Finite Group Databasebeta

← #11807964

Subgroups — #11807964

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic
3C3×#4980C211yesmaximal, characteristic
4#10591272C211yesmaximal, characteristic
5#10591270C211yesmaximal, characteristic
6#10591269C211yesmaximal, characteristic
7#10591262C211yesmaximal, characteristic
8#10591261C211yesmaximal, characteristic
9#10591261C211yesmaximal, characteristic
10#10591223C211yesmaximal, characteristic
11#10591223C211yesmaximal, characteristic
12#10591221C211yesmaximal, characteristic
13#10591220C211yesmaximal, characteristic
14#10591201C211yesmaximal, characteristic
15#10591192C211yesmaximal, characteristic
16#83231—31nomaximal
17#74977—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#888C418yescomplemented
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic32C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2211yescharacteristic
36#63658C2211yescharacteristic
37#63658C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42#63579C2211yescharacteristic
43#63579C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×C4⋊Q8—31no—
55C2×#888D311yescharacteristic
56C3×#387—31no—
57#5229—31no—
58#5229—31no—
59#5229—31no—
60#5229—31no—
61#4980—31no—
62#4980—31no—
63#4980—31no—
64#4980—31no—
65#4980—31no—
66#4980—31no—
67#4980—31no—
68#4980—31no—
69#4980—61no—
70#4980D311yescharacteristic
71#4978—31no—
72#4973—31no—
73#4937—31no—
74#4937—31no—
75#4933—31no—
76#4929—31no—
77#4655—31no—
78#4654—31no—
79#4653—31no—
80#4652—31no—
81#4651—31no—
82#4651—31no—
83#4646—31no—
84#4646—31no—
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
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×Dic6—41no—
101C2×C3×Dic6—41no—
102C2×C3×Dic6—41no—
103C2×C3×Dic6—41no—
104C2×C3×Dic6C2×C414yes—
105C2×C3×Dic6C2×C414yes—
106C32×C4⋊C4C2×C414yes—
107C4⋊(C3⋊Dic3)—41no—
108C4×C3⋊Dic3—41no—
109C3×C4⋊Dic3—41no—
110C3×C4⋊Dic3C2×C414yes—
111C3×Dic3⋊C4C2×C414yes—
112C3×Dic3⋊C4C2×C414yes—
113C3×C4×Dic3—41no—
114C3×C4×Dic3C2×C414yes—
115Dic3⋊Dic3—41no—
116Dic3⋊Dic3—41no—
117Dic32—41no—
118Dic32—41no—
119#2381—91noSylow
120C22×C3×Q8—31no—
121C22×C3×Q8—31no—
122C22×Dic6C2×D311yescharacteristic
123C22×Dic6C2×D311yescharacteristic
124C3×C4⋊Q8—38no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C42—31no—
133C2×C3×C42—31no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—61no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
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—61no—
152C2×C4×Dic3C2×D311yescharacteristic
153C2×C4×Dic3C2×D311yescharacteristic
154#888Dic318yescomplemented
155C3×#95—31no—
156C3×#95—31no—
157C3×#95—31no—
158C3×#95—31no—
159C3⋊#95—31no—
160C3⋊#95—31no—
161C3⋊#95—31no—
162C3⋊#95—31no—
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—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—61no—
192C3⋊#95—61no—
193C3⋊#95—61no—
194C3⋊#95—61no—
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C3⋊#95C2×D311yescharacteristic
199C23×C32C2411yescharacteristic
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4C22×C412yes—
207C2×C32×C4C22×C412yes—
208C2×C32×C4C22×C412yes—
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⋊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—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×Dic3C22×C412yes—
242C2×C3×Dic3C22×C412yes—
243C2×C3×Dic3C22×C412yes—
244C2×C3×Dic3C22×C412yes—
245C3×Dic6—44no—
246C3×Dic6—44no—
247C2×C4⋊Q8—31no—
248#391—91no—
249#391—91no—
250#391—91no—
251#391—91no—
252#387—31no—
253#387—91no—
254#387—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#387—91no—
259#387—91no—
260#383—91no—
261#383—91no—
262C2×C3×Q8—34no—
263C2×C3×Q8—34no—
264C2×C3×Q8—121no—
265C2×C3×Q8—121no—
266C2×C3×Q8—121no—
267C2×C3×Q8—121no—
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—31no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C2×Dic6—41no—
306C2×Dic6—41no—
307C2×Dic6—41no—
308C2×Dic6—41no—
309C2×Dic6C2×Dic314yes—
310C2×Dic6C2×Dic314yes—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—34no—
313C3×C4⋊C4—34no—
314C3×C4⋊C4—34no—
315C3×C4⋊C4—121no—
316C3×C4⋊C4C4×D314yes—
317C3×C4⋊C4C2×Dic314yes—
318C3×C42—34no—
319C3×C42—121no—
320C4⋊Dic3—41no—
321C4⋊Dic3—121no—
322C4⋊Dic3—121no—
323C4⋊Dic3—121no—
324C4⋊Dic3—121no—
325C4⋊Dic3—122no—
326C4⋊Dic3C2×Dic314yes—
327Dic3⋊C4—121no—
328Dic3⋊C4—121no—
329Dic3⋊C4C2×Dic314yes—
330Dic3⋊C4C2×Dic314yes—
331C4×Dic3—41no—
332C4×Dic3—121no—
333C4×Dic3—121no—
334C4×Dic3—121no—
335C4×Dic3—121no—
336C4×Dic3—121no—
337C4×Dic3—121no—
338C4×Dic3—122no—
339C4×Dic3C2×Dic314yes—
340C22×C32C23×C411yescharacteristic
341C22×C32H(5,𝔽2)11yescharacteristic
342C22×C32H(5,𝔽2)11yescharacteristic
343C22×C322−1+411yescharacteristic
344C22×C322−1+411yescharacteristic
345C22×C322−1+411yescharacteristic
346C22×C322−1+411yescharacteristic
347C32×C4—22no—
348C32×C4—22no—
349C32×C4—22no—
350C3⋊Dic3—41no—
351C3⋊Dic3—41no—
352C3⋊Dic3—41no—
353C3⋊Dic3—41no—
354C3×Dic3—22no—
355C3×Dic3—22no—
356C3×Dic3—22no—
357C3×Dic3—22no—
358C3×Dic3—41no—
359C3×Dic3—41no—
360C3×Dic3—41no—
361C3×Dic3—41no—
362C22×Q8—31no—
363C22×Q8—31no—
364C4⋊Q8—38no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—91no—
371C2×C4⋊C4—91no—
372C2×C4⋊C4D3211yescharacteristic
373C2×C42—31no—
374C2×C42—31no—
375C2×C42—91no—
376C2×C42—91no—
377C2×C42—91no—
378#95—31no—
379#95—31no—
380#95—31no—
381#95—31no—
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#95—91no—
391#95—91no—
392#95—91no—
393#95—91no—
394#95—91no—
395#95—91no—
396#95—91no—
397#95—91no—
398C23×C3—21no—
399C23×C3C23×D311yescharacteristic
400C23×C3C23×D311yescharacteristic
401C3×Q8—124no—
402C3×Q8—124no—
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—22no—
417C2×C3×C4—22no—
418C2×C3×C4—32no—
419C2×C3×C4—32no—
420C2×C3×C4—32no—
421C2×C3×C4—32no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
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—61no—
447C2×C3×C4—61no—
448C2×C3×C4C2×C4×D312yes—
449C2×C3×C4C2×C4×D312yes—
450C2×C3×C4C2×C4×D312yes—
451C2×C3×C4C22×Dic312yes—
452C2×C3×C4C22×Dic312yes—
453C2×C3×C4C22×Dic312yes—
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—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—62no—
475C2×Dic3—62no—
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—61no—
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—121no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3—121no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3C22×Dic312yes—
511C2×Dic3C22×Dic312yes—
512C2×Dic3C22×Dic312yes—
513C2×Dic3C22×Dic312yes—
514Dic6—44no—
515Dic6—44no—
516C2×C32#51811yescharacteristic
517C2×C32#51911yescharacteristic
518C2×C32#51911yescharacteristic
519C2×C32#56311yescharacteristic
520C2×C32#56311yescharacteristic
521C2×C32#56311yescharacteristic
522C2×C32#56311yescharacteristic
523C2×Q8—34no—
524C2×Q8—34no—
525C2×Q8—121no—
526C2×Q8—121no—
527C2×Q8—121no—
528C2×Q8—121no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4C2×D3211yescharacteristic
542C22×C4C2×D3211yescharacteristic
543C22×C4C2×D3211yescharacteristic
544C4⋊C4—34no—
545C4⋊C4—34no—
546C4⋊C4—34no—
547C4⋊C4—121no—
548C4⋊C4—361no—
549C4⋊C4—361no—
550C4⋊C4—361no—
551C4⋊C4D3×Dic314yes—
552C42—34no—
553C42—121no—
554C42—361no—
555C42—361no—
556C42—361no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3C22×C4×D311yescharacteristic
565C22×C3#100411yescharacteristic
566C22×C3#100411yescharacteristic
567C22×C3#100411yescharacteristic
568C22×C3#100711yescharacteristic
569C22×C3#100711yescharacteristic
570C22×C3#100711yescharacteristic
571C22×C3#100711yescharacteristic
572C22×C3#100711yescharacteristic
573C22×C3#100911yescharacteristic
574C22×C3#101011yescharacteristic
575C22×C3#101011yescharacteristic
576C22×C3#101011yescharacteristic
577C22×C3C23×Dic311yescharacteristic
578C3×C4—22no—
579C3×C4—22no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—22no—
584C3×C4—42no—
585C3×C4—42no—
586C3×C4—42no—
587C3×C4—62no—
588C3×C4—62no—
589C3×C4—62no—
590C3×C4—62no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4—121no—
595Dic3—22no—
596Dic3—22no—
597Dic3—22no—
598Dic3—22no—
599Dic3—41no—
600Dic3—41no—
601Dic3—41no—
602Dic3—41no—
603Dic3—122no—
604Dic3—122no—
605Dic3—121no—
606Dic3—121no—
607Dic3—121no—
608Dic3—121no—
609Dic3—121no—
610Dic3—121no—
611Dic3—121no—
612Dic3—121no—
613Dic3—241no—
614Dic3—241no—
615C32#238111yescharacteristic, complemented, Sylow
616C23C22×D3211yescharacteristic
617Q8—124no—
618Q8—124no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—32no—
626C2×C4—32no—
627C2×C4—32no—
628C2×C4—32no—
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—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4C2×D3×Dic312yes—
662C2×C4C2×D3×Dic312yes—
663C2×C4C2×D3×Dic312yes—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3#551611yescharacteristic
672C2×C3#554511yescharacteristic
673C2×C3#557211yescharacteristic
674C2×C3#564611yescharacteristic
675C2×C3#565111yescharacteristic
676C2×C3#569911yescharacteristic
677C2×C3#571211yescharacteristic
678C2×C3#573511yescharacteristic
679C2×C3#573511yescharacteristic
680C2×C3#573511yescharacteristic
681C2×C3#573511yescharacteristic
682C2×C3#579811yescharacteristic
683C2×C3#581211yescharacteristic
684C2×C3#581211yescharacteristic
685C22#6429711yescharacteristic
686C22#6429711yescharacteristic
687C22#6431311yescharacteristic
688C22#6431411yescharacteristic
689C22#6431511yescharacteristic
690C22#6431611yescharacteristic
691C22C22×D3×Dic311yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—62no—
696C4—62no—
697C4—62no—
698C4—62no—
699C4—121no—
700C4—121no—
701C4—121no—
702C4—121no—
703C4—361no—
704C4—361no—
705C4—361no—
706C4—361no—
707C3—21no—
708C3#7497711yescharacteristic, complemented
709C3#8323111yescharacteristic, complemented
710C2#1059434011yescharacteristic
711C2#1059435311yescharacteristic
712C2#1059449511yescharacteristic
713C2#1059450311yescharacteristic
714C2#1059481811yescharacteristic
715C2#1059521511yescharacteristic
716C2#1059534711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
29. C3×#888C4semidirect
154. #888Dic3semidirect
615. C32#2381semidirect
708. C3#74977semidirect
709. C3#83231semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
#105926792
C3×#49802
#105912722
#105912702
#105912692
#105912622
#105912612
#105912232
#105912212
#105912202
#105912012
#105911922
#832313
#749773