Finite Group Databasebeta

← #10720206

Subgroups — #10720206

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C22×C3⋊#95C211yesmaximal, characteristic, complemented
4C2×#4958C211yesmaximal, characteristic
5C2×#4958C211yesmaximal, characteristic
6C2×#4946C211yesmaximal, characteristic, complemented
7C2×#4940C211yesmaximal, characteristic, complemented
8#71544C211yesmaximal, characteristic, complemented
9#71537C211yesmaximal, characteristic, complemented
10#71536C211yesmaximal, characteristic, complemented
11#71534C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69418C211yesmaximal, characteristic, complemented
15#69413C211yesmaximal, characteristic, complemented
16#14140—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C3×C4×C22⋊C4—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37#5213C418yescomplemented
38C2×C3⋊#95—24no—
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
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4958—24no—
56#4958—24no—
57#4946—24no—
58#4940—24no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#385—31no—
64C2×C4×C22⋊C4D311yescharacteristic, complemented
65C22×#95—31no—
66#1443—31no—
67#1442—31no—
68#1440—31no—
69#1439—31no—
70#1437—31no—
71#1436—31no—
72#1434—31no—
73C22⋊#95—31no—
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—41no—
81C23×C3×C4—41no—
82C23×C3×C4C2×C414yes—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67C2×C414yes—
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—22no—
99C23×Dic3—22no—
100C23×Dic3—22no—
101C23×Dic3—22no—
102C23×Dic3—22no—
103C23×Dic3—22no—
104C23×Dic3—22no—
105C23×Dic3—22no—
106C23×Dic3—41no—
107C23×Dic3—41no—
108C23×Dic3—41no—
109C23×Dic3—41no—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4D414yes—
122C2×C3×C22⋊C4D414yes—
123C2×C3×C42—22no—
124C2×C3×C42—22no—
125C2×C3×C42—22no—
126C2×C3×C42—22no—
127C2×C3×C42—41no—
128C2×C3×C42—41no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217C2×C414yes—
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—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4C2×C414yescomplemented
149C2×(C2×D3)⋊C4C2×C414yescomplemented
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4—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—22no—
168C3⋊#95—22no—
169C3⋊#95—41no—
170C3⋊#95—41no—
171C3⋊#95C2×C414yescomplemented
172C3⋊#95C2×C414yescomplemented
173C3⋊#95D414yescomplemented
174C23×D4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C24×C4C2×D311yescharacteristic
178C22×C4⋊C4—31no—
179C22×C4⋊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⋊C4C2×D311yescharacteristic
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C42C2×D311yescharacteristic
190C22×C42C2×D311yescharacteristic
191#388—64no—
192#386—38no—
193#386—64no—
194#386—64no—
195#385—64no—
196C4×C22⋊C4—24no—
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—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—64no—
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
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×C3C22×C412yes—
225C24×C3C2×D412yes—
226C24×C3C2×D412yes—
227C24×C3#4112yes—
228C24×C3#4112yes—
229C24×C3#4112yes—
230C24×C3#4112yes—
231C24×C3C2411yescharacteristic
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—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3C22×C412yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—28no—
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×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—28no—
283C22×C3×C4—44no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—44no—
288C22×C3×C4C22×C412yes—
289C22×C3×C4C22×C412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4#4112yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—28no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C22×Dic3—28no—
304C22×Dic3—28no—
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×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—44no—
348C22×Dic3—44no—
349C22×Dic3—44no—
350C22×Dic3—44no—
351C22×Dic3—44no—
352C22×Dic3—44no—
353C22×Dic3—44no—
354C22×Dic3—44no—
355C22×Dic3—44no—
356C22×Dic3—44no—
357C22×Dic3—44no—
358C22×Dic3—44no—
359C22×Dic3C22×C412yes—
360C22×Dic3C22×C412yes—
361C22×Dic3C22×C412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×D412yes—
364C22×Dic3#4112yes—
365C22×Dic3#4112yes—
366C3×C22⋊C4—28no—
367C3×C22⋊C4—28no—
368C3×C42—44no—
369C3×C42—44no—
370#217—28no—
371(C2×D3)⋊C4—28no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375(C2×D3)⋊C4—44no—
376(C2×D3)⋊C4—44no—
377Dic3⋊C4—44no—
378Dic3⋊C4—44no—
379C25—31no—
380C25C22×D311yescharacteristic
381C22×D4—34no—
382C22×D4—62no—
383C22×D4—62no—
384C22×D4—62no—
385C22×D4—62no—
386C22×D4—62no—
387C22×D4—62no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—41no—
400C23×C4—41no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—121no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4—121no—
415C23×C4C4×D314yes—
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—121no—
427C2×C4⋊C4—121no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—34no—
434C2×C22⋊C4—34no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—121no—
448C2×C22⋊C4—121no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4D1214yes—
454C2×C22⋊C4#6714yes—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—41no—
460C2×C42—41no—
461#95—22no—
462#95—22no—
463#95—34no—
464#95—34no—
465#95—34no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—62no—
477#95—121no—
478#95—121no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3#11714yes—
508C23×C3C4×D414yes—
509C23×C3C4×D414yes—
510C23×C3#12114yes—
511C23×C3#12314yes—
512C23×C3#12414yes—
513C23×C3#12614yes—
514C23×C3C23×C411yescharacteristic
515C23×C3C22×D411yescharacteristic
516C23×C3C22×D411yescharacteristic
517C23×C3C22×D411yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3C2×#4111yescharacteristic
521C23×C3C2×#4111yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3C2×#4111yescharacteristic
524C23×C3C2×#4111yescharacteristic
525C23×C3H(5,𝔽2)11yescharacteristic
526C23×C3H(5,𝔽2)11yescharacteristic
527C23×C3H(5,𝔽2)11yescharacteristic
528C23×C32−1+411yescharacteristic
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
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—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—416no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4C4×D414yes—
607#67—416no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—416no—
630C2×Dic3—416no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—32no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24C2×C4×D312yes—
683C24C2×D1212yes—
684C24#23512yes—
685C24#23512yes—
686C24#23512yes—
687C24#23512yes—
688C24C2×#6712yes—
689C24C23×D311yescharacteristic
690C2×D4—68no—
691C2×D4—68no—
692C2×D4—68no—
693C2×D4—124no—
694C2×D4—124no—
695C2×D4—124no—
696C2×D4—124no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—28no—
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—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—28no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—68no—
746C22×C4—68no—
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—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4—124no—
801C22×C4C2×C4×D312yes—
802C22×C4C2×C4×D312yes—
803C22×C4C2×D1212yes—
804C22×C4C2×D1212yes—
805C22×C4D3×D412yes—
806C22×C4#23712yes—
807C22×C4C2×#6712yes—
808C22×C4C2×#6712yes—
809C4⋊C4—124no—
810C4⋊C4—124no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—68no—
814C22⋊C4—68no—
815C22⋊C4—124no—
816C22⋊C4—124no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C22⋊C4—124no—
820C42—44no—
821C42—44no—
822C22×C3—24no—
823C22×C3—24no—
824C22×C3—24no—
825C22×C3—24no—
826C22×C3—24no—
827C22×C3—24no—
828C22×C3—24no—
829C22×C3—24no—
830C22×C3—24no—
831C22×C3—24no—
832C22×C3—24no—
833C22×C3—24no—
834C22×C3—24no—
835C22×C3—24no—
836C22×C3#38818yescomplemented
837C22×C3C2×#11711yescharacteristic
838C22×C3C2×C4×D411yescharacteristic
839C22×C3C2×C4×D411yescharacteristic
840C22×C3C2×C4×D411yescharacteristic
841C22×C3C4×#4111yescharacteristic
842C22×C3#51811yescharacteristic
843C22×C3#52011yescharacteristic
844C22×C3C2×#12111yescharacteristic
845C22×C3C2×#12311yescharacteristic
846C22×C3#52511yescharacteristic
847C22×C3#52511yescharacteristic
848C22×C3C2×#12411yescharacteristic
849C22×C3C2×#12611yescharacteristic
850C22×C3#52911yescharacteristic
851C22×C3#52911yescharacteristic
852C22×C3#53811yescharacteristic
853C22×C3#53811yescharacteristic
854C22×C3#53911yescharacteristic
855C22×C3#53911yescharacteristic
856C22×C3D4211yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54611yescharacteristic
860C22×C3#54611yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54711yescharacteristic
864C22×C3#54711yescharacteristic
865C22×C3#54811yescharacteristic
866C22×C3#55111yescharacteristic
867C22×C3#55111yescharacteristic
868C22×C3#55211yescharacteristic
869C22×C3#55311yescharacteristic
870C22×C3#55311yescharacteristic
871C22×C3#55311yescharacteristic
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—81no—
880C2×D3—81no—
881C2×D3—81no—
882C2×D3—81no—
883C2×D3—81no—
884C2×D3—81no—
885C2×D3—81no—
886C2×D3—81no—
887C3×C4—24no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893Dic3—42no—
894Dic3—42no—
895Dic3—42no—
896Dic3—42no—
897Dic3—42no—
898Dic3—42no—
899Dic3—42no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23#87214yes—
964C23C4×D1214yes—
965C23#87514yes—
966C23#87614yes—
967C23C4×#6714yes—
968C23#92914yes—
969C23#93014yes—
970C23C22×C4×D311yescharacteristic
971C23C22×D1211yescharacteristic
972C23C2×#23511yescharacteristic
973C23C2×#23511yescharacteristic
974C23C2×#23511yescharacteristic
975C23C2×#23511yescharacteristic
976C23C2×D3×D411yescharacteristic
977C23C2×#23711yescharacteristic
978C23#100411yescharacteristic
979C23#100411yescharacteristic
980C23D3×#4111yescharacteristic
981C23D3×#4111yescharacteristic
982C23#100911yescharacteristic
983C23#101011yescharacteristic
984C23C22×#6711yescharacteristic
985D4—1216no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—416no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—1216no—
1050C2×C4—1216no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4#67⋊C414yes—
1080C2×C3—28no—
1081C2×C3C2×#38811yescharacteristic
1082C2×C3#229011yescharacteristic
1083C2×C3#231811yescharacteristic
1084C2×C3#235811yescharacteristic
1085C2×C3#235911yescharacteristic
1086C2×C3#236111yescharacteristic
1087C2×C3#236411yescharacteristic
1088C2×C3#242411yescharacteristic
1089C2×C3#242511yescharacteristic
1090C2×C3#244311yescharacteristic
1091C2×C3#244411yescharacteristic
1092C2×C3#247211yescharacteristic
1093C2×C3#248111yescharacteristic
1094C2×C3#248811yescharacteristic
1095C2×C3#251011yescharacteristic
1096D3—82no—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—241no—
1119C22—241no—
1120C22—241no—
1121C22—241no—
1122C22—241no—
1123C22—241no—
1124C22—241no—
1125C22—241no—
1126C22#494018yescomplemented
1127C22C2×#87211yescharacteristic
1128C22C2×C4×D1211yescharacteristic
1129C22C2×#87511yescharacteristic
1130C22C2×#87611yescharacteristic
1131C22C2×#67⋊C411yescharacteristic
1132C22#548611yescharacteristic
1133C22#549011yescharacteristic
1134C22#549511yescharacteristic
1135C22#552211yescharacteristic
1136C22#552311yescharacteristic
1137C22#552711yescharacteristic
1138C22#553111yescharacteristic
1139C22#553811yescharacteristic
1140C22#553811yescharacteristic
1141C22#554011yescharacteristic
1142C22#554011yescharacteristic
1143C22#554711yescharacteristic
1144C22#554711yescharacteristic
1145C22D4×D1211yescharacteristic
1146C22#555211yescharacteristic
1147C22#555411yescharacteristic
1148C22#555411yescharacteristic
1149C22#555511yescharacteristic
1150C22#556011yescharacteristic
1151C22#556011yescharacteristic
1152C22#556411yescharacteristic
1153C22#556411yescharacteristic
1154C22#556511yescharacteristic
1155C22C2×C4×#6711yescharacteristic
1156C22C2×#92911yescharacteristic
1157C22C2×#93011yescharacteristic
1158C22D4×#6711yescharacteristic
1159C22#580611yescharacteristic
1160C22#582411yescharacteristic
1161C22#582911yescharacteristic
1162C4—24no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—122no—
1169C4—122no—
1170C4—122no—
1171C4—122no—
1172C4—122no—
1173C4—122no—
1174C4—122no—
1175C3#1414011yescharacteristic, complemented, Sylow
1176C2—28no—
1177C2—242no—
1178C2#7343811yescharacteristic
1179C2#7346711yescharacteristic
1180C2#7347111yescharacteristic
1181C2#7350311yescharacteristic
1182C2#7350411yescharacteristic
1183C2#7352111yescharacteristic
1184C2#7356811yescharacteristic
1185C2#7359411yescharacteristic
1186C2C2×#494011yescharacteristic
1187C2#8209911yescharacteristic
1188C2#8224211yescharacteristic
1189C2#8235511yescharacteristic
1190C2#8235611yescharacteristic
1191C2#8235711yescharacteristic
1192C2#8240711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×C4×C22⋊C4C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#14140
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C22⋊C4C2semidirect
3. C22×C3⋊#95C2semidirect
6. C2×#4946C2semidirect
7. C2×#4940C2semidirect
8. #71544C2semidirect
9. #71537C2semidirect
10. #71536C2semidirect
11. #71534C2semidirect
12. #69429C2semidirect
13. #69428C2semidirect
14. #69418C2semidirect
15. #69413C2semidirect
37. #5213C4semidirect
64. C2×C4×C22⋊C4D3semidirect
148. C2×(C2×D3)⋊C4C2×C4semidirect
149. C2×(C2×D3)⋊C4C2×C4semidirect
171. C3⋊#95C2×C4semidirect
172. C3⋊#95C2×C4semidirect
173. C3⋊#95D4semidirect
836. C22×C3#388semidirect
1126. C22#4940semidirect
1175. C3#14140semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊C42
C2×#52132
C22×C3⋊#952
C2×#49582
C2×#49462
C2×#49402
#715442
#715372
#715362
#715342
#694292
#694282
#694182
#694132
#141403