Finite Group Databasebeta

← #10733739

Subgroups — #10733739

Order 768.

1982 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#936C211yesmaximal, characteristic
2C2×C3×#394C211yesmaximal, characteristic
3C2×#4979C211yesmaximal, characteristic, complemented
4C2×#4948C211yesmaximal, characteristic, complemented
5C2×#4944C211yesmaximal, characteristic, complemented
6C2×#4646C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic
8#71564C211yesmaximal, characteristic, complemented
9#71549C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#71546C211yesmaximal, characteristic, complemented
14#71545C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#15321—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
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×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C2×#936—24no—
33C2×#936—24no—
34C2×#936—24no—
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C3×#394—24no—
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
56#4979—24no—
57#4948—24no—
58#4944—24no—
59#4646—24no—
60C22×#124—31no—
61C2×#396—31no—
62C2×#395—31no—
63C2×#394D311yescharacteristic
64C2×#391—31no—
65C2×#388—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1438—31no—
72#1437—31no—
73#1436—31no—
74#1436—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—41no—
83C22×C3×D4—41no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C22×Dic6—22no—
98C22×Dic6—22no—
99C22×Dic6—22no—
100C22×Dic6—22no—
101C22×Dic6—41no—
102C22×Dic6—41no—
103C22×Dic6D414yes—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—41no—
116C2×C3×C22⋊C4—41no—
117C2×C3×C22⋊C4—41no—
118C2×C3×C22⋊C4—41no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
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—41no—
138C2×#217—41no—
139C2×#217—41no—
140C2×#217—41no—
141C2×#217D414yes—
142C2×#217D414yes—
143#936—232no—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—41no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—41no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4—41no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3—22no—
161C2×C4×Dic3—41no—
162C3×#95D414yes—
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—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—41no—
176C23×Q8—31no—
177C23×D4C2×D311yescharacteristic
178C2×#124—64no—
179C2×#124—64no—
180C2×#124—64no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4C2×D311yescharacteristic
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4C2×D311yescharacteristic
195C22×C22⋊C4C2×D311yescharacteristic
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C42—31no—
199C22×C42—31no—
200#396—64no—
201#395—64no—
202#394—24no—
203#391—64no—
204#388—64no—
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—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95C2×D311yescharacteristic
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×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3C2×D412yes—
248C24×C3C2×D412yes—
249C24×C3C2411yescharacteristic
250C2×C3×D4—28no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C2×C3×D4—44no—
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—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4C2×D412yes—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4#4112yes—
291C22×C3×C4#4112yes—
292C22×Dic3—21no—
293C22×Dic3—21no—
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×Dic3C2×D412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3#4112yes—
346C22×Dic3#4112yes—
347C22×Dic3#4112yes—
348C2×Dic6—28no—
349C2×Dic6—28no—
350C2×Dic6—44no—
351C2×Dic6—44no—
352C2×Dic6—44no—
353C2×Dic6—44no—
354C2×Dic6—44no—
355C3×C4⋊C4—44no—
356C3×C22⋊C4—44no—
357C3×C22⋊C4—44no—
358C3×C22⋊C4—44no—
359C3×C22⋊C4—44no—
360#217—28no—
361#217—28no—
362#217—28no—
363#217—28no—
364#217—28no—
365#217—44no—
366#217—44no—
367#217—44no—
368C4⋊Dic3—44no—
369Dic3⋊C4—44no—
370Dic3⋊C4—44no—
371Dic3⋊C4—44no—
372C4×Dic3—28no—
373C4×Dic3—44no—
374C25C22×D311yescharacteristic
375C25C22×D311yescharacteristic
376C22×Q8—34no—
377C22×Q8—62no—
378C22×Q8—62no—
379C22×Q8—62no—
380C22×Q8—62no—
381C22×Q8—121no—
382C22×Q8—121no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—41no—
389C22×D4—41no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403#124—632no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—62no—
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—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—41no—
430C2×C22⋊C4—41no—
431C2×C22⋊C4—41no—
432C2×C22⋊C4—41no—
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—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4—121no—
454C2×C22⋊C4—121no—
455C2×C42—62no—
456C2×C42—62no—
457C2×C42—62no—
458C2×C42—62no—
459C2×C42—62no—
460C2×C42—121no—
461#95—62no—
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—121no—
474#95#6714yes—
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—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×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—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3C22×D411yescharacteristic
546C23×C3C22×D411yescharacteristic
547C23×C3C22×D411yescharacteristic
548C23×C3C22×D411yescharacteristic
549C23×C3C2×#4111yescharacteristic
550C23×C3C2×#4111yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3C2×#4111yescharacteristic
553C23×C3C2×#4111yescharacteristic
554C23×C3H(5,𝔽2)11yescharacteristic
555C23×C3H(5,𝔽2)11yescharacteristic
556C23×C3H(5,𝔽2)11yescharacteristic
557C23×C32−1+411yescharacteristic
558C23×C32−1+411yescharacteristic
559C23×C32−1+411yescharacteristic
560C3×D4—416no—
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—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
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×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4#12114yes—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
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—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3#12014yes—
652Dic6—416no—
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—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24D3×D412yes—
682C24D3×D412yes—
683C24C23×D311yescharacteristic
684C2×Q8—68no—
685C2×Q8—68no—
686C2×Q8—124no—
687C2×Q8—124no—
688C2×Q8—124no—
689C2×Q8—124no—
690C2×Q8—124no—
691C2×D4—28no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
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—32no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—32no—
732C22×C4—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
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×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4D3×D412yes—
784C22×C4#23712yes—
785C22×C4#23712yes—
786C22×C4C2×#6712yes—
787C22×C4C2×#6712yes—
788C22×C4C2×#6712yes—
789C4⋊C4—44no—
790C4⋊C4—124no—
791C4⋊C4—124no—
792C4⋊C4—124no—
793C4⋊C4—124no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—68no—
799C22⋊C4—68no—
800C22⋊C4—68no—
801C22⋊C4—68no—
802C22⋊C4—68no—
803C22⋊C4—124no—
804C22⋊C4—124no—
805C22⋊C4—124no—
806C42—68no—
807C42—124no—
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—81no—
823C22×C3—81no—
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×C3—81no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3C2×#12011yescharacteristic
839C22×C3C2×#12111yescharacteristic
840C22×C3#52511yescharacteristic
841C22×C3#52911yescharacteristic
842C22×C3#53211yescharacteristic
843C22×C3#53211yescharacteristic
844C22×C3#53411yescharacteristic
845C22×C3#53611yescharacteristic
846C22×C3#53611yescharacteristic
847C22×C3#53711yescharacteristic
848C22×C3#53811yescharacteristic
849C22×C3#54211yescharacteristic
850C22×C3#54211yescharacteristic
851C22×C3#54211yescharacteristic
852C22×C3#54211yescharacteristic
853C22×C3D4211yescharacteristic
854C22×C3D4211yescharacteristic
855C22×C3#54611yescharacteristic
856C22×C3#54611yescharacteristic
857C22×C3#54611yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54711yescharacteristic
860C22×C3#54711yescharacteristic
861C22×C3#54711yescharacteristic
862C22×C3#54811yescharacteristic
863C22×C3#54811yescharacteristic
864C22×C3#54811yescharacteristic
865C22×C3#54811yescharacteristic
866C22×C3#55011yescharacteristic
867C22×C3#55111yescharacteristic
868C22×C3#55511yescharacteristic
869C22×C3#55611yescharacteristic
870C22×C3#55611yescharacteristic
871C22×C3#56211yescharacteristic
872C22×C3#56311yescharacteristic
873C3×C4—24no—
874C3×C4—42no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—81no—
878Dic3—24no—
879Dic3—42no—
880Dic3—42no—
881Dic3—42no—
882Dic3—42no—
883Dic3—42no—
884Dic3—42no—
885Dic3—81no—
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—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
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—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23C2×D3×D411yescharacteristic
957C23C2×D3×D411yescharacteristic
958C23C2×D3×D411yescharacteristic
959C23C2×#23711yescharacteristic
960C23C2×#23711yescharacteristic
961C23#100411yescharacteristic
962C23#100411yescharacteristic
963C23#100411yescharacteristic
964C23D3×#4111yescharacteristic
965C23D3×#4111yescharacteristic
966C23D3×#4111yescharacteristic
967C23#101011yescharacteristic
968C23#101011yescharacteristic
969C23#101011yescharacteristic
970C23C22×#6711yescharacteristic
971Q8—1216no—
972D4—416no—
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—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—34no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
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—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4#93814yes—
1064C2×C3—82no—
1065C2×C3—82no—
1066C2×C3#240711yescharacteristic
1067C2×C3#241011yescharacteristic
1068C2×C3#242611yescharacteristic
1069C2×C3#243211yescharacteristic
1070C2×C3#246111yescharacteristic
1071C2×C3#247411yescharacteristic
1072C2×C3#252111yescharacteristic
1073C2×C3#254511yescharacteristic
1074C2×C3#255511yescharacteristic
1075C2×C3#267211yescharacteristic
1076C2×C3#267411yescharacteristic
1077C2×C3#270011yescharacteristic
1078C2×C3#271511yescharacteristic
1079C2×C3#273011yescharacteristic
1080C2×C3#273111yescharacteristic
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—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22D3×#12011yescharacteristic
1112C22#558911yescharacteristic
1113C22#559111yescharacteristic
1114C22#559111yescharacteristic
1115C22#559611yescharacteristic
1116C22#559711yescharacteristic
1117C22#559811yescharacteristic
1118C22#559911yescharacteristic
1119C22#560011yescharacteristic
1120C22#560311yescharacteristic
1121C22#560311yescharacteristic
1122C22#561011yescharacteristic
1123C22#561111yescharacteristic
1124C22#561311yescharacteristic
1125C22#561611yescharacteristic
1126C22#562111yescharacteristic
1127C22#564811yescharacteristic
1128C22#565111yescharacteristic
1129C22#565511yescharacteristic
1130C22#565511yescharacteristic
1131C22#565611yescharacteristic
1132C22#565911yescharacteristic
1133C22#566211yescharacteristic
1134C22#566211yescharacteristic
1135C22#567111yescharacteristic
1136C22#567111yescharacteristic
1137C22#567711yescharacteristic
1138C22#567711yescharacteristic
1139C22C2×#93811yescharacteristic
1140C22D4×#6711yescharacteristic
1141C22D4×#6711yescharacteristic
1142C22#580611yescharacteristic
1143C22#582511yescharacteristic
1144C22#583111yescharacteristic
1145C22#583211yescharacteristic
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—64no—
1151C4—81no—
1152C4—122no—
1153C4—122no—
1154C4—122no—
1155C4—122no—
1156C4—122no—
1157C4—122no—
1158C4—241no—
1159C3#1532111yescharacteristic, complemented, Sylow
1160C2—82no—
1161C2—82no—
1162C2#7689411yescharacteristic
1163C2#7690411yescharacteristic
1164C2#7692711yescharacteristic
1165C2#7694011yescharacteristic
1166C2#7701911yescharacteristic
1167C2#7703811yescharacteristic
1168C2#7704411yescharacteristic
1169C2#7704611yescharacteristic
1170C2#8260511yescharacteristic
1171C2#8264611yescharacteristic
1172C2#8267211yescharacteristic
1173C2#8268211yescharacteristic
1174C2#8285211yescharacteristic
1175C2#8287011yescharacteristic
1176C2#8297111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC23×C3×D4C22
hypercenterC2×#394D3
hypocenterC3#15321
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
3. C2×#4979C2semidirect
4. C2×#4948C2semidirect
5. C2×#4944C2semidirect
6. C2×#4646C2semidirect
8. #71564C2semidirect
9. #71549C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. #71547C2semidirect
13. #71546C2semidirect
14. #71545C2semidirect
15. #69407C2semidirect
1159. C3#15321semidirect

Maximal subgroups

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

subgroupindex
C22×#9362
C2×C3×#3942
C2×#49792
C2×#49482
C2×#49442
C2×#46462
#721312
#715642
#715492
#715472
#715462
#715452
#694072
#153213