Finite Group Databasebeta

← #11808954

Subgroups — #11808954

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 705 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592358C211yesmaximal, characteristic
2C3×#4657C211yesmaximal, characteristic
3C3×#4649C211yesmaximal, characteristic
4#10591353C211yesmaximal, characteristic
5#10591342C211yesmaximal, characteristic
6#10591341C211yesmaximal, characteristic
7Dic3×C4⋊Dic3C211yesmaximal, characteristic
8#10591243C211yesmaximal, characteristic
9Dic3×Dic3⋊C4C211yesmaximal, characteristic
10Dic3×Dic3⋊C4C211yesmaximal, characteristic
11Dic3×Dic3⋊C4C211yesmaximal, characteristic
12#10591239C211yesmaximal, characteristic
13#10591200C211yesmaximal, characteristic
14#10591199C211yesmaximal, characteristic
15#10591196C211yesmaximal, characteristic
16#77741—31nomaximal
17#73670—31nomaximal
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34C2×Dic32C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C32×#95C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
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×#398—31no—
54C3×C4×C4⋊C4—31no—
55#4986—31no—
56#4985—31no—
57#4985—31no—
58#4983—31no—
59#4982—31no—
60#4982—31no—
61#4981—31no—
62#4981—31no—
63Dic3×C4⋊C4—31no—
64Dic3×C4⋊C4—31no—
65Dic3×C4⋊C4—31no—
66Dic3×C4⋊C4—31no—
67C4×C4⋊Dic3—31no—
68#4932—31no—
69C4×Dic3⋊C4—31no—
70C4×Dic3⋊C4—31no—
71C4×Dic3⋊C4—31no—
72C4×Dic3⋊C4—31no—
73#4661—31no—
74#4660—31no—
75#4659—31no—
76#4659—31no—
77#4659—61no—
78#4658—31no—
79#4658—31no—
80#4657D311yescharacteristic
81#4649—31no—
82#4649D311yescharacteristic
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
99C4⋊(C3⋊Dic3)—22no—
100#3750—22no—
101C3×C4⋊Dic3—22no—
102C3×Dic3⋊C4—22no—
103C3×Dic3⋊C4—22no—
104C3×Dic3⋊C4—22no—
105C3×Dic3⋊C4—22no—
106C3×Dic3⋊C4—22no—
107C3×C4×Dic3—22no—
108C3×C4×Dic3—22no—
109C3×C4×Dic3—22no—
110#3724—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×C3×C42—31no—
126C2×C3×C42—31no—
127C2×C3×C42—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—61no—
143C2×Dic3⋊C4C2×D311yescharacteristic
144C2×Dic3⋊C4C2×D311yescharacteristic
145C2×Dic3⋊C4C2×D311yescharacteristic
146C2×Dic3⋊C4C2×D311yescharacteristic
147C2×Dic3⋊C4C2×D311yescharacteristic
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×Dic3C2×D311yescharacteristic
157C2×C4×Dic3C2×D311yescharacteristic
158C2×C4×Dic3C2×D311yescharacteristic
159C3×#95—21no—
160C3×#95—31no—
161C3×#95—31no—
162C3×#95—31no—
163C3×#95C2×D311yescharacteristic
164C3×#95C2×D311yescharacteristic
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—31no—
188C3⋊#95—31no—
189C3⋊#95—61no—
190C3⋊#95—61no—
191C3⋊#95—61no—
192C3⋊#95—61no—
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⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3C2×Q812yes—
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×Dic3C2×Q812yes—
236C2×C3×Dic3C2×Q812yes—
237C2×C3×Dic3#4112yes—
238C2×C3×Dic3#4112yes—
239C2×C3×Dic3#4112yes—
240C2×C3×Dic3#4112yes—
241C2×C3×Dic3#4112yes—
242#400—91no—
243#400—91no—
244#400—91no—
245#400—91no—
246#398—31no—
247#398—91no—
248#398—91no—
249#398—91no—
250C4×C4⋊C4—31no—
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—
300C3×C42—62no—
301C3×C42—62no—
302C3×C42—62no—
303C4⋊Dic3—22no—
304C4⋊Dic3—62no—
305C4⋊Dic3—62no—
306C4⋊Dic3—62no—
307C4⋊Dic3—62no—
308C4⋊Dic3—62no—
309C4⋊Dic3—122no—
310Dic3⋊C4—22no—
311Dic3⋊C4—22no—
312Dic3⋊C4—22no—
313Dic3⋊C4—22no—
314Dic3⋊C4—22no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317Dic3⋊C4—62no—
318Dic3⋊C4—62no—
319Dic3⋊C4—62no—
320Dic3⋊C4—62no—
321Dic3⋊C4—62no—
322Dic3⋊C4—122no—
323C4×Dic3—22no—
324C4×Dic3—22no—
325C4×Dic3—22no—
326C4×Dic3—34no—
327C4×Dic3—34no—
328C4×Dic3—62no—
329C4×Dic3—62no—
330C4×Dic3—62no—
331C4×Dic3—62no—
332C4×Dic3—62no—
333C4×Dic3—62no—
334C22×C32C22×Q811yescharacteristic
335C22×C32C2×#4111yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C32×C4—22no—
342C32×C4—41no—
343C32×C4—41no—
344C3⋊Dic3—22no—
345C3⋊Dic3—41no—
346C3⋊Dic3—41no—
347C3⋊Dic3—41no—
348C3×Dic3—22no—
349C3×Dic3—22no—
350C3×Dic3—22no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3—41no—
354C3×Dic3—41no—
355C3×Dic3#12514yes—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—31no—
371C2×C42—91no—
372C2×C42—91no—
373C2×C42—91no—
374C2×C42—91no—
375#95—31no—
376#95—31no—
377#95—31no—
378#95—91no—
379#95—91no—
380#95—91no—
381#95—91no—
382#95—91no—
383#95—91no—
384#95—91no—
385#95—91no—
386#95—91no—
387#95—91no—
388#95—91no—
389#95—91no—
390#95D3211yescharacteristic
391C23×C3—21no—
392C23×C3C23×D311yescharacteristic
393C23×C3C23×D311yescharacteristic
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
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—22no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
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#23512yes—
444C2×C3×C4#23912yes—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
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—32no—
463C2×Dic3—32no—
464C2×Dic3—62no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—121no—
488C2×Dic3—121no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3#23512yes—
499C2×Dic3#23512yes—
500C2×Dic3#23712yes—
501C2×Dic3#23712yes—
502C2×Dic3#23712yes—
503C2×Dic3D3×Q812yes—
504C2×Dic3D3×Q812yes—
505C2×C32C2×#12511yescharacteristic
506C2×C32#52911yescharacteristic
507C2×C32#52911yescharacteristic
508C2×C32#52911yescharacteristic
509C2×C32#52911yescharacteristic
510C2×C32#53311yescharacteristic
511C2×C32#53311yescharacteristic
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4C2×D3211yescharacteristic
525C22×C4C2×D3211yescharacteristic
526C22×C4C2×D3211yescharacteristic
527C4⋊C4—62no—
528C4⋊C4—62no—
529C4⋊C4—62no—
530C4⋊C4—62no—
531C4⋊C4—62no—
532C4⋊C4—62no—
533C4⋊C4—182no—
534C4⋊C4—182no—
535C4⋊C4—182no—
536C4⋊C4—182no—
537C4⋊C4—182no—
538C4⋊C4—182no—
539C42—62no—
540C42—62no—
541C42—62no—
542C42—94no—
543C42—182no—
544C42—182no—
545C42—182no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3C2×#23511yescharacteristic
554C22×C3C2×#23511yescharacteristic
555C22×C3C2×#23511yescharacteristic
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
567C3×C4—22no—
568C3×C4—22no—
569C3×C4—34no—
570C3×C4—42no—
571C3×C4—41no—
572C3×C4—41no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—62no—
576C3×C4—62no—
577C3×C4—62no—
578C3×C4—62no—
579C3×C4—81no—
580C3×C4—81no—
581C3×C4—121no—
582C3×C4—121no—
583C3×C4—121no—
584Dic3—22no—
585Dic3—22no—
586Dic3—22no—
587Dic3—22no—
588Dic3—41no—
589Dic3—41no—
590Dic3—41no—
591Dic3—62no—
592Dic3—62no—
593Dic3—122no—
594Dic3—121no—
595Dic3—121no—
596Dic3—121no—
597Dic3—121no—
598Dic3—121no—
599Dic3—121no—
600Dic3—241no—
601Dic3—241no—
602Dic3—241no—
603Dic3#88914yes—
604C32#240211yescharacteristic, complemented, Sylow
605C23C22×D3211yescharacteristic
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—32no—
615C2×C4—32no—
616C2×C4—32no—
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—92no—
639C2×C4—181no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4#379912yes—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3#547911yescharacteristic
659C2×C3C2×#88911yescharacteristic
660C2×C3#552811yescharacteristic
661C2×C3#553811yescharacteristic
662C2×C3#555711yescharacteristic
663C2×C3#557811yescharacteristic
664C2×C3#557811yescharacteristic
665C2×C3#560011yescharacteristic
666C2×C3#562211yescharacteristic
667C2×C3#562411yescharacteristic
668C2×C3#564911yescharacteristic
669C2×C3D3×#12511yescharacteristic
670C2×C3#569111yescharacteristic
671C2×C3#572811yescharacteristic
672C22C2×#379911yescharacteristic
673C22D3×#23511yescharacteristic
674C22D3×#23511yescharacteristic
675C22D3×#23711yescharacteristic
676C22D3×#23711yescharacteristic
677C22D3×#23711yescharacteristic
678C22D32×Q811yescharacteristic
679C4—22no—
680C4—34no—
681C4—41no—
682C4—41no—
683C4—62no—
684C4—62no—
685C4—62no—
686C4—62no—
687C4—121no—
688C4—121no—
689C4—121no—
690C4—182no—
691C4—361no—
692C4—361no—
693C4—361no—
694C3—21no—
695C3#7367011yescharacteristic, complemented
696C3#7774111yescharacteristic, complemented
697C2#1059397611yescharacteristic
698C2#1059408611yescharacteristic
699C2#1059409811yescharacteristic
700C2#1059421611yescharacteristic
701C2D3×#88911yescharacteristic
702C2#1059438611yescharacteristic
703C2#1059439711yescharacteristic
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
604. C32#2402semidirect
695. C3#73670semidirect
696. C3#77741semidirect

Maximal subgroups

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

subgroupindex
#105923582
C3×#46572
C3×#46492
#105913532
#105913422
#105913412
Dic3×C4⋊Dic32
#105912432
Dic3×Dic3⋊C42
#105912392
#105912002
#105911992
#105911962
#777413
#736703