Finite Group Databasebeta

← #10716823

Subgroups — #10716823

Order 768.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4940C211yesmaximal, characteristic
2C2×#4668C211yesmaximal, characteristic
3C2×#4670C211yesmaximal, characteristic
4C3×#1434C211yesmaximal, characteristic, complemented
5#71535C211yesmaximal, characteristic, complemented
6(C2×D3)⋊#95C211yesmaximal, characteristic
7(C2×D3)⋊#95C211yesmaximal, characteristic
8#69408C211yesmaximal, characteristic
9#69408C211yesmaximal, characteristic
10#69407C211yesmaximal, characteristic, complemented
11#69407C211yesmaximal, characteristic, complemented
12#69406C211yesmaximal, characteristic, complemented
13#69406C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#13831—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊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×C4×Dic3C2211yescharacteristic
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#4940C418yescomplemented
53#4670C418yescomplemented
54#4668C418yescomplemented
55C2×#388—31no—
56C2×#388—31no—
57C2×#385—31no—
58#1437—31no—
59#1437—31no—
60#1436—31no—
61#1436—31no—
62#1436—31no—
63#1436—31no—
64C4⋊#95—31no—
65C4⋊#95—31no—
66#1434—31no—
67#1434D311yescharacteristic, complemented
68C22⋊#95—31no—
69C22⋊#95—31no—
70C24×D3C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C22×C4×D3—41no—
86C22×C4×D3—41no—
87C22×C4×D3—41no—
88C22×C4×D3—41no—
89C22×C4×D3—41no—
90C22×C4×D3—41no—
91C22×C4×D3C2×C414yes—
92C2×C3×C42—41no—
93C2×C3×C42—41no—
94C2×C3×C42C2×C414yescomplemented
95C2×(C2×D3)⋊C4—41no—
96C2×(C2×D3)⋊C4—41no—
97C2×(C2×D3)⋊C4—41no—
98C2×(C2×D3)⋊C4—41no—
99C2×(C2×D3)⋊C4—41no—
100C2×(C2×D3)⋊C4—41no—
101C2×(C2×D3)⋊C4—41no—
102C2×(C2×D3)⋊C4—41no—
103C2×(C2×D3)⋊C4—41no—
104C2×(C2×D3)⋊C4—41no—
105C2×(C2×D3)⋊C4C2×C414yes—
106C2×(C2×D3)⋊C4C2×C414yes—
107C2×(C2×D3)⋊C4C2×C414yes—
108C2×(C2×D3)⋊C4C2×C414yes—
109C2×(C2×D3)⋊C4C2×C414yes—
110C2×(C2×D3)⋊C4C2×C414yes—
111C2×(C2×D3)⋊C4C2×C414yes—
112C2×(C2×D3)⋊C4C2×C414yes—
113C2×C4⋊Dic3—41no—
114C2×C4⋊Dic3—41no—
115C2×C4⋊Dic3—41no—
116C2×C4⋊Dic3—41no—
117C2×C4⋊Dic3C2×C414yes—
118C2×C4⋊Dic3C2×C414yescomplemented
119C2×Dic3⋊C4—41no—
120C2×Dic3⋊C4—41no—
121C2×Dic3⋊C4—41no—
122C2×Dic3⋊C4—41no—
123C2×Dic3⋊C4C2×C414yes—
124C2×Dic3⋊C4C2×C414yescomplemented
125C2×C4×Dic3—41no—
126C2×C4×Dic3—41no—
127C2×C4×Dic3—41no—
128C2×C4×Dic3—41no—
129C2×C4×Dic3—41no—
130C2×C4×Dic3—41no—
131C2×C4×Dic3—41no—
132C2×C4×Dic3—41no—
133C2×C4×Dic3C2×C414yescomplemented
134C3×#95—41no—
135C3×#95—41no—
136C3×#95—41no—
137C3×#95—41no—
138C3×#95C2×C414yes—
139C3×#95C2×C414yescomplemented
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95C2×C414yes—
151C3⋊#95C2×C414yescomplemented
152C3⋊#95C2×C414yescomplemented
153C3⋊#95C2×C414yescomplemented
154C24×C4—31no—
155C22×C4⋊C4—31no—
156C22×C4⋊C4—31no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C42—31no—
166C22×C42—31no—
167C22×C42—31no—
168C22×C42C2×D311yescharacteristic
169#388—38no—
170#388—38no—
171#385—38no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95C2×D311yescharacteristic
187C2×#95C2×D311yescharacteristic
188C2×#95C2×D311yescharacteristic
189C2×#95C2×D311yescharacteristic
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C24×C3C2411yescharacteristic
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3C22×C412yes—
206C23×D3C22×C412yes—
207C23×D3C22×C412yes—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
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×C4C22×C412yes—
249C22×C3×C4C22×C412yes—
250C22×C3×C4C22×C412yes—
251C22×C3×C4C22×C412yes—
252C22×C3×C4C22×C412yes—
253C22×C3×C4C22×C412yes—
254C22×C3×C4C22×C412yes—
255C22×C3×C4C22×C412yes—
256C22×C3×C4C22×C412yes—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
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×Dic3C22×C412yes—
298C22×Dic3C22×C412yes—
299C22×Dic3C22×C412yes—
300C22×Dic3C22×C412yes—
301C22×Dic3C22×C412yes—
302C22×Dic3C22×C412yes—
303C22×Dic3C22×C412yes—
304C22×Dic3C22×C412yes—
305C22×Dic3C22×C412yes—
306C2×C4×D3—44no—
307C2×C4×D3—44no—
308C2×C4×D3—44no—
309C2×C4×D3—44no—
310C2×C4×D3—44no—
311C2×C4×D3—44no—
312C2×C4×D3—44no—
313C3×C42—44no—
314(C2×D3)⋊C4—44no—
315(C2×D3)⋊C4—44no—
316(C2×D3)⋊C4—44no—
317(C2×D3)⋊C4—44no—
318(C2×D3)⋊C4—44no—
319(C2×D3)⋊C4C42116yescomplemented
320C4⋊Dic3—44no—
321C4⋊Dic3—44no—
322Dic3⋊C4—44no—
323Dic3⋊C4—44no—
324C4×Dic3—44no—
325C4×Dic3—44no—
326C4×Dic3—44no—
327C25—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—34no—
336C23×C4—121no—
337C23×C4—121no—
338C23×C4—121no—
339C23×C4—121no—
340C23×C4—121no—
341C23×C4—121no—
342C23×C4C22×D311yescharacteristic
343C23×C4C22×D311yescharacteristic
344C23×C4C22×D311yescharacteristic
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C2×C4⋊C4—34no—
350C2×C4⋊C4—34no—
351C2×C4⋊C4—34no—
352C2×C4⋊C4—34no—
353C2×C4⋊C4—121no—
354C2×C4⋊C4—121no—
355C2×C4⋊C4—121no—
356C2×C4⋊C4—121no—
357C2×C4⋊C4—121no—
358C2×C4⋊C4—121no—
359C2×C4⋊C4—121no—
360C2×C4⋊C4—121no—
361C2×C22⋊C4—34no—
362C2×C22⋊C4—34no—
363C2×C22⋊C4—34no—
364C2×C22⋊C4—34no—
365C2×C22⋊C4—34no—
366C2×C22⋊C4—34no—
367C2×C22⋊C4—34no—
368C2×C22⋊C4—34no—
369C2×C22⋊C4—121no—
370C2×C22⋊C4—121no—
371C2×C22⋊C4—121no—
372C2×C22⋊C4—121no—
373C2×C22⋊C4—121no—
374C2×C22⋊C4—121no—
375C2×C22⋊C4—121no—
376C2×C22⋊C4—121no—
377C2×C22⋊C4—121no—
378C2×C22⋊C4—121no—
379C2×C42—34no—
380C2×C42—41no—
381C2×C42—41no—
382C2×C42—121no—
383C2×C42—121no—
384C2×C42—121no—
385C2×C42—121no—
386C2×C42—121no—
387C2×C42—121no—
388C2×C42—121no—
389C2×C42—121no—
390C2×C42C4×D314yescomplemented
391#95—34no—
392#95—34no—
393#95—34no—
394#95—34no—
395#95—41no—
396#95—41no—
397#95—41no—
398#95—41no—
399#95—121no—
400#95—121no—
401#95—121no—
402#95—121no—
403#95—121no—
404#95—121no—
405#95—121no—
406#95—121no—
407#95—121no—
408#95—121no—
409#95C4×D314yes—
410#95C4×D314yescomplemented
411C23×C3C23×C411yescharacteristic
412C23×C3C23×C411yescharacteristic
413C23×C3C23×C411yescharacteristic
414C23×C3H(5,𝔽2)11yescharacteristic
415C23×C3H(5,𝔽2)11yescharacteristic
416C23×C3H(5,𝔽2)11yescharacteristic
417C23×C3H(5,𝔽2)11yescharacteristic
418C23×C3H(5,𝔽2)11yescharacteristic
419C23×C3H(5,𝔽2)11yescharacteristic
420C23×C3H(5,𝔽2)11yescharacteristic
421C23×C3H(5,𝔽2)11yescharacteristic
422C23×C32−1+411yescharacteristic
423C23×C32−1+411yescharacteristic
424C23×C32−1+411yescharacteristic
425C23×C32−1+411yescharacteristic
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3C2×C4214yes—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
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—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
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×C4C2×C4214yes—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
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—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
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×Dic3C2×C4214yes—
559C4×D3—416no—
560C24—32no—
561C24—32no—
562C24—32no—
563C24—61no—
564C24—61no—
565C24—61no—
566C24—61no—
567C24—61no—
568C24—61no—
569C24—61no—
570C24—61no—
571C24—61no—
572C24—61no—
573C24—61no—
574C24—61no—
575C24C23×D311yescharacteristic
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
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—32no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—32no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
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—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—124no—
666C22×C4—124no—
667C22×C4—124no—
668C22×C4—124no—
669C22×C4—124no—
670C22×C4—124no—
671C22×C4—124no—
672C22×C4C2×C4×D312yes—
673C22×C4C2×C4×D312yes—
674C22×C4C2×C4×D312yes—
675C22×C4C2×C4×D312yes—
676C22×C4C2×C4×D312yes—
677C22×C4C2×C4×D312yes—
678C22×C4C2×C4×D312yes—
679C22×C4C2×C4×D312yes—
680C22×C4C2×C4×D312yes—
681C4⋊C4—124no—
682C4⋊C4—124no—
683C4⋊C4—124no—
684C4⋊C4—124no—
685C22⋊C4—316no—
686C22⋊C4—124no—
687C22⋊C4—124no—
688C22⋊C4—124no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C42—44no—
692C42—124no—
693C42—124no—
694C42—124no—
695C22×C3C22×C4211yescharacteristic
696C22×C3#51811yescharacteristic
697C22×C3#51811yescharacteristic
698C22×C3#51811yescharacteristic
699C22×C3#51811yescharacteristic
700C22×C3#51811yescharacteristic
701C22×C3#51811yescharacteristic
702C22×C3#51811yescharacteristic
703C22×C3#51911yescharacteristic
704C22×C3#52011yescharacteristic
705C22×C3#52011yescharacteristic
706C22×C3#52011yescharacteristic
707C22×C3#52011yescharacteristic
708C22×C3#52011yescharacteristic
709C22×C3#52011yescharacteristic
710C22×C3#52011yescharacteristic
711C22×C3#52011yescharacteristic
712C22×C3#52011yescharacteristic
713C22×C3#52011yescharacteristic
714C22×C3#56011yescharacteristic
715C22×C3#56011yescharacteristic
716C22×C3#56011yescharacteristic
717C22×C3#56011yescharacteristic
718C22×C3H(3,𝔽4)11yescharacteristic
719C22×C3#56211yescharacteristic
720C22×C3#56211yescharacteristic
721C22×C3#56211yescharacteristic
722C22×C3#56211yescharacteristic
723C22×C3#56211yescharacteristic
724C22×C3#56211yescharacteristic
725C22×C3#56311yescharacteristic
726C22×C3#56311yescharacteristic
727C22×C3#56311yescharacteristic
728C22×C3#56311yescharacteristic
729C22×C3#56311yescharacteristic
730C2×D3—24no—
731C2×D3—24no—
732C2×D3—24no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C3×C4—24no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—42no—
752Dic3—24no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757Dic3—42no—
758Dic3—42no—
759C23—34no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—62no—
766C23—62no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—121no—
779C23—121no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23C22×C4×D311yescharacteristic
795C23C22×C4×D311yescharacteristic
796C23C22×C4×D311yescharacteristic
797C23#100411yescharacteristic
798C23#100411yescharacteristic
799C23#100411yescharacteristic
800C23#100711yescharacteristic
801C23#100911yescharacteristic
802C23#100911yescharacteristic
803C23#100911yescharacteristic
804C23#100911yescharacteristic
805C23#100911yescharacteristic
806C23#101011yescharacteristic
807C23#101011yescharacteristic
808C23#101011yescharacteristic
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
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—34no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
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—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
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—1216no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
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×C4C42×D314yes—
908C2×C3#227411yescharacteristic
909C2×C3#227511yescharacteristic
910C2×C3#227511yescharacteristic
911C2×C3#237511yescharacteristic
912C2×C3#237611yescharacteristic
913C2×C3#237611yescharacteristic
914C2×C3#237611yescharacteristic
915C2×C3#237711yescharacteristic
916C2×C3#237711yescharacteristic
917C2×C3#237811yescharacteristic
918C2×C3#237811yescharacteristic
919C2×C3#237911yescharacteristic
920C2×C3#237911yescharacteristic
921C2×C3#238311yescharacteristic
922C2×C3#238311yescharacteristic
923D3—44no—
924C22—64no—
925C22—64no—
926C22—64no—
927C22—122no—
928C22—122no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—122no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22C2×C42×D311yescharacteristic
940C22#548611yescharacteristic
941C22#550411yescharacteristic
942C22#552111yescharacteristic
943C22#552111yescharacteristic
944C22#552111yescharacteristic
945C22#552311yescharacteristic
946C22#552311yescharacteristic
947C22#552311yescharacteristic
948C22#552311yescharacteristic
949C22#552311yescharacteristic
950C22#554511yescharacteristic
951C22#554511yescharacteristic
952C22#554511yescharacteristic
953C22#554611yescharacteristic
954C22#554611yescharacteristic
955C22#554611yescharacteristic
956C22#557211yescharacteristic
957C22#557411yescharacteristic
958C22#562011yescharacteristic
959C22#562111yescharacteristic
960C22#564611yescharacteristic
961C22#564711yescharacteristic
962C22#566611yescharacteristic
963C22#566611yescharacteristic
964C22#566711yescharacteristic
965C22#566711yescharacteristic
966C22#568311yescharacteristic
967C22#568411yescharacteristic
968C22#569911yescharacteristic
969C22#570011yescharacteristic
970C22#571111yescharacteristic
971C22#571211yescharacteristic
972C22#571211yescharacteristic
973C22#571211yescharacteristic
974C4—24no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—64no—
982C4—122no—
983C4—122no—
984C4—122no—
985C4—122no—
986C4—122no—
987C4—122no—
988C3#1383111yescharacteristic, complemented, Sylow
989C2—124no—
990C2#7341211yescharacteristic
991C2#7343611yescharacteristic
992C2#7375011yescharacteristic
993C2#7401311yescharacteristic
994C2#7412411yescharacteristic
995C2#7423011yescharacteristic
996C2#7429911yescharacteristic
997C2#7497611yescharacteristic
998C2#7498011yescharacteristic
999C2#7531311yescharacteristic
1000C2#7531411yescharacteristic
1001C2#7548911yescharacteristic
1002C2#7549311yescharacteristic
1003C2#7584011yescharacteristic
1004C2#7584111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC22×C3C22×C42
FittingC3×#1434C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1434D3
hypocenterC3#13831
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. C3×#1434C2semidirect
5. #71535C2semidirect
10. #69407C2semidirect
11. #69407C2semidirect
12. #69406C2semidirect
13. #69406C2semidirect
14. Dic3⋊#95C2semidirect
15. #69403C2semidirect
52. #4940C4semidirect
53. #4670C4semidirect
54. #4668C4semidirect
67. #1434D3semidirect
94. C2×C3×C42C2×C4semidirect
118. C2×C4⋊Dic3C2×C4semidirect
124. C2×Dic3⋊C4C2×C4semidirect
133. C2×C4×Dic3C2×C4semidirect
139. C3×#95C2×C4semidirect
151. C3⋊#95C2×C4semidirect
152. C3⋊#95C2×C4semidirect
153. C3⋊#95C2×C4semidirect
319. (C2×D3)⋊C4C42semidirect
390. C2×C42C4×D3semidirect
410. #95C4×D3semidirect
988. C3#13831semidirect

Maximal subgroups

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

subgroupindex
C2×#49402
C2×#46682
C2×#46702
C3×#14342
#715352
(C2×D3)⋊#952
#694082
#694072
#694062
Dic3⋊#952
#694032
#138313