Finite Group Databasebeta

← #10720219

Subgroups — #10720219

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×#4956C211yesmaximal, characteristic
2C2×#4956C211yesmaximal, characteristic
3C2×#4956C211yesmaximal, characteristic
4C2×#4951C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×#4668C211yesmaximal, characteristic, complemented
7C2×D3×#95C211yesmaximal, characteristic, complemented
8C3×#1437C211yesmaximal, characteristic, complemented
9#71549C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71534C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69417C211yesmaximal, characteristic, complemented
14#69415C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14140—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
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#4956—24no—
53#4956—24no—
54#4956C418yescomplemented
55#4951—24no—
56C4×(C2×D3)⋊C4—24no—
57#4668—24no—
58D3×#95—24no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#385—31no—
64C2×C4×C22⋊C4—31no—
65C22×#95—31no—
66#1443—31no—
67#1442—31no—
68#1440—31no—
69#1439—31no—
70#1437D311yescharacteristic, complemented
71#1436—31no—
72#1434—31no—
73C22⋊#95—31no—
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67C2×C414yes—
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3C2×C414yes—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4C2×C414yescomplemented
126C2×C3×C42—22no—
127C2×C3×C42—22no—
128C2×C3×C42—41no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—41no—
134C2×#217—41no—
135C2×#217—41no—
136C2×#217—41no—
137C2×#217C2×C414yescomplemented
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4C2×C414yes—
145C2×(C2×D3)⋊C4D414yes—
146C2×(C2×D3)⋊C4D414yes—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—41no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—41no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—41no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—41no—
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—22no—
170C3⋊#95—41no—
171C3⋊#95C2×C414yescomplemented
172C3⋊#95C2×C414yescomplemented
173C3⋊#95D414yescomplemented
174C23×D4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C24×C4—31no—
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⋊C4C2×D311yescharacteristic
187C22×C22⋊C4C2×D311yescharacteristic
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C42—31no—
190C22×C42C2×D311yescharacteristic
191#388—64no—
192#386—38no—
193#386—64no—
194#386—64no—
195#385—64no—
196C4×C22⋊C4—64no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—64no—
213C2×#95C2×D311yescharacteristic
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×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3C22×C412yes—
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×D3C22×C412yes—
241C23×D3C2×D412yes—
242C23×D3C2×D412yes—
243C23×D3#4112yes—
244C23×D3#4112yes—
245C23×D3#4112yes—
246C23×D3#4112yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4C22×C412yes—
282C22×C3×C4C22×C412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
288C22×C3×C4#4112yes—
289C2×#67—28no—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67—44no—
295C2×#67—44no—
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×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3C22×C412yes—
339C22×Dic3C22×C412yes—
340C22×Dic3C22×C412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—28no—
348C2×C4×D3—28no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C3×C22⋊C4—28no—
367C3×C22⋊C4—44no—
368C3×C22⋊C4—44no—
369C3×C42—44no—
370#217—44no—
371#217—44no—
372#217—44no—
373(C2×D3)⋊C4—28no—
374(C2×D3)⋊C4—28no—
375(C2×D3)⋊C4—28no—
376C4⋊Dic3—44no—
377Dic3⋊C4—44no—
378C4×Dic3—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—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—34no—
396C23×C4—62no—
397C23×C4—62no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4—62no—
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—121no—
411C23×C4—121no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4—121no—
415C23×C4—121no—
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—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—34no—
435C2×C22⋊C4—34no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4—34no—
438C2×C22⋊C4—41no—
439C2×C22⋊C4—41no—
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—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4—121no—
454C2×C22⋊C4C4×D314yescomplemented
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—41no—
458C2×C42—62no—
459C2×C42—62no—
460C2×C42—121no—
461#95—22no—
462#95—22no—
463#95—34no—
464#95—34no—
465#95—34no—
466#95—41no—
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—62no—
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—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×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
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—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3#11714yes—
558C22×D3C4×D414yes—
559C22×D3C4×D414yes—
560C22×D3#12114yes—
561C22×D3#12314yes—
562C22×D3#12414yes—
563C22×D3#12614yes—
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—41no—
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×C4C4×D414yes—
606#67—416no—
607C2×Dic3—22no—
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—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—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—
656C4×D3—416no—
657C4×D3—416no—
658C4×D3—416no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—32no—
674C24—32no—
675C24—32no—
676C24—32no—
677C24—32no—
678C24—32no—
679C24—32no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24C2×C4×D312yes—
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—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—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—32no—
732C22×C4—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—68no—
739C22×C4—68no—
740C22×C4—68no—
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—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—68no—
784C22×C4—124no—
785C22×C4—124no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4—124no—
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×C4#23512yes—
804C22×C4#23512yes—
805C22×C4D3×D412yes—
806C22×C4D3×D412yes—
807C22×C4D3×D412yes—
808C22×C4#23712yes—
809C4⋊C4—124no—
810C4⋊C4—124no—
811C22⋊C4—28no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—68no—
815C22⋊C4—68no—
816C22⋊C4—68no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C22⋊C4—124no—
820C42—44no—
821C42—124no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
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—24no—
873C2×D3—24no—
874C2×D3—24no—
875C2×D3—24no—
876C2×D3—24no—
877C2×D3—24no—
878C2×D3—24no—
879C2×D3—24no—
880C2×D3—24no—
881C2×D3—24no—
882C2×D3—24no—
883C2×D3—24no—
884C2×D3—24no—
885C2×D3—24no—
886C2×D3#38818yescomplemented
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—34no—
908C23—34no—
909C23—34no—
910C23—34no—
911C23—34no—
912C23—34no—
913C23—34no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23C22×C4×D311yescharacteristic
971C23C2×#23511yescharacteristic
972C23C2×#23511yescharacteristic
973C23C2×D3×D411yescharacteristic
974C23C2×D3×D411yescharacteristic
975C23C2×D3×D411yescharacteristic
976C23C2×#23711yescharacteristic
977C23#100411yescharacteristic
978C23#100411yescharacteristic
979C23D3×#4111yescharacteristic
980C23D3×#4111yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983C23#100911yescharacteristic
984C23#101011yescharacteristic
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—41no—
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—62no—
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—1216no—
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—82no—
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—28no—
1097C22—38no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—64no—
1106C22—64no—
1107C22—64no—
1108C22—64no—
1109C22—64no—
1110C22—64no—
1111C22—64no—
1112C22—64no—
1113C22—64no—
1114C22—64no—
1115C22—64no—
1116C22—64no—
1117C22—64no—
1118C22—64no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22C4×#23511yescharacteristic
1128C22C2×#67⋊C411yescharacteristic
1129C22#549011yescharacteristic
1130C22#549011yescharacteristic
1131C22D3×#11711yescharacteristic
1132C22#552911yescharacteristic
1133C22#553011yescharacteristic
1134C22C4×D3×D411yescharacteristic
1135C22C4×D3×D411yescharacteristic
1136C22#554511yescharacteristic
1137C22#554611yescharacteristic
1138C22#554711yescharacteristic
1139C22#554711yescharacteristic
1140C22#555011yescharacteristic
1141C22#555111yescharacteristic
1142C22#555611yescharacteristic
1143C22#555711yescharacteristic
1144C22#555711yescharacteristic
1145C22#555811yescharacteristic
1146C22#559111yescharacteristic
1147C22D3×#12111yescharacteristic
1148C22#560911yescharacteristic
1149C22#561011yescharacteristic
1150C22#561111yescharacteristic
1151C22#561311yescharacteristic
1152C22#561411yescharacteristic
1153C22D3×#12311yescharacteristic
1154C22#565811yescharacteristic
1155C22#566011yescharacteristic
1156C22D3×#12411yescharacteristic
1157C22#567711yescharacteristic
1158C22#567811yescharacteristic
1159C22D3×#12611yescharacteristic
1160C22#570711yescharacteristic
1161C22#571711yescharacteristic
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—68no—
1177C2—82no—
1178C2#7356211yescharacteristic
1179C2#7357811yescharacteristic
1180C2#7357911yescharacteristic
1181C2#7487911yescharacteristic
1182C2#7489511yescharacteristic
1183C2#7489711yescharacteristic
1184C2#7545711yescharacteristic
1185C2#7554211yescharacteristic
1186C2D3×#38811yescharacteristic
1187C2#7584811yescharacteristic
1188C2#7586811yescharacteristic
1189C2#7587011yescharacteristic
1190C2#7633011yescharacteristic
1191C2#7643311yescharacteristic
1192C2#7644211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1437D3
hypocenterC3#14140
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#4951C2semidirect
5. C2×C4×(C2×D3)⋊C4C2semidirect
6. C2×#4668C2semidirect
7. C2×D3×#95C2semidirect
8. C3×#1437C2semidirect
9. #71549C2semidirect
10. #71547C2semidirect
11. #71534C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69417C2semidirect
14. #69415C2semidirect
15. #69406C2semidirect
54. #4956C4semidirect
70. #1437D3semidirect
125. C2×C3×C22⋊C4C2×C4semidirect
137. C2×#217C2×C4semidirect
171. C3⋊#95C2×C4semidirect
172. C3⋊#95C2×C4semidirect
173. C3⋊#95D4semidirect
454. C2×C22⋊C4C4×D3semidirect
886. C2×D3#388semidirect
1175. C3#14140semidirect

Maximal subgroups

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

subgroupindex
C2×#49562
C2×#49512
C2×C4×(C2×D3)⋊C42
C2×#46682
C2×D3×#952
C3×#14372
#715492
#715472
#715342
(C2×D3)⋊#952
#694172
#694152
#694062
#141403