Finite Group Databasebeta

← #10733807

Subgroups — #10733807

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×#897C211yesmaximal, characteristic, complemented
2C2×#4994C211yesmaximal, characteristic, complemented
3C2×#4939C211yesmaximal, characteristic
4C2×#4677C211yesmaximal, characteristic, complemented
5C2×#4673C211yesmaximal, characteristic, complemented
6C2×#4665C211yesmaximal, characteristic
7C2×#4668C211yesmaximal, characteristic, complemented
8C2×#4656C211yesmaximal, characteristic, complemented
9C3×#1436C211yesmaximal, characteristic, complemented
10#71535C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69426C211yesmaximal, characteristic
15#69419C211yesmaximal, characteristic, complemented
16#15325—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C2×#897—24no—
41C2×#897—24no—
42C2×#897—24no—
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
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4994—24no—
56#4939—24no—
57#4677—24no—
58#4673—24no—
59#4668—24no—
60#4665—24no—
61#4656—24no—
62C22×C22⋊Q8—31no—
63C2×#399—31no—
64C2×#396—31no—
65C2×#395—31no—
66C2×#393—31no—
67C2×#390—31no—
68C2×#386—31no—
69C2×#385—31no—
70#1444—31no—
71#1439—31no—
72#1439—31no—
73#1439—31no—
74#1438—31no—
75#1436D311yescharacteristic, complemented
76C4⋊#95—31no—
77C24×D3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—41no—
97C22×D12—41no—
98C22×D12Q814yescomplemented
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
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⋊C4D414yescomplemented
116C2×C3×C42—22no—
117C2×C3×C42—22no—
118C2×C3×C42—41no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4—41no—
149C2×(C2×D3)⋊C4—41no—
150C2×(C2×D3)⋊C4—41no—
151C2×(C2×D3)⋊C4D414yes—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—22no—
160C2×C4⋊Dic3—22no—
161C2×C4⋊Dic3—22no—
162C2×C4⋊Dic3—22no—
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—41no—
166C2×C4⋊Dic3—41no—
167C2×C4⋊Dic3—41no—
168C2×C4⋊Dic3—41no—
169C2×C4⋊Dic3D414yescomplemented
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173#897—232no—
174C3×#95—22no—
175C3×#95—22no—
176C3×#95—41no—
177C3×#95D414yes—
178C3×#95D414yescomplemented
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C23×Q8—31no—
187C23×D4—31no—
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⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C42C2×D311yescharacteristic
212#399—64no—
213#396—64no—
214#395—64no—
215#393—64no—
216#390—64no—
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×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C24×C3C2411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3C2×D412yes—
259C23×D3C2×Q812yes—
260C23×D3C2×Q812yes—
261C23×D3#4112yes—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
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×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
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×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3#4112yes—
353C2×D12—28no—
354C2×D12—28no—
355C2×D12—44no—
356C2×D12—44no—
357C2×D12—44no—
358C2×D12—44no—
359C2×D12—44no—
360C2×C4×D3—28no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×Dic6—28no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C2×Dic6—44no—
371C2×Dic6—44no—
372C2×Dic6—44no—
373C2×Dic6—44no—
374C3×C4⋊C4—28no—
375C3×C42—44no—
376(C2×D3)⋊C4—28no—
377(C2×D3)⋊C4—28no—
378(C2×D3)⋊C4—28no—
379(C2×D3)⋊C4—44no—
380(C2×D3)⋊C4—44no—
381(C2×D3)⋊C4—44no—
382(C2×D3)⋊C4—44no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4—44no—
385(C2×D3)⋊C4—44no—
386(C2×D3)⋊C4—44no—
387C4⋊Dic3—28no—
388C4⋊Dic3—28no—
389C4⋊Dic3—44no—
390C4⋊Dic3—44no—
391C4⋊Dic3—44no—
392C4⋊Dic3—44no—
393Dic3⋊C4—44no—
394C25—31no—
395C25—31no—
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—62no—
399C22×Q8—62no—
400C22×Q8—62no—
401C22×Q8—121no—
402C22×Q8—121no—
403C22×D4—34no—
404C22×D4—62no—
405C22×D4—62no—
406C22×D4—62no—
407C22×D4—62no—
408C22×D4—121no—
409C22×D4—121no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—62no—
417C23×C4—62no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—121no—
422C23×C4—121no—
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
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—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—121no—
451C2×C4⋊C4—121no—
452C2×C4⋊C4—121no—
453C2×C4⋊C4—121no—
454C2×C4⋊C4D1214yescomplemented
455C2×C22⋊C4—34no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
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—121no—
483C2×C22⋊C4—121no—
484C2×C22⋊C4—121no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4—121no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—41no—
491#95—22no—
492#95—22no—
493#95—41no—
494#95—62no—
495#95—62no—
496#95—62no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95D1214yes—
502#95D1214yescomplemented
503C23×C3C22×D411yescharacteristic
504C23×C3C22×D411yescharacteristic
505C23×C3C22×D411yescharacteristic
506C23×C3C22×D411yescharacteristic
507C23×C3C22×D411yescharacteristic
508C23×C3C22×Q811yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4111yescharacteristic
512C23×C3H(5,𝔽2)11yescharacteristic
513C23×C3H(5,𝔽2)11yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C23×C32−1+411yescharacteristic
516C23×C32−1+411yescharacteristic
517C23×C32−1+411yescharacteristic
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3C22⋊Q814yes—
588C2×C3×C4—22no—
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—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4#12014yes—
635C2×C3×C4C22⋊Q814yescomplemented
636C2×C3×C4#12714yes—
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—
679D12—416no—
680C4×D3—416no—
681Dic6—416no—
682C24—32no—
683C24—32no—
684C24—32no—
685C24—32no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—61no—
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—68no—
721C2×D4—68no—
722C2×D4—124no—
723C2×D4—124no—
724C2×D4—124no—
725C2×D4—124no—
726C2×D4—124no—
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—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—32no—
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—124no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4—124no—
810C22×C4—124no—
811C22×C4—124no—
812C22×C4C2×D1212yes—
813C22×C4C2×D1212yes—
814C22×C4C2×D1212yes—
815C22×C4C2×D1212yes—
816C22×C4C2×D1212yes—
817C22×C4C2×D1212yes—
818C22×C4C2×D1212yes—
819C22×C4C2×D1212yes—
820C22×C4C2×D1212yes—
821C22×C4D3×D412yes—
822C22×C4D3×D412yes—
823C22×C4#23712yes—
824C22×C4D3×Q812yes—
825C4⋊C4—28no—
826C4⋊C4—68no—
827C4⋊C4—68no—
828C4⋊C4—124no—
829C4⋊C4—124no—
830C4⋊C4—124no—
831C4⋊C4—124no—
832C4⋊C4—124no—
833C22⋊C4—68no—
834C22⋊C4—68no—
835C22⋊C4—68no—
836C22⋊C4—124no—
837C22⋊C4—124no—
838C22⋊C4—124no—
839C22⋊C4—124no—
840C22⋊C4—124no—
841C22⋊C4—124no—
842C22⋊C4—124no—
843C22⋊C4—124no—
844C42—44no—
845C22×C3C2×#12011yescharacteristic
846C22×C3C2×C22⋊Q811yescharacteristic
847C22×C3C2×C22⋊Q811yescharacteristic
848C22×C3#52511yescharacteristic
849C22×C3C2×#12711yescharacteristic
850C22×C3#53211yescharacteristic
851C22×C3#53511yescharacteristic
852C22×C3#53611yescharacteristic
853C22×C3#53611yescharacteristic
854C22×C3#53711yescharacteristic
855C22×C3#53711yescharacteristic
856C22×C3#53911yescharacteristic
857C22×C3#54211yescharacteristic
858C22×C3#54211yescharacteristic
859C22×C3#54311yescharacteristic
860C22×C3D4211yescharacteristic
861C22×C3D4211yescharacteristic
862C22×C3D4211yescharacteristic
863C22×C3D4211yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54611yescharacteristic
867C22×C3#54711yescharacteristic
868C22×C3#54711yescharacteristic
869C22×C3#54711yescharacteristic
870C22×C3#54811yescharacteristic
871C22×C3#54811yescharacteristic
872C22×C3#54811yescharacteristic
873C22×C3D4×Q811yescharacteristic
874C22×C3D4×Q811yescharacteristic
875C22×C3D4×Q811yescharacteristic
876C22×C3#55111yescharacteristic
877C22×C3#55411yescharacteristic
878C22×C3#56211yescharacteristic
879C22×C3#56311yescharacteristic
880C2×D3—24no—
881C2×D3—24no—
882C2×D3—24no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—42no—
887C2×D3—42no—
888C2×D3—42no—
889C2×D3—42no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—42no—
893C2×D3—42no—
894C2×D3—42no—
895C2×D3—42no—
896C2×D3—42no—
897C2×D3—42no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C2×D3—81no—
903C2×D3—81no—
904C2×D3—81no—
905C2×D3—81no—
906C2×D3—81no—
907C2×D3—81no—
908C2×D3—81no—
909C2×D3—81no—
910C3×C4—24no—
911C3×C4—24no—
912C3×C4—24no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—42no—
916C3×C4—42no—
917Dic3—42no—
918Dic3—42no—
919Dic3—42no—
920Dic3—42no—
921Dic3—81no—
922Dic3—81no—
923C23—34no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23—121no—
983C23—121no—
984C23—121no—
985C23—121no—
986C23—121no—
987C23—121no—
988C23—121no—
989C23—121no—
990C23—121no—
991C23—121no—
992C23—121no—
993C23C22×D1211yescharacteristic
994C23C22×D1211yescharacteristic
995C23C22×D1211yescharacteristic
996C23C2×D3×D411yescharacteristic
997C23C2×D3×D411yescharacteristic
998C23C2×#23711yescharacteristic
999C23#100411yescharacteristic
1000C23C2×D3×Q811yescharacteristic
1001C23#100711yescharacteristic
1002C23D3×#4111yescharacteristic
1003C23D3×#4111yescharacteristic
1004C23#100911yescharacteristic
1005C23#100911yescharacteristic
1006C23#101011yescharacteristic
1007C23#101011yescharacteristic
1008Q8—1216no—
1009D4—1216no—
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—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
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#87414yes—
1100C2×C4#88214yes—
1101C2×C4#89714yescomplemented
1102C2×C3#240911yescharacteristic
1103C2×C3#243011yescharacteristic
1104C2×C3#243311yescharacteristic
1105C2×C3#243711yescharacteristic
1106C2×C3#244911yescharacteristic
1107C2×C3#245211yescharacteristic
1108C2×C3#246111yescharacteristic
1109C2×C3#254011yescharacteristic
1110C2×C3#254211yescharacteristic
1111C2×C3#267211yescharacteristic
1112C2×C3#267411yescharacteristic
1113C2×C3#268111yescharacteristic
1114C2×C3#268311yescharacteristic
1115C2×C3#269211yescharacteristic
1116C2×C3#272311yescharacteristic
1117D3—44no—
1118D3—82no—
1119C22—64no—
1120C22—64no—
1121C22—64no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—122no—
1126C22—122no—
1127C22—122no—
1128C22—122no—
1129C22—122no—
1130C22—122no—
1131C22—122no—
1132C22—122no—
1133C22—122no—
1134C22—122no—
1135C22—122no—
1136C22—122no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—241no—
1142C22—241no—
1143C22—241no—
1144C22—241no—
1145C22—241no—
1146C22—241no—
1147C22—241no—
1148C22—241no—
1149C22C2×#87411yescharacteristic
1150C22C2×#88211yescharacteristic
1151C22C2×#89711yescharacteristic
1152C22#551011yescharacteristic
1153C22#552411yescharacteristic
1154C22#552511yescharacteristic
1155C22#552611yescharacteristic
1156C22D4×D1211yescharacteristic
1157C22D4×D1211yescharacteristic
1158C22D4×D1211yescharacteristic
1159C22D4×D1211yescharacteristic
1160C22#555411yescharacteristic
1161C22#555411yescharacteristic
1162C22#555511yescharacteristic
1163C22#555511yescharacteristic
1164C22Q8×D1211yescharacteristic
1165C22Q8×D1211yescharacteristic
1166C22#557611yescharacteristic
1167C22#557611yescharacteristic
1168C22#559111yescharacteristic
1169C22#559611yescharacteristic
1170C22#559711yescharacteristic
1171C22D3×C22⋊Q811yescharacteristic
1172C22#562811yescharacteristic
1173C22#563411yescharacteristic
1174C22#564311yescharacteristic
1175C22#565511yescharacteristic
1176C22#565811yescharacteristic
1177C22#566711yescharacteristic
1178C22#567711yescharacteristic
1179C22#569011yescharacteristic
1180C22#569911yescharacteristic
1181C22#570711yescharacteristic
1182C22#571011yescharacteristic
1183C22#572711yescharacteristic
1184C4—24no—
1185C4—24no—
1186C4—24no—
1187C4—42no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—122no—
1192C4—122no—
1193C4—122no—
1194C4—122no—
1195C4—241no—
1196C4—241no—
1197C3#1532511yescharacteristic, complemented, Sylow
1198C2—124no—
1199C2—242no—
1200C2#7358711yescharacteristic
1201C2#7379811yescharacteristic
1202C2#7380011yescharacteristic
1203C2#7441311yescharacteristic
1204C2#7462911yescharacteristic
1205C2#7469911yescharacteristic
1206C2#7517411yescharacteristic
1207C2#7532111yescharacteristic
1208C2#7538811yescharacteristic
1209C2#7539411yescharacteristic
1210C2#7551311yescharacteristic
1211C2#7566911yescharacteristic
1212C2#7601111yescharacteristic
1213C2#7626111yescharacteristic
1214C2#7661911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#15325
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×#897C2semidirect
2. C2×#4994C2semidirect
4. C2×#4677C2semidirect
5. C2×#4673C2semidirect
7. C2×#4668C2semidirect
8. C2×#4656C2semidirect
9. C3×#1436C2semidirect
10. #71535C2semidirect
11. #69427C2semidirect
12. #69427C2semidirect
13. #69427C2semidirect
15. #69419C2semidirect
75. #1436D3semidirect
98. C22×D12Q8semidirect
115. C2×C3×C4⋊C4D4semidirect
169. C2×C4⋊Dic3D4semidirect
178. C3×#95D4semidirect
454. C2×C4⋊C4D12semidirect
502. #95D12semidirect
635. C2×C3×C4C22⋊Q8semidirect
1101. C2×C4#897semidirect
1197. C3#15325semidirect

Maximal subgroups

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

subgroupindex
C22×#8972
C2×#49942
C2×#49392
C2×#46772
C2×#46732
C2×#46652
C2×#46682
C2×#46562
C3×#14362
#715352
#694272
#694262
#694192
#153253