Finite Group Databasebeta

← #10733800

Subgroups — #10733800

Order 768.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic, complemented
2C2×C3×#390C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#4979C211yesmaximal, characteristic, complemented
5C2×#4949C211yesmaximal, characteristic, complemented
6C2×#4948C211yesmaximal, characteristic, complemented
7C2×#4947C211yesmaximal, characteristic, complemented
8C2×#4946C211yesmaximal, characteristic, complemented
9#72131C211yesmaximal, characteristic
10#71568C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#71546C211yesmaximal, characteristic, complemented
14#71536C211yesmaximal, characteristic, complemented
15#71535C211yesmaximal, characteristic, complemented
16#15325—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C2×#878—24no—
41C2×#878—24no—
42C2×#878—24no—
43C3×#390—24no—
44#5220—24no—
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57#4979—24no—
58#4949—24no—
59#4948—24no—
60#4947—24no—
61#4946—24no—
62C22×C22⋊Q8—31no—
63C2×#399—31no—
64C2×#396—31no—
65C2×#395—31no—
66C2×#393—31no—
67C2×#390D311yescharacteristic
68C2×#386—31no—
69C2×#385—31no—
70#1444—31no—
71#1439—31no—
72#1439—31no—
73#1439—31no—
74#1438—31no—
75#1436—31no—
76C4⋊#95—31no—
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—41no—
84C22×C3×D4—41no—
85C22×C3×D4Q814yescomplemented
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—41no—
97C23×Dic3—41no—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—22no—
109C22×Dic6—22no—
110C22×Dic6—22no—
111C22×Dic6—41no—
112C22×Dic6—41no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4D414yes—
128C2×C3×C42—22no—
129C2×C3×C42—22no—
130C2×C3×C42—41no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—22no—
148C2×#217—41no—
149C2×#217—41no—
150C2×#217—41no—
151C2×#217—41no—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—41no—
157C2×C4⋊Dic3D414yescomplemented
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—41no—
171C2×Dic3⋊C4—41no—
172C2×Dic3⋊C4D414yescomplemented
173#878—232no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—41no—
184C3⋊#95D414yes—
185C3⋊#95D414yescomplemented
186C23×Q8—31no—
187C23×D4C2×D311yescharacteristic
188C24×C4—31no—
189C2×C22⋊Q8—64no—
190C2×C22⋊Q8—64no—
191C2×C22⋊Q8—64no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4C2×D311yescharacteristic
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42C2×D311yescharacteristic
212#399—64no—
213#396—64no—
214#395—64no—
215#393—64no—
216#390—24no—
217#386—64no—
218#385—64no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3C2×D412yes—
258C24×C3C2×Q812yes—
259C24×C3C2×Q812yes—
260C24×C3#4112yes—
261C24×C3C2411yescharacteristic
262C2×C3×D4—28no—
263C2×C3×D4—28no—
264C2×C3×D4—44no—
265C2×C3×D4—44no—
266C2×C3×D4—44no—
267C2×C3×D4—44no—
268C2×C3×D4—44no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×Q812yes—
303C22×C3×C4#4112yes—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—28no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
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—44no—
353C22×Dic3—44no—
354C22×Dic3—44no—
355C22×Dic3—44no—
356C22×Dic3—44no—
357C22×Dic3—44no—
358C22×Dic3C2×D412yes—
359C22×Dic3C2×D412yes—
360C22×Dic3C2×D412yes—
361C22×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×D412yes—
364C22×Dic3C2×D412yes—
365C22×Dic3C2×D412yes—
366C22×Dic3#4112yes—
367C2×Dic6—28no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C2×Dic6—44no—
371C2×Dic6—44no—
372C2×Dic6—44no—
373C2×Dic6—44no—
374C3×C4⋊C4—44no—
375C3×C22⋊C4—28no—
376C3×C22⋊C4—44no—
377C3×C22⋊C4—44no—
378C3×C22⋊C4—44no—
379C3×C42—44no—
380#217—28no—
381#217—28no—
382#217—44no—
383#217—44no—
384#217—44no—
385#217—44no—
386#217—44no—
387C4⋊Dic3—28no—
388C4⋊Dic3—44no—
389Dic3⋊C4—28no—
390Dic3⋊C4—28no—
391Dic3⋊C4—44no—
392Dic3⋊C4—44no—
393Dic3⋊C4—44no—
394C25C22×D311yescharacteristic
395C25C22×D311yescharacteristic
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—62no—
399C22×Q8—62no—
400C22×Q8—62no—
401C22×Q8—121no—
402C22×Q8—121no—
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—41no—
408C22×D4—41no—
409C22×D4Dic614yescomplemented
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—121no—
424C23×C4—121no—
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C22⋊Q8—632no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—62no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—62no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—121no—
453C2×C4⋊C4—121no—
454C2×C4⋊C4—121no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—41no—
465C2×C22⋊C4—41no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—121no—
484C2×C22⋊C4—121no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4#6714yes—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—41no—
491#95—34no—
492#95—34no—
493#95—62no—
494#95—62no—
495#95—62no—
496#95—62no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95—62no—
502#95—121no—
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—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3C22⋊Q814yes—
573C23×C3C22×D411yescharacteristic
574C23×C3C22×D411yescharacteristic
575C23×C3C22×D411yescharacteristic
576C23×C3C22×D411yescharacteristic
577C23×C3C22×D411yescharacteristic
578C23×C3C22×Q811yescharacteristic
579C23×C3C2×#4111yescharacteristic
580C23×C3C2×#4111yescharacteristic
581C23×C3C2×#4111yescharacteristic
582C23×C3H(5,𝔽2)11yescharacteristic
583C23×C3H(5,𝔽2)11yescharacteristic
584C23×C3H(5,𝔽2)11yescharacteristic
585C23×C32−1+411yescharacteristic
586C23×C32−1+411yescharacteristic
587C23×C32−1+411yescharacteristic
588C3×D4—416no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4#12014yes—
623C2×C3×C4C22⋊Q814yescomplemented
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—416no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—41no—
678C2×Dic3—41no—
679C2×Dic3—41no—
680C2×Dic3#12714yes—
681Dic6—416no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24C2×Dic612yes—
709C24C2×Dic612yes—
710C24#23512yes—
711C24C2×#6712yes—
712C24C23×D311yescharacteristic
713C2×Q8—68no—
714C2×Q8—124no—
715C2×Q8—124no—
716C2×Q8—124no—
717C2×Q8—124no—
718C2×Q8—124no—
719C2×Q8—124no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—32no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—68no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
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—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4C2×Dic612yes—
818C22×C4D3×D412yes—
819C22×C4D3×D412yes—
820C22×C4D3×D412yes—
821C22×C4D3×D412yes—
822C22×C4#23712yes—
823C22×C4C2×#6712yes—
824C22×C4C2×#6712yes—
825C4⋊C4—44no—
826C4⋊C4—68no—
827C4⋊C4—68no—
828C4⋊C4—68no—
829C4⋊C4—124no—
830C4⋊C4—124no—
831C4⋊C4—124no—
832C4⋊C4—124no—
833C22⋊C4—28no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—68no—
838C22⋊C4—68no—
839C22⋊C4—124no—
840C22⋊C4—124no—
841C22⋊C4—124no—
842C22⋊C4—124no—
843C22⋊C4—124no—
844C42—44no—
845C22×C3—24no—
846C22×C3—24no—
847C22×C3—24no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—42no—
862C22×C3—42no—
863C22×C3—42no—
864C22×C3—42no—
865C22×C3—42no—
866C22×C3—42no—
867C22×C3—81no—
868C22×C3—81no—
869C22×C3—81no—
870C22×C3—81no—
871C22×C3—81no—
872C22×C3—81no—
873C22×C3—81no—
874C22×C3—81no—
875C22×C3C2×#12011yescharacteristic
876C22×C3C2×C22⋊Q811yescharacteristic
877C22×C3C2×C22⋊Q811yescharacteristic
878C22×C3#52511yescharacteristic
879C22×C3C2×#12711yescharacteristic
880C22×C3#53211yescharacteristic
881C22×C3#53511yescharacteristic
882C22×C3#53611yescharacteristic
883C22×C3#53611yescharacteristic
884C22×C3#53711yescharacteristic
885C22×C3#53711yescharacteristic
886C22×C3#53911yescharacteristic
887C22×C3#54211yescharacteristic
888C22×C3#54211yescharacteristic
889C22×C3#54311yescharacteristic
890C22×C3D4211yescharacteristic
891C22×C3D4211yescharacteristic
892C22×C3D4211yescharacteristic
893C22×C3D4211yescharacteristic
894C22×C3#54611yescharacteristic
895C22×C3#54611yescharacteristic
896C22×C3#54611yescharacteristic
897C22×C3#54711yescharacteristic
898C22×C3#54711yescharacteristic
899C22×C3#54711yescharacteristic
900C22×C3#54811yescharacteristic
901C22×C3#54811yescharacteristic
902C22×C3#54811yescharacteristic
903C22×C3D4×Q811yescharacteristic
904C22×C3D4×Q811yescharacteristic
905C22×C3D4×Q811yescharacteristic
906C22×C3#55111yescharacteristic
907C22×C3#55411yescharacteristic
908C22×C3#56211yescharacteristic
909C22×C3#56311yescharacteristic
910C3×C4—24no—
911C3×C4—24no—
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—81no—
915Dic3—24no—
916Dic3—42no—
917Dic3—42no—
918Dic3—42no—
919Dic3—42no—
920Dic3—42no—
921Dic3—42no—
922Dic3—81no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23#92414yes—
993C23C22×Dic611yescharacteristic
994C23C2×#23511yescharacteristic
995C23C2×D3×D411yescharacteristic
996C23C2×D3×D411yescharacteristic
997C23C2×D3×D411yescharacteristic
998C23C2×D3×D411yescharacteristic
999C23C2×#23711yescharacteristic
1000C23#100411yescharacteristic
1001C23#100411yescharacteristic
1002C23#100411yescharacteristic
1003C23D3×#4111yescharacteristic
1004C23#101011yescharacteristic
1005C23#101011yescharacteristic
1006C23#101011yescharacteristic
1007C23C22×#6711yescharacteristic
1008Q8—1216no—
1009D4—416no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—34no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—1216no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4#87814yescomplemented
1101C2×C4#93714yes—
1102C2×C3—44no—
1103C2×C3—82no—
1104C2×C3#240911yescharacteristic
1105C2×C3#243011yescharacteristic
1106C2×C3#243311yescharacteristic
1107C2×C3#243711yescharacteristic
1108C2×C3#244911yescharacteristic
1109C2×C3#245211yescharacteristic
1110C2×C3#246111yescharacteristic
1111C2×C3#254011yescharacteristic
1112C2×C3#254211yescharacteristic
1113C2×C3#267211yescharacteristic
1114C2×C3#267411yescharacteristic
1115C2×C3#268111yescharacteristic
1116C2×C3#268311yescharacteristic
1117C2×C3#269211yescharacteristic
1118C2×C3#272311yescharacteristic
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
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—42no—
1139C22—42no—
1140C22—42no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22C2×#87811yescharacteristic
1150C22#548311yescharacteristic
1151C22#549011yescharacteristic
1152C22#549511yescharacteristic
1153C22D4×Dic611yescharacteristic
1154C22D4×Dic611yescharacteristic
1155C22D4×Dic611yescharacteristic
1156C22#553911yescharacteristic
1157C22#554711yescharacteristic
1158C22#555211yescharacteristic
1159C22#555211yescharacteristic
1160C22#556411yescharacteristic
1161C22#559611yescharacteristic
1162C22#559711yescharacteristic
1163C22#559711yescharacteristic
1164C22#560311yescharacteristic
1165C22#561011yescharacteristic
1166C22#561111yescharacteristic
1167C22#561111yescharacteristic
1168C22#562111yescharacteristic
1169C22#566911yescharacteristic
1170C22#567211yescharacteristic
1171C22#567511yescharacteristic
1172C22#567711yescharacteristic
1173C22D3×#12711yescharacteristic
1174C22#571511yescharacteristic
1175C22#571711yescharacteristic
1176C22#571711yescharacteristic
1177C22C2×#92411yescharacteristic
1178C22C2×#93711yescharacteristic
1179C22D4×#6711yescharacteristic
1180C22D4×#6711yescharacteristic
1181C22#580611yescharacteristic
1182C22#582411yescharacteristic
1183C22#582511yescharacteristic
1184C4—24no—
1185C4—24no—
1186C4—42no—
1187C4—42no—
1188C4—64no—
1189C4—81no—
1190C4—122no—
1191C4—122no—
1192C4—122no—
1193C4—122no—
1194C4—122no—
1195C4—122no—
1196C4—241no—
1197C3#1532511yescharacteristic, complemented, Sylow
1198C2—44no—
1199C2—82no—
1200C2#7632311yescharacteristic
1201C2#7632711yescharacteristic
1202C2#7634711yescharacteristic
1203C2#7634911yescharacteristic
1204C2#7638011yescharacteristic
1205C2#7638211yescharacteristic
1206C2#7639711yescharacteristic
1207C2#7646511yescharacteristic
1208C2#8211011yescharacteristic
1209C2#8234911yescharacteristic
1210C2#8236011yescharacteristic
1211C2#8265111yescharacteristic
1212C2#8268211yescharacteristic
1213C2#8298211yescharacteristic
1214C2#8317511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
prime radicalC23×C3×D4C22
hypercenterC2×#390D3
hypocenterC3#15325
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#878C2semidirect
4. C2×#4979C2semidirect
5. C2×#4949C2semidirect
6. C2×#4948C2semidirect
7. C2×#4947C2semidirect
8. C2×#4946C2semidirect
10. #71568C2semidirect
11. #71547C2semidirect
12. #71547C2semidirect
13. #71546C2semidirect
14. #71536C2semidirect
15. #71535C2semidirect
85. C22×C3×D4Q8semidirect
157. C2×C4⋊Dic3D4semidirect
172. C2×Dic3⋊C4D4semidirect
185. C3⋊#95D4semidirect
409. C22×D4Dic6semidirect
623. C2×C3×C4C22⋊Q8semidirect
1100. C2×C4#878semidirect
1197. C3#15325semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×C3×#3902
C2×#52202
C2×#49792
C2×#49492
C2×#49482
C2×#49472
C2×#49462
#721312
#715682
#715472
#715462
#715362
#715352
#153253