Finite Group Databasebeta

← #10723151

Subgroups — #10723151

Order 768.

1346 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4978C211yesmaximal, characteristic
2C2×#4977C211yesmaximal, characteristic
3C2×#4647C211yesmaximal, characteristic
4C2×#4647C211yesmaximal, characteristic
5C2×#4652C211yesmaximal, characteristic
6C3×#1442C211yesmaximal, characteristic
7#69420C211yesmaximal, characteristic
8#69419C211yesmaximal, characteristic
9#69414C211yesmaximal, characteristic
10#69413C211yesmaximal, characteristic
11#69409C211yesmaximal, characteristic
12#69407C211yesmaximal, characteristic
13#69407C211yesmaximal, characteristic
14#69405C211yesmaximal, characteristic
15Dic3⋊#95C211yesmaximal, characteristic
16#14404—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic3C2211yescharacteristic
19C22×C4⋊Dic3C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×Dic3⋊C4C2211yescharacteristic
22C22×Dic3⋊C4C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
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#4978—24no—
53#4977—24no—
54#4652C418yescomplemented
55#4647—24no—
56#4647—24no—
57C2×#389—31no—
58C2×#389—31no—
59C2×#387—31no—
60C2×#387—31no—
61C2×#382—31no—
62#1444—31no—
63#1444—31no—
64#1442—31no—
65#1442—31no—
66#1442D311yescharacteristic
67#1441—31no—
68#1436—31no—
69#1436—31no—
70#1436—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×C4⋊Dic3—22no—
91C2×C4⋊Dic3—22no—
92C2×C4⋊Dic3—22no—
93C2×C4⋊Dic3—22no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3—41no—
96C2×C4⋊Dic3—41no—
97C2×C4⋊Dic3—41no—
98C2×C4⋊Dic3—41no—
99C2×Dic3⋊C4—22no—
100C2×Dic3⋊C4—22no—
101C2×Dic3⋊C4—22no—
102C2×Dic3⋊C4—22no—
103C2×Dic3⋊C4—22no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4—22no—
106C2×Dic3⋊C4—22no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—41no—
109C2×Dic3⋊C4—41no—
110C2×Dic3⋊C4—41no—
111C2×Dic3⋊C4—41no—
112C2×Dic3⋊C4—41no—
113C2×Dic3⋊C4C2×C414yes—
114C2×Dic3⋊C4C2×C414yes—
115C2×Dic3⋊C4D414yes—
116C2×Dic3⋊C4Q814yes—
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
122C2×C4×Dic3—41no—
123C2×C4×Dic3—41no—
124C2×C4×Dic3—41no—
125C2×C4×Dic3C2×C414yes—
126C3×#95—22no—
127C3×#95—22no—
128C3×#95—22no—
129C3×#95—22no—
130C3×#95—41no—
131C3×#95C2×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—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95C2×C414yes—
145C3⋊#95C2×C414yes—
146C3⋊#95C2×C414yes—
147C3⋊#95D414yes—
148C22×C4⋊C4—31no—
149C22×C4⋊C4—31no—
150C22×C4⋊C4—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⋊C4C2×D311yescharacteristic
158C22×C42—31no—
159C22×C42—31no—
160C22×C42—31no—
161#389—64no—
162#389—64no—
163#387—38no—
164#387—64no—
165#382—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×#95C2×D311yescharacteristic
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×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×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×Dic3C22×C412yes—
283C22×Dic3C22×C412yes—
284C22×Dic3C22×C412yes—
285C22×Dic3C22×C412yes—
286C22×Dic3C2×D412yes—
287C22×Dic3C2×D412yes—
288C22×Dic3C2×D412yes—
289C22×Dic3C2×D412yes—
290C22×Dic3C2×Q812yes—
291C22×Dic3C2×Q812yes—
292C22×Dic3#4112yes—
293C22×Dic3#4112yes—
294C3×C4⋊C4—44no—
295C4⋊Dic3—44no—
296C4⋊Dic3—44no—
297C4⋊Dic3—44no—
298Dic3⋊C4—28no—
299Dic3⋊C4—44no—
300Dic3⋊C4—44no—
301Dic3⋊C4—44no—
302Dic3⋊C4—44no—
303Dic3⋊C4C4⋊C4116yescomplemented
304C4×Dic3—28no—
305C4×Dic3—44no—
306C4×Dic3—44no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320C23×C4C22×D311yescharacteristic
321C23×C4C22×D311yescharacteristic
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—34no—
325C2×C4⋊C4—34no—
326C2×C4⋊C4—34no—
327C2×C4⋊C4—34no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—62no—
330C2×C4⋊C4—62no—
331C2×C4⋊C4—62no—
332C2×C4⋊C4—62no—
333C2×C4⋊C4—62no—
334C2×C4⋊C4—62no—
335C2×C4⋊C4—62no—
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—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×C42—34no—
353C2×C42—62no—
354C2×C42—62no—
355C2×C42—62no—
356C2×C42—62no—
357C2×C42—62no—
358C2×C42—121no—
359C2×C42—121no—
360C2×C42—121no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—22no—
365#95—34no—
366#95—34no—
367#95—34no—
368#95—34no—
369#95—41no—
370#95—62no—
371#95—62no—
372#95—62no—
373#95—62no—
374#95—62no—
375#95—62no—
376#95—62no—
377#95—62no—
378#95—121no—
379#95—121no—
380#95—121no—
381#95—121no—
382#95C4×D314yes—
383C23×C3C23×C411yescharacteristic
384C23×C3C22×D411yescharacteristic
385C23×C3C22×D411yescharacteristic
386C23×C3C22×Q811yescharacteristic
387C23×C3C2×#4111yescharacteristic
388C23×C3C2×#4111yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3H(5,𝔽2)11yescharacteristic
391C23×C3H(5,𝔽2)11yescharacteristic
392C23×C3H(5,𝔽2)11yescharacteristic
393C23×C32−1+411yescharacteristic
394C23×C32−1+411yescharacteristic
395C23×C32−1+411yescharacteristic
396C23×C32−1+411yescharacteristic
397C23×C32−1+411yescharacteristic
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
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—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
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×C4C2×C4⋊C414yes—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
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—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
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×Dic3C2×C4⋊C414yes—
501C2×Dic3C2×C4⋊C414yes—
502C2×Dic3C4×D414yes—
503C24C23×D311yescharacteristic
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
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—32no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
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×C4C2×C4×D312yes—
603C22×C4C2×C4×D312yes—
604C22×C4C2×C4×D312yes—
605C22×C4D3×D412yes—
606C22×C4D3×D412yes—
607C22×C4#23712yes—
608C22×C4D3×Q812yes—
609C4⋊C4—316no—
610C4⋊C4—44no—
611C4⋊C4—68no—
612C4⋊C4—124no—
613C4⋊C4—124no—
614C4⋊C4—124no—
615C4⋊C4—124no—
616C4⋊C4—124no—
617C4⋊C4—124no—
618C4⋊C4—124no—
619C42—68no—
620C42—124no—
621C42—124no—
622C22×C3C22×C4⋊C411yescharacteristic
623C22×C3C2×C4×D411yescharacteristic
624C22×C3C4×#4111yescharacteristic
625C22×C3#51911yescharacteristic
626C22×C3#52011yescharacteristic
627C22×C3#52011yescharacteristic
628C22×C3#52011yescharacteristic
629C22×C3#53511yescharacteristic
630C22×C3#53611yescharacteristic
631C22×C3#53611yescharacteristic
632C22×C3#53711yescharacteristic
633C22×C3#53811yescharacteristic
634C22×C3#53911yescharacteristic
635C22×C3#54111yescharacteristic
636C22×C3#54111yescharacteristic
637C22×C3#54211yescharacteristic
638C22×C3#54211yescharacteristic
639C22×C3#54411yescharacteristic
640C22×C3#54411yescharacteristic
641C22×C3D4211yescharacteristic
642C22×C3#54611yescharacteristic
643C22×C3#54711yescharacteristic
644C22×C3#54711yescharacteristic
645C22×C3#54811yescharacteristic
646C22×C3#54811yescharacteristic
647C22×C3D4×Q811yescharacteristic
648C22×C3#55111yescharacteristic
649C22×C3#55211yescharacteristic
650C22×C3#55411yescharacteristic
651C22×C3#55711yescharacteristic
652C22×C3#55711yescharacteristic
653C22×C3#56211yescharacteristic
654C22×C3#56311yescharacteristic
655C22×C3#56311yescharacteristic
656C22×C3#56411yescharacteristic
657C3×C4—24no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—81no—
663C3×C4—81no—
664Dic3—24no—
665Dic3—24no—
666Dic3—24no—
667Dic3—42no—
668Dic3—42no—
669Dic3—42no—
670Dic3—81no—
671Dic3—81no—
672C23C22×C4×D311yescharacteristic
673C23C2×D3×D411yescharacteristic
674C23C2×D3×D411yescharacteristic
675C23C2×#23711yescharacteristic
676C23#100411yescharacteristic
677C23C2×D3×Q811yescharacteristic
678C23#100711yescharacteristic
679C23D3×#4111yescharacteristic
680C23D3×#4111yescharacteristic
681C23#100911yescharacteristic
682C23#100911yescharacteristic
683C23#101011yescharacteristic
684C23#101011yescharacteristic
685C23#101011yescharacteristic
686C23#101011yescharacteristic
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—34no—
706C2×C4—34no—
707C2×C4—34no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
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—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
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—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
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×C4D3×C4⋊C414yes—
792C2×C3#231711yescharacteristic
793C2×C3#232311yescharacteristic
794C2×C3#233411yescharacteristic
795C2×C3D4×C4⋊C411yescharacteristic
796C2×C3#235111yescharacteristic
797C2×C3#235911yescharacteristic
798C2×C3#238211yescharacteristic
799C2×C3#267411yescharacteristic
800C2×C3#267611yescharacteristic
801C2×C3#271311yescharacteristic
802C2×C3#271911yescharacteristic
803C2×C3#272311yescharacteristic
804C2×C3#272611yescharacteristic
805C2×C3#275511yescharacteristic
806C2×C3#277411yescharacteristic
807C22C2×D3×C4⋊C411yescharacteristic
808C22#552311yescharacteristic
809C22#552311yescharacteristic
810C22C4×#23711yescharacteristic
811C22C4×D3×D411yescharacteristic
812C22#554611yescharacteristic
813C22#557211yescharacteristic
814C22#559011yescharacteristic
815C22#559811yescharacteristic
816C22#560311yescharacteristic
817C22#561111yescharacteristic
818C22#562911yescharacteristic
819C22#563211yescharacteristic
820C22#563311yescharacteristic
821C22#563611yescharacteristic
822C22#564711yescharacteristic
823C22#564811yescharacteristic
824C22#565111yescharacteristic
825C22#565511yescharacteristic
826C22#565811yescharacteristic
827C22#566511yescharacteristic
828C22#567411yescharacteristic
829C22#567511yescharacteristic
830C22#567611yescharacteristic
831C22#567811yescharacteristic
832C22#568511yescharacteristic
833C22C3⋊#56411yescharacteristic
834C22#568911yescharacteristic
835C22#568911yescharacteristic
836C22#569611yescharacteristic
837C22#570111yescharacteristic
838C22#570811yescharacteristic
839C22#571011yescharacteristic
840C22#571211yescharacteristic
841C22#572111yescharacteristic
842C4—24no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—64no—
848C4—64no—
849C4—64no—
850C4—81no—
851C4—81no—
852C4—122no—
853C4—122no—
854C4—122no—
855C4—241no—
856C4—241no—
857C3#1440411yescharacteristic, complemented, Sylow
858C2#7422511yescharacteristic
859C2#7439311yescharacteristic
860C2#7494711yescharacteristic
861C2#7497911yescharacteristic
862C2#7546711yescharacteristic
863C2#7583811yescharacteristic
864C2#7598211yescharacteristic
865C2#7682211yescharacteristic
866C2#7700211yescharacteristic
867C2#7759411yescharacteristic
868C2#7786811yescharacteristic
869C2#7787611yescharacteristic
870C2#7824211yescharacteristic
871C2#7824611yescharacteristic
872C2#7827911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1442C2
socle, prime radical, cosocleC24×C3C24
hypercenter#1442D3
hypocenterC3#14404
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
54. #4652C4semidirect
303. Dic3⋊C4C4⋊C4semidirect
857. C3#14404semidirect

Maximal subgroups

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

subgroupindex
C2×#49782
C2×#49772
C2×#46472
C2×#46522
C3×#14422
#694202
#694192
#694142
#694132
#694092
#694072
#694052
Dic3⋊#952
#144043