Finite Group Databasebeta

← #10728184

Subgroups — #10728184

Order 768.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4989C211yesmaximal, characteristic
2C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×#4667C211yesmaximal, characteristic
4C2×#4657C211yesmaximal, characteristic, complemented
5C3×#1436C211yesmaximal, characteristic, complemented
6#71564C211yesmaximal, characteristic, complemented
7#71535C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic
9#69428C211yesmaximal, characteristic
10#69427C211yesmaximal, characteristic
11#69427C211yesmaximal, characteristic
12#69421C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69409C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#14840—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×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
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#4989—24no—
53C4×(C2×D3)⋊C4—24no—
54#4667—24no—
55#4657—24no—
56C2×#398—31no—
57C2×#385—31no—
58C2×#380—31no—
59C2×C4×C22⋊C4—31no—
60#1445—31no—
61#1444—31no—
62#1441—31no—
63#1439—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1436—31no—
68#1436D311yescharacteristic, complemented
69C4⋊#95—31no—
70C4⋊#95—31no—
71C24×D3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—41no—
91C22×C4×D3—41no—
92C22×C4×D3D414yes—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C42—22no—
97C2×C3×C42—22no—
98C2×C3×C42—41no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—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—41no—
110C2×(C2×D3)⋊C4—41no—
111C2×(C2×D3)⋊C4—41no—
112C2×(C2×D3)⋊C4—41no—
113C2×(C2×D3)⋊C4—41no—
114C2×(C2×D3)⋊C4—41no—
115C2×(C2×D3)⋊C4Q814yes—
116C2×(C2×D3)⋊C4Q814yes—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—22no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—41no—
121C2×C4⋊Dic3—41no—
122C2×C4⋊Dic3—41no—
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—22no—
133C2×Dic3⋊C4—41no—
134C2×Dic3⋊C4—41no—
135C2×Dic3⋊C4—41no—
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4—41no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3—22no—
140C2×C4×Dic3—41no—
141C3×#95—22no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—41no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95D414yes—
159C24×C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C42—31no—
175C22×C42C2×D311yescharacteristic
176#398—64no—
177#385—64no—
178#380—64no—
179C4×C22⋊C4—64no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95C2×D311yescharacteristic
194C2×#95C2×D311yescharacteristic
195C2×#95C2×D311yescharacteristic
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C24×C3C2411yescharacteristic
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3C2×D412yes—
212C23×D3C2×Q812yes—
213C23×D3C2×Q812yes—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
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×C4C2×D412yes—
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×Q812yes—
258C22×C3×C4C2×Q812yes—
259C22×C3×C4#4112yes—
260C22×C3×C4#4112yes—
261C22×C3×C4#4112yes—
262C22×C3×C4#4112yes—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
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×Dic3C2×D412yes—
305C22×Dic3C2×D412yes—
306C22×Dic3C2×D412yes—
307C22×Dic3C2×Q812yes—
308C22×Dic3C2×Q812yes—
309C22×Dic3#4112yes—
310C22×Dic3#4112yes—
311C22×Dic3#4112yes—
312C2×C4×D3—28no—
313C2×C4×D3—28no—
314C2×C4×D3—44no—
315C2×C4×D3—44no—
316C2×C4×D3—44no—
317C2×C4×D3—44no—
318C2×C4×D3—44no—
319C3×C4⋊C4—44no—
320C3×C42—44no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—28no—
324(C2×D3)⋊C4—44no—
325(C2×D3)⋊C4—44no—
326(C2×D3)⋊C4—44no—
327C4⋊Dic3—44no—
328C4⋊Dic3—44no—
329Dic3⋊C4—44no—
330Dic3⋊C4—44no—
331Dic3⋊C4—44no—
332Dic3⋊C4—44no—
333Dic3⋊C4—44no—
334C4×Dic3—44no—
335C25—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—34no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—62no—
347C23×C4—62no—
348C23×C4—121no—
349C23×C4—121no—
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—62no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—121no—
374C2×C4⋊C4—121no—
375C2×C4⋊C4—121no—
376C2×C4⋊C4—121no—
377C2×C4⋊C4—121no—
378C2×C4⋊C4—121no—
379C2×C4⋊C4—121no—
380C2×C4⋊C4—121no—
381C2×C22⋊C4—34no—
382C2×C22⋊C4—34no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—62no—
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—121no—
394C2×C22⋊C4—121no—
395C2×C22⋊C4—121no—
396C2×C22⋊C4—121no—
397C2×C22⋊C4—121no—
398C2×C22⋊C4—121no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—41no—
402C2×C42—62no—
403C2×C42—62no—
404C2×C42—121no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—34no—
410#95—41no—
411#95—62no—
412#95—62no—
413#95—62no—
414#95—62no—
415#95—62no—
416#95—62no—
417#95—62no—
418#95—121no—
419#95—121no—
420#95—121no—
421#95—121no—
422#95—121no—
423C23×C3C22×D411yescharacteristic
424C23×C3C22×D411yescharacteristic
425C23×C3C22×Q811yescharacteristic
426C23×C3C22×Q811yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3C2×#4111yescharacteristic
431C23×C3C2×#4111yescharacteristic
432C23×C3C2×#4111yescharacteristic
433C23×C3C2×#4111yescharacteristic
434C23×C3H(5,𝔽2)11yescharacteristic
435C23×C3H(5,𝔽2)11yescharacteristic
436C23×C3H(5,𝔽2)11yescharacteristic
437C23×C3H(5,𝔽2)11yescharacteristic
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
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—41no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
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×D3C4⋊Q814yes—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
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—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
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×C4C22⋊Q814yes—
521C2×C3×C4#12314yes—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
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—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
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#12114yes—
570C2×Dic3C22⋊Q814yes—
571C4×D3—416no—
572C24—32no—
573C24—32no—
574C24—32no—
575C24—61no—
576C24—61no—
577C24—61no—
578C24—61no—
579C24—61no—
580C24—61no—
581C24—61no—
582C24—61no—
583C24—61no—
584C24—61no—
585C24—61no—
586C24—61no—
587C24C23×D311yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
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—32no—
630C22×C4—32no—
631C22×C4—32no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—32no—
635C22×C4—32no—
636C22×C4—32no—
637C22×C4—68no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—68no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
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—124no—
681C22×C4—124no—
682C22×C4—124no—
683C22×C4—124no—
684C22×C4—124no—
685C22×C4#23512yes—
686C22×C4#23512yes—
687C22×C4#23512yes—
688C22×C4D3×D412yes—
689C22×C4D3×D412yes—
690C22×C4#23712yes—
691C22×C4D3×Q812yes—
692C22×C4D3×Q812yes—
693C4⋊C4—44no—
694C4⋊C4—124no—
695C4⋊C4—124no—
696C4⋊C4—124no—
697C4⋊C4—124no—
698C4⋊C4—124no—
699C4⋊C4—124no—
700C4⋊C4—124no—
701C22⋊C4—68no—
702C22⋊C4—68no—
703C22⋊C4—68no—
704C22⋊C4—124no—
705C22⋊C4—124no—
706C22⋊C4—124no—
707C42—44no—
708C42—124no—
709C22×C3C2×#12111yescharacteristic
710C22×C3C2×C22⋊Q811yescharacteristic
711C22×C3C2×C22⋊Q811yescharacteristic
712C22×C3C2×#12311yescharacteristic
713C22×C3#52511yescharacteristic
714C22×C3#52911yescharacteristic
715C22×C3#52911yescharacteristic
716C22×C3#52911yescharacteristic
717C22×C3#52911yescharacteristic
718C22×C3C2×C4⋊Q811yescharacteristic
719C22×C3#53211yescharacteristic
720C22×C3#53311yescharacteristic
721C22×C3#53311yescharacteristic
722C22×C3#53411yescharacteristic
723C22×C3#53511yescharacteristic
724C22×C3#53811yescharacteristic
725C22×C3#53811yescharacteristic
726C22×C3#54011yescharacteristic
727C22×C3#54011yescharacteristic
728C22×C3#54611yescharacteristic
729C22×C3#54611yescharacteristic
730C22×C3#54611yescharacteristic
731C22×C3#55011yescharacteristic
732C22×C3#55111yescharacteristic
733C22×C3#55111yescharacteristic
734C22×C3#55311yescharacteristic
735C22×C3#55411yescharacteristic
736C22×C3#55411yescharacteristic
737C22×C3#55411yescharacteristic
738C22×C3#55411yescharacteristic
739C22×C3#55411yescharacteristic
740C22×C3#55411yescharacteristic
741C22×C3#55411yescharacteristic
742C22×C3#55411yescharacteristic
743C22×C3#55511yescharacteristic
744C2×D3—24no—
745C2×D3—24no—
746C2×D3—24no—
747C2×D3—42no—
748C2×D3—42no—
749C2×D3—42no—
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—42no—
759C3×C4—24no—
760C3×C4—24no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4—81no—
764C3×C4—81no—
765C3×C4—81no—
766Dic3—24no—
767Dic3—24no—
768Dic3—42no—
769Dic3—42no—
770Dic3—81no—
771Dic3—81no—
772Dic3—81no—
773C23—34no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—121no—
802C23—121no—
803C23—121no—
804C23—121no—
805C23—121no—
806C23—121no—
807C23—121no—
808C23C2×#23511yescharacteristic
809C23C2×#23511yescharacteristic
810C23C2×#23511yescharacteristic
811C23C2×D3×D411yescharacteristic
812C23C2×D3×D411yescharacteristic
813C23C2×#23711yescharacteristic
814C23#100411yescharacteristic
815C23C2×D3×Q811yescharacteristic
816C23C2×D3×Q811yescharacteristic
817C23D3×#4111yescharacteristic
818C23D3×#4111yescharacteristic
819C23D3×#4111yescharacteristic
820C23#100911yescharacteristic
821C23#100911yescharacteristic
822C23#100911yescharacteristic
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
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—34no—
842C2×C4—34no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
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—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
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—1216no—
891C2×C4—121no—
892C2×C4—121no—
893C2×C4—121no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C4—121no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
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#88314yes—
921C2×C4#89614yes—
922C2×C3#239511yescharacteristic
923C2×C3#241211yescharacteristic
924C2×C3#241411yescharacteristic
925C2×C3#245011yescharacteristic
926C2×C3#245011yescharacteristic
927C2×C3#245411yescharacteristic
928C2×C3#245411yescharacteristic
929C2×C3#250211yescharacteristic
930C2×C3#252211yescharacteristic
931C2×C3#252211yescharacteristic
932C2×C3#257411yescharacteristic
933C2×C3#257411yescharacteristic
934C2×C3#258311yescharacteristic
935C2×C3#266111yescharacteristic
936C2×C3#285711yescharacteristic
937D3—44no—
938C22—64no—
939C22—64no—
940C22—64no—
941C22—122no—
942C22—122no—
943C22—122no—
944C22—122no—
945C22—122no—
946C22—122no—
947C22—122no—
948C22—122no—
949C22—122no—
950C22—122no—
951C22—122no—
952C22—122no—
953C22#547911yescharacteristic
954C22C2×#88311yescharacteristic
955C22C2×#89611yescharacteristic
956C22#551111yescharacteristic
957C22#552811yescharacteristic
958C22#553211yescharacteristic
959C22#553511yescharacteristic
960C22#553811yescharacteristic
961C22#553811yescharacteristic
962C22#554711yescharacteristic
963C22#554811yescharacteristic
964C22#555011yescharacteristic
965C22#555311yescharacteristic
966C22#555611yescharacteristic
967C22#556011yescharacteristic
968C22#557811yescharacteristic
969C22#557911yescharacteristic
970C22#557911yescharacteristic
971C22#557911yescharacteristic
972C22#559111yescharacteristic
973C22D3×#12111yescharacteristic
974C22#560511yescharacteristic
975C22D3×C22⋊Q811yescharacteristic
976C22#563511yescharacteristic
977C22#563511yescharacteristic
978C22#563611yescharacteristic
979C22#565411yescharacteristic
980C22#565811yescharacteristic
981C22#566311yescharacteristic
982C22#567411yescharacteristic
983C22#568811yescharacteristic
984C22#569011yescharacteristic
985C22#570411yescharacteristic
986C22#570911yescharacteristic
987C22D3×C4⋊Q811yescharacteristic
988C4—24no—
989C4—24no—
990C4—42no—
991C4—42no—
992C4—64no—
993C4—64no—
994C4—81no—
995C4—81no—
996C4—81no—
997C4—122no—
998C4—122no—
999C4—241no—
1000C4—241no—
1001C4—241no—
1002C3#1484011yescharacteristic, complemented, Sylow
1003C2—124no—
1004C2#7358211yescharacteristic
1005C2#7367711yescharacteristic
1006C2#7372611yescharacteristic
1007C2#7442311yescharacteristic
1008C2#7442611yescharacteristic
1009C2#7489011yescharacteristic
1010C2#7508111yescharacteristic
1011C2#7532211yescharacteristic
1012C2#7534811yescharacteristic
1013C2#7534911yescharacteristic
1014C2#7549511yescharacteristic
1015C2#7591011yescharacteristic
1016C2#7624711yescharacteristic
1017C2#7628811yescharacteristic
1018C2#7651911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14840
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#4657C2semidirect
5. C3×#1436C2semidirect
6. #71564C2semidirect
7. #71535C2semidirect
12. #69421C2semidirect
13. #69420C2semidirect
14. #69409C2semidirect
15. Dic3⋊#95C2semidirect
68. #1436D3semidirect
1002. C3#14840semidirect

Maximal subgroups

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

subgroupindex
C2×#49892
C2×C4×(C2×D3)⋊C42
C2×#46672
C2×#46572
C3×#14362
#715642
#715352
#694282
#694272
#694212
#694202
#694092
Dic3⋊#952
#148403