Finite Group Databasebeta

← #10719149

Subgroups — #10719149

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#872C211yesmaximal, characteristic
2C2×#4989C211yesmaximal, characteristic
3C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#4669C211yesmaximal, characteristic
5C2×#4652C211yesmaximal, characteristic, complemented
6C3×#1436C211yesmaximal, characteristic, complemented
7#71536C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic
9#69427C211yesmaximal, characteristic
10(C2×D3)⋊#95C211yesmaximal, characteristic
11#69420C211yesmaximal, characteristic, complemented
12#69409C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic
14#69406C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14063—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×#872—24no—
35C2×#872—24no—
36C2×#872—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4989C418yescomplemented
56Dic3×C4⋊C4—24no—
57#4669—24no—
58#4652—24no—
59C22×#117—31no—
60C2×#388—31no—
61C2×#387—31no—
62C2×#385—31no—
63C2×C4×C4⋊C4—31no—
64#1444—31no—
65#1441—31no—
66#1440—31no—
67#1439—31no—
68#1437—31no—
69#1436—31no—
70#1436—31no—
71#1436D311yescharacteristic, complemented
72#1434—31no—
73C22⋊#95—31no—
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3C2×C414yes—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4C2×C414yes—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
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—41no—
116C2×(C2×D3)⋊C4—41no—
117C2×(C2×D3)⋊C4C2×C414yes—
118C2×(C2×D3)⋊C4C2×C414yes—
119C2×(C2×D3)⋊C4D414yes—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—41no—
133C2×Dic3⋊C4C2×C414yes—
134C2×Dic3⋊C4D414yes—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—22no—
137C2×C4×Dic3—22no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3—22no—
140C2×C4×Dic3—22no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3D414yes—
144#872—232no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95C2×C414yes—
162C3⋊#95C2×C414yes—
163C24×C4—31no—
164C2×#117—64no—
165C2×#117—64no—
166C2×#117—64no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4C2×D311yescharacteristic
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×C42—31no—
180C22×C42—31no—
181C22×C42—31no—
182C22×C42C2×D311yescharacteristic
183#388—64no—
184#387—64no—
185#385—38no—
186C4×C4⋊C4—64no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
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×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C2×#95C2×D311yescharacteristic
203C2×#95C2×D311yescharacteristic
204C2×#95C2×D311yescharacteristic
205C24×C3C2411yescharacteristic
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
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×D3C22×C412yes—
219C23×D3C2×D412yes—
220C23×D3#4112yes—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
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×C4C22×C412yes—
262C22×C3×C4C22×C412yes—
263C22×C3×C4C22×C412yes—
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×D412yes—
267C22×C3×C4#4112yes—
268C22×C3×C4#4112yes—
269C22×C3×C4#4112yes—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
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×Dic3C22×C412yes—
309C22×Dic3C22×C412yes—
310C22×Dic3C22×C412yes—
311C22×Dic3C2×D412yes—
312C22×Dic3C2×D412yes—
313C22×Dic3C2×D412yes—
314C22×Dic3C2×D412yes—
315C22×Dic3C2×D412yes—
316C22×Dic3#4112yes—
317C22×Dic3#4112yes—
318C22×Dic3#4112yes—
319C2×C4×D3—28no—
320C2×C4×D3—28no—
321C2×C4×D3—28no—
322C2×C4×D3—28no—
323C2×C4×D3—28no—
324C2×C4×D3—28no—
325C2×C4×D3—28no—
326C3×C4⋊C4—28no—
327C3×C42—28no—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—28no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334C4⋊Dic3—28no—
335Dic3⋊C4—28no—
336Dic3⋊C4—28no—
337Dic3⋊C4—28no—
338Dic3⋊C4—44no—
339C4×Dic3—28no—
340C4×Dic3—28no—
341C4×Dic3—44no—
342C25—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—34no—
351C23×C4—62no—
352C23×C4—62no—
353C23×C4—62no—
354C23×C4—62no—
355C23×C4—62no—
356C23×C4—62no—
357C23×C4C22×D311yescharacteristic
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D311yescharacteristic
362C23×C4C22×D311yescharacteristic
363C23×C4C22×D311yescharacteristic
364#117—632no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—34no—
368C2×C4⋊C4—34no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—62no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—121no—
382C2×C4⋊C4C4×D314yes—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—121no—
400C2×C22⋊C4—121no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—34no—
405C2×C42—62no—
406C2×C42—62no—
407C2×C42—62no—
408C2×C42—62no—
409C2×C42—62no—
410C2×C42—62no—
411C2×C42—62no—
412C2×C42—62no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—34no—
419#95—34no—
420#95—62no—
421#95—62no—
422#95—62no—
423#95—62no—
424#95—62no—
425#95—62no—
426#95—62no—
427#95—62no—
428#95—121no—
429#95—121no—
430#95—121no—
431C23×C3C23×C411yescharacteristic
432C23×C3C22×D411yescharacteristic
433C23×C3C22×D411yescharacteristic
434C23×C3C22×D411yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3H(5,𝔽2)11yescharacteristic
443C23×C32−1+411yescharacteristic
444C23×C32−1+411yescharacteristic
445C23×C32−1+411yescharacteristic
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3C4×D414yes—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4#11714yescomplemented
529C2×C3×C4C4×D414yes—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3C4×D414yes—
578C2×Dic3#12014yes—
579C4×D3—232no—
580C24—32no—
581C24—32no—
582C24—32no—
583C24—61no—
584C24—61no—
585C24—61no—
586C24—61no—
587C24—61no—
588C24—61no—
589C24—61no—
590C24—61no—
591C24—61no—
592C24—61no—
593C24—61no—
594C24—61no—
595C24C23×D311yescharacteristic
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—68no—
648C22×C4—68no—
649C22×C4—68no—
650C22×C4—68no—
651C22×C4—68no—
652C22×C4—68no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—68no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4C2×C4×D312yes—
693C22×C4C2×C4×D312yes—
694C22×C4C2×C4×D312yes—
695C22×C4#23512yes—
696C22×C4#23512yes—
697C22×C4D3×D412yes—
698C22×C4D3×D412yes—
699C22×C4D3×D412yes—
700C22×C4#23712yes—
701C4⋊C4—28no—
702C4⋊C4—68no—
703C4⋊C4—68no—
704C4⋊C4—68no—
705C4⋊C4—68no—
706C4⋊C4—124no—
707C22⋊C4—68no—
708C22⋊C4—68no—
709C22⋊C4—68no—
710C22⋊C4—68no—
711C22⋊C4—124no—
712C22⋊C4—124no—
713C42—28no—
714C42—68no—
715C42—68no—
716C42—124no—
717C22×C3C2×#11711yescharacteristic
718C22×C3C2×C4×D411yescharacteristic
719C22×C3C2×C4×D411yescharacteristic
720C22×C3C2×C4×D411yescharacteristic
721C22×C3C4×#4111yescharacteristic
722C22×C3#51911yescharacteristic
723C22×C3#52011yescharacteristic
724C22×C3C2×#12011yescharacteristic
725C22×C3#52511yescharacteristic
726C22×C3#52511yescharacteristic
727C22×C3#52511yescharacteristic
728C22×C3#52511yescharacteristic
729C22×C3#52511yescharacteristic
730C22×C3#52911yescharacteristic
731C22×C3#52911yescharacteristic
732C22×C3#53611yescharacteristic
733C22×C3#53711yescharacteristic
734C22×C3#54111yescharacteristic
735C22×C3#54211yescharacteristic
736C22×C3#54611yescharacteristic
737C22×C3#54711yescharacteristic
738C22×C3#54711yescharacteristic
739C22×C3#54711yescharacteristic
740C22×C3#54711yescharacteristic
741C22×C3#54711yescharacteristic
742C22×C3#54811yescharacteristic
743C22×C3#55011yescharacteristic
744C22×C3#55111yescharacteristic
745C22×C3#55211yescharacteristic
746C22×C3#55211yescharacteristic
747C22×C3#55211yescharacteristic
748C22×C3#55211yescharacteristic
749C22×C3#55511yescharacteristic
750C22×C3#55611yescharacteristic
751C22×C3#55611yescharacteristic
752C2×D3—24no—
753C2×D3—24no—
754C2×D3—24no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—42no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C3×C4—24no—
768C3×C4—24no—
769C3×C4—42no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—81no—
773C3×C4—81no—
774Dic3—24no—
775Dic3—24no—
776Dic3—42no—
777Dic3—42no—
778Dic3—42no—
779Dic3—42no—
780Dic3—42no—
781C23—34no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—121no—
801C23—121no—
802C23—121no—
803C23—121no—
804C23—121no—
805C23—121no—
806C23—121no—
807C23—121no—
808C23—121no—
809C23—121no—
810C23—121no—
811C23—121no—
812C23—121no—
813C23—121no—
814C23—121no—
815C23—121no—
816C23C22×C4×D311yescharacteristic
817C23C2×#23511yescharacteristic
818C23C2×#23511yescharacteristic
819C23C2×D3×D411yescharacteristic
820C23C2×D3×D411yescharacteristic
821C23C2×D3×D411yescharacteristic
822C23C2×#23711yescharacteristic
823C23#100711yescharacteristic
824C23#100711yescharacteristic
825C23D3×#4111yescharacteristic
826C23D3×#4111yescharacteristic
827C23D3×#4111yescharacteristic
828C23D3×#4111yescharacteristic
829C23#100911yescharacteristic
830C23#101011yescharacteristic
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—34no—
853C2×C4—34no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—632no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4#87214yescomplemented
929C2×C4#67⋊C414yes—
930C2×C3#229011yescharacteristic
931C2×C3C4×#12011yescharacteristic
932C2×C3#232311yescharacteristic
933C2×C3#234411yescharacteristic
934C2×C3#235411yescharacteristic
935C2×C3#235911yescharacteristic
936C2×C3#236211yescharacteristic
937C2×C3#240611yescharacteristic
938C2×C3#240711yescharacteristic
939C2×C3#247411yescharacteristic
940C2×C3#247511yescharacteristic
941C2×C3#247811yescharacteristic
942C2×C3#247911yescharacteristic
943C2×C3#259911yescharacteristic
944C2×C3#260911yescharacteristic
945D3—44no—
946C22—64no—
947C22—64no—
948C22—64no—
949C22—122no—
950C22—122no—
951C22—122no—
952C22—122no—
953C22—122no—
954C22—122no—
955C22—122no—
956C22—122no—
957C22—122no—
958C22—122no—
959C22—122no—
960C22—122no—
961C22C2×#87211yescharacteristic
962C22C2×#67⋊C411yescharacteristic
963C22#550711yescharacteristic
964C22#550711yescharacteristic
965C22#552211yescharacteristic
966C22#552911yescharacteristic
967C22#553211yescharacteristic
968C22#553811yescharacteristic
969C22#553811yescharacteristic
970C22C4×D3×D411yescharacteristic
971C22C4×D3×D411yescharacteristic
972C22#554711yescharacteristic
973C22#554711yescharacteristic
974C22#555111yescharacteristic
975C22#555311yescharacteristic
976C22#556811yescharacteristic
977C22#557211yescharacteristic
978C22#557411yescharacteristic
979C22#558111yescharacteristic
980C22D3×#12011yescharacteristic
981C22#560611yescharacteristic
982C22#560611yescharacteristic
983C22#562811yescharacteristic
984C22#562911yescharacteristic
985C22#563111yescharacteristic
986C22#563311yescharacteristic
987C22#565411yescharacteristic
988C22#565511yescharacteristic
989C22#565611yescharacteristic
990C22#568211yescharacteristic
991C22#569311yescharacteristic
992C22#569311yescharacteristic
993C22#570211yescharacteristic
994C22#570511yescharacteristic
995C22#573111yescharacteristic
996C4—24no—
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—64no—
1002C4—64no—
1003C4—81no—
1004C4—81no—
1005C4—122no—
1006C4—122no—
1007C4—122no—
1008C4—122no—
1009C4—122no—
1010C3#1406311yescharacteristic, complemented, Sylow
1011C2—124no—
1012C2#7343811yescharacteristic
1013C2#7363911yescharacteristic
1014C2#7376711yescharacteristic
1015C2#7440411yescharacteristic
1016C2#7460011yescharacteristic
1017C2#7465911yescharacteristic
1018C2#7496611yescharacteristic
1019C2#7530711yescharacteristic
1020C2#7537111yescharacteristic
1021C2#7537511yescharacteristic
1022C2#7553111yescharacteristic
1023C2#7553811yescharacteristic
1024C2#7602411yescharacteristic
1025C2#7602611yescharacteristic
1026C2#7661111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14063
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×C4⋊C4C2semidirect
5. C2×#4652C2semidirect
6. C3×#1436C2semidirect
7. #71536C2semidirect
11. #69420C2semidirect
12. #69409C2semidirect
14. #69406C2semidirect
15. #69401C2semidirect
55. #4989C4semidirect
71. #1436D3semidirect
528. C2×C3×C4#117semidirect
928. C2×C4#872semidirect
1010. C3#14063semidirect

Maximal subgroups

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

subgroupindex
C22×#8722
C2×#49892
C2×Dic3×C4⋊C42
C2×#46692
C2×#46522
C3×#14362
#715362
#694292
#694272
(C2×D3)⋊#952
#694202
#694092
#694082
#694062
#694012
#140633