Finite Group Databasebeta

← #10729233

Subgroups — #10729233

Order 768.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#126C211yesmaximal, characteristic, complemented
2C2×#4990C211yesmaximal, characteristic, complemented
3C2×#4957C211yesmaximal, characteristic
4C2×#4940C211yesmaximal, characteristic, complemented
5#71570C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71568C211yesmaximal, characteristic, complemented
8#71566C211yesmaximal, characteristic, complemented
9#71564C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic
11#71550C211yesmaximal, characteristic
12#71549C211yesmaximal, characteristic, complemented
13#71547C211yesmaximal, characteristic, complemented
14#71545C211yesmaximal, characteristic, complemented
15C4×C3⋊#95C211yesmaximal, characteristic, complemented
16#14930—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C2×C3×#126—24no—
19C2×C3×#126—24no—
20C2×C3×#126—24no—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
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#4990—24no—
56#4957—24no—
57#4940—24no—
58C22×#126D311yescharacteristic, complemented
59C2×#390—31no—
60C2×#388—31no—
61C2×#388—31no—
62#1444—31no—
63#1441—31no—
64#1440—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69#1438—31no—
70#1437—31no—
71#1436—31no—
72C4×#95—31no—
73C25×C3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—41no—
87C22×#67—41no—
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C3×#126—232no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4D414yescomplemented
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4D414yes—
114C2×C3×C42—22no—
115C2×C3×C42—22no—
116C2×C3×C42D414yescomplemented
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—41no—
123C2×#217—41no—
124C2×#217—41no—
125C2×#217—41no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—41no—
148C2×Dic3⋊C4—41no—
149C2×Dic3⋊C4—41no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—41no—
155C2×C4×Dic3—41no—
156C3⋊#95—22no—
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—22no—
167C3⋊#95—41no—
168C3⋊#95—41no—
169C3⋊#95—41no—
170C23×D4—31no—
171C2×#126—24no—
172C2×#126—24no—
173C2×#126—24no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4C2×D311yescharacteristic
177C22×C4⋊C4C2×D311yescharacteristic
178C22×C4⋊C4C2×D311yescharacteristic
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C42—31no—
192C22×C42—31no—
193C22×C42C2×D311yescharacteristic
194#390—64no—
195#388—64no—
196#388—64no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3C2×D412yes—
226C24×C3C2411yescharacteristic
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×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3#4112yes—
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×C4C2×D412yes—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C2×#67—28no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67—44no—
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×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3#4112yes—
334C22×Dic3#4112yes—
335C22×Dic3#4112yes—
336C22×Dic3#4112yes—
337C22×Dic3#4112yes—
338C22×Dic3#4112yes—
339C22×Dic3#4112yes—
340C3×C4⋊C4—28no—
341C3×C4⋊C4—28no—
342C3×C4⋊C4—28no—
343C3×C22⋊C4—28no—
344C3×C22⋊C4—28no—
345C3×C22⋊C4—28no—
346C3×C42—28no—
347#217—44no—
348#217—44no—
349#217—44no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—28no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356Dic3⋊C4—44no—
357Dic3⋊C4—44no—
358C4×Dic3—44no—
359C4×Dic3—44no—
360C25—31no—
361C25C22×D311yescharacteristic
362C22×D4—62no—
363C22×D4—62no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—62no—
367C22×D4—121no—
368C22×D4—121no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382#126—232no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4—121no—
396C2×C4⋊C4—121no—
397C2×C4⋊C4#6714yescomplemented
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
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—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4—121no—
429C2×C22⋊C4—121no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4#6714yes—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42—121no—
441C2×C42—121no—
442C2×C42#6714yescomplemented
443#95—62no—
444#95—62no—
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#95—121no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3C22×D411yescharacteristic
493C23×C3C22×D411yescharacteristic
494C23×C3C22×D411yescharacteristic
495C23×C3C2×#4111yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3C2×#4111yescharacteristic
498C23×C3C2×#4111yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3C2×#4111yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C23×C3H(5,𝔽2)11yescharacteristic
506C23×C32−1+411yescharacteristic
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
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—41no—
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—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
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#12014yes—
584#67—416no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
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—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
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×Dic3—41no—
633C2×Dic3#12614yescomplemented
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—32no—
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—
663C24C2×#6712yes—
664C24C23×D311yescharacteristic
665C2×D4—68no—
666C2×D4—124no—
667C2×D4—124no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C2×D4—124no—
672C22×C4—21no—
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—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
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×C4C2×#6712yes—
756C22×C4C2×#6712yes—
757C22×C4C2×#6712yes—
758C22×C4C2×#6712yes—
759C22×C4C2×#6712yes—
760C22×C4C2×#6712yes—
761C22×C4C2×#6712yes—
762C22×C4C2×#6712yes—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—124no—
767C4⋊C4—124no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—68no—
772C22⋊C4—68no—
773C22⋊C4—124no—
774C22⋊C4—124no—
775C22⋊C4—124no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C42—28no—
781C42—124no—
782C42—124no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—81no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—81no—
794C22×C3—81no—
795C22×C3—81no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3C2×#12011yescharacteristic
799C22×C3#52511yescharacteristic
800C22×C3#52511yescharacteristic
801C22×C3#52511yescharacteristic
802C22×C3C2×#12611yescharacteristic
803C22×C3#52911yescharacteristic
804C22×C3#52911yescharacteristic
805C22×C3#52911yescharacteristic
806C22×C3#53211yescharacteristic
807C22×C3#53211yescharacteristic
808C22×C3#53211yescharacteristic
809C22×C3#53211yescharacteristic
810C22×C3#53211yescharacteristic
811C22×C3#53511yescharacteristic
812C22×C3#53711yescharacteristic
813C22×C3#53811yescharacteristic
814C22×C3#53811yescharacteristic
815C22×C3#54211yescharacteristic
816C22×C3#54211yescharacteristic
817C22×C3#54611yescharacteristic
818C22×C3#54611yescharacteristic
819C22×C3#54611yescharacteristic
820C22×C3#54611yescharacteristic
821C22×C3#54711yescharacteristic
822C22×C3#54711yescharacteristic
823C22×C3#55011yescharacteristic
824C22×C3#55011yescharacteristic
825C22×C3#55111yescharacteristic
826C22×C3#55111yescharacteristic
827C22×C3#55111yescharacteristic
828C22×C3#55211yescharacteristic
829C22×C3#55311yescharacteristic
830C22×C3#55311yescharacteristic
831C22×C3#55311yescharacteristic
832C22×C3#55611yescharacteristic
833C2×D3—42no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—81no—
841C2×D3—81no—
842C2×D3—81no—
843C2×D3—81no—
844C2×D3—81no—
845C2×D3—81no—
846C2×D3—81no—
847C2×D3—81no—
848C3×C4—24no—
849C3×C4—42no—
850C3×C4—42no—
851C3×C4—42no—
852C3×C4—42no—
853C3×C4—42no—
854Dic3—24no—
855Dic3—42no—
856Dic3—42no—
857Dic3—42no—
858Dic3—42no—
859Dic3—81no—
860Dic3—81no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
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—
931C23D3×#4111yescharacteristic
932C23D3×#4111yescharacteristic
933C23D3×#4111yescharacteristic
934C23D3×#4111yescharacteristic
935C23D3×#4111yescharacteristic
936C23D3×#4111yescharacteristic
937C23D3×#4111yescharacteristic
938C23D3×#4111yescharacteristic
939C23#100911yescharacteristic
940C23#100911yescharacteristic
941C23#100911yescharacteristic
942C23#101011yescharacteristic
943C23C22×#6711yescharacteristic
944C23C22×#6711yescharacteristic
945C23C22×#6711yescharacteristic
946D4—1216no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
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—34no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
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—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
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#95314yes—
1038C2×C3—82no—
1039C2×C3#238811yescharacteristic
1040C2×C3#243011yescharacteristic
1041C2×C3#243111yescharacteristic
1042C2×C3#246711yescharacteristic
1043C2×C3#246811yescharacteristic
1044C2×C3#247911yescharacteristic
1045C2×C3#248011yescharacteristic
1046C2×C3#251211yescharacteristic
1047C2×C3#252111yescharacteristic
1048C2×C3#255411yescharacteristic
1049C2×C3#255911yescharacteristic
1050C2×C3#260111yescharacteristic
1051C2×C3#260311yescharacteristic
1052C2×C3#266211yescharacteristic
1053C2×C3#286011yescharacteristic
1054D3—82no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—122no—
1071C22—122no—
1072C22—122no—
1073C22—122no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22—241no—
1078C22—241no—
1079C22—241no—
1080C22—241no—
1081C22—241no—
1082C22—241no—
1083C22—241no—
1084C22—241no—
1085C22#570211yescharacteristic
1086C22D3×#12611yescharacteristic
1087C22#570411yescharacteristic
1088C22#570411yescharacteristic
1089C22#570511yescharacteristic
1090C22#570511yescharacteristic
1091C22#570511yescharacteristic
1092C22#570611yescharacteristic
1093C22#570611yescharacteristic
1094C22#570611yescharacteristic
1095C22#570811yescharacteristic
1096C22#570911yescharacteristic
1097C22#570911yescharacteristic
1098C22#570911yescharacteristic
1099C22#571011yescharacteristic
1100C22#571011yescharacteristic
1101C22#582411yescharacteristic
1102C22#582411yescharacteristic
1103C22#582811yescharacteristic
1104C22#582811yescharacteristic
1105C22#582811yescharacteristic
1106C22#582911yescharacteristic
1107C22#582911yescharacteristic
1108C22#582911yescharacteristic
1109C22#582911yescharacteristic
1110C22#583011yescharacteristic
1111C22#583211yescharacteristic
1112C22#583211yescharacteristic
1113C22#583211yescharacteristic
1114C22#583211yescharacteristic
1115C22#583211yescharacteristic
1116C22#583311yescharacteristic
1117C22#583411yescharacteristic
1118C22#583411yescharacteristic
1119C22C2×#95311yescharacteristic
1120C4—24no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—64no—
1127C4—122no—
1128C4—122no—
1129C4—122no—
1130C4—122no—
1131C4—241no—
1132C4—241no—
1133C3#1493011yescharacteristic, complemented, Sylow
1134C2—82no—
1135C2—242no—
1136C2#8307711yescharacteristic
1137C2#8308011yescharacteristic
1138C2#8308111yescharacteristic
1139C2#8308411yescharacteristic
1140C2#8308611yescharacteristic
1141C2#8308711yescharacteristic
1142C2#8310411yescharacteristic
1143C2#8310611yescharacteristic
1144C2#8310811yescharacteristic
1145C2#8310911yescharacteristic
1146C2#8311111yescharacteristic
1147C2#8311311yescharacteristic
1148C2#8409111yescharacteristic
1149C2#8409211yescharacteristic
1150C2#8409511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#126C2
prime radicalC23×#67C22
hypercenterC22×#126D3
hypocenterC3#14930
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C3×#126C2semidirect
2. C2×#4990C2semidirect
4. C2×#4940C2semidirect
5. #71570C2semidirect
6. #71570C2semidirect
7. #71568C2semidirect
8. #71566C2semidirect
9. #71564C2semidirect
12. #71549C2semidirect
13. #71547C2semidirect
14. #71545C2semidirect
15. C4×C3⋊#95C2semidirect
58. C22×#126D3semidirect
104. C2×C3×C4⋊C4D4semidirect
116. C2×C3×C42D4semidirect
397. C2×C4⋊C4#67semidirect
442. C2×C42#67semidirect
633. C2×Dic3#126semidirect
1133. C3#14930semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1262
C2×#49902
C2×#49572
C2×#49402
#715702
#715682
#715662
#715642
#715502
#715492
#715472
#715452
C4×C3⋊#952
#149303