Finite Group Databasebeta

← #10735708

Subgroups — #10735708

Order 768.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#399C211yesmaximal, characteristic, complemented
2C2×#4990C211yesmaximal, characteristic, complemented
3C2×#4978C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic
5#71570C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71564C211yesmaximal, characteristic, complemented
8#71564C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic
10#71550C211yesmaximal, characteristic
11#71549C211yesmaximal, characteristic, complemented
12#71549C211yesmaximal, characteristic, complemented
13#71545C211yesmaximal, characteristic, complemented
14#69429C211yesmaximal, characteristic, complemented
15#69421C211yesmaximal, characteristic, complemented
16#15456—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C3×#399—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
53#4990—24no—
54#4978—24no—
55#4957—24no—
56C2×#399D311yescharacteristic, complemented
57C2×#390—31no—
58C2×#388—31no—
59C2×#387—31no—
60#1445—31no—
61#1440—31no—
62#1440—31no—
63#1440—31no—
64#1439—31no—
65#1439—31no—
66#1438—31no—
67#1438—31no—
68#1437—31no—
69#1436—31no—
70#1436—31no—
71C25×C3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—41no—
85C22×#67—41no—
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—41no—
98C2×C3×C4⋊C4—41no—
99C2×C3×C4⋊C4—41no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C4⋊C4D414yescomplemented
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—41no—
108C2×C3×C22⋊C4—41no—
109C2×C3×C22⋊C4—41no—
110C2×C3×C22⋊C4—41no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—41no—
117C2×#217—41no—
118C2×#217—41no—
119C2×#217—41no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4D414yes—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—41no—
145C2×C4×Dic3—41no—
146C2×C4×Dic3—41no—
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⋊#95—41no—
162C3⋊#95—41no—
163C23×D4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4C2×D311yescharacteristic
166C22×C4⋊C4C2×D311yescharacteristic
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×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C22⋊C4C2×D311yescharacteristic
180C22×C42—31no—
181C22×C42—31no—
182#399—24no—
183#390—64no—
184#388—64no—
185#387—64no—
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—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95C2×D311yescharacteristic
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3#4112yes—
217C24×C3C2411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3#4112yes—
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×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×C4C2×D412yes—
271C22×C3×C4C2×D412yes—
272C22×C3×C4C2×D412yes—
273C22×C3×C4C2×D412yes—
274C22×C3×C4#4112yes—
275C2×#67—28no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67—44no—
279C2×#67—44no—
280C2×#67—44no—
281C2×#67—44no—
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×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×Dic3C2×D412yes—
326C22×Dic3C2×D412yes—
327C22×Dic3#4112yes—
328C22×Dic3#4112yes—
329C22×Dic3#4112yes—
330C22×Dic3#4112yes—
331C3×C4⋊C4—44no—
332C3×C4⋊C4—44no—
333C3×C4⋊C4—44no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337#217—44no—
338#217—44no—
339#217—44no—
340(C2×D3)⋊C4—28no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346Dic3⋊C4—28no—
347C4×Dic3—44no—
348C4×Dic3—44no—
349C25—31no—
350C25C22×D311yescharacteristic
351C22×D4—62no—
352C22×D4—62no—
353C22×D4—62no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—121no—
357C22×D4—121no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4#6714yescomplemented
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—41no—
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—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—121no—
408C2×C22⋊C4—121no—
409C2×C22⋊C4—121no—
410C2×C22⋊C4—121no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C42—62no—
420C2×C42—62no—
421C2×C42—62no—
422C2×C42—121no—
423C2×C42—121no—
424C2×C42—121no—
425#95—22no—
426#95—62no—
427#95—62no—
428#95—62no—
429#95—62no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—121no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95—121no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
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×C3C22×D411yescharacteristic
477C23×C3C22×D411yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C3H(5,𝔽2)11yescharacteristic
487C23×C3H(5,𝔽2)11yescharacteristic
488C23×C3H(5,𝔽2)11yescharacteristic
489C23×C3H(5,𝔽2)11yescharacteristic
490C23×C32−1+411yescharacteristic
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
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—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568#67—416no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
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#12314yes—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—32no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24#23912yes—
648C24C23×D311yescharacteristic
649C2×D4—68no—
650C2×D4—124no—
651C2×D4—124no—
652C2×D4—124no—
653C2×D4—124no—
654C2×D4—124no—
655C2×D4—124no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
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—32no—
694C22×C4—32no—
695C22×C4—32no—
696C22×C4—32no—
697C22×C4—32no—
698C22×C4—32no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
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×C4D3×D412yes—
743C22×C4#23712yes—
744C22×C4C2×#6712yes—
745C22×C4C2×#6712yes—
746C22×C4C2×#6712yes—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—68no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—68no—
755C22⋊C4—124no—
756C22⋊C4—124no—
757C22⋊C4—124no—
758C22⋊C4—124no—
759C22⋊C4—124no—
760C22⋊C4—124no—
761C22⋊C4—124no—
762C22⋊C4—124no—
763C42—124no—
764C42—124no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3—81no—
778C22×C3—81no—
779C22×C3—81no—
780C22×C3C2×#12311yescharacteristic
781C22×C3#52511yescharacteristic
782C22×C3#52511yescharacteristic
783C22×C3#52911yescharacteristic
784C22×C3#52911yescharacteristic
785C22×C3#53211yescharacteristic
786C22×C3#53411yescharacteristic
787C22×C3#53511yescharacteristic
788C22×C3#53811yescharacteristic
789C22×C3#53911yescharacteristic
790C22×C3#53911yescharacteristic
791C22×C3#54011yescharacteristic
792C22×C3#54011yescharacteristic
793C22×C3#54011yescharacteristic
794C22×C3#54211yescharacteristic
795C22×C3D4211yescharacteristic
796C22×C3#54611yescharacteristic
797C22×C3#54611yescharacteristic
798C22×C3#54811yescharacteristic
799C22×C3#54811yescharacteristic
800C22×C3#55011yescharacteristic
801C22×C3#55011yescharacteristic
802C22×C3#55111yescharacteristic
803C22×C3#55111yescharacteristic
804C22×C3#55111yescharacteristic
805C22×C3#55111yescharacteristic
806C22×C3#55111yescharacteristic
807C22×C3#55111yescharacteristic
808C22×C3#55311yescharacteristic
809C22×C3#55311yescharacteristic
810C22×C3#55611yescharacteristic
811C22×C3#55911yescharacteristic
812C22×C3#55911yescharacteristic
813C22×C3#56011yescharacteristic
814C22×C3#56211yescharacteristic
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—81no—
823C2×D3—81no—
824C2×D3—81no—
825C2×D3—81no—
826C2×D3—81no—
827C2×D3—81no—
828C2×D3—81no—
829C2×D3—81no—
830C3×C4—42no—
831C3×C4—42no—
832C3×C4—42no—
833C3×C4—42no—
834C3×C4—42no—
835C3×C4—81no—
836Dic3—24no—
837Dic3—42no—
838Dic3—42no—
839Dic3—42no—
840Dic3—81no—
841Dic3—81no—
842Dic3—81no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23C2×D3×D411yescharacteristic
914C23C2×#23711yescharacteristic
915C23#100411yescharacteristic
916C23#100411yescharacteristic
917C23#100411yescharacteristic
918C23#100411yescharacteristic
919C23C2×#23911yescharacteristic
920C23#100711yescharacteristic
921C23D3×#4111yescharacteristic
922C23D3×#4111yescharacteristic
923C23D3×#4111yescharacteristic
924C23D3×#4111yescharacteristic
925C23D3×#4111yescharacteristic
926C23#100911yescharacteristic
927C23C22×#6711yescharacteristic
928D4—1216no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—34no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
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×C3—82no—
1021C2×C3#244511yescharacteristic
1022C2×C3#244811yescharacteristic
1023C2×C3#246311yescharacteristic
1024C2×C3#246711yescharacteristic
1025C2×C3#247111yescharacteristic
1026C2×C3#248211yescharacteristic
1027C2×C3#251611yescharacteristic
1028C2×C3#256011yescharacteristic
1029C2×C3#260211yescharacteristic
1030C2×C3#267311yescharacteristic
1031C2×C3#271111yescharacteristic
1032C2×C3#273011yescharacteristic
1033C2×C3#274011yescharacteristic
1034C2×C3#275211yescharacteristic
1035C2×C3#279611yescharacteristic
1036D3—82no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22—241no—
1060C22—241no—
1061C22—241no—
1062C22—241no—
1063C22—241no—
1064C22—241no—
1065C22—241no—
1066C22—241no—
1067C22#562411yescharacteristic
1068C22#562711yescharacteristic
1069C22#563311yescharacteristic
1070C22#563711yescharacteristic
1071C22#563711yescharacteristic
1072C22#563711yescharacteristic
1073C22#563811yescharacteristic
1074C22#563811yescharacteristic
1075C22#564011yescharacteristic
1076C22#564111yescharacteristic
1077C22#564411yescharacteristic
1078C22#564711yescharacteristic
1079C22#564911yescharacteristic
1080C22D3×#12311yescharacteristic
1081C22#565411yescharacteristic
1082C22#565811yescharacteristic
1083C22#565911yescharacteristic
1084C22#565911yescharacteristic
1085C22#566111yescharacteristic
1086C22#566111yescharacteristic
1087C22#566311yescharacteristic
1088C22#566311yescharacteristic
1089C22#566411yescharacteristic
1090C22#566411yescharacteristic
1091C22#571511yescharacteristic
1092C22#571811yescharacteristic
1093C22#571911yescharacteristic
1094C22#572011yescharacteristic
1095C22D4×#6711yescharacteristic
1096C22#580411yescharacteristic
1097C22#580611yescharacteristic
1098C22#581711yescharacteristic
1099C22#582811yescharacteristic
1100C22#583211yescharacteristic
1101C22#583411yescharacteristic
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—64no—
1108C4—81no—
1109C4—122no—
1110C4—122no—
1111C4—122no—
1112C4—241no—
1113C4—241no—
1114C4—241no—
1115C3#1545611yescharacteristic, complemented, Sylow
1116C2—82no—
1117C2—242no—
1118C2#7802211yescharacteristic
1119C2#7802511yescharacteristic
1120C2#7803111yescharacteristic
1121C2#7806711yescharacteristic
1122C2#7807811yescharacteristic
1123C2#7810511yescharacteristic
1124C2#7812111yescharacteristic
1125C2#7812411yescharacteristic
1126C2#8278311yescharacteristic
1127C2#8280611yescharacteristic
1128C2#8281811yescharacteristic
1129C2#8284911yescharacteristic
1130C2#8285511yescharacteristic
1131C2#8290211yescharacteristic
1132C2#8318211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#399C2
prime radicalC23×#67C22
hypercenterC2×#399D3
hypocenterC3#15456
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×C3×#399C2semidirect
2. C2×#4990C2semidirect
3. C2×#4978C2semidirect
5. #71570C2semidirect
6. #71570C2semidirect
7. #71564C2semidirect
8. #71564C2semidirect
11. #71549C2semidirect
12. #71549C2semidirect
13. #71545C2semidirect
14. #69429C2semidirect
15. #69421C2semidirect
56. C2×#399D3semidirect
101. C2×C3×C4⋊C4D4semidirect
382. C2×C4⋊C4#67semidirect
1115. C3#15456semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3992
C2×#49902
C2×#49782
C2×#49572
#715702
#715642
#715502
#715492
#715452
#694292
#694212
#154563