Finite Group Databasebeta

← #11857053

Subgroups — #11857053

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592650C211yesmaximal, characteristic
2C3×#4945C211yesmaximal, characteristic
3C3×#4944C211yesmaximal, characteristic
4#10591703C211yesmaximal, characteristic
5#10591703C211yesmaximal, characteristic
6#10591702C211yesmaximal, characteristic
7#10591701C211yesmaximal, characteristic
8#10591333C211yesmaximal, characteristic, complemented
9#10591272C211yesmaximal, characteristic, complemented
10#10591271C211yesmaximal, characteristic, complemented
11#10591254C211yesmaximal, characteristic, complemented
12#10591250C211yesmaximal, characteristic, complemented
13C4×Dic32C211yesmaximal, characteristic, complemented
14#10591193C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#75823—31nomaximal
17#75823—31nomaximal
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63658C2211yescharacteristic
40#63658C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#388—31no—
54C3×#388—31no—
55#4980—31no—
56#4980—31no—
57#4978—31no—
58#4978—31no—
59#4951—31no—
60#4951—31no—
61#4951—31no—
62#4951—31no—
63#4951—61no—
64#4945—31no—
65#4945—31no—
66#4945—31no—
67#4945D311yescharacteristic
68#4944—31no—
69#4944—31no—
70#4944—31no—
71#4944D311yescharacteristic
72#4933—31no—
73#4933—31no—
74C42×Dic3—31no—
75C42×Dic3—31no—
76#4655—31no—
77#4655—31no—
78#4654—31no—
79#4654—31no—
80#4653—31no—
81#4653—31no—
82#4652—31no—
83#4652—31no—
84C24×C32C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C32×C22⋊C4—22no—
100#3757—22no—
101#3757—22no—
102C4⋊(C3⋊Dic3)—22no—
103C4×C3⋊Dic3—22no—
104C3×#217—22no—
105C3×#217—22no—
106C3×#217—22no—
107C3×#217—22no—
108C3×Dic3⋊C4—22no—
109C3×Dic3⋊C4—22no—
110C3×C4×Dic3—22no—
111C3×C4×Dic3—22no—
112#3724—22no—
113#3724—22no—
114Dic3⋊Dic3—22no—
115Dic3⋊Dic3—22no—
116Dic32—22no—
117Dic32—22no—
118Dic32—22no—
119Dic32—22no—
120#2866—91noSylow
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4C2×D311yescharacteristic
129C2×C3×C22⋊C4C2×D311yescharacteristic
130C2×C3×C42—31no—
131C2×C3×C42—31no—
132C2×#217—31no—
133C2×#217—31no—
134C2×#217—31no—
135C2×#217—31no—
136C2×#217—61no—
137C2×#217—61no—
138C2×#217C2×D311yescharacteristic
139C2×#217C2×D311yescharacteristic
140C2×#217C2×D311yescharacteristic
141C2×#217C2×D311yescharacteristic
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—61no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4C2×D311yescharacteristic
154C2×Dic3⋊C4C2×D311yescharacteristic
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—61no—
166C2×C4×Dic3C2×D311yescharacteristic
167C2×C4×Dic3C2×D311yescharacteristic
168C3×#95—31no—
169C3×#95—31no—
170C3×#95—31no—
171C3×#95—31no—
172C3⋊#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—61no—
193C3⋊#95—61no—
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32C2411yescharacteristic
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4#4112yes—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3#4112yes—
223C2×C3⋊Dic3#4112yes—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3#4112yes—
245C2×C3×Dic3#4112yes—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248#388—31no—
249#388—31no—
250#388—91no—
251#388—91no—
252#388—91no—
253#388—91no—
254#388—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#387—91no—
259#387—91no—
260#387—91no—
261#387—91no—
262C43—91no—
263C24×C3—21no—
264C24×C3C22×D311yescharacteristic
265C24×C3C22×D311yescharacteristic
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—61no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C3×C4⋊C4—62no—
301C3×C4⋊C4—62no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—62no—
306C3×C22⋊C4—62no—
307C3×C22⋊C4—62no—
308C3×C22⋊C4—62no—
309C3×C42—62no—
310C3×C42—62no—
311#217—22no—
312#217—22no—
313#217—22no—
314#217—22no—
315#217—62no—
316#217—62no—
317#217—62no—
318#217—62no—
319#217—122no—
320#217—122no—
321C4⋊Dic3—62no—
322C4⋊Dic3—62no—
323C4⋊Dic3—62no—
324C4⋊Dic3—62no—
325C4⋊Dic3—122no—
326Dic3⋊C4—22no—
327Dic3⋊C4—22no—
328Dic3⋊C4—62no—
329Dic3⋊C4—62no—
330Dic3⋊C4—62no—
331Dic3⋊C4—62no—
332Dic3⋊C4—62no—
333Dic3⋊C4—62no—
334C4×Dic3—22no—
335C4×Dic3—22no—
336C4×Dic3—62no—
337C4×Dic3—62no—
338C4×Dic3—62no—
339C4×Dic3—62no—
340C4×Dic3—62no—
341C4×Dic3—62no—
342C4×Dic3—62no—
343C4×Dic3—62no—
344C4×Dic3—62no—
345C4×Dic3—62no—
346C4×Dic3—122no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32—41no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4111yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C22×C32C2×#4111yescharacteristic
358C22×C32C2×#4111yescharacteristic
359C22×C32C2×#4111yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C32×C4—22no—
362C32×C4—41no—
363C3⋊Dic3—22no—
364C3⋊Dic3—22no—
365C3⋊Dic3—41no—
366C3⋊Dic3—41no—
367C3×Dic3—22no—
368C3×Dic3—22no—
369C3×Dic3—22no—
370C3×Dic3—22no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—91no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—91no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4D3211yescharacteristic
389C2×C42—31no—
390C2×C42—31no—
391C2×C42—91no—
392C2×C42—91no—
393C2×C42—91no—
394C2×C42—91no—
395C2×C42—91no—
396#95—31no—
397#95—31no—
398#95—31no—
399#95—31no—
400#95—91no—
401#95—91no—
402#95—91no—
403#95—91no—
404#95—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3C23×D311yescharacteristic
433C23×C3C23×D311yescharacteristic
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4#23712yes—
475C2×C3×C4#23712yes—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—32no—
497C2×Dic3—32no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3#23512yes—
533C2×Dic3#23512yes—
534C2×Dic3#23712yes—
535C2×Dic3#23712yes—
536C2×C32—81no—
537C2×C32#52911yescharacteristic
538C2×C32#52911yescharacteristic
539C2×C32#52911yescharacteristic
540C2×C32#52911yescharacteristic
541C2×C32#52911yescharacteristic
542C2×C32#52911yescharacteristic
543C2×C32#52911yescharacteristic
544C24C2×D3211yescharacteristic
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—91no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4—91no—
557C22×C4C2×D3211yescharacteristic
558C22×C4C2×D3211yescharacteristic
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—182no—
562C4⋊C4—182no—
563C4⋊C4—182no—
564C4⋊C4—182no—
565C4⋊C4—182no—
566C22⋊C4—22no—
567C22⋊C4—62no—
568C22⋊C4—62no—
569C22⋊C4—62no—
570C22⋊C4—62no—
571C22⋊C4—182no—
572C22⋊C4—182no—
573C42—62no—
574C42—62no—
575C42—182no—
576C42—182no—
577C42—182no—
578C42—182no—
579C42—182no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—42no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3C2×#23511yescharacteristic
609C22×C3C2×#23511yescharacteristic
610C22×C3C2×#23711yescharacteristic
611C22×C3C2×#23711yescharacteristic
612C22×C3C2×#23711yescharacteristic
613C22×C3C2×#23711yescharacteristic
614C22×C3D3×#4111yescharacteristic
615C22×C3D3×#4111yescharacteristic
616C22×C3D3×#4111yescharacteristic
617C22×C3D3×#4111yescharacteristic
618C22×C3D3×#4111yescharacteristic
619C22×C3D3×#4111yescharacteristic
620C22×C3D3×#4111yescharacteristic
621C22×C3D3×#4111yescharacteristic
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—42no—
625C3×C4—42no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—62no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—121no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4—121no—
636Dic3—22no—
637Dic3—22no—
638Dic3—22no—
639Dic3—22no—
640Dic3—41no—
641Dic3—41no—
642Dic3—41no—
643Dic3—41no—
644Dic3—62no—
645Dic3—62no—
646Dic3—62no—
647Dic3—62no—
648Dic3—122no—
649Dic3—122no—
650Dic3—121no—
651Dic3—121no—
652Dic3—121no—
653Dic3—121no—
654Dic3—241no—
655Dic3—241no—
656C32#286611yescharacteristic, complemented, Sylow
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23C22×D3211yescharacteristic
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—92no—
695C2×C4—92no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—181no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4#380512yes—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—82no—
715C2×C3—81no—
716C2×C3—81no—
717C2×C3#552811yescharacteristic
718C2×C3#552811yescharacteristic
719C2×C3#553811yescharacteristic
720C2×C3#553811yescharacteristic
721C2×C3#555711yescharacteristic
722C2×C3#555711yescharacteristic
723C2×C3#560011yescharacteristic
724C2×C3#560011yescharacteristic
725C2×C3#564911yescharacteristic
726C2×C3#564911yescharacteristic
727C2×C3#568011yescharacteristic
728C2×C3#568011yescharacteristic
729C2×C3#570611yescharacteristic
730C2×C3#570611yescharacteristic
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22D3×#23511yescharacteristic
739C22D3×#23511yescharacteristic
740C22D3×#23711yescharacteristic
741C22D3×#23711yescharacteristic
742C22#6431211yescharacteristic
743C22#6431211yescharacteristic
744C22C2×#380511yescharacteristic
745C4—22no—
746C4—41no—
747C4—62no—
748C4—62no—
749C4—62no—
750C4—62no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—121no—
755C4—182no—
756C4—182no—
757C4—361no—
758C4—361no—
759C3—21no—
760C3#7582311yescharacteristic, complemented
761C3#7582311yescharacteristic, complemented
762C2—81no—
763C2#1059408711yescharacteristic
764C2#1059408811yescharacteristic
765C2#1059410611yescharacteristic
766C2#1059410711yescharacteristic
767C2#1059493411yescharacteristic
768C2#1059517311yescharacteristic
769C2#1059520211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2866
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591333C2semidirect
9. #10591272C2semidirect
10. #10591271C2semidirect
11. #10591254C2semidirect
12. #10591250C2semidirect
13. C4×Dic32C2semidirect
14. #10591193C2semidirect
15. #10591192C2semidirect
656. C32#2866semidirect
760. C3#75823semidirect
761. C3#75823semidirect

Maximal subgroups

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

subgroupindex
#105926502
C3×#49452
C3×#49442
#105917032
#105917022
#105917012
#105913332
#105912722
#105912712
#105912542
#105912502
C4×Dic322
#105911932
#105911922
#758233