Finite Group Databasebeta

← #10733881

Subgroups — #10733881

Order 768.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C2×#5210C211yesmaximal, characteristic, complemented
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×#4948C211yesmaximal, characteristic, complemented
6C2×#4657C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic
8#71547C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71546C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#15330—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×#386—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41#5221—24no—
42#5210—24no—
43#5210—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56#4948—24no—
57#4657—24no—
58C2×#398—31no—
59C2×#396—31no—
60C2×#390—31no—
61C2×#386D311yescharacteristic
62C2×#385—31no—
63C2×#385—31no—
64#1444—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1438—31no—
71#1436—31no—
72#1434—31no—
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—41no—
80C22×C3×D4—41no—
81C22×C3×D4Q814yes—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—41no—
108C2×C3×C22⋊C4—41no—
109C2×C3×C22⋊C4—41no—
110C2×C3×C22⋊C4—41no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—41no—
127C2×#217—41no—
128C2×#217—41no—
129C2×#217—41no—
130C2×#217—41no—
131C2×#217—41no—
132C2×#217—41no—
133C2×#217—41no—
134C2×#217D414yes—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3—22no—
139C2×C4⋊Dic3—41no—
140C2×C4⋊Dic3—41no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—41no—
151C2×Dic3⋊C4—41no—
152C2×Dic3⋊C4—41no—
153C2×Dic3⋊C4—41no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4—41no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—41no—
159C3×#95—22no—
160C3×#95D414yes—
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⋊#95—41no—
172C3⋊#95D414yescomplemented
173C23×D4C2×D311yescharacteristic
174C24×C4C2×D311yescharacteristic
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C22⋊C4C2×D311yescharacteristic
193C22×C42—31no—
194#398—64no—
195#396—64no—
196#390—64no—
197#386—24no—
198#385—64no—
199#385—64no—
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×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C24×C3—21no—
215C24×C3—21no—
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×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3C2×D412yes—
241C24×C3C2×Q812yes—
242C24×C3C2×Q812yes—
243C24×C3#4112yes—
244C24×C3C2411yescharacteristic
245C2×C3×D4—28no—
246C2×C3×D4—28no—
247C2×C3×D4—44no—
248C2×C3×D4—44no—
249C2×C3×D4—44no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
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—44no—
282C22×C3×C4—44no—
283C22×C3×C4—44no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—44no—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×Q812yes—
293C22×C3×C4#4112yes—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×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×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3#4112yes—
348C22×Dic3#4112yes—
349C22×Dic3#4112yes—
350C3×C22⋊C4—44no—
351C3×C22⋊C4—44no—
352C3×C22⋊C4—44no—
353#217—28no—
354#217—28no—
355#217—44no—
356#217—44no—
357#217—44no—
358#217—44no—
359#217—44no—
360#217—44no—
361C4⋊Dic3—44no—
362C4⋊Dic3—44no—
363Dic3⋊C4—44no—
364Dic3⋊C4—44no—
365Dic3⋊C4—44no—
366Dic3⋊C4—44no—
367Dic3⋊C4—44no—
368C4×Dic3—44no—
369C25C22×D311yescharacteristic
370C25C22×D311yescharacteristic
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—41no—
376C22×D4—41no—
377C22×D4Dic614yes—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—41no—
390C23×C4—41no—
391C23×C4—41no—
392C23×C4—41no—
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—121no—
412C2×C4⋊C4—121no—
413C2×C4⋊C4—121no—
414C2×C4⋊C4—121no—
415C2×C4⋊C4—121no—
416C2×C4⋊C4—121no—
417C2×C4⋊C4—121no—
418C2×C4⋊C4—121no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—41no—
426C2×C22⋊C4—41no—
427C2×C22⋊C4—41no—
428C2×C22⋊C4—41no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
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—121no—
445C2×C22⋊C4—121no—
446C2×C22⋊C4—121no—
447C2×C22⋊C4—121no—
448C2×C22⋊C4—121no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C42—62no—
453C2×C42—62no—
454C2×C42—121no—
455#95—22no—
456#95—34no—
457#95—62no—
458#95—62no—
459#95—62no—
460#95—62no—
461#95—62no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—121no—
466#95—121no—
467#95—121no—
468#95#6714yes—
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—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—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×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3C22⋊Q814yes—
539C23×C3C22×D411yescharacteristic
540C23×C3C22×D411yescharacteristic
541C23×C3C22×D411yescharacteristic
542C23×C3C22×Q811yescharacteristic
543C23×C3C2×#4111yescharacteristic
544C23×C3C2×#4111yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3C2×#4111yescharacteristic
548C23×C3H(5,𝔽2)11yescharacteristic
549C23×C3H(5,𝔽2)11yescharacteristic
550C23×C3H(5,𝔽2)11yescharacteristic
551C23×C3H(5,𝔽2)11yescharacteristic
552C23×C3H(5,𝔽2)11yescharacteristic
553C23×C32−1+411yescharacteristic
554C3×D4—416no—
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—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
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—416no—
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×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4C22⋊Q814yes—
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—41no—
613C2×Dic3—41no—
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—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—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
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—
673C24C2×Dic612yes—
674C24C2×Dic612yes—
675C24D3×D412yes—
676C24#23712yes—
677C24C23×D311yescharacteristic
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
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—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—32no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
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—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×C4C2×Dic612yes—
778C22×C4#23512yes—
779C22×C4D3×D412yes—
780C22×C4C2×#6712yes—
781C22×C4C2×#6712yes—
782C22×C4C2×#6712yes—
783C4⋊C4—124no—
784C4⋊C4—124no—
785C4⋊C4—124no—
786C4⋊C4—124no—
787C4⋊C4—124no—
788C4⋊C4—124no—
789C4⋊C4—124no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—68no—
794C22⋊C4—68no—
795C22⋊C4—124no—
796C22⋊C4—124no—
797C22⋊C4—124no—
798C22⋊C4—124no—
799C22⋊C4—124no—
800C22⋊C4—124no—
801C42—124no—
802C22×C3—24no—
803C22×C3—24no—
804C22×C3—24no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3C2×C22⋊Q811yescharacteristic
833C22×C3C2×C22⋊Q811yescharacteristic
834C22×C3#52511yescharacteristic
835C22×C3#52511yescharacteristic
836C22×C3#53211yescharacteristic
837C22×C3#53211yescharacteristic
838C22×C3#53411yescharacteristic
839C22×C3#53511yescharacteristic
840C22×C3#53511yescharacteristic
841C22×C3#53911yescharacteristic
842C22×C3#54011yescharacteristic
843C22×C3#54011yescharacteristic
844C22×C3#54211yescharacteristic
845C22×C3#54211yescharacteristic
846C22×C3#54311yescharacteristic
847C22×C3D4211yescharacteristic
848C22×C3D4211yescharacteristic
849C22×C3D4211yescharacteristic
850C22×C3#54611yescharacteristic
851C22×C3#54611yescharacteristic
852C22×C3#54611yescharacteristic
853C22×C3#54711yescharacteristic
854C22×C3#54811yescharacteristic
855C22×C3D4×Q811yescharacteristic
856C22×C3#55111yescharacteristic
857C22×C3#55111yescharacteristic
858C22×C3#55311yescharacteristic
859C22×C3#55311yescharacteristic
860C22×C3#55311yescharacteristic
861C22×C3#55311yescharacteristic
862C22×C3#55411yescharacteristic
863C22×C3#55411yescharacteristic
864C22×C3#55411yescharacteristic
865C22×C3#56011yescharacteristic
866C22×C3#56211yescharacteristic
867C3×C4—24no—
868C3×C4—42no—
869C3×C4—42no—
870C3×C4—42no—
871C3×C4—81no—
872Dic3—42no—
873Dic3—42no—
874Dic3—42no—
875Dic3—42no—
876Dic3—42no—
877Dic3—42no—
878Dic3—42no—
879Dic3—81no—
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—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
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—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23#87814yes—
950C23C22×Dic611yescharacteristic
951C23C2×#23511yescharacteristic
952C23C2×D3×D411yescharacteristic
953C23C2×D3×D411yescharacteristic
954C23C2×#23711yescharacteristic
955C23#100411yescharacteristic
956C23#100411yescharacteristic
957C23#100411yescharacteristic
958C23#100411yescharacteristic
959C23#100411yescharacteristic
960C23D3×#4111yescharacteristic
961C23D3×#4111yescharacteristic
962C23D3×#4111yescharacteristic
963C23#101011yescharacteristic
964C23C22×#6711yescharacteristic
965D4—416no—
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—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—416no—
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—62no—
1002C2×C4—62no—
1003C2×C4—62no—
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—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
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—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4#92414yes—
1058C2×C3—44no—
1059C2×C3—82no—
1060C2×C3#243711yescharacteristic
1061C2×C3#244911yescharacteristic
1062C2×C3#245211yescharacteristic
1063C2×C3#246111yescharacteristic
1064C2×C3#246411yescharacteristic
1065C2×C3#246411yescharacteristic
1066C2×C3#256611yescharacteristic
1067C2×C3#257911yescharacteristic
1068C2×C3#260311yescharacteristic
1069C2×C3#266911yescharacteristic
1070C2×C3#269211yescharacteristic
1071C2×C3#270111yescharacteristic
1072C2×C3#271111yescharacteristic
1073C2×C3#274811yescharacteristic
1074C2×C3#275711yescharacteristic
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22C2×#87811yescharacteristic
1106C22#548311yescharacteristic
1107C22#549011yescharacteristic
1108C22#549511yescharacteristic
1109C22D4×Dic611yescharacteristic
1110C22#553911yescharacteristic
1111C22#553911yescharacteristic
1112C22#553911yescharacteristic
1113C22#554811yescharacteristic
1114C22#555811yescharacteristic
1115C22#555811yescharacteristic
1116C22#556111yescharacteristic
1117C22#558911yescharacteristic
1118C22#559011yescharacteristic
1119C22#559211yescharacteristic
1120C22#559511yescharacteristic
1121C22#560111yescharacteristic
1122C22#560111yescharacteristic
1123C22#560211yescharacteristic
1124C22#560611yescharacteristic
1125C22#561211yescharacteristic
1126C22#561511yescharacteristic
1127C22#561511yescharacteristic
1128C22#562111yescharacteristic
1129C22#565511yescharacteristic
1130C22#565611yescharacteristic
1131C22#565911yescharacteristic
1132C22#566211yescharacteristic
1133C22C2×#92411yescharacteristic
1134C22D4×#6711yescharacteristic
1135C22D4×#6711yescharacteristic
1136C22#580511yescharacteristic
1137C22#580611yescharacteristic
1138C22#583111yescharacteristic
1139C22#583211yescharacteristic
1140C4—24no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—81no—
1145C4—122no—
1146C4—122no—
1147C4—122no—
1148C4—122no—
1149C4—122no—
1150C4—122no—
1151C4—122no—
1152C4—241no—
1153C3#1533011yescharacteristic, complemented, Sylow
1154C2—44no—
1155C2—82no—
1156C2#7470911yescharacteristic
1157C2#7472011yescharacteristic
1158C2#7477011yescharacteristic
1159C2#7477811yescharacteristic
1160C2#7480311yescharacteristic
1161C2#7483911yescharacteristic
1162C2#7485011yescharacteristic
1163C2#7492511yescharacteristic
1164C2#8211011yescharacteristic
1165C2#8236211yescharacteristic
1166C2#8238611yescharacteristic
1167C2#8260911yescharacteristic
1168C2#8265911yescharacteristic
1169C2#8269511yescharacteristic
1170C2#8285211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#15330
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#5210C2semidirect
4. C2×#5210C2semidirect
5. C2×#4948C2semidirect
6. C2×#4657C2semidirect
8. #71547C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. #71546C2semidirect
13. #69420C2semidirect
14. #69407C2semidirect
15. #69403C2semidirect
172. C3⋊#95D4semidirect
1153. C3#15330semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52212
C2×#52102
C2×#49482
C2×#46572
#721312
#715472
#715462
#694202
#694072
#694032
#153303