Finite Group Databasebeta

← #10723909

Subgroups — #10723909

Order 768.

1398 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4929C211yesmaximal, characteristic
2C2×#4646C211yesmaximal, characteristic
3C2×#4646C211yesmaximal, characteristic
4C3×#1436C211yesmaximal, characteristic
5#71564C211yesmaximal, characteristic
6#71563C211yesmaximal, characteristic
7#71536C211yesmaximal, characteristic
8#69420C211yesmaximal, characteristic
9#69420C211yesmaximal, characteristic
10#69420C211yesmaximal, characteristic
11#69419C211yesmaximal, characteristic
12#69410C211yesmaximal, characteristic
13#69409C211yesmaximal, characteristic
14#69406C211yesmaximal, characteristic
15Dic3⋊#95C211yesmaximal, characteristic
16#14467—31nomaximal, Sylow
17C23×Dic6C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
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
52#4929—24no—
53#4646—24no—
54#4646C418yescomplemented
55C2×#391—31no—
56C2×#391—31no—
57C2×#391—31no—
58#1444—31no—
59#1444—31no—
60#1444—31no—
61#1444—31no—
62#1441—31no—
63#1441—31no—
64#1436—31no—
65#1436—31no—
66#1436—31no—
67#1436D311yescharacteristic
68C4⋊#95—31no—
69C4⋊#95—31no—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C22×Dic6—41no—
86C22×Dic6—41no—
87C22×Dic6—41no—
88C22×Dic6—41no—
89C22×Dic6C2×C414yes—
90C22×Dic6D414yes—
91C22×Dic6Q814yes—
92C2×C3×C4⋊C4—41no—
93C2×C3×C4⋊C4—41no—
94C2×C3×C4⋊C4Q814yescomplemented
95C2×C3×C42—22no—
96C2×C3×C42—41no—
97C2×C3×C42—41no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—41no—
101C2×C4⋊Dic3—41no—
102C2×C4⋊Dic3—41no—
103C2×C4⋊Dic3—41no—
104C2×C4⋊Dic3—41no—
105C2×C4⋊Dic3—41no—
106C2×C4⋊Dic3—41no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—41no—
110C2×Dic3⋊C4—41no—
111C2×Dic3⋊C4—41no—
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⋊C4C2×C414yes—
121C2×Dic3⋊C4Q814yescomplemented
122C2×C4×Dic3—22no—
123C2×C4×Dic3—41no—
124C2×C4×Dic3—41no—
125C2×C4×Dic3—41no—
126C2×C4×Dic3—41no—
127C2×C4×Dic3C2×C414yes—
128C3×#95—22no—
129C3×#95—22no—
130C3×#95—41no—
131C3×#95—41no—
132C3×#95C2×C414yes—
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—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95C2×C414yes—
148C3⋊#95C2×C414yes—
149C3⋊#95C2×C414yes—
150C23×Q8—31no—
151C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
160C22×C42—31no—
161C22×C42—31no—
162C22×C42C2×D311yescharacteristic
163#391—38no—
164#391—64no—
165#391—64no—
166C2×#95—31no—
167C2×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
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×#95C2×D311yescharacteristic
184C2×#95C2×D311yescharacteristic
185C2×#95C2×D311yescharacteristic
186C2×#95C2×D311yescharacteristic
187C2×#95C2×D311yescharacteristic
188C24×C3C2411yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
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×C4C22×C412yes—
229C22×C3×C4C22×C412yes—
230C22×C3×C4C22×C412yes—
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2×Q812yes—
233C22×C3×C4C2×Q812yes—
234C22×C3×C4C2×Q812yes—
235C22×C3×C4C2×Q812yes—
236C22×C3×C4C2×Q812yes—
237C22×C3×C4#4112yes—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
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×Dic3C22×C412yes—
284C22×Dic3C22×C412yes—
285C22×Dic3C22×C412yes—
286C22×Dic3C22×C412yes—
287C22×Dic3C2×D412yes—
288C22×Dic3C2×D412yes—
289C22×Dic3C2×Q812yes—
290C22×Dic3C2×Q812yes—
291C22×Dic3C2×Q812yes—
292C22×Dic3C2×Q812yes—
293C22×Dic3#4112yes—
294C2×Dic6—44no—
295C2×Dic6—44no—
296C2×Dic6—44no—
297C2×Dic6—44no—
298C2×Dic6—44no—
299C2×Dic6—44no—
300C2×Dic6C4⋊C4116yescomplemented
301C3×C4⋊C4—44no—
302C3×C42—44no—
303C4⋊Dic3—44no—
304C4⋊Dic3—44no—
305C4⋊Dic3—44no—
306Dic3⋊C4—44no—
307Dic3⋊C4—44no—
308Dic3⋊C4—44no—
309Dic3⋊C4—44no—
310Dic3⋊C4—44no—
311C4×Dic3—44no—
312C4×Dic3—44no—
313C22×Q8—34no—
314C22×Q8—34no—
315C22×Q8—34no—
316C22×Q8—121no—
317C22×Q8—121no—
318C22×Q8—121no—
319C22×Q8—121no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4C22×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C2×C4⋊C4—34no—
336C2×C4⋊C4—34no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—62no—
341C2×C4⋊C4—62no—
342C2×C4⋊C4—62no—
343C2×C4⋊C4—121no—
344C2×C4⋊C4—121no—
345C2×C4⋊C4—121no—
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⋊C4Dic614yescomplemented
362C2×C42—22no—
363C2×C42—34no—
364C2×C42—41no—
365C2×C42—41no—
366C2×C42—62no—
367C2×C42—121no—
368C2×C42—121no—
369C2×C42—121no—
370C2×C42—121no—
371#95—22no—
372#95—22no—
373#95—34no—
374#95—34no—
375#95—34no—
376#95—41no—
377#95—41no—
378#95—62no—
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—121no—
389#95—121no—
390#95—121no—
391#95—121no—
392#95C4×D314yes—
393C23×C3C23×C411yescharacteristic
394C23×C3C22×D411yescharacteristic
395C23×C3C22×Q811yescharacteristic
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×C3H(5,𝔽2)11yescharacteristic
405C23×C3H(5,𝔽2)11yescharacteristic
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×C4—41no—
455C2×C3×C4C2×C4⋊C414yes—
456C2×C3×C4C4×Q814yes—
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×Dic3C2×C4⋊C414yes—
511C2×Dic3C2×C4⋊C414yes—
512C2×Dic3C4×Q814yes—
513Dic6—416no—
514C24C23×D311yescharacteristic
515C2×Q8—316no—
516C2×Q8—124no—
517C2×Q8—124no—
518C2×Q8—124no—
519C2×Q8—124no—
520C2×Q8—124no—
521C2×Q8—124no—
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—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—32no—
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×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×C4C2×Dic612yes—
618C22×C4C2×Dic612yes—
619C22×C4C2×Dic612yes—
620C22×C4C2×C4×D312yes—
621C22×C4C2×C4×D312yes—
622C22×C4C2×C4×D312yes—
623C22×C4#23512yes—
624C22×C4D3×D412yes—
625C22×C4D3×Q812yes—
626C22×C4D3×Q812yes—
627C4⋊C4—44no—
628C4⋊C4—124no—
629C4⋊C4—124no—
630C4⋊C4—124no—
631C4⋊C4—124no—
632C4⋊C4—124no—
633C4⋊C4—124no—
634C4⋊C4—124no—
635C4⋊C4—124no—
636C42—44no—
637C42—124no—
638C42—124no—
639C22×C3C22×C4⋊C411yescharacteristic
640C22×C3C2×C4×Q811yescharacteristic
641C22×C3C2×C4×Q811yescharacteristic
642C22×C3#51811yescharacteristic
643C22×C3#51811yescharacteristic
644C22×C3#52011yescharacteristic
645C22×C3#52011yescharacteristic
646C22×C3#53411yescharacteristic
647C22×C3#53411yescharacteristic
648C22×C3#53811yescharacteristic
649C22×C3#53811yescharacteristic
650C22×C3#53911yescharacteristic
651C22×C3#53911yescharacteristic
652C22×C3#54311yescharacteristic
653C22×C3#54311yescharacteristic
654C22×C3#54311yescharacteristic
655C22×C3#54311yescharacteristic
656C22×C3#54411yescharacteristic
657C22×C3#54411yescharacteristic
658C22×C3D4×Q811yescharacteristic
659C22×C3D4×Q811yescharacteristic
660C22×C3#55011yescharacteristic
661C22×C3#55011yescharacteristic
662C22×C3#55411yescharacteristic
663C22×C3#55411yescharacteristic
664C22×C3#55511yescharacteristic
665C22×C3#55711yescharacteristic
666C22×C3#55711yescharacteristic
667C22×C3Q8211yescharacteristic
668C22×C3Q8211yescharacteristic
669C22×C3Q8211yescharacteristic
670C22×C3H(3,𝔽4)11yescharacteristic
671C22×C3#56211yescharacteristic
672C22×C3#56211yescharacteristic
673C22×C3#56311yescharacteristic
674C3×C4—24no—
675C3×C4—24no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—42no—
680C3×C4—81no—
681Dic3—24no—
682Dic3—24no—
683Dic3—24no—
684Dic3—42no—
685Dic3—42no—
686Dic3—81no—
687Dic3—81no—
688Dic3—81no—
689C23C22×Dic611yescharacteristic
690C23C22×C4×D311yescharacteristic
691C23C2×#23511yescharacteristic
692C23C2×D3×D411yescharacteristic
693C23#100411yescharacteristic
694C23#100411yescharacteristic
695C23#100411yescharacteristic
696C23C2×D3×Q811yescharacteristic
697C23C2×D3×Q811yescharacteristic
698C23D3×#4111yescharacteristic
699C23#100911yescharacteristic
700C23#100911yescharacteristic
701C23#100911yescharacteristic
702C23#101011yescharacteristic
703C23#101011yescharacteristic
704Q8—1216no—
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—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—34no—
730C2×C4—34no—
731C2×C4—34no—
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—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
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—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
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×C4—121no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4C4×Dic614yes—
809C2×C4D3×C4⋊C414yes—
810C2×C3#231511yescharacteristic
811C2×C3#232911yescharacteristic
812C2×C3#232911yescharacteristic
813C2×C3Q8×C4⋊C411yescharacteristic
814C2×C3Q8×C4⋊C411yescharacteristic
815C2×C3#236911yescharacteristic
816C2×C3#237911yescharacteristic
817C2×C3#273211yescharacteristic
818C2×C3#273211yescharacteristic
819C2×C3#273311yescharacteristic
820C2×C3#273411yescharacteristic
821C2×C3#280611yescharacteristic
822C2×C3#280611yescharacteristic
823C2×C3#280911yescharacteristic
824C2×C3#281111yescharacteristic
825C22C2×C4×Dic611yescharacteristic
826C22#548311yescharacteristic
827C22C2×D3×C4⋊C411yescharacteristic
828C22#551111yescharacteristic
829C22#551911yescharacteristic
830C22#552311yescharacteristic
831C22#553211yescharacteristic
832C22D4×Dic611yescharacteristic
833C22#553911yescharacteristic
834C22#554511yescharacteristic
835C22#554511yescharacteristic
836C22#554611yescharacteristic
837C22#555311yescharacteristic
838C22#556011yescharacteristic
839C22#556411yescharacteristic
840C22Q8×Dic611yescharacteristic
841C22Q8×Dic611yescharacteristic
842C22#556711yescharacteristic
843C22C4×D3×Q811yescharacteristic
844C22#558911yescharacteristic
845C22#559911yescharacteristic
846C22#562111yescharacteristic
847C22#563211yescharacteristic
848C22#563411yescharacteristic
849C22#563411yescharacteristic
850C22#563411yescharacteristic
851C22#565311yescharacteristic
852C22#566011yescharacteristic
853C22#566711yescharacteristic
854C22#568311yescharacteristic
855C22#568511yescharacteristic
856C22#568911yescharacteristic
857C22#570411yescharacteristic
858C22#571211yescharacteristic
859C22#572211yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—64no—
867C4—64no—
868C4—64no—
869C4—81no—
870C4—122no—
871C4—122no—
872C4—241no—
873C4—241no—
874C4—241no—
875C3#1446711yescharacteristic, complemented, Sylow
876C2#7344711yescharacteristic
877C2C4⋊C4×Dic611yescharacteristic
878C2#7365711yescharacteristic
879C2#7454111yescharacteristic
880C2#7459111yescharacteristic
881C2#7483011yescharacteristic
882C2#7517911yescharacteristic
883C2#7528111yescharacteristic
884C2#7528311yescharacteristic
885C2#7529911yescharacteristic
886C2#7549311yescharacteristic
887C2#7571211yescharacteristic
888C2#7598111yescharacteristic
889C2#7618411yescharacteristic
890C2#7660411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, prime radical, cosocleC24×C3C24
hypercenter#1436D3
hypocenterC3#14467
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
54. #4646C4semidirect
94. C2×C3×C4⋊C4Q8semidirect
121. C2×Dic3⋊C4Q8semidirect
300. C2×Dic6C4⋊C4semidirect
361. C2×C4⋊C4Dic6semidirect
875. C3#14467semidirect

Maximal subgroups

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

subgroupindex
C2×#49292
C2×#46462
C3×#14362
#715642
#715632
#715362
#694202
#694192
#694102
#694092
#694062
Dic3⋊#952
#144673