Finite Group Databasebeta

← #10722776

Subgroups — #10722776

Order 768.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4957C211yesmaximal, characteristic
2C2×#4958C211yesmaximal, characteristic
3C2×#4651C211yesmaximal, characteristic, complemented
4C3×#1437C211yesmaximal, characteristic, complemented
5#71550C211yesmaximal, characteristic
6#71547C211yesmaximal, characteristic, complemented
7#71544C211yesmaximal, characteristic, complemented
8#71544C211yesmaximal, characteristic, complemented
9#71537C211yesmaximal, characteristic, complemented
10#71536C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69409C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14379—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4958—24no—
53#4957C418yescomplemented
54#4651—24no—
55C2×#390—31no—
56C2×#386—31no—
57C2×#383—31no—
58#1441—31no—
59#1440—31no—
60#1440—31no—
61#1439—31no—
62#1439—31no—
63#1438—31no—
64#1437—31no—
65#1437D311yescharacteristic, complemented
66#1436—31no—
67#1434—31no—
68C22⋊#95—31no—
69C22⋊#95—31no—
70C25×C3C2311yescharacteristic
71C24×D3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C22×#67—22no—
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—41no—
83C22×#67—41no—
84C22×#67C2×C414yes—
85C23×Dic3—22no—
86C23×Dic3—22no—
87C23×Dic3—22no—
88C23×Dic3—41no—
89C23×Dic3—41no—
90C23×Dic3—41no—
91C23×Dic3—41no—
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4—41no—
105C2×C3×C22⋊C4—41no—
106C2×C3×C22⋊C4—41no—
107C2×C3×C22⋊C4C2×C414yes—
108C2×C3×C42—41no—
109C2×C3×C42—41no—
110C2×C3×C42—41no—
111C2×#217—22no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×#217—41no—
116C2×#217C2×C414yes—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—41no—
122C2×(C2×D3)⋊C4—41no—
123C2×(C2×D3)⋊C4—41no—
124C2×(C2×D3)⋊C4—41no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4C2×C414yescomplemented
134C2×(C2×D3)⋊C4C2×C414yescomplemented
135C2×Dic3⋊C4—41no—
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4C2×C414yescomplemented
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3C2×C414yescomplemented
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—41no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95D414yes—
162C23×D4—31no—
163C24×C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
175C22×C22⋊C4C2×D311yescharacteristic
176C22×C22⋊C4C2×D311yescharacteristic
177C22×C42—31no—
178C22×C42C2×D311yescharacteristic
179#390—38no—
180#386—64no—
181#383—64no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C24×C3—21no—
201C24×C3—21no—
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×C3C22×C412yes—
213C24×C3#4112yes—
214C24×C3#4112yes—
215C24×C3C2411yescharacteristic
216C23×D3—21no—
217C23×D3—21no—
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×D3C22×C412yes—
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×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×C4C22×C412yes—
270C22×C3×C4C22×C412yes—
271C22×C3×C4C2×D412yes—
272C22×C3×C4#4112yes—
273C2×#67—28no—
274C2×#67—28no—
275C2×#67—44no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67—44no—
279C2×#67—44no—
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×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—44no—
323C22×Dic3—44no—
324C22×Dic3—44no—
325C22×Dic3—44no—
326C22×Dic3—44no—
327C22×Dic3—44no—
328C22×Dic3—44no—
329C22×Dic3C22×C412yes—
330C22×Dic3C22×C412yes—
331C22×Dic3C22×C412yes—
332C22×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3#4112yes—
335C22×Dic3#4112yes—
336C3×C22⋊C4—44no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339C3×C42—44no—
340#217—44no—
341#217—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348Dic3⋊C4—44no—
349Dic3⋊C4—44no—
350C4×Dic3—28no—
351C25—31no—
352C25C22×D311yescharacteristic
353C22×D4—34no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—121no—
359C22×D4—121no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—62no—
368C23×C4—62no—
369C23×C4—62no—
370C23×C4—121no—
371C23×C4—121no—
372C23×C4—121no—
373C23×C4—121no—
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C2×C4⋊C4—34no—
381C2×C4⋊C4—121no—
382C2×C4⋊C4—121no—
383C2×C4⋊C4—121no—
384C2×C4⋊C4—121no—
385C2×C4⋊C4—121no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—34no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—121no—
403C2×C22⋊C4—121no—
404C2×C22⋊C4—121no—
405C2×C22⋊C4—121no—
406C2×C22⋊C4—121no—
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⋊C4C4×D314yes—
419C2×C42—34no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42—62no—
424C2×C42—62no—
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—121no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95—121no—
441#95—121no—
442#95—121no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
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×C3—41no—
477C23×C3#11714yes—
478C23×C3C23×C411yescharacteristic
479C23×C3C22×D411yescharacteristic
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×C3H(5,𝔽2)11yescharacteristic
491C23×C3H(5,𝔽2)11yescharacteristic
492C23×C32−1+411yescharacteristic
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
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—
526C22×D3—41no—
527C22×D3—41no—
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—41no—
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—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570#67—416no—
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—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—416no—
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—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3C4×D414yes—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—32no—
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—61no—
648C24C2×C4×D312yes—
649C24#23512yes—
650C24#23512yes—
651C24C23×D311yescharacteristic
652C2×D4—68no—
653C2×D4—68no—
654C2×D4—124no—
655C2×D4—124no—
656C2×D4—124no—
657C2×D4—124no—
658C2×D4—124no—
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—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—32no—
698C22×C4—32no—
699C22×C4—32no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—32no—
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×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—124no—
747C22×C4—124no—
748C22×C4—124no—
749C22×C4—124no—
750C22×C4—124no—
751C22×C4—124no—
752C22×C4—124no—
753C22×C4C2×C4×D312yes—
754C22×C4C2×C4×D312yes—
755C22×C4D3×D412yes—
756C22×C4#23712yes—
757C4⋊C4—124no—
758C4⋊C4—124no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—124no—
763C22⋊C4—124no—
764C22⋊C4—124no—
765C22⋊C4—124no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C42—44no—
771C42—68no—
772C22×C3—24no—
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3C2×#11711yescharacteristic
788C22×C3C2×C4×D411yescharacteristic
789C22×C3C4×#4111yescharacteristic
790C22×C3#51811yescharacteristic
791C22×C3#51811yescharacteristic
792C22×C3#51811yescharacteristic
793C22×C3#52011yescharacteristic
794C22×C3#53511yescharacteristic
795C22×C3#53711yescharacteristic
796C22×C3#53811yescharacteristic
797C22×C3#53811yescharacteristic
798C22×C3#53811yescharacteristic
799C22×C3#53811yescharacteristic
800C22×C3#53911yescharacteristic
801C22×C3#53911yescharacteristic
802C22×C3#54011yescharacteristic
803C22×C3#54211yescharacteristic
804C22×C3#54211yescharacteristic
805C22×C3#54211yescharacteristic
806C22×C3#54611yescharacteristic
807C22×C3#54611yescharacteristic
808C22×C3#54611yescharacteristic
809C22×C3#55011yescharacteristic
810C22×C3#55111yescharacteristic
811C22×C3#55111yescharacteristic
812C22×C3#55111yescharacteristic
813C22×C3#55111yescharacteristic
814C22×C3#55311yescharacteristic
815C22×C3#55311yescharacteristic
816C22×C3#55311yescharacteristic
817C22×C3#55511yescharacteristic
818C22×C3#56011yescharacteristic
819C22×C3#56011yescharacteristic
820C22×C3#56011yescharacteristic
821C22×C3#56011yescharacteristic
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—81no—
830C2×D3—81no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C3×C4—42no—
838C3×C4—42no—
839C3×C4—42no—
840C3×C4—42no—
841C3×C4—81no—
842C3×C4—81no—
843Dic3—24no—
844Dic3—42no—
845Dic3—42no—
846Dic3—42no—
847Dic3—42no—
848Dic3—81no—
849Dic3—81no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
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—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
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—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23#87214yes—
920C23C22×C4×D311yescharacteristic
921C23C2×#23511yescharacteristic
922C23C2×#23511yescharacteristic
923C23C2×D3×D411yescharacteristic
924C23C2×#23711yescharacteristic
925C23#100411yescharacteristic
926C23#100411yescharacteristic
927C23#100411yescharacteristic
928C23#100411yescharacteristic
929C23D3×#4111yescharacteristic
930C23D3×#4111yescharacteristic
931C23#100911yescharacteristic
932C23#100911yescharacteristic
933C23#100911yescharacteristic
934C23#101011yescharacteristic
935D4—1216no—
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—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—34no—
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—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
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—62no—
988C2×C4—62no—
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—1216no—
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×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C3—44no—
1029C2×C3#231811yescharacteristic
1030C2×C3#232411yescharacteristic
1031C2×C3#233711yescharacteristic
1032C2×C3#234211yescharacteristic
1033C2×C3#235311yescharacteristic
1034C2×C3#236311yescharacteristic
1035C2×C3#238011yescharacteristic
1036C2×C3#268511yescharacteristic
1037C2×C3#269111yescharacteristic
1038C2×C3#270511yescharacteristic
1039C2×C3#271411yescharacteristic
1040C2×C3#273711yescharacteristic
1041C2×C3#274911yescharacteristic
1042C2×C3#275611yescharacteristic
1043C2×C3#275711yescharacteristic
1044D3—82no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—241no—
1068C22—241no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22C2×#87211yescharacteristic
1076C22#548611yescharacteristic
1077C22#549011yescharacteristic
1078C22#549511yescharacteristic
1079C22#552311yescharacteristic
1080C22#552711yescharacteristic
1081C22#552711yescharacteristic
1082C22C4×#23711yescharacteristic
1083C22#554011yescharacteristic
1084C22C4×D3×D411yescharacteristic
1085C22#554511yescharacteristic
1086C22#554511yescharacteristic
1087C22#555011yescharacteristic
1088C22#555611yescharacteristic
1089C22#556011yescharacteristic
1090C22#556011yescharacteristic
1091C22#556411yescharacteristic
1092C22#556411yescharacteristic
1093C22#556511yescharacteristic
1094C22#559511yescharacteristic
1095C22#559711yescharacteristic
1096C22#560111yescharacteristic
1097C22#561011yescharacteristic
1098C22#561711yescharacteristic
1099C22#562011yescharacteristic
1100C22#562011yescharacteristic
1101C22#566211yescharacteristic
1102C22#566311yescharacteristic
1103C22#566611yescharacteristic
1104C22#567011yescharacteristic
1105C22#567411yescharacteristic
1106C22#568211yescharacteristic
1107C22#570411yescharacteristic
1108C22#571011yescharacteristic
1109C22#571811yescharacteristic
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—64no—
1115C4—81no—
1116C4—81no—
1117C4—122no—
1118C4—122no—
1119C4—122no—
1120C4—122no—
1121C4—241no—
1122C4—241no—
1123C3#1437911yescharacteristic, complemented, Sylow
1124C2—44no—
1125C2—242no—
1126C2#7346211yescharacteristic
1127C2#7356811yescharacteristic
1128C2#7357411yescharacteristic
1129C2#7468511yescharacteristic
1130C2#7480011yescharacteristic
1131C2#7484111yescharacteristic
1132C2#7546111yescharacteristic
1133C2#7547211yescharacteristic
1134C2#7571311yescharacteristic
1135C2#7574111yescharacteristic
1136C2#7574311yescharacteristic
1137C2#7591911yescharacteristic
1138C2#7630511yescharacteristic
1139C2#7638811yescharacteristic
1140C2#7639611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1437D3
hypocenterC3#14379
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#4651C2semidirect
4. C3×#1437C2semidirect
6. #71547C2semidirect
7. #71544C2semidirect
8. #71544C2semidirect
9. #71537C2semidirect
10. #71536C2semidirect
11. #69429C2semidirect
12. #69429C2semidirect
13. #69428C2semidirect
14. #69409C2semidirect
15. #69401C2semidirect
53. #4957C4semidirect
65. #1437D3semidirect
133. C2×(C2×D3)⋊C4C2×C4semidirect
134. C2×(C2×D3)⋊C4C2×C4semidirect
140. C2×Dic3⋊C4C2×C4semidirect
143. C2×C4×Dic3C2×C4semidirect
1123. C3#14379semidirect

Maximal subgroups

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

subgroupindex
C2×#49572
C2×#49582
C2×#46512
C3×#14372
#715502
#715472
#715442
#715372
#715362
#694292
#694282
#694092
#694012
#143793