×Dic3⋊C4—41no—
116C2×Dic3⋊C4—41no—
117C2×Dic3⋊C4—41no—
118C2×Dic3⋊C4—41no—
119C2×Dic3⋊C4—41no—
120C2×Dic3⋊C4—41no—
121C2×Dic3⋊C4—41no—
122C2×Dic3⋊C4—41no—
123C2×Dic3⋊C4—41no—
124C2×Dic3⋊C4D414yes—
125C2×Dic3⋊C4Q814yes—
126C2×C4×Dic3—22no—
127C2×C4×Dic3—22no—
128C2×C4×Dic3—41no—
129C2×C4×Dic3—41no—
130C2×C4×Dic3—41no—
131C2×C4×Dic3C2×C414yes—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3⋊#95—22no—
137C3⋊#95—22no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95C2×C414yes—
151C3⋊#95C2×C414yes—
152C22×C4⋊C4—31no—
153C22×C4⋊C4—31no—
154C22×C4⋊C4—31no—
155C22×C4⋊C4—31no—
156C22×C4⋊C4—31no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4C2×D311yescharacteristic
163C22×C4⋊C4C2×D311yescharacteristic
164C22×C42—31no—
165C22×C42—31no—
166C22×C42C2×D311yescharacteristic
167#389—38no—
168#389—64no—
169#389—64no—
170#387—24no—
171#387—64no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95C2×D311yescharacteristic
189C2×#95C2×D311yescharacteristic
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C24×C3C2411yescharacteristic
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
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—21no—
220C22×C3×C4—21no—
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×C4C22×C412yes—
232C22×C3×C4C22×C412yes—
233C22×C3×C4C22×C412yes—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D412yes—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×Q812yes—
239C22×C3×C4C2×Q812yes—
240C22×C3×C4C2×Q812yes—
241C22×C3×C4C2×Q812yes—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
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—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×Dic3C22×C412yes—
289C22×Dic3C22×C412yes—
290C22×Dic3C22×C412yes—
291C22×Dic3C22×C412yes—
292C22×Dic3C2×D412yes—
293C22×Dic3C2×D412yes—
294C22×Dic3C2×Q812yes—
295C22×Dic3C2×Q812yes—
296C22×Dic3#4112yes—
297C22×Dic3#4112yes—
298C3×C4⋊C4—44no—
299C3×C4⋊C4C4⋊C4116yescomplemented
300C3×C42—44no—
301C4⋊Dic3—28no—
302C4⋊Dic3—28no—
303C4⋊Dic3—44no—
304C4⋊Dic3—44no—
305Dic3⋊C4—44no—
306Dic3⋊C4—44no—
307Dic3⋊C4—44no—
308Dic3⋊C4—44no—
309Dic3⋊C4—44no—
310Dic3⋊C4—44no—
311C4×Dic3—44no—
312C4×Dic3—44no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4C22×D311yescharacteristic
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D311yescharacteristic
324C23×C4C22×D311yescharacteristic
325C23×C4C22×D311yescharacteristic
326C23×C4C22×D311yescharacteristic
327C23×C4C22×D311yescharacteristic
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—34no—
331C2×C4⋊C4—34no—
332C2×C4⋊C4—34no—
333C2×C4⋊C4—34no—
334C2×C4⋊C4—34no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—62no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—62no—
341C2×C4⋊C4—62no—
342C2×C4⋊C4—62no—
343C2×C4⋊C4—62no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—62no—
346C2×C4⋊C4—121no—
347C2×C4⋊C4—121no—
348C2×C4⋊C4—121no—
349C2×C4⋊C4—121no—
350C2×C4⋊C4—121no—
351C2×C4⋊C4—121no—
352C2×C4⋊C4—121no—
353C2×C4⋊C4—121no—
354C2×C4⋊C4—121no—
355C2×C4⋊C4—121no—
356C2×C4⋊C4—121no—
357C2×C4⋊C4—121no—
358C2×C4⋊C4—121no—
359C2×C4⋊C4—121no—
360C2×C4⋊C4—121no—
361C2×C4⋊C4Dic614yes—
362C2×C4⋊C4C4×D314yes—
363C2×C4⋊C4#6714yes—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—34no—
367C2×C42—41no—
368C2×C42—62no—
369C2×C42—62no—
370C2×C42—121no—
371C2×C42—121no—
372C2×C42—121no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—22no—
377#95—34no—
378#95—34no—
379#95—62no—
380#95—62no—
381#95—62no—
382#95—62no—
383#95—62no—
384#95—62no—
385#95—62no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—121no—
390#95—121no—
391#95—121no—
392#95—121no—
393C23×C3C23×C411yescharacteristic
394C23×C3C22×D411yescharacteristic
395C23×C3C22×D411yescharacteristic
396C23×C3C22×Q811yescharacteristic
397C23×C3C22×Q811yescharacteristic
398C23×C3C2×#4111yescharacteristic
399C23×C3C2×#4111yescharacteristic
400C23×C3H(5,𝔽2)11yescharacteristic
401C23×C3H(5,𝔽2)11yescharacteristic
402C23×C3H(5,𝔽2)11yescharacteristic
403C23×C3H(5,𝔽2)11yescharacteristic
404C23×C32−1+411yescharacteristic
405C23×C32−1+411yescharacteristic
406C23×C32−1+411yescharacteristic
407C23×C32−1+411yescharacteristic
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
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—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4C2×C4⋊C414yes—
455C2×C3×C4C2×C4⋊C414yes—
456C2×C3×C4C2×C4⋊C414yes—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
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—41no—
510C2×Dic3—41no—
511C2×Dic3C4×D414yes—
512C2×Dic3C4×Q814yes—
513C24C23×D311yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
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—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4C2×Dic612yes—
609C22×C4C2×Dic612yes—
610C22×C4C2×Dic612yes—
611C22×C4C2×C4×D312yes—
612C22×C4C2×C4×D312yes—
613C22×C4C2×C4×D312yes—
614C22×C4D3×D412yes—
615C22×C4D3×Q812yes—
616C22×C4C2×#6712yes—
617C22×C4C2×#6712yes—
618C22×C4C2×#6712yes—
619C4⋊C4—44no—
620C4⋊C4—68no—
621C4⋊C4—68no—
622C4⋊C4—124no—
623C4⋊C4—124no—
624C4⋊C4—124no—
625C4⋊C4—124no—
626C4⋊C4—124no—
627C4⋊C4—124no—
628C4⋊C4—124no—
629C4⋊C4—124no—
630C4⋊C4Dic3⋊C4116yescomplemented
631C42—44no—
632C42—124no—
633C42—124no—
634C22×C3C22×C4⋊C411yescharacteristic
635C22×C3C2×C4×D411yescharacteristic
636C22×C3C2×C4×Q811yescharacteristic
637C22×C3#51811yescharacteristic
638C22×C3#51911yescharacteristic
639C22×C3#52011yescharacteristic
640C22×C3#52011yescharacteristic
641C22×C3#53411yescharacteristic
642C22×C3#53711yescharacteristic
643C22×C3#53711yescharacteristic
644C22×C3#53711yescharacteristic
645C22×C3#53811yescharacteristic
646C22×C3#53811yescharacteristic
647C22×C3#53911yescharacteristic
648C22×C3#53911yescharacteristic
649C22×C3#54311yescharacteristic
650C22×C3#54411yescharacteristic
651C22×C3#54411yescharacteristic
652C22×C3#54411yescharacteristic
653C22×C3D4211yescharacteristic
654C22×C3#54711yescharacteristic
655C22×C3#54711yescharacteristic
656C22×C3D4×Q811yescharacteristic
657C22×C3D4×Q811yescharacteristic
658C22×C3D4×Q811yescharacteristic
659C22×C3#55011yescharacteristic
660C22×C3#55411yescharacteristic
661C22×C3#55611yescharacteristic
662C22×C3#55711yescharacteristic
663C22×C3#55711yescharacteristic
664C22×C3Q8211yescharacteristic
665C22×C3#56211yescharacteristic
666C22×C3#56311yescharacteristic
667C22×C3#56311yescharacteristic
668C22×C3#56411yescharacteristic
669C3×C4—24no—
670C3×C4—24no—
671C3×C4—24no—
672C3×C4—42no—
673C3×C4—42no—
674C3×C4—81no—
675C3×C4—81no—
676Dic3—24no—
677Dic3—24no—
678Dic3—42no—
679Dic3—42no—
680Dic3—42no—
681Dic3—42no—
682Dic3—81no—
683Dic3—81no—
684C23C22×Dic611yescharacteristic
685C23C22×C4×D311yescharacteristic
686C23C2×D3×D411yescharacteristic
687C23#100411yescharacteristic
688C23C2×D3×Q811yescharacteristic
689C23#100711yescharacteristic
690C23D3×#4111yescharacteristic
691C23D3×#4111yescharacteristic
692C23#100911yescharacteristic
693C23#100911yescharacteristic
694C23#100911yescharacteristic
695C23#101011yescharacteristic
696C23#101011yescharacteristic
697C23#101011yescharacteristic
698C23C22×#6711yescharacteristic
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—34no—
724C2×C4—34no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
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—121no—
772C2×C4—121no—
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—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4C2×Dic3⋊C414yes—
802C2×C4C2×Dic3⋊C414yes—
803C2×C4C2×Dic3⋊C414yes—
804C2×C3#231611yescharacteristic
805C2×C3#232511yescharacteristic
806C2×C3#232911yescharacteristic
807C2×C3D4×C4⋊C411yescharacteristic
808C2×C3Q8×C4⋊C411yescharacteristic
809C2×C3#236511yescharacteristic
810C2×C3#238211yescharacteristic
811C2×C3#268211yescharacteristic
812C2×C3#268311yescharacteristic
813C2×C3#272611yescharacteristic
814C2×C3#272611yescharacteristic
815C2×C3#272711yescharacteristic
816C2×C3#273411yescharacteristic
817C2×C3#280511yescharacteristic
818C2×C3#280611yescharacteristic
819C22#551611yescharacteristic
820C22#551911yescharacteristic
821C22#551911yescharacteristic
822C22#552111yescharacteristic
823C22D4×Dic611yescharacteristic
824C22#553911yescharacteristic
825C22C4×D3×D411yescharacteristic
826C22#554611yescharacteristic
827C22Q8×Dic611yescharacteristic
828C22#556911yescharacteristic
829C22C4×D3×Q811yescharacteristic
830C22#557411yescharacteristic
831C22#562911yescharacteristic
832C22#563211yescharacteristic
833C22#563411yescharacteristic
834C22#564611yescharacteristic
835C22#565311yescharacteristic
836C22#565511yescharacteristic
837C22#565711yescharacteristic
838C22#566711yescharacteristic
839C22#568511yescharacteristic
840C22C3⋊#56411yescharacteristic
841C22#568911yescharacteristic
842C22#569211yescharacteristic
843C22#570211yescharacteristic
844C22#570411yescharacteristic
845C22#570711yescharacteristic
846C22#571211yescharacteristic
847C22C22×Dic3⋊C411yescharacteristic
848C22D4×#6711yescharacteristic
849C22Q8×#6711yescharacteristic
850C22#582411yescharacteristic
851C22#583311yescharacteristic
852C22#583311yescharacteristic
853C22#583411yescharacteristic
854C4—24no—
855C4—24no—
856C4—24no—
857C4—42no—
858C4—42no—
859C4—64no—
860C4—64no—
861C4—81no—
862C4—81no—
863C4—122no—
864C4—122no—
865C4—122no—
866C4—122no—
867C4—241no—
868C4—241no—
869C3#1444111yescharacteristic, complemented, Sylow
870C2#7496711yescharacteristic
871C2#7497811yescharacteristic
872C2#7517611yescharacteristic
873C2#7517911yescharacteristic
874C2#7528011yescharacteristic
875C2#7528111yescharacteristic
876C2#7529811yescharacteristic
877C2#7530011yescharacteristic
878C2#8223211yescharacteristic
879C2D4×Dic3⋊C411yescharacteristic
880C2Q8×Dic3⋊C411yescharacteristic
881C2#8279311yescharacteristic
882C2#8287311yescharacteristic
883C2#8305411yescharacteristic
884C2#8310211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#387C2
socle, prime radical, cosocleC24×C3C24
hypercenterC2×#387D3
hypocenterC3#14441
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
53. #4984C4semidirect
299. C3×C4⋊C4C4⋊C4semidirect
630. C4⋊C4Dic3⋊C4semidirect
869. C3#14441semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3872
C2×#49842
C2×#49722
C2×#49802
C2×#49282
#715682
#715362
#694202
#694112
#694062
Dic3⋊#952
#144413