Finite Group Databasebeta

← #10733806

Subgroups — #10733806

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×#924C211yesmaximal, characteristic, complemented
2C2×C3×#386C211yesmaximal, characteristic
3C2×#5221C211yesmaximal, characteristic
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×#4949C211yesmaximal, characteristic, complemented
6C2×#4948C211yesmaximal, characteristic, complemented
7C2×#4947C211yesmaximal, characteristic, complemented
8C2×#4656C211yesmaximal, characteristic, complemented
9#72131C211yesmaximal, characteristic
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71546C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#15325—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C2×#924—24no—
35C2×#924—24no—
36C2×#924—24no—
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C3×#386—24no—
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46#5221—24no—
47#5210—24no—
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
57C2×C3⋊#95C2211yescharacteristic
58#4949—24no—
59#4948—24no—
60#4947—24no—
61#4656—24no—
62C22×C22⋊Q8—31no—
63C2×#399—31no—
64C2×#396—31no—
65C2×#395—31no—
66C2×#393—31no—
67C2×#390—31no—
68C2×#386D311yescharacteristic
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×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—41no—
92C23×C3×C4—41no—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
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×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
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—41no—
142C2×#217—41no—
143C2×#217—41no—
144C2×#217—41no—
145C2×#217D414yes—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—22no—
152C2×C4⋊Dic3—41no—
153C2×C4⋊Dic3—41no—
154C2×C4⋊Dic3D414yescomplemented
155#924—232no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
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—41no—
169C2×Dic3⋊C4—41no—
170C2×Dic3⋊C4D414yescomplemented
171C2×C4×Dic3—22no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—41no—
174C3×#95—22no—
175C3×#95D414yes—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—41no—
185C3⋊#95D414yescomplemented
186C23×Q8—31no—
187C23×D4C2×D311yescharacteristic
188C24×C4C2×D311yescharacteristic
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⋊C4—31no—
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⋊C4—31no—
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#399—64no—
213#396—64no—
214#395—64no—
215#393—64no—
216#390—64no—
217#386—24no—
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×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
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—28no—
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×C4—21no—
297C22×C3×C4—44no—
298C22×C3×C4—44no—
299C22×C3×C4—44no—
300C22×C3×C4—44no—
301C22×C3×C4—44no—
302C22×C3×C4—44no—
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2×Q812yes—
310C22×C3×C4#4112yes—
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—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
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×C22⋊C4—44no—
375C3×C22⋊C4—44no—
376C3×C22⋊C4—44no—
377#217—28no—
378#217—28no—
379#217—28no—
380#217—44no—
381#217—44no—
382#217—44no—
383#217—44no—
384#217—44no—
385C4⋊Dic3—28no—
386C4⋊Dic3—44no—
387C4⋊Dic3—44no—
388Dic3⋊C4—28no—
389Dic3⋊C4—28no—
390Dic3⋊C4—44no—
391Dic3⋊C4—44no—
392Dic3⋊C4—44no—
393C4×Dic3—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—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—41no—
424C23×C4—41no—
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C22⋊Q8—632no—
431C2×C4⋊C4—34no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—62no—
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—121no—
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—34no—
463C2×C22⋊C4—41no—
464C2×C22⋊C4—41no—
465C2×C22⋊C4—62no—
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—62no—
484C2×C22⋊C4—121no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4—121no—
488C2×C42—62no—
489C2×C42—62no—
490C2×C42—121no—
491#95—22no—
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—121no—
502#95#6714yes—
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—416no—
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—41no—
623C2×C3×C4C22⋊Q814yescomplemented
624C2×C3×C4#12714yes—
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—22no—
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#12014yes—
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—
710C24D3×D412yes—
711C24#23712yes—
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—28no—
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—21no—
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—32no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
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—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4—61no—
815C22×C4—61no—
816C22×C4—61no—
817C22×C4C2×Dic612yes—
818C22×C4#23512yes—
819C22×C4D3×D412yes—
820C22×C4D3×D412yes—
821C22×C4D3×D412yes—
822C22×C4C2×#6712yes—
823C22×C4C2×#6712yes—
824C22×C4C2×#6712yes—
825C4⋊C4—68no—
826C4⋊C4—68no—
827C4⋊C4—68no—
828C4⋊C4—124no—
829C4⋊C4—124no—
830C4⋊C4—124no—
831C4⋊C4—124no—
832C4⋊C4—124no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—68no—
837C22⋊C4—68no—
838C22⋊C4—68no—
839C22⋊C4—124no—
840C22⋊C4—124no—
841C22⋊C4—124no—
842C22⋊C4—124no—
843C22⋊C4—124no—
844C42—124no—
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#87814yes—
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—416no—
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—41no—
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—62no—
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#92414yescomplemented
1101C2×C4#94014yes—
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#554811yescharacteristic
1158C22#555111yescharacteristic
1159C22#555111yescharacteristic
1160C22#556111yescharacteristic
1161C22D3×#12011yescharacteristic
1162C22#559011yescharacteristic
1163C22#559011yescharacteristic
1164C22#559211yescharacteristic
1165C22#559811yescharacteristic
1166C22#559811yescharacteristic
1167C22#560211yescharacteristic
1168C22#560611yescharacteristic
1169C22#560811yescharacteristic
1170C22#560811yescharacteristic
1171C22#561211yescharacteristic
1172C22#562111yescharacteristic
1173C22#564811yescharacteristic
1174C22#565111yescharacteristic
1175C22#565511yescharacteristic
1176C22#566211yescharacteristic
1177C22C2×#92411yescharacteristic
1178C22D4×#6711yescharacteristic
1179C22D4×#6711yescharacteristic
1180C22C2×#94011yescharacteristic
1181C22#580611yescharacteristic
1182C22#582511yescharacteristic
1183C22#583111yescharacteristic
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#7468911yescharacteristic
1201C2#7470911yescharacteristic
1202C2#7471811yescharacteristic
1203C2#7479511yescharacteristic
1204C2#7480311yescharacteristic
1205C2#7482611yescharacteristic
1206C2#7489611yescharacteristic
1207C2#7491411yescharacteristic
1208C2#8211011yescharacteristic
1209C2#8236211yescharacteristic
1210C2#8237911yescharacteristic
1211C2#8258811yescharacteristic
1212C2#8266811yescharacteristic
1213C2#8268511yescharacteristic
1214C2#8287011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#15325
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#924C2semidirect
4. C2×#5210C2semidirect
5. C2×#4949C2semidirect
6. C2×#4948C2semidirect
7. C2×#4947C2semidirect
8. C2×#4656C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. #71546C2semidirect
13. #69420C2semidirect
14. #69407C2semidirect
15. Dic3⋊#95C2semidirect
85. C22×C3×D4Q8semidirect
154. C2×C4⋊Dic3D4semidirect
170. C2×Dic3⋊C4D4semidirect
185. C3⋊#95D4semidirect
409. C22×D4Dic6semidirect
623. C2×C3×C4C22⋊Q8semidirect
1100. C2×C4#924semidirect
1197. C3#15325semidirect

Maximal subgroups

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

subgroupindex
C22×#9242
C2×C3×#3862
C2×#52212
C2×#52102
C2×#49492
C2×#49482
C2×#49472
C2×#46562
#721312
#715472
#715462
#694202
#694072
Dic3⋊#952
#153253