Finite Group Databasebeta

← #11808953

Subgroups — #11808953

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592348C211yesmaximal, characteristic
2C3×#4659C211yesmaximal, characteristic
3C3×#4657C211yesmaximal, characteristic
4#10591358C211yesmaximal, characteristic
5#10591342C211yesmaximal, characteristic
6#10591341C211yesmaximal, characteristic
7#10591340C211yesmaximal, characteristic
8#10591274C211yesmaximal, characteristic
9#10591252C211yesmaximal, characteristic
10#10591241C211yesmaximal, characteristic
11#10591241C211yesmaximal, characteristic
12#10591241C211yesmaximal, characteristic
13#10591241C211yesmaximal, characteristic
14#10591210C211yesmaximal, characteristic
15#10591196C211yesmaximal, characteristic
16#78133—31nomaximal
17#77741—31nomaximal
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34C2×Dic32C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C32×#95C2211yescharacteristic
38#63658C2211yescharacteristic
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×#400—31no—
54C3×#398—31no—
55#4986—31no—
56#4985—31no—
57#4983—31no—
58#4982—31no—
59#4982—31no—
60#4981—31no—
61Dic3×C4⋊C4—31no—
62Dic3×C4⋊C4—31no—
63Dic3×C4⋊C4—31no—
64Dic3×C4⋊C4—31no—
65Dic3×C4⋊C4—31no—
66Dic3×C4⋊C4—31no—
67#4661—31no—
68#4660—31no—
69#4660—31no—
70#4659D311yescharacteristic
71#4658—31no—
72#4658—31no—
73#4657—31no—
74#4657D311yescharacteristic
75#4649—31no—
76#4649—31no—
77#4649—31no—
78#4649—31no—
79#4649—31no—
80#4649—31no—
81#4649—61no—
82#4648—31no—
83#4648—31no—
84C22×C32×C4C2311yescharacteristic
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
99#3750—22no—
100#3750—22no—
101C4×C3⋊Dic3—22no—
102C4×C3⋊Dic3—22no—
103C4×C3⋊Dic3—22no—
104C3×C4⋊Dic3—22no—
105C3×C4⋊Dic3—22no—
106C3×Dic3⋊C4—22no—
107C3×Dic3⋊C4—22no—
108C3×Dic3⋊C4—22no—
109C3×Dic3⋊C4—22no—
110Dic3⋊Dic3—22no—
111Dic3⋊Dic3—22no—
112Dic3⋊Dic3—22no—
113Dic3⋊Dic3—22no—
114Dic32—22no—
115Dic32—22no—
116Dic32—22no—
117Dic32Q814yes—
118#2402—91noSylow
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—61no—
140C2×Dic3⋊C4—61no—
141C2×Dic3⋊C4C2×D311yescharacteristic
142C2×Dic3⋊C4C2×D311yescharacteristic
143C2×Dic3⋊C4C2×D311yescharacteristic
144C2×Dic3⋊C4C2×D311yescharacteristic
145C2×C4×Dic3—31no—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—61no—
160C2×C4×Dic3—61no—
161C2×C4×Dic3—61no—
162C3×#95—21no—
163C3×#95—31no—
164C3×#95—31no—
165C3×#95—31no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95C2×D311yescharacteristic
170C3×#95C2×D311yescharacteristic
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—61no—
190C3⋊#95C2×D311yescharacteristic
191C3⋊#95C2×D311yescharacteristic
192C3⋊#95C2×D311yescharacteristic
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C23×C32C2411yescharacteristic
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4#4112yes—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3C2×Q812yes—
215C2×C3⋊Dic3#4112yes—
216C2×C3⋊Dic3#4112yes—
217C2×C3⋊Dic3#4112yes—
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—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×Dic3C2×Q812yes—
239C2×C3×Dic3C2×Q812yes—
240C2×C3×Dic3#4112yes—
241C2×C3×Dic3#4112yes—
242#400—31no—
243#400—91no—
244#400—91no—
245#400—91no—
246#398—31no—
247#398—91no—
248#398—91no—
249#398—91no—
250C4×C4⋊C4—91no—
251C4×C4⋊C4—91no—
252C4×C4⋊C4—91no—
253C4×C4⋊C4—91no—
254C4×C4⋊C4—91no—
255C4×C4⋊C4—91no—
256#376—91no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C22×D311yescharacteristic
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—61no—
283C22×Dic3—61no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D311yescharacteristic
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D311yescharacteristic
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C3×C4⋊C4—62no—
295C3×C4⋊C4—62no—
296C3×C4⋊C4—62no—
297C3×C4⋊C4—62no—
298C3×C4⋊C4—62no—
299C3×C4⋊C4—62no—
300C4⋊Dic3—22no—
301C4⋊Dic3—22no—
302C4⋊Dic3—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3—62no—
305C4⋊Dic3—62no—
306Dic3⋊C4—22no—
307Dic3⋊C4—22no—
308Dic3⋊C4—22no—
309Dic3⋊C4—22no—
310Dic3⋊C4—62no—
311Dic3⋊C4—62no—
312Dic3⋊C4—62no—
313Dic3⋊C4—62no—
314Dic3⋊C4—62no—
315Dic3⋊C4—64no—
316Dic3⋊C4—64no—
317Dic3⋊C4—62no—
318Dic3⋊C4—62no—
319Dic3⋊C4—62no—
320C4×Dic3—34no—
321C4×Dic3—34no—
322C4×Dic3—62no—
323C4×Dic3—62no—
324C4×Dic3—62no—
325C4×Dic3—62no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328C4×Dic3—62no—
329C4×Dic3—62no—
330C4×Dic3—62no—
331C4×Dic3—62no—
332C4×Dic3—62no—
333C4×Dic3—62no—
334C4×Dic3—64no—
335C4×Dic3—122no—
336C4×Dic3—122no—
337C22×C32C22×Q811yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C22×C32C2×#4111yescharacteristic
344C32×C4—22no—
345C32×C4—41no—
346C32×C4—41no—
347C3⋊Dic3—22no—
348C3⋊Dic3—41no—
349C3⋊Dic3—41no—
350C3⋊Dic3#12514yes—
351C3×Dic3—22no—
352C3×Dic3—22no—
353C3×Dic3—22no—
354C3×Dic3—22no—
355C3×Dic3—41no—
356C3×Dic3—41no—
357C3×Dic3—41no—
358C3×Dic3—41no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—91no—
371C2×C42—91no—
372C2×C42—91no—
373C2×C42—91no—
374C2×C42—91no—
375C2×C42—91no—
376C2×C42—91no—
377C2×C42—91no—
378#95—31no—
379#95—31no—
380#95—31no—
381#95—31no—
382#95—31no—
383#95—31no—
384#95—91no—
385#95—91no—
386#95—91no—
387#95—91no—
388#95—91no—
389#95—91no—
390#95—91no—
391#95—91no—
392#95—91no—
393#95D3211yescharacteristic
394C23×C3—21no—
395C23×C3C23×D311yescharacteristic
396C23×C3C23×D311yescharacteristic
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—32no—
419C2×C3×C4—32no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4#23712yes—
447C2×C3×C4#23912yes—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—32no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—32no—
472C2×Dic3—32no—
473C2×Dic3—32no—
474C2×Dic3—32no—
475C2×Dic3—32no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—62no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3—121no—
503C2×Dic3—121no—
504C2×Dic3#23712yes—
505C2×Dic3#23712yes—
506C2×Dic3D3×Q812yes—
507C2×Dic3D3×Q812yes—
508C2×C32C2×#12511yescharacteristic
509C2×C32#52911yescharacteristic
510C2×C32#52911yescharacteristic
511C2×C32#52911yescharacteristic
512C2×C32#52911yescharacteristic
513C2×C32#53311yescharacteristic
514C2×C32#53311yescharacteristic
515C22×C4—31no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4C2×D3211yescharacteristic
528C22×C4C2×D3211yescharacteristic
529C22×C4C2×D3211yescharacteristic
530C4⋊C4—62no—
531C4⋊C4—62no—
532C4⋊C4—62no—
533C4⋊C4—62no—
534C4⋊C4—62no—
535C4⋊C4—62no—
536C4⋊C4—182no—
537C4⋊C4—182no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—182no—
541C4⋊C4—182no—
542C42—94no—
543C42—182no—
544C42—182no—
545C42—182no—
546C42—182no—
547C42—182no—
548C42—182no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3C2×#23711yescharacteristic
557C22×C3C2×#23711yescharacteristic
558C22×C3C2×#23711yescharacteristic
559C22×C3C2×D3×Q811yescharacteristic
560C22×C3C2×D3×Q811yescharacteristic
561C22×C3C2×#23911yescharacteristic
562C22×C3D3×#4111yescharacteristic
563C22×C3D3×#4111yescharacteristic
564C22×C3D3×#4111yescharacteristic
565C22×C3D3×#4111yescharacteristic
566C22×C3D3×#4111yescharacteristic
567C22×C3D3×#4111yescharacteristic
568C22×C3D3×#4111yescharacteristic
569C22×C3D3×#4111yescharacteristic
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—42no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—62no—
580C3×C4—62no—
581C3×C4—62no—
582C3×C4—62no—
583C3×C4—121no—
584C3×C4—121no—
585C3×C4—121no—
586C3×C4—121no—
587Dic3—22no—
588Dic3—22no—
589Dic3—22no—
590Dic3—22no—
591Dic3—34no—
592Dic3—34no—
593Dic3—41no—
594Dic3—41no—
595Dic3—41no—
596Dic3—41no—
597Dic3—64no—
598Dic3—64no—
599Dic3—62no—
600Dic3—62no—
601Dic3—122no—
602Dic3—122no—
603Dic3—121no—
604Dic3—121no—
605Dic3—121no—
606Dic3—121no—
607C32#240211yescharacteristic, complemented, Sylow
608C23C22×D3211yescharacteristic
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—32no—
618C2×C4—32no—
619C2×C4—32no—
620C2×C4—32no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—92no—
642C2×C4—92no—
643C2×C4—92no—
644C2×C4—92no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4#379612yes—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3#560011yescharacteristic
662C2×C3#562211yescharacteristic
663C2×C3#562211yescharacteristic
664C2×C3#562411yescharacteristic
665C2×C3#564911yescharacteristic
666C2×C3#564911yescharacteristic
667C2×C3#568011yescharacteristic
668C2×C3D3×#12511yescharacteristic
669C2×C3D3×#12511yescharacteristic
670C2×C3#568811yescharacteristic
671C2×C3#569111yescharacteristic
672C2×C3#570611yescharacteristic
673C2×C3#570611yescharacteristic
674C2×C3#572811yescharacteristic
675C22C2×#379611yescharacteristic
676C22#6430611yescharacteristic
677C22#6430611yescharacteristic
678C22D3×#23711yescharacteristic
679C22D3×#23711yescharacteristic
680C22#6431211yescharacteristic
681C22D32×Q811yescharacteristic
682C4—22no—
683C4—41no—
684C4—41no—
685C4—62no—
686C4—62no—
687C4—62no—
688C4—62no—
689C4—94no—
690C4—121no—
691C4—121no—
692C4—121no—
693C4—121no—
694C4—182no—
695C4—361no—
696C4—361no—
697C3—21no—
698C3#7774111yescharacteristic, complemented
699C3#7813311yescharacteristic, complemented
700C2#1059394311yescharacteristic
701C2#1059411211yescharacteristic
702C2#1059413011yescharacteristic
703C2#1059414411yescharacteristic
704C2#1059438711yescharacteristic
705C2#1059438811yescharacteristic
706C2#1059439911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2402
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
607. C32#2402semidirect
698. C3#77741semidirect
699. C3#78133semidirect

Maximal subgroups

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

subgroupindex
#105923482
C3×#46592
C3×#46572
#105913582
#105913422
#105913412
#105913402
#105912742
#105912522
#105912412
#105912102
#105911962
#781333
#777413