Finite Group Databasebeta

← #10720214

Subgroups — #10720214

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×#386C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×C4×#217C211yesmaximal, characteristic, complemented
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#4951C211yesmaximal, characteristic, complemented
7C2×#4950C211yesmaximal, characteristic, complemented
8#71548C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69416C211yesmaximal, characteristic, complemented
13#69412C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14140—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C3×#386C418yescomplemented
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37#5220—24no—
38#5220—24no—
39C4×#217—24no—
40C2×C3⋊#95—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57#4951—24no—
58#4950—24no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386—31no—
62C2×#386D311yescharacteristic
63C2×#385—31no—
64C2×C4×C22⋊C4—31no—
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
75C25×C3C2311yescharacteristic
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4C2×C414yes—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4C2×C414yes—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×Dic3—22no—
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—41no—
106C23×Dic3—41no—
107C23×Dic3—41no—
108C23×Dic3—41no—
109C23×Dic3C2311yescharacteristic
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⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4C2×C414yes—
124C2×C3×C22⋊C4C2×C414yescomplemented
125C2×C3×C22⋊C4C2×C414yescomplemented
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—41no—
139C2×#217—41no—
140C2×#217—41no—
141C2×#217—41no—
142C2×#217D414yes—
143C2×#217D414yes—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—41no—
149C2×C4⋊Dic3—41no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—41no—
155C2×C4×Dic3—41no—
156C3×#95C2×C414yescomplemented
157C3×#95C2×C414yescomplemented
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—22no—
170C3⋊#95—22no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C3⋊#95D414yescomplemented
174C23×D4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
187C22×C22⋊C4C2×D311yescharacteristic
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C42—31no—
190C22×C42—31no—
191#388—64no—
192#386—64no—
193#386—64no—
194#386Dic318yescomplemented
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—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×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×C3C22×C412yes—
239C24×C3C22×C412yes—
240C24×C3C2×D412yes—
241C24×C3C2×D412yes—
242C24×C3#4112yes—
243C24×C3#4112yes—
244C24×C3#4112yes—
245C24×C3#4112yes—
246C24×C3C2411yescharacteristic
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—28no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—28no—
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—21no—
283C22×C3×C4—28no—
284C22×C3×C4—44no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—44no—
288C22×C3×C4—44no—
289C22×C3×C4C22×C412yes—
290C22×C3×C4C22×C412yes—
291C22×C3×C4C22×C412yes—
292C22×C3×C4C22×C412yes—
293C22×C3×C4C22×C412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4#4112yes—
296C22×Dic3—28no—
297C22×Dic3—28no—
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×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—44no—
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×Dic3C2×D412yes—
359C22×Dic3C2×D412yes—
360C22×Dic3C2×D412yes—
361C22×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×D412yes—
364C22×Dic3#4112yes—
365C22×Dic3#4112yes—
366C3×C22⋊C4—28no—
367C3×C22⋊C4—28no—
368C3×C22⋊C4—44no—
369#217—28no—
370#217—28no—
371#217—44no—
372#217—44no—
373#217—44no—
374#217—44no—
375C4⋊Dic3—44no—
376C4⋊Dic3—44no—
377C4×Dic3—44no—
378C4×Dic3—44no—
379C25C22×D311yescharacteristic
380C25C22×D311yescharacteristic
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4C2×Dic314yes—
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—31no—
400C23×C4—41no—
401C23×C4—41no—
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—62no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4—121no—
415C23×C4—121no—
416C23×C4C2×Dic314yes—
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—41no—
435C2×C22⋊C4—41no—
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—62no—
448C2×C22⋊C4—121no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4C2×Dic314yes—
453C2×C22⋊C4C2×Dic314yescomplemented
454C2×C22⋊C4C2×Dic314yescomplemented
455C2×C42—62no—
456C2×C42—62no—
457C2×C42—62no—
458C2×C42—62no—
459C2×C42—121no—
460C2×C42—121no—
461#95—34no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
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—121no—
476#95—121no—
477#95C2×Dic314yescomplemented
478#95C2×Dic314yescomplemented
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—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
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×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3#11714yes—
543C23×C3C4×D414yes—
544C23×C3C4×D414yes—
545C23×C3#12114yes—
546C23×C3#12314yes—
547C23×C3#12414yes—
548C23×C3#12614yes—
549C23×C3C23×C411yescharacteristic
550C23×C3C22×D411yescharacteristic
551C23×C3C22×D411yescharacteristic
552C23×C3C22×D411yescharacteristic
553C23×C3C2×#4111yescharacteristic
554C23×C3C2×#4111yescharacteristic
555C23×C3C2×#4111yescharacteristic
556C23×C3C2×#4111yescharacteristic
557C23×C3C2×#4111yescharacteristic
558C23×C3C2×#4111yescharacteristic
559C23×C3C2×#4111yescharacteristic
560C23×C3H(5,𝔽2)11yescharacteristic
561C23×C3H(5,𝔽2)11yescharacteristic
562C23×C3H(5,𝔽2)11yescharacteristic
563C23×C32−1+411yescharacteristic
564C3×D4—416no—
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—416no—
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×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×C4C4×D414yes—
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—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—416no—
626C2×Dic3—416no—
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—
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—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24#23512yes—
682C24#23512yes—
683C24D3×D412yes—
684C24D3×D412yes—
685C24#23712yes—
686C24#23712yes—
687C24C22×Dic312yes—
688C24C22×Dic312yes—
689C24C23×D311yescharacteristic
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
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—28no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—32no—
732C22×C4—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—68no—
741C22×C4—68no—
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—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
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×C4—124no—
802C22×C4D3×D412yes—
803C22×C4#23712yes—
804C22×C4C22×Dic312yes—
805C22×C4C22×Dic312yes—
806C22×C4C22×Dic312yes—
807C22×C4C22×Dic312yes—
808C22×C4C22×Dic312yes—
809C4⋊C4—124no—
810C4⋊C4—124no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—44no—
814C22⋊C4—68no—
815C22⋊C4—68no—
816C22⋊C4—124no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C22⋊C4—124no—
820C42—124no—
821C42—124no—
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—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—81no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3#38818yescomplemented
852C22×C3C2×#11711yescharacteristic
853C22×C3C2×C4×D411yescharacteristic
854C22×C3C2×C4×D411yescharacteristic
855C22×C3C2×C4×D411yescharacteristic
856C22×C3C4×#4111yescharacteristic
857C22×C3#51811yescharacteristic
858C22×C3#52011yescharacteristic
859C22×C3C2×#12111yescharacteristic
860C22×C3C2×#12311yescharacteristic
861C22×C3#52511yescharacteristic
862C22×C3#52511yescharacteristic
863C22×C3C2×#12411yescharacteristic
864C22×C3C2×#12611yescharacteristic
865C22×C3#52911yescharacteristic
866C22×C3#52911yescharacteristic
867C22×C3#53811yescharacteristic
868C22×C3#53811yescharacteristic
869C22×C3#53911yescharacteristic
870C22×C3#53911yescharacteristic
871C22×C3D4211yescharacteristic
872C22×C3D4211yescharacteristic
873C22×C3#54611yescharacteristic
874C22×C3#54611yescharacteristic
875C22×C3#54611yescharacteristic
876C22×C3#54611yescharacteristic
877C22×C3#54611yescharacteristic
878C22×C3#54711yescharacteristic
879C22×C3#54711yescharacteristic
880C22×C3#54811yescharacteristic
881C22×C3#55111yescharacteristic
882C22×C3#55111yescharacteristic
883C22×C3#55211yescharacteristic
884C22×C3#55311yescharacteristic
885C22×C3#55311yescharacteristic
886C22×C3#55311yescharacteristic
887C3×C4—24no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892Dic3—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—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
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—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23#87914yes—
964C23#88314yes—
965C23#88414yes—
966C23#88514yes—
967C23#92614yes—
968C23D4×Dic314yes—
969C23D4×Dic314yes—
970C23C2×#23511yescharacteristic
971C23C2×#23511yescharacteristic
972C23C2×D3×D411yescharacteristic
973C23C2×D3×D411yescharacteristic
974C23C2×D3×D411yescharacteristic
975C23C2×#23711yescharacteristic
976C23C2×#23711yescharacteristic
977C23C2×#23711yescharacteristic
978C23#100411yescharacteristic
979C23#100411yescharacteristic
980C23D3×#4111yescharacteristic
981C23D3×#4111yescharacteristic
982C23#100911yescharacteristic
983C23#101011yescharacteristic
984C23C23×Dic311yescharacteristic
985D4—416no—
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—416no—
1005C2×C4—41no—
1006C2×C4—41no—
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—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
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—1216no—
1046C2×C4—1216no—
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—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×C4D4×Dic314yes—
1080C2×C3—28no—
1081C2×C3—82no—
1082C2×C3C2×#38811yescharacteristic
1083C2×C3#229011yescharacteristic
1084C2×C3#231811yescharacteristic
1085C2×C3#235811yescharacteristic
1086C2×C3#235911yescharacteristic
1087C2×C3#236111yescharacteristic
1088C2×C3#236411yescharacteristic
1089C2×C3#242411yescharacteristic
1090C2×C3#242511yescharacteristic
1091C2×C3#244311yescharacteristic
1092C2×C3#244411yescharacteristic
1093C2×C3#247211yescharacteristic
1094C2×C3#248111yescharacteristic
1095C2×C3#248811yescharacteristic
1096C2×C3#251011yescharacteristic
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—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22#495118yescomplemented
1127C22C2×#87911yescharacteristic
1128C22C2×#88311yescharacteristic
1129C22C2×#88411yescharacteristic
1130C22C2×#88511yescharacteristic
1131C22#553811yescharacteristic
1132C22#553811yescharacteristic
1133C22#554711yescharacteristic
1134C22#554711yescharacteristic
1135C22#556011yescharacteristic
1136C22#556011yescharacteristic
1137C22#556411yescharacteristic
1138C22#556411yescharacteristic
1139C22#558711yescharacteristic
1140C22#559011yescharacteristic
1141C22#559111yescharacteristic
1142C22#559111yescharacteristic
1143C22#559811yescharacteristic
1144C22#560111yescharacteristic
1145C22#560111yescharacteristic
1146C22#560911yescharacteristic
1147C22#561011yescharacteristic
1148C22#561011yescharacteristic
1149C22#561111yescharacteristic
1150C22#561811yescharacteristic
1151C22#565011yescharacteristic
1152C22#565411yescharacteristic
1153C22#565511yescharacteristic
1154C22#565811yescharacteristic
1155C22C2×#92611yescharacteristic
1156C22C2×D4×Dic311yescharacteristic
1157C22C2×D4×Dic311yescharacteristic
1158C22C2×D4×Dic311yescharacteristic
1159C22#579811yescharacteristic
1160C22Dic3×#4111yescharacteristic
1161C22#582711yescharacteristic
1162C4—24no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—122no—
1168C4—122no—
1169C4—122no—
1170C4—122no—
1171C4—122no—
1172C4—122no—
1173C4—122no—
1174C4—122no—
1175C3#1414011yescharacteristic, complemented, Sylow
1176C2—28no—
1177C2—82no—
1178C2#7469611yescharacteristic
1179C2#7470211yescharacteristic
1180C2#7470511yescharacteristic
1181C2#7472711yescharacteristic
1182C2#7473511yescharacteristic
1183C2#7473911yescharacteristic
1184C2#7474411yescharacteristic
1185C2#7489311yescharacteristic
1186C2C2×#495111yescharacteristic
1187C2#8231811yescharacteristic
1188C2#8232411yescharacteristic
1189C2#8257911yescharacteristic
1190C2#8263611yescharacteristic
1191C2#8263811yescharacteristic
1192C2#8283811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14140
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×C4×#217C2semidirect
5. C22×C3⋊#95C2semidirect
6. C2×#4951C2semidirect
7. C2×#4950C2semidirect
8. #71548C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. #71544C2semidirect
12. #69416C2semidirect
13. #69412C2semidirect
14. #69407C2semidirect
15. #69401C2semidirect
34. C3×#386C4semidirect
124. C2×C3×C22⋊C4C2×C4semidirect
125. C2×C3×C22⋊C4C2×C4semidirect
156. C3×#95C2×C4semidirect
157. C3×#95C2×C4semidirect
173. C3⋊#95D4semidirect
194. #386Dic3semidirect
453. C2×C22⋊C4C2×Dic3semidirect
454. C2×C22⋊C4C2×Dic3semidirect
477. #95C2×Dic3semidirect
478. #95C2×Dic3semidirect
851. C22×C3#388semidirect
1126. C22#4951semidirect
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×#3862
C2×#52202
C2×C4×#2172
C22×C3⋊#952
C2×#49512
C2×#49502
#715482
#715462
#715452
#715442
#694162
#694122
#694072
#694012
#141403