Finite Group Databasebeta

← #10719427

Subgroups — #10719427

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4988C211yesmaximal, characteristic
2C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4670C211yesmaximal, characteristic, complemented
5C2×#4648C211yesmaximal, characteristic, complemented
6C3×#1436C211yesmaximal, characteristic, complemented
7#71565C211yesmaximal, characteristic, complemented
8#71537C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14082—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
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#4988C418yescomplemented
53C4×(C2×D3)⋊C4—24no—
54#4670—24no—
55#4665—24no—
56#4648—24no—
57C2×#390—31no—
58C2×#388—31no—
59C2×#386—31no—
60C2×C4×C22⋊C4—31no—
61C2×#376—31no—
62#1441—31no—
63#1440—31no—
64#1439—31no—
65#1438—31no—
66#1437—31no—
67#1437—31no—
68#1437—31no—
69#1436D311yescharacteristic, complemented
70#1434—31no—
71C22⋊#95—31no—
72C24×D3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C22×D12—22no—
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—41no—
92C22×D12—41no—
93C22×D12C2×C414yes—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—41no—
100C22×C4×D3—41no—
101C2×C3×C4⋊C4—41no—
102C2×C3×C4⋊C4—41no—
103C2×C3×C4⋊C4C2×C414yescomplemented
104C2×C3×C42—22no—
105C2×C3×C42—41no—
106C2×C3×C42—41no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
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—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4C2×C414yes—
137C2×(C2×D3)⋊C4C2×C414yes—
138C2×(C2×D3)⋊C4C2×C414yescomplemented
139C2×(C2×D3)⋊C4C2×C414yescomplemented
140C2×C4⋊Dic3—22no—
141C2×C4⋊Dic3—41no—
142C2×C4⋊Dic3—41no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—22no—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3C2×C414yescomplemented
151C2×C4×Dic3D414yescomplemented
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—41no—
155C3×#95—41no—
156C3×#95D414yes—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—41no—
167C3⋊#95—41no—
168C23×D4—31no—
169C24×C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4C2×D311yescharacteristic
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C42—31no—
184C22×C42—31no—
185C22×C42—31no—
186C22×C42C2×D311yescharacteristic
187#390—38no—
188#388—64no—
189#386—64no—
190C4×C22⋊C4—64no—
191#376—64no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95C2×D311yescharacteristic
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C24×C3C2411yescharacteristic
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3C22×C412yes—
236C23×D3C22×C412yes—
237C23×D3#4112yes—
238C23×D3#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
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×C4C22×C412yes—
279C22×C3×C4C22×C412yes—
280C22×C3×C4C22×C412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4#4112yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
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×Dic3C22×C412yes—
324C22×Dic3C22×C412yes—
325C22×Dic3C2×D412yes—
326C22×Dic3C2×D412yes—
327C22×Dic3#4112yes—
328C22×Dic3#4112yes—
329C22×Dic3#4112yes—
330C2×D12—28no—
331C2×D12—28no—
332C2×D12—44no—
333C2×D12—44no—
334C2×D12—44no—
335C2×D12—44no—
336C2×D12—44no—
337C2×C4×D3—28no—
338C2×C4×D3—44no—
339C2×C4×D3—44no—
340C2×C4×D3—44no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C3×C4⋊C4—44no—
345C3×C42—44no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—44no—
358C4×Dic3—28no—
359C4×Dic3—28no—
360C4×Dic3—28no—
361C25—31no—
362C25—31no—
363C22×D4—34no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—62no—
367C22×D4—62no—
368C22×D4—121no—
369C22×D4—121no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—62no—
377C23×C4—62no—
378C23×C4—62no—
379C23×C4—62no—
380C23×C4—62no—
381C23×C4—121no—
382C23×C4—121no—
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C2×C4⋊C4—41no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—121no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4C4×D314yescomplemented
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4—121no—
429C2×C42—22no—
430C2×C42—34no—
431C2×C42—34no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—62no—
435C2×C42—62no—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42—62no—
441#95—22no—
442#95—22no—
443#95—41no—
444#95—41no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—121no—
455#95—121no—
456#95D1214yes—
457C23×C3C23×C411yescharacteristic
458C23×C3C22×D411yescharacteristic
459C23×C3C22×D411yescharacteristic
460C23×C3C2×#4111yescharacteristic
461C23×C3C2×#4111yescharacteristic
462C23×C3C2×#4111yescharacteristic
463C23×C3C2×#4111yescharacteristic
464C23×C3C2×#4111yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3H(5,𝔽2)11yescharacteristic
469C23×C3H(5,𝔽2)11yescharacteristic
470C23×C3H(5,𝔽2)11yescharacteristic
471C23×C3H(5,𝔽2)11yescharacteristic
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3#11714yes—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4C4×D414yes—
590C2×C3×C4#12114yes—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3C4×D414yes—
633D12—416no—
634C4×D3—416no—
635C24—32no—
636C24—32no—
637C24—32no—
638C24—32no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24C23×D311yescharacteristic
666C2×D4—68no—
667C2×D4—68no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C2×D4—124no—
672C2×D4—124no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—32no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—68no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—124no—
756C22×C4—124no—
757C22×C4—124no—
758C22×C4—124no—
759C22×C4—124no—
760C22×C4—124no—
761C22×C4C2×C4×D312yes—
762C22×C4C2×C4×D312yes—
763C22×C4C2×C4×D312yes—
764C22×C4C2×D1212yes—
765C22×C4C2×D1212yes—
766C22×C4C2×D1212yes—
767C22×C4#23512yes—
768C22×C4D3×D412yes—
769C22×C4#23912yes—
770C22×C4#23912yes—
771C4⋊C4—44no—
772C4⋊C4—124no—
773C22⋊C4—68no—
774C22⋊C4—68no—
775C22⋊C4—68no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C22⋊C4—124no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C42—44no—
785C42—68no—
786C42—68no—
787C42—68no—
788C22×C3C2×#11711yescharacteristic
789C22×C3C2×C4×D411yescharacteristic
790C22×C3C2×C4×D411yescharacteristic
791C22×C3C4×#4111yescharacteristic
792C22×C3C4×#4111yescharacteristic
793C22×C3#51811yescharacteristic
794C22×C3#51811yescharacteristic
795C22×C3C2×#12111yescharacteristic
796C22×C3#52511yescharacteristic
797C22×C3#52511yescharacteristic
798C22×C3#52511yescharacteristic
799C22×C3#52911yescharacteristic
800C22×C3#52911yescharacteristic
801C22×C3#52911yescharacteristic
802C22×C3#53211yescharacteristic
803C22×C3#53511yescharacteristic
804C22×C3#53511yescharacteristic
805C22×C3#54011yescharacteristic
806C22×C3#54011yescharacteristic
807C22×C3#54611yescharacteristic
808C22×C3#54611yescharacteristic
809C22×C3#54611yescharacteristic
810C22×C3#55011yescharacteristic
811C22×C3#55111yescharacteristic
812C22×C3#55111yescharacteristic
813C22×C3#55111yescharacteristic
814C22×C3#55111yescharacteristic
815C22×C3#55111yescharacteristic
816C22×C3#55111yescharacteristic
817C22×C3#55311yescharacteristic
818C22×C3#55311yescharacteristic
819C22×C3#55311yescharacteristic
820C22×C3#55511yescharacteristic
821C22×C3#55511yescharacteristic
822C22×C3#55511yescharacteristic
823C2×D3—24no—
824C2×D3—24no—
825C2×D3—24no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—42no—
832C2×D3—42no—
833C2×D3—42no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—81no—
846C2×D3—81no—
847C2×D3—81no—
848C2×D3—81no—
849C2×D3—81no—
850C2×D3—81no—
851C2×D3—81no—
852C2×D3—81no—
853C3×C4—24no—
854C3×C4—24no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4—81no—
860Dic3—24no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864Dic3—42no—
865Dic3—81no—
866C23—34no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23C22×C4×D311yescharacteristic
937C23C22×D1211yescharacteristic
938C23C2×#23511yescharacteristic
939C23C2×D3×D411yescharacteristic
940C23#100411yescharacteristic
941C23#100411yescharacteristic
942C23#100411yescharacteristic
943C23C2×#23911yescharacteristic
944C23C2×#23911yescharacteristic
945C23D3×#4111yescharacteristic
946C23D3×#4111yescharacteristic
947C23D3×#4111yescharacteristic
948C23D3×#4111yescharacteristic
949C23D3×#4111yescharacteristic
950C23#100911yescharacteristic
951D4—1216no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—34no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—1216no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4C4×D1214yes—
1043C2×C4#89514yes—
1044C2×C3#229011yescharacteristic
1045C2×C3C4×#12111yescharacteristic
1046C2×C3#232811yescharacteristic
1047C2×C3#234211yescharacteristic
1048C2×C3#235311yescharacteristic
1049C2×C3#236311yescharacteristic
1050C2×C3#237211yescharacteristic
1051C2×C3#241111yescharacteristic
1052C2×C3#241411yescharacteristic
1053C2×C3#247111yescharacteristic
1054C2×C3#247611yescharacteristic
1055C2×C3#252611yescharacteristic
1056C2×C3#253111yescharacteristic
1057C2×C3#260311yescharacteristic
1058C2×C3#261011yescharacteristic
1059D3—44no—
1060D3—82no—
1061C22—64no—
1062C22—64no—
1063C22—64no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—122no—
1070C22—122no—
1071C22—122no—
1072C22—122no—
1073C22—122no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—241no—
1084C22—241no—
1085C22—241no—
1086C22—241no—
1087C22—241no—
1088C22—241no—
1089C22—241no—
1090C22—241no—
1091C22C2×C4×D1211yescharacteristic
1092C22#548611yescharacteristic
1093C22C2×#89511yescharacteristic
1094C22#551411yescharacteristic
1095C22D3×#11711yescharacteristic
1096C22#552411yescharacteristic
1097C22#553211yescharacteristic
1098C22C4×D3×D411yescharacteristic
1099C22#554511yescharacteristic
1100C22#554811yescharacteristic
1101C22#555411yescharacteristic
1102C22#555411yescharacteristic
1103C22#555411yescharacteristic
1104C22#555611yescharacteristic
1105C22#555611yescharacteristic
1106C22C4×#23911yescharacteristic
1107C22C4×#23911yescharacteristic
1108C22#557711yescharacteristic
1109C22#558011yescharacteristic
1110C22#559211yescharacteristic
1111C22#560711yescharacteristic
1112C22#561511yescharacteristic
1113C22#562711yescharacteristic
1114C22#563711yescharacteristic
1115C22#563711yescharacteristic
1116C22#563711yescharacteristic
1117C22#565611yescharacteristic
1118C22#566111yescharacteristic
1119C22#566311yescharacteristic
1120C22#567011yescharacteristic
1121C22#569111yescharacteristic
1122C22#569511yescharacteristic
1123C22#570511yescharacteristic
1124C22#570611yescharacteristic
1125C22#573411yescharacteristic
1126C4—24no—
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—64no—
1133C4—81no—
1134C4—122no—
1135C4—122no—
1136C4—122no—
1137C4—122no—
1138C4—241no—
1139C3#1408211yescharacteristic, complemented, Sylow
1140C2—124no—
1141C2—242no—
1142C2#7357511yescharacteristic
1143C2#7364911yescharacteristic
1144C2C4×#89511yescharacteristic
1145C2#7449911yescharacteristic
1146C2#7460211yescharacteristic
1147C2#7466711yescharacteristic
1148C2#7493711yescharacteristic
1149C2#7530611yescharacteristic
1150C2#7533211yescharacteristic
1151C2#7535611yescharacteristic
1152C2#7586311yescharacteristic
1153C2#7590011yescharacteristic
1154C2#7620911yescharacteristic
1155C2#7624311yescharacteristic
1156C2#7649511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#14082
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×C4×(C2×D3)⋊C4C2semidirect
4. C2×#4670C2semidirect
5. C2×#4648C2semidirect
6. C3×#1436C2semidirect
7. #71565C2semidirect
8. #71537C2semidirect
9. #69429C2semidirect
10. #69427C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69408C2semidirect
14. #69408C2semidirect
15. #69402C2semidirect
52. #4988C4semidirect
69. #1436D3semidirect
103. C2×C3×C4⋊C4C2×C4semidirect
138. C2×(C2×D3)⋊C4C2×C4semidirect
139. C2×(C2×D3)⋊C4C2×C4semidirect
150. C2×C4×Dic3C2×C4semidirect
151. C2×C4×Dic3D4semidirect
395. C2×C4⋊C4C4×D3semidirect
1139. C3#14082semidirect

Maximal subgroups

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

subgroupindex
C2×#49882
C2×C4×(C2×D3)⋊C42
C2×#46652
C2×#46702
C2×#46482
C3×#14362
#715652
#715372
#694292
#694272
#694262
(C2×D3)⋊#952
#694082
#694022
#140823