Finite Group Databasebeta

← #10718895

Subgroups — #10718895

Order 768.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4989C211yesmaximal, characteristic
2C2×#4668C211yesmaximal, characteristic
3C2×#4668C211yesmaximal, characteristic
4C2×D3×#95C211yesmaximal, characteristic
5C2×#4666C211yesmaximal, characteristic
6C3×#1442C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C211yesmaximal, characteristic
9(C2×D3)⋊#95C211yesmaximal, characteristic
10#69413C211yesmaximal, characteristic, complemented
11#69411C211yesmaximal, characteristic, complemented
12#69409C211yesmaximal, characteristic, complemented
13#69407C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#14044—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
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—
53#4668—24no—
54#4668C418yescomplemented
55#4666—24no—
56D3×#95—24no—
57C2×#385—31no—
58C2×#385—31no—
59C2×#385—31no—
60C2×C4×C22⋊C4—31no—
61C22×#95—31no—
62#1442—31no—
63#1442D311yescharacteristic, complemented
64#1441—31no—
65#1441—31no—
66#1436—31no—
67#1436—31no—
68C4⋊#95—31no—
69C4⋊#95—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C22×C4×D3—22no—
88C22×C4×D3—22no—
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×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—41no—
99C22×C4×D3—41no—
100C22×C4×D3—41no—
101C22×C4×D3—41no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
106C22×C4×D3C2×C414yes—
107C22×C4×D3D414yes—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—41no—
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)⋊C4C2×C414yes—
119C2×(C2×D3)⋊C4C2×C414yes—
120C2×(C2×D3)⋊C4D414yes—
121C2×(C2×D3)⋊C4Q814yes—
122C2×(C2×D3)⋊C4Q814yes—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×C4⋊Dic3—41no—
127C2×C4⋊Dic3—41no—
128C2×C4⋊Dic3C2×C414yescomplemented
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—41no—
133C2×Dic3⋊C4—41no—
134C2×Dic3⋊C4—41no—
135C2×Dic3⋊C4—41no—
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4C2×C414yescomplemented
138C2×C4×Dic3—22no—
139C2×C4×Dic3—22no—
140C2×C4×Dic3—22no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—41no—
143C2×C4×Dic3—41no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—41no—
149C3×#95C2×C414yescomplemented
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⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95C2×C414yescomplemented
164C24×C4—31no—
165C24×C4—31no—
166C24×C4—31no—
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×C42—31no—
178C22×C42—31no—
179#385—38no—
180#385—64no—
181#385—64no—
182C4×C22⋊C4—64no—
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×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—64no—
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C2×#95C2×D311yescharacteristic
203C2×#95C2×D311yescharacteristic
204C24×C3C2411yescharacteristic
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3C22×C412yes—
214C23×D3C2×D412yes—
215C23×D3C2×D412yes—
216C23×D3C2×Q812yes—
217C23×D3C2×Q812yes—
218C23×D3#4112yes—
219C23×D3#4112yes—
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×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×Q812yes—
267C22×C3×C4C2×Q812yes—
268C22×C3×C4#4112yes—
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×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×Q812yes—
314C22×Dic3C2×Q812yes—
315C22×Dic3#4112yes—
316C22×Dic3#4112yes—
317C22×Dic3#4112yes—
318C2×C4×D3—28no—
319C2×C4×D3—28no—
320C2×C4×D3—28no—
321C2×C4×D3—28no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3—44no—
326C2×C4×D3—44no—
327C2×C4×D3—44no—
328C2×C4×D3—44no—
329C2×C4×D3—44no—
330C2×C4×D3—44no—
331C2×C4×D3—44no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
339C3×C4⋊C4—44no—
340(C2×D3)⋊C4—28no—
341(C2×D3)⋊C4—28no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4C4⋊C4116yescomplemented
344C4⋊Dic3—44no—
345C4⋊Dic3—44no—
346Dic3⋊C4—44no—
347Dic3⋊C4—44no—
348Dic3⋊C4—44no—
349C4×Dic3—44no—
350C4×Dic3—44no—
351C25—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—34no—
359C23×C4—34no—
360C23×C4—31no—
361C23×C4—62no—
362C23×C4—62no—
363C23×C4—62no—
364C23×C4—62no—
365C23×C4—62no—
366C23×C4—62no—
367C23×C4—62no—
368C23×C4—62no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—121no—
373C23×C4—121no—
374C23×C4—121no—
375C23×C4—121no—
376C23×C4—121no—
377C23×C4—121no—
378C23×C4—121no—
379C23×C4—121no—
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D311yescharacteristic
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—121no—
399C2×C4⋊C4—121no—
400C2×C4⋊C4—121no—
401C2×C4⋊C4—121no—
402C2×C4⋊C4—121no—
403C2×C4⋊C4—121no—
404C2×C4⋊C4—121no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
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×C42—62no—
418C2×C42—62no—
419C2×C42—62no—
420C2×C42—62no—
421C2×C42—121no—
422C2×C42—121no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—34no—
428#95—41no—
429#95—62no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95—121no—
441#95—121no—
442#95C4×D314yescomplemented
443C23×C3C23×C411yescharacteristic
444C23×C3C22×D411yescharacteristic
445C23×C3C22×D411yescharacteristic
446C23×C3C22×Q811yescharacteristic
447C23×C3C22×Q811yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3C2×#4111yescharacteristic
450C23×C3C2×#4111yescharacteristic
451C23×C3C2×#4111yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3C2×#4111yescharacteristic
454C23×C3H(5,𝔽2)11yescharacteristic
455C23×C3H(5,𝔽2)11yescharacteristic
456C23×C3H(5,𝔽2)11yescharacteristic
457C23×C3H(5,𝔽2)11yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
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×D3C2×C4⋊C414yes—
487C22×D3C4×D414yes—
488C22×D3C4×Q814yes—
489C22×D3#12114yes—
490C22×D3C22⋊Q814yes—
491C22×D3#12514yes—
492C22×D3C4⋊Q814yes—
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—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
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—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4C2×C4⋊C414yes—
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—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
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×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3C2×C4⋊C414yes—
590C2×Dic3#12314yes—
591C4×D3—416no—
592C4×D3—416no—
593C4×D3—416no—
594C24—32no—
595C24—32no—
596C24—32no—
597C24—32no—
598C24—32no—
599C24—32no—
600C24—32no—
601C24—61no—
602C24—61no—
603C24—61no—
604C24—61no—
605C24—61no—
606C24—61no—
607C24—61no—
608C24—61no—
609C24C23×D311yescharacteristic
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—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—32no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—68no—
662C22×C4—68no—
663C22×C4—68no—
664C22×C4—68no—
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×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—124no—
705C22×C4—124no—
706C22×C4—124no—
707C22×C4—124no—
708C22×C4—124no—
709C22×C4—124no—
710C22×C4—124no—
711C22×C4—124no—
712C22×C4—124no—
713C22×C4—124no—
714C22×C4—124no—
715C22×C4—124no—
716C22×C4—124no—
717C22×C4—124no—
718C22×C4—124no—
719C22×C4—124no—
720C22×C4—124no—
721C22×C4C2×C4×D312yes—
722C22×C4C2×C4×D312yes—
723C22×C4C2×C4×D312yes—
724C22×C4D3×D412yes—
725C22×C4D3×D412yes—
726C22×C4#23712yes—
727C22×C4D3×Q812yes—
728C22×C4D3×Q812yes—
729C4⋊C4—44no—
730C4⋊C4—124no—
731C4⋊C4—124no—
732C4⋊C4—124no—
733C4⋊C4—124no—
734C4⋊C4—124no—
735C22⋊C4—316no—
736C22⋊C4—68no—
737C22⋊C4—68no—
738C22⋊C4—124no—
739C42—124no—
740C42—124no—
741C22×C3C22×C4⋊C411yescharacteristic
742C22×C3C2×C4×D411yescharacteristic
743C22×C3C2×C4×Q811yescharacteristic
744C22×C3C4×#4111yescharacteristic
745C22×C3C4×#4111yescharacteristic
746C22×C3#51811yescharacteristic
747C22×C3#51811yescharacteristic
748C22×C3C2×#12111yescharacteristic
749C22×C3C2×C22⋊Q811yescharacteristic
750C22×C3C2×#12311yescharacteristic
751C22×C3#52511yescharacteristic
752C22×C3C2×#12511yescharacteristic
753C22×C3#52911yescharacteristic
754C22×C3#52911yescharacteristic
755C22×C3C2×C4⋊Q811yescharacteristic
756C22×C3#53411yescharacteristic
757C22×C3#53511yescharacteristic
758C22×C3#53811yescharacteristic
759C22×C3#53811yescharacteristic
760C22×C3#54611yescharacteristic
761C22×C3#54611yescharacteristic
762C22×C3#54611yescharacteristic
763C22×C3#54611yescharacteristic
764C22×C3#55111yescharacteristic
765C22×C3#55111yescharacteristic
766C22×C3#55111yescharacteristic
767C22×C3#55111yescharacteristic
768C22×C3#55411yescharacteristic
769C22×C3#55411yescharacteristic
770C22×C3#55411yescharacteristic
771C22×C3#55411yescharacteristic
772C22×C3#55411yescharacteristic
773C22×C3#55411yescharacteristic
774C22×C3#55411yescharacteristic
775C22×C3#55411yescharacteristic
776C2×D3—24no—
777C2×D3—24no—
778C2×D3—24no—
779C2×D3—24no—
780C2×D3—24no—
781C2×D3—24no—
782C2×D3—24no—
783C2×D3—24no—
784C2×D3—24no—
785C2×D3—24no—
786C2×D3—24no—
787C2×D3—24no—
788C2×D3—24no—
789C2×D3—24no—
790C2×D3#38918yes—
791C3×C4—24no—
792C3×C4—42no—
793C3×C4—42no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—42no—
797C3×C4—81no—
798Dic3—24no—
799Dic3—24no—
800Dic3—42no—
801Dic3—42no—
802Dic3—42no—
803Dic3—42no—
804Dic3—81no—
805C23—34no—
806C23—34no—
807C23—34no—
808C23—34no—
809C23—34no—
810C23—34no—
811C23—34no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23C22×C4×D311yescharacteristic
841C23C2×D3×D411yescharacteristic
842C23C2×D3×D411yescharacteristic
843C23C2×#23711yescharacteristic
844C23#100411yescharacteristic
845C23C2×D3×Q811yescharacteristic
846C23C2×D3×Q811yescharacteristic
847C23D3×#4111yescharacteristic
848C23D3×#4111yescharacteristic
849C23D3×#4111yescharacteristic
850C23D3×#4111yescharacteristic
851C23D3×#4111yescharacteristic
852C23#100911yescharacteristic
853C23#100911yescharacteristic
854C23#100911yescharacteristic
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—34no—
877C2×C4—34no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—1216no—
930C2×C4—1216no—
931C2×C4—1216no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4—121no—
946C2×C4—121no—
947C2×C4—121no—
948C2×C4—121no—
949C2×C4—121no—
950C2×C4—121no—
951C2×C4—121no—
952C2×C4—121no—
953C2×C4—121no—
954C2×C4—121no—
955C2×C4D3×C4⋊C414yes—
956C2×C3C2×#38911yescharacteristic
957C2×C3C4×#12311yescharacteristic
958C2×C3#232111yescharacteristic
959C2×C3#234911yescharacteristic
960C2×C3#234911yescharacteristic
961C2×C3#236811yescharacteristic
962C2×C3#236811yescharacteristic
963C2×C3#241111yescharacteristic
964C2×C3#241211yescharacteristic
965C2×C3#245011yescharacteristic
966C2×C3#245011yescharacteristic
967C2×C3#250211yescharacteristic
968C2×C3#250511yescharacteristic
969C2×C3#250511yescharacteristic
970C2×C3#258311yescharacteristic
971D3—28no—
972C22—38no—
973C22—64no—
974C22—64no—
975C22—64no—
976C22—64no—
977C22—64no—
978C22—64no—
979C22—64no—
980C22—64no—
981C22—64no—
982C22—64no—
983C22—64no—
984C22—64no—
985C22—64no—
986C22—64no—
987C22C2×D3×C4⋊C411yescharacteristic
988C22#552111yescharacteristic
989C22#552211yescharacteristic
990C22C4×#23711yescharacteristic
991C22C4×D3×D411yescharacteristic
992C22#554511yescharacteristic
993C22C4×D3×Q811yescharacteristic
994C22#559111yescharacteristic
995C22D3×#12111yescharacteristic
996C22#560611yescharacteristic
997C22#560711yescharacteristic
998C22D3×C22⋊Q811yescharacteristic
999C22#563511yescharacteristic
1000C22#563511yescharacteristic
1001C22#563611yescharacteristic
1002C22#563611yescharacteristic
1003C22D3×#12311yescharacteristic
1004C22#565311yescharacteristic
1005C22#565411yescharacteristic
1006C22#565811yescharacteristic
1007C22#565911yescharacteristic
1008C22#567611yescharacteristic
1009C22#567611yescharacteristic
1010C22#567811yescharacteristic
1011C22#568011yescharacteristic
1012C22D3×#12511yescharacteristic
1013C22#569011yescharacteristic
1014C22#569011yescharacteristic
1015C22#569011yescharacteristic
1016C22#569011yescharacteristic
1017C22#570411yescharacteristic
1018C22#570511yescharacteristic
1019C22#570511yescharacteristic
1020C22#570611yescharacteristic
1021C22D3×C4⋊Q811yescharacteristic
1022C4—24no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—64no—
1029C4—64no—
1030C4—81no—
1031C4—122no—
1032C4—122no—
1033C4—122no—
1034C4—122no—
1035C4—241no—
1036C3#1404411yescharacteristic, complemented, Sylow
1037C2—68no—
1038C2#7422811yescharacteristic
1039C2#7439411yescharacteristic
1040C2#7531011yescharacteristic
1041C2#7531111yescharacteristic
1042C2#7545311yescharacteristic
1043C2#7582711yescharacteristic
1044C2D3×#38911yescharacteristic
1045C2#7686611yescharacteristic
1046C2#7710911yescharacteristic
1047C2#7766811yescharacteristic
1048C2#7776511yescharacteristic
1049C2#7796111yescharacteristic
1050C2#7834411yescharacteristic
1051C2#7835211yescharacteristic
1052C2#7835411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1442C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1442D3
hypocenterC3#14044
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
6. C3×#1442C2semidirect
7. #71563C2semidirect
10. #69413C2semidirect
11. #69411C2semidirect
12. #69409C2semidirect
13. #69407C2semidirect
14. #69407C2semidirect
15. Dic3⋊#95C2semidirect
54. #4668C4semidirect
63. #1442D3semidirect
128. C2×C4⋊Dic3C2×C4semidirect
137. C2×Dic3⋊C4C2×C4semidirect
149. C3×#95C2×C4semidirect
163. C3⋊#95C2×C4semidirect
343. (C2×D3)⋊C4C4⋊C4semidirect
442. #95C4×D3semidirect
1036. C3#14044semidirect

Maximal subgroups

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

subgroupindex
C2×#49892
C2×#46682
C2×D3×#952
C2×#46662
C3×#14422
#715632
(C2×D3)⋊#952
#694132
#694112
#694092
#694072
Dic3⋊#952
#140443