Finite Group Databasebeta

← #10719214

Subgroups — #10719214

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5213C211yesmaximal, characteristic
2C2×C4×#217C211yesmaximal, characteristic, complemented
3C2×#4956C211yesmaximal, characteristic
4C2×#4945C211yesmaximal, characteristic, complemented
5C2×#4666C211yesmaximal, characteristic, complemented
6C3×C22⋊#95C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic
8#71549C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11#69417C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69406C211yesmaximal, characteristic, complemented
14#69403C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14068—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38#5213C418yescomplemented
39C4×#217—24no—
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
53C2×C3⋊#95C2211yescharacteristic
54#4956—24no—
55#4945—24no—
56#4666—24no—
57C2×#388—31no—
58C2×#386—31no—
59C2×#386—31no—
60C2×C4×C22⋊C4—31no—
61C2×C4×C22⋊C4—31no—
62#1443—31no—
63#1440—31no—
64#1439—31no—
65#1438—31no—
66#1437—31no—
67#1436—31no—
68#1434—31no—
69#1434—31no—
70C22⋊#95—31no—
71C22⋊#95D311yescharacteristic, complemented
72C25×C3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—41no—
77C23×C3×C4—41no—
78C23×C3×C4—41no—
79C23×C3×C4—41no—
80C23×C3×C4C2×C414yescomplemented
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—41no—
92C22×#67—41no—
93C22×#67C2×C414yes—
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217C2×C414yescomplemented
122C2×#217D414yes—
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—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4C2×C414yes—
137C2×(C2×D3)⋊C4C2×C414yes—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—41no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—41no—
146C2×C4×Dic3—41no—
147C2×C4×Dic3—41no—
148C2×C4×Dic3—41no—
149C2×C4×Dic3D414yescomplemented
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—41no—
153C3×#95—41no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95C2×C414yescomplemented
167C3⋊#95C2×C414yescomplemented
168C23×D4—31no—
169C24×C4—31no—
170C24×C4C2×D311yescharacteristic
171C22×C4⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4C2×D311yescharacteristic
181C22×C22⋊C4C2×D311yescharacteristic
182C22×C42—31no—
183C22×C42—31no—
184C22×C42—31no—
185#388—64no—
186#386—38no—
187#386—64no—
188C4×C22⋊C4—64no—
189C4×C22⋊C4—64no—
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×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
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—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3C22×C412yes—
221C24×C3C2×D412yes—
222C24×C3#4112yes—
223C24×C3C2411yescharacteristic
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—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3C22×C412yes—
237C23×D3#4112yes—
238C23×D3#4112yes—
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—28no—
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×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4—44no—
279C22×C3×C4—44no—
280C22×C3×C4—44no—
281C22×C3×C4—44no—
282C22×C3×C4C22×C412yes—
283C22×C3×C4C22×C412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4#4112yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
288C2×#67—28no—
289C2×#67—28no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67—44no—
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—21no—
334C22×Dic3—21no—
335C22×Dic3C22×C412yes—
336C22×Dic3C22×C412yes—
337C22×Dic3C22×C412yes—
338C22×Dic3C2×D412yes—
339C22×Dic3C2×D412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3#4112yes—
343C22×Dic3#4112yes—
344C2×C4×D3—28no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C3×C22⋊C4—44no—
352C3×C22⋊C4—44no—
353#217—28no—
354#217—28no—
355#217—28no—
356(C2×D3)⋊C4—28no—
357(C2×D3)⋊C4—28no—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4—44no—
360(C2×D3)⋊C4—44no—
361Dic3⋊C4—44no—
362C4×Dic3—44no—
363C4×Dic3—44no—
364C4×Dic3—44no—
365C25—31no—
366C25C22×D311yescharacteristic
367C22×D4—34no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—121no—
373C22×D4—121no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—41no—
384C23×C4—41no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—62no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4C4×D314yescomplemented
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—121no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
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—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C42—34no—
435C2×C42—62no—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—121no—
440C2×C42—121no—
441C2×C42—121no—
442C2×C42—121no—
443#95—22no—
444#95—22no—
445#95—34no—
446#95—34no—
447#95—41no—
448#95—41no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—62no—
456#95—62no—
457#95—62no—
458#95—121no—
459#95—121no—
460#95—121no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
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×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3C4×D414yes—
496C23×C3C23×C411yescharacteristic
497C23×C3C22×D411yescharacteristic
498C23×C3C22×D411yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3C2×#4111yescharacteristic
503C23×C3C2×#4111yescharacteristic
504C23×C3C2×#4111yescharacteristic
505C23×C3C2×#4111yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3H(5,𝔽2)11yescharacteristic
508C23×C3H(5,𝔽2)11yescharacteristic
509C23×C3H(5,𝔽2)11yescharacteristic
510C23×C3H(5,𝔽2)11yescharacteristic
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
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—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3#11714yes—
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—416no—
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—
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—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4C4×D414yes—
589#67—416no—
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—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
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—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3#12114yes—
639C4×D3—416no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—32no—
653C24—32no—
654C24—32no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24C2×C4×D312yes—
668C24D3×D412yes—
669C24#23912yes—
670C24C23×D311yescharacteristic
671C2×D4—68no—
672C2×D4—68no—
673C2×D4—124no—
674C2×D4—124no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—124no—
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—28no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—68no—
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×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4C2×C4×D312yes—
778C22×C4C2×C4×D312yes—
779C22×C4#23512yes—
780C22×C4#23512yes—
781C22×C4D3×D412yes—
782C22×C4#23712yes—
783C4⋊C4—124no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—68no—
787C22⋊C4—68no—
788C22⋊C4—68no—
789C22⋊C4—68no—
790C22⋊C4—68no—
791C22⋊C4—124no—
792C22⋊C4—124no—
793C22⋊C4—124no—
794C42—124no—
795C42—124no—
796C42—124no—
797C22×C3—24no—
798C22×C3—24no—
799C22×C3—24no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3C2×#11711yescharacteristic
813C22×C3C2×C4×D411yescharacteristic
814C22×C3C2×C4×D411yescharacteristic
815C22×C3C4×#4111yescharacteristic
816C22×C3C4×#4111yescharacteristic
817C22×C3#51811yescharacteristic
818C22×C3#51811yescharacteristic
819C22×C3C2×#12111yescharacteristic
820C22×C3#52511yescharacteristic
821C22×C3#52511yescharacteristic
822C22×C3#52511yescharacteristic
823C22×C3#52911yescharacteristic
824C22×C3#52911yescharacteristic
825C22×C3#52911yescharacteristic
826C22×C3#53211yescharacteristic
827C22×C3#53411yescharacteristic
828C22×C3#53511yescharacteristic
829C22×C3#53811yescharacteristic
830C22×C3#53811yescharacteristic
831C22×C3#54611yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#54611yescharacteristic
834C22×C3#54611yescharacteristic
835C22×C3#55111yescharacteristic
836C22×C3#55111yescharacteristic
837C22×C3#55111yescharacteristic
838C22×C3#55111yescharacteristic
839C22×C3#55111yescharacteristic
840C22×C3#55311yescharacteristic
841C22×C3#55311yescharacteristic
842C22×C3#55311yescharacteristic
843C22×C3#55311yescharacteristic
844C22×C3#55311yescharacteristic
845C22×C3#55311yescharacteristic
846C22×C3#55911yescharacteristic
847C2×D3—24no—
848C2×D3—24no—
849C2×D3—24no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C3×C4—24no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—81no—
867C3×C4—81no—
868Dic3—24no—
869Dic3—42no—
870Dic3—42no—
871Dic3—42no—
872Dic3—42no—
873Dic3—42no—
874Dic3—42no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—34no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23#89314yes—
945C23C22×C4×D311yescharacteristic
946C23C2×#23511yescharacteristic
947C23C2×#23511yescharacteristic
948C23C2×D3×D411yescharacteristic
949C23C2×D3×D411yescharacteristic
950C23C2×#23711yescharacteristic
951C23#100411yescharacteristic
952C23#100411yescharacteristic
953C23#100411yescharacteristic
954C23#100411yescharacteristic
955C23C2×#23911yescharacteristic
956C23D3×#4111yescharacteristic
957C23D3×#4111yescharacteristic
958C23D3×#4111yescharacteristic
959C23D3×#4111yescharacteristic
960D4—1216no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—34no—
977C2×C4—416no—
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—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—1216no—
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—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4#67⋊C414yes—
1054C2×C3—44no—
1055C2×C3#229011yescharacteristic
1056C2×C3C4×#12111yescharacteristic
1057C2×C3#232111yescharacteristic
1058C2×C3#234211yescharacteristic
1059C2×C3#235311yescharacteristic
1060C2×C3#236411yescharacteristic
1061C2×C3#237411yescharacteristic
1062C2×C3#253411yescharacteristic
1063C2×C3#253511yescharacteristic
1064C2×C3#255711yescharacteristic
1065C2×C3#255911yescharacteristic
1066C2×C3#257611yescharacteristic
1067C2×C3#257811yescharacteristic
1068C2×C3#259811yescharacteristic
1069C2×C3#260011yescharacteristic
1070D3—44no—
1071C22—24no—
1072C22—24no—
1073C22—24no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—64no—
1087C22—64no—
1088C22—64no—
1089C22—122no—
1090C22—122no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22C4×#23511yescharacteristic
1102C22C2×#67⋊C411yescharacteristic
1103C22#548611yescharacteristic
1104C22#548611yescharacteristic
1105C22#549011yescharacteristic
1106C22#549011yescharacteristic
1107C22C2×#89311yescharacteristic
1108C22#551411yescharacteristic
1109C22#551411yescharacteristic
1110C22D3×#11711yescharacteristic
1111C22#552211yescharacteristic
1112C22#554011yescharacteristic
1113C22#554711yescharacteristic
1114C22#554711yescharacteristic
1115C22#555611yescharacteristic
1116C22#555711yescharacteristic
1117C22#555711yescharacteristic
1118C22#555811yescharacteristic
1119C22#555911yescharacteristic
1120C22#558911yescharacteristic
1121C22#559211yescharacteristic
1122C22#559311yescharacteristic
1123C22#559311yescharacteristic
1124C22#559611yescharacteristic
1125C22D3×#12111yescharacteristic
1126C22#561011yescharacteristic
1127C22#561011yescharacteristic
1128C22#562411yescharacteristic
1129C22#562711yescharacteristic
1130C22#563711yescharacteristic
1131C22#563711yescharacteristic
1132C22#565911yescharacteristic
1133C22#565911yescharacteristic
1134C22#566111yescharacteristic
1135C22#566111yescharacteristic
1136C4—24no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—64no—
1141C4—81no—
1142C4—81no—
1143C4—122no—
1144C4—122no—
1145C4—122no—
1146C4—122no—
1147C4—122no—
1148C4—122no—
1149C3#1406811yescharacteristic, complemented, Sylow
1150C2—44no—
1151C2—124no—
1152C2#7333811yescharacteristic
1153C2#7347811yescharacteristic
1154C2#7356211yescharacteristic
1155C2#7382111yescharacteristic
1156C2#7386511yescharacteristic
1157C2#7400911yescharacteristic
1158C2#7412311yescharacteristic
1159C2#7448211yescharacteristic
1160C2#7448411yescharacteristic
1161C2#7449611yescharacteristic
1162C2#7461711yescharacteristic
1163C2#7475111yescharacteristic
1164C2#7475911yescharacteristic
1165C2#7476111yescharacteristic
1166C2#7490111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#14068
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#217C2semidirect
4. C2×#4945C2semidirect
5. C2×#4666C2semidirect
6. C3×C22⋊#95C2semidirect
8. #71549C2semidirect
9. #69428C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. #69417C2semidirect
12. #69408C2semidirect
13. #69406C2semidirect
14. #69403C2semidirect
15. #69401C2semidirect
38. #5213C4semidirect
71. C22⋊#95D3semidirect
80. C23×C3×C4C2×C4semidirect
121. C2×#217C2×C4semidirect
149. C2×C4×Dic3D4semidirect
166. C3⋊#95C2×C4semidirect
167. C3⋊#95C2×C4semidirect
394. C23×C4C4×D3semidirect
1149. C3#14068semidirect

Maximal subgroups

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

subgroupindex
C2×#52132
C2×C4×#2172
C2×#49562
C2×#49452
C2×#46662
C3×C22⋊#952
#715502
#715492
#694282
(C2×D3)⋊#952
#694172
#694082
#694062
#694032
#694012
#140683