Finite Group Databasebeta

← #11819162

Subgroups — #11819162

Order 1152.

947 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592357C211yesmaximal, characteristic, complemented
2C3×#4666C211yesmaximal, characteristic
3C3×C3⋊#401C211yesmaximal, characteristic, complemented
4#10591373C211yesmaximal, characteristic
5#10591369C211yesmaximal, characteristic
6#10591362C211yesmaximal, characteristic
7#10591362C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic
9#10591333C211yesmaximal, characteristic, complemented
10#10591332C211yesmaximal, characteristic, complemented
11#10591331C211yesmaximal, characteristic, complemented
12#10591278C211yesmaximal, characteristic
13#10591223C211yesmaximal, characteristic, complemented
14#10591217C211yesmaximal, characteristic, complemented
15#10591211C211yesmaximal, characteristic, complemented
16#78430—31nomaximal
17#73509—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C32×#95C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2211yescharacteristic
36#63658C2211yescharacteristic
37#63658C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
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×#401—31no—
54C3×C4×C22⋊C4—31no—
55#5210—31no—
56C2×C3⋊#95—31no—
57#4946—31no—
58#4943—31no—
59#4943—31no—
60#4942—31no—
61#4937—31no—
62#4933—31no—
63#4933—31no—
64#4933—31no—
65#4668—31no—
66#4668—31no—
67#4667—31no—
68#4666D311yescharacteristic
69#4664—31no—
70#4664—31no—
71D3×#95—31no—
72C3⋊#401D311yescharacteristic, complemented
73#4660—31no—
74#4658—31no—
75#4658—31no—
76#4658—31no—
77#4658—31no—
78#4658—31no—
79#4658—61no—
80#4655—31no—
81#4654—31no—
82#4653—31no—
83#4651—31no—
84C23×C3×D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
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
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—41no—
102C2×D3×Dic3—22no—
103C2×D3×Dic3—22no—
104C2×D3×Dic3—22no—
105C2×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107C2×D3×Dic3—41no—
108#3750—41no—
109#3750—41no—
110C3×(C2×D3)⋊C4—22no—
111C3×(C2×D3)⋊C4—22no—
112C3×C4×Dic3—22no—
113C3×C4×Dic3—41no—
114#3724—22no—
115#3724—41no—
116Dic3⋊Dic3—22no—
117Dic3⋊Dic3—22no—
118(C2×D3)⋊Dic3—22no—
119(C2×D3)⋊Dic3—22no—
120#2493—91noSylow
121C23×C3×C4—31no—
122C23×Dic3—31no—
123C23×Dic3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—31no—
126C22×C4×D3C2×D311yescharacteristic
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C42—31no—
130C2×C3×C42—31no—
131C2×#217—31no—
132C2×#217—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4C2×D311yescharacteristic
136C2×(C2×D3)⋊C4C2×D311yescharacteristic
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—61no—
150C2×Dic3⋊C4—61no—
151C2×C4×Dic3C2×D311yescharacteristic
152C2×C4×Dic3C2×D311yescharacteristic
153C3×#95—21no—
154C3×#95—31no—
155C3×#95—31no—
156C3×#95—31no—
157C3×#95—31no—
158C3×#95—31no—
159C3×#95—31no—
160C3×#95—31no—
161C3×#95C2×D311yescharacteristic
162C3×#95C2×D311yescharacteristic
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95—31no—
167C3⋊#95—31no—
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—61no—
188C3⋊#95—61no—
189C3⋊#95—61no—
190C3⋊#95—61no—
191C3⋊#95C2×D311yescharacteristic
192C3⋊#95C2×D311yescharacteristic
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32C2411yescharacteristic
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3#4112yes—
204C22×C3×D3#4112yes—
205C22×C3×D3#4112yes—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—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—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3#4112yes—
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—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3#4112yes—
248C3×C4×D3—44no—
249D3×Dic3—44no—
250D3×Dic3—44no—
251#401—31no—
252#400—91no—
253#400—91no—
254#400—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#385—91no—
259#385—91no—
260#383—91no—
261#381—91no—
262#381—91no—
263#380—91no—
264C4×C22⋊C4—31no—
265C2×#95—91no—
266C24×C3—31no—
267C23×D3C22×D311yescharacteristic
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—62no—
279C22×C3×C4—62no—
280C22×C3×C4—121no—
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—62no—
300C22×Dic3—62no—
301C22×Dic3—62no—
302C22×Dic3—62no—
303C22×Dic3—62no—
304C22×Dic3—121no—
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—41no—
315C2×C4×D3—62no—
316C2×C4×D3—62no—
317C2×C4×D3—62no—
318C2×C4×D3—62no—
319C2×C4×D3—62no—
320C2×C4×D3—121no—
321C3×C22⋊C4—62no—
322C3×C22⋊C4—62no—
323C3×C42—62no—
324C3×C42—121no—
325#217—62no—
326#217—62no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—22no—
329(C2×D3)⋊C4—62no—
330(C2×D3)⋊C4—62no—
331C4⋊Dic3—62no—
332C4⋊Dic3—62no—
333Dic3⋊C4—62no—
334Dic3⋊C4—62no—
335Dic3⋊C4—62no—
336Dic3⋊C4—62no—
337Dic3⋊C4—121no—
338Dic3⋊C4—121no—
339Dic3⋊C4—121no—
340Dic3⋊C4—121no—
341Dic3⋊C4—121no—
342Dic3⋊C4—121no—
343Dic3⋊C4—122no—
344Dic3⋊C4—122no—
345C4×Dic3—22no—
346C4×Dic3—41no—
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32H(5,𝔽2)11yescharacteristic
353C22×C322−1+411yescharacteristic
354C2×C3×D3—22no—
355C2×C3×D3—22no—
356C2×C3×D3—22no—
357C2×C3×D3—22no—
358C2×C3×D3—22no—
359C2×C3×D3—22no—
360C2×C3×D3#12614yes—
361C32×C4—41no—
362C32×C4—41no—
363C32×C4—41no—
364C3⋊Dic3—22no—
365C3⋊Dic3—41no—
366C3⋊Dic3—41no—
367C3⋊Dic3—41no—
368C3×Dic3—22no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C23×C4—31no—
376C23×C4—91no—
377C23×C4—91no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4—91no—
388C2×C42—31no—
389C2×C42—31no—
390#95—31no—
391#95—31no—
392#95—31no—
393#95—31no—
394#95—31no—
395#95—31no—
396#95—31no—
397#95—91no—
398#95—91no—
399#95—91no—
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#95D3211yescharacteristic
410C23×C3—21no—
411C23×C3—32no—
412C23×C3—32no—
413C23×C3—32no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—61no—
417C23×C3—61no—
418C23×C3C23×D311yescharacteristic
419C23×C3C23×D311yescharacteristic
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3#23512yes—
425C22×D3#23512yes—
426C22×D3#23512yes—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
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—32no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
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—61no—
475C2×C3×C4—124no—
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—62no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—62no—
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—124no—
533C2×Dic3—124no—
534C2×Dic3#23712yes—
535C4×D3—44no—
536C4×D3—124no—
537C4×D3—124no—
538C2×C32C2×#12611yescharacteristic
539C2×C32#52911yescharacteristic
540C2×C32#53911yescharacteristic
541C2×C32#55111yescharacteristic
542C2×C32#55111yescharacteristic
543C2×C32#55211yescharacteristic
544C2×C32#55211yescharacteristic
545C3×D3—24no—
546C24—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—91no—
560C22×C4—121no—
561C22×C4—182no—
562C22×C4—182no—
563C22×C4—182no—
564C22×C4—182no—
565C22×C4—182no—
566C22×C4—361no—
567C22×C4C2×D3211yescharacteristic
568C22×C4C2×D3211yescharacteristic
569C22×C4C2×D3211yescharacteristic
570C4⋊C4—182no—
571C4⋊C4—182no—
572C4⋊C4—182no—
573C4⋊C4—361no—
574C4⋊C4—361no—
575C4⋊C4—361no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—182no—
579C22⋊C4—182no—
580C42—62no—
581C42—121no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—34no—
590C22×C3—62no—
591C22×C3—62no—
592C22×C3—62no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—62no—
596C22×C3C2×#23511yescharacteristic
597C22×C3C2×#23511yescharacteristic
598C22×C3C2×#23511yescharacteristic
599C22×C3C2×#23711yescharacteristic
600C22×C3#100411yescharacteristic
601C22×C3D3×#4111yescharacteristic
602C22×C3D3×#4111yescharacteristic
603C22×C3D3×#4111yescharacteristic
604C22×C3D3×#4111yescharacteristic
605C22×C3D3×#4111yescharacteristic
606C22×C3D3×#4111yescharacteristic
607C22×C3#100911yescharacteristic
608C22×C3#101011yescharacteristic
609C22×C3#101011yescharacteristic
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3#87614yes—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—62no—
624C3×C4—81no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—121no—
628C3×C4—121no—
629C3×C4—121no—
630C3×C4—121no—
631C3×C4—121no—
632C3×C4—121no—
633Dic3—22no—
634Dic3—41no—
635Dic3—41no—
636Dic3—41no—
637Dic3—41no—
638Dic3—41no—
639Dic3—41no—
640Dic3—62no—
641Dic3—62no—
642Dic3—122no—
643Dic3—122no—
644Dic3—121no—
645Dic3—121no—
646Dic3—121no—
647Dic3—121no—
648Dic3—121no—
649Dic3—121no—
650Dic3—241no—
651Dic3—241no—
652C32#249311yescharacteristic, complemented, Sylow
653C23—32no—
654C23—32no—
655C23—32no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23C22×D3211yescharacteristic
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—32no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
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—92no—
692C2×C4—124no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
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—364no—
705C2×C4—364no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—64no—
714C2×C3C2×#87611yescharacteristic
715C2×C3#549511yescharacteristic
716C2×C3#553111yescharacteristic
717C2×C3#553811yescharacteristic
718C2×C3#554111yescharacteristic
719C2×C3#555611yescharacteristic
720C2×C3#556411yescharacteristic
721C2×C3D3×#12611yescharacteristic
722C2×C3#570511yescharacteristic
723C2×C3#570511yescharacteristic
724C2×C3#570611yescharacteristic
725C2×C3#570711yescharacteristic
726C2×C3#570811yescharacteristic
727C2×C3#570811yescharacteristic
728D3—24no—
729C22—34no—
730C22—62no—
731C22—62no—
732C22—62no—
733C22—62no—
734C22—62no—
735C22—62no—
736C22D3×#23511yescharacteristic
737C22D3×#23511yescharacteristic
738C22D3×#23511yescharacteristic
739C22#6430911yescharacteristic
740C22D3×#23711yescharacteristic
741C22#6431411yescharacteristic
742C22#6431911yescharacteristic
743C4—41no—
744C4—41no—
745C4—41no—
746C4—62no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4—182no—
754C4—361no—
755C4—361no—
756C4—361no—
757C3—21no—
758C3#7350911yescharacteristic, complemented
759C3#7843011yescharacteristic, complemented
760C2—64no—
761C2D3×#87611yescharacteristic
762C2#1059409011yescharacteristic
763C2#1059409411yescharacteristic
764C2#1059409511yescharacteristic
765C2#1059440511yescharacteristic
766C2#1059440911yescharacteristic
767C2#1059464511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2493
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #10592357C2semidirect
3. C3×C3⋊#401C2semidirect
9. #10591333C2semidirect
10. #10591332C2semidirect
11. #10591331C2semidirect
13. #10591223C2semidirect
14. #10591217C2semidirect
15. #10591211C2semidirect
72. C3⋊#401D3semidirect
652. C32#2493semidirect
758. C3#73509semidirect
759. C3#78430semidirect

Maximal subgroups

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

subgroupindex
#105923572
C3×#46662
C3×C3⋊#4012
#105913732
#105913692
#105913622
D3×C3⋊#952
#105913332
#105913322
#105913312
#105912782
#105912232
#105912172
#105912112
#784303
#735093