Finite Group Databasebeta

← #11808006

Subgroups — #11808006

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#889C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic
3C3×#4984C211yesmaximal, characteristic
4#10591357C211yesmaximal, characteristic
5#10591272C211yesmaximal, characteristic
6#10591270C211yesmaximal, characteristic
7#10591265C211yesmaximal, characteristic
8#10591265C211yesmaximal, characteristic
9#10591262C211yesmaximal, characteristic
10#10591262C211yesmaximal, characteristic
11#10591224C211yesmaximal, characteristic
12#10591206C211yesmaximal, characteristic
13#10591201C211yesmaximal, characteristic
14#10591201C211yesmaximal, characteristic
15#10591192C211yesmaximal, characteristic
16#83027—31nomaximal
17#75993—31nomaximal
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊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×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#889C418yescomplemented
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#125—31no—
55C2×#889D311yescharacteristic
56C3×#389—31no—
57#4984—31no—
58#4984—31no—
59#4984—31no—
60#4984D311yescharacteristic
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—31no—
70#4980—61no—
71#4978—31no—
72#4978—31no—
73#4977—31no—
74#4976—31no—
75#4976—31no—
76#4972—31no—
77#4936—31no—
78#4936—31no—
79#4933—31no—
80#4933—31no—
81#4655—31no—
82#4654—31no—
83#4652—31no—
84#4650—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
100C32×C4⋊C4C2×C414yes—
101C4⋊(C3⋊Dic3)—41no—
102C4×C3⋊Dic3—41no—
103C3×C4⋊Dic3—41no—
104C3×C4⋊Dic3—41no—
105C3×C4⋊Dic3—41no—
106C3×C4⋊Dic3C2×C414yes—
107C3×Dic3⋊C4C2×C414yes—
108C3×Dic3⋊C4C2×C414yes—
109C3×Dic3⋊C4C2×C414yes—
110C3×Dic3⋊C4C2×C414yes—
111C3×C4×Dic3—41no—
112C3×C4×Dic3C2×C414yes—
113Dic3⋊Dic3—41no—
114Dic3⋊Dic3—41no—
115Dic3⋊Dic3—41no—
116Dic3⋊Dic3—41no—
117Dic32—41no—
118Dic32—41no—
119#2382—91noSylow
120C3×#125—38no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
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—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—61no—
141C2×C4⋊Dic3C2×D311yescharacteristic
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×C4⋊Dic3C2×D311yescharacteristic
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4C2×D311yescharacteristic
150C2×Dic3⋊C4C2×D311yescharacteristic
151C2×Dic3⋊C4C2×D311yescharacteristic
152C2×Dic3⋊C4C2×D311yescharacteristic
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×Dic3C2×D311yescharacteristic
161C2×C4×Dic3C2×D311yescharacteristic
162#889Dic318yescomplemented
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—31no—
192C3⋊#95—31no—
193C3⋊#95—61no—
194C3⋊#95—61no—
195C3⋊#95—61no—
196C3⋊#95—61no—
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—
245C2×#125—31no—
246#389—31no—
247#389—91no—
248#389—91no—
249#389—91no—
250#387—91no—
251#387—91no—
252#387—91no—
253#387—91no—
254#387—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#382—91no—
259#382—91no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C22×Dic3—61no—
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D311yescharacteristic
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C3×C4⋊C4—24no—
298C3×C4⋊C4—34no—
299C3×C4⋊C4—34no—
300C3×C4⋊C4—34no—
301C3×C4⋊C4—34no—
302C3×C4⋊C4—34no—
303C3×C4⋊C4—121no—
304C3×C4⋊C4—121no—
305C3×C4⋊C4—121no—
306C3×C4⋊C4C4×D314yes—
307C3×C4⋊C4C2×Dic314yes—
308C3×C42—34no—
309C3×C42—121no—
310C4⋊Dic3—41no—
311C4⋊Dic3—41no—
312C4⋊Dic3—41no—
313C4⋊Dic3—121no—
314C4⋊Dic3—121no—
315C4⋊Dic3—121no—
316C4⋊Dic3—121no—
317C4⋊Dic3—121no—
318C4⋊Dic3—121no—
319C4⋊Dic3—122no—
320C4⋊Dic3C2×Dic314yes—
321Dic3⋊C4—121no—
322Dic3⋊C4—121no—
323Dic3⋊C4—121no—
324Dic3⋊C4—121no—
325Dic3⋊C4C2×Dic314yes—
326Dic3⋊C4C2×Dic314yes—
327Dic3⋊C4C2×Dic314yes—
328Dic3⋊C4C2×Dic314yes—
329C4×Dic3—41no—
330C4×Dic3—121no—
331C4×Dic3—121no—
332C4×Dic3—121no—
333C4×Dic3—121no—
334C4×Dic3—121no—
335C4×Dic3—121no—
336C4×Dic3—122no—
337C4×Dic3C2×Dic314yes—
338C22×C32C23×C411yescharacteristic
339C22×C32H(5,𝔽2)11yescharacteristic
340C22×C32H(5,𝔽2)11yescharacteristic
341C22×C322−1+411yescharacteristic
342C22×C322−1+411yescharacteristic
343C22×C322−1+411yescharacteristic
344C22×C322−1+411yescharacteristic
345C32×C4—22no—
346C32×C4—22no—
347C32×C4—22no—
348C3⋊Dic3—41no—
349C3⋊Dic3—41no—
350C3⋊Dic3—41no—
351C3⋊Dic3—41no—
352C3×Dic3—22no—
353C3×Dic3—22no—
354C3×Dic3—22no—
355C3×Dic3—22no—
356C3×Dic3—41no—
357C3×Dic3—41no—
358C3×Dic3—41no—
359C3×Dic3—41no—
360#125—38no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
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⋊C4—91no—
373C2×C4⋊C4—91no—
374C2×C4⋊C4D3211yescharacteristic
375C2×C42—31no—
376C2×C42—31no—
377C2×C42—91no—
378C2×C42—91no—
379C2×C42—91no—
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—
396C23×C3—21no—
397C23×C3C23×D311yescharacteristic
398C23×C3C23×D311yescharacteristic
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—21no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
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—61no—
425C2×C3×C4—61no—
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×C4C2×C4×D312yes—
445C2×C3×C4C2×C4×D312yes—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4C22×Dic312yes—
448C2×C3×C4C22×Dic312yes—
449C2×C3×C4C22×Dic312yes—
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—21no—
469C2×Dic3—21no—
470C2×Dic3—62no—
471C2×Dic3—62no—
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—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—121no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3—121no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3C22×Dic312yes—
507C2×Dic3C22×Dic312yes—
508C2×Dic3C22×Dic312yes—
509C2×Dic3C22×Dic312yes—
510C2×C32#51911yescharacteristic
511C2×C32#52011yescharacteristic
512C2×C32#52011yescharacteristic
513C2×C32#56211yescharacteristic
514C2×C32#56311yescharacteristic
515C2×C32#56311yescharacteristic
516C2×C32#56411yescharacteristic
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4C2×D3211yescharacteristic
530C22×C4C2×D3211yescharacteristic
531C22×C4C2×D3211yescharacteristic
532C4⋊C4—34no—
533C4⋊C4—34no—
534C4⋊C4—34no—
535C4⋊C4—34no—
536C4⋊C4—34no—
537C4⋊C4—121no—
538C4⋊C4—121no—
539C4⋊C4—121no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C4⋊C4—361no—
543C4⋊C4—361no—
544C4⋊C4—361no—
545C4⋊C4D3×Dic314yes—
546C42—34no—
547C42—121no—
548C42—361no—
549C42—361no—
550C42—361no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3C22×C4×D311yescharacteristic
559C22×C3#100411yescharacteristic
560C22×C3#100411yescharacteristic
561C22×C3#100711yescharacteristic
562C22×C3#100711yescharacteristic
563C22×C3#100711yescharacteristic
564C22×C3#100711yescharacteristic
565C22×C3#100911yescharacteristic
566C22×C3#100911yescharacteristic
567C22×C3#101011yescharacteristic
568C22×C3#101011yescharacteristic
569C22×C3#101011yescharacteristic
570C22×C3#101011yescharacteristic
571C22×C3C23×Dic311yescharacteristic
572C3×C4—22no—
573C3×C4—22no—
574C3×C4—22no—
575C3×C4—22no—
576C3×C4—22no—
577C3×C4—22no—
578C3×C4—42no—
579C3×C4—42no—
580C3×C4—42no—
581C3×C4—62no—
582C3×C4—62no—
583C3×C4—62no—
584C3×C4—62no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4—121no—
589Dic3—22no—
590Dic3—22no—
591Dic3—22no—
592Dic3—22no—
593Dic3—41no—
594Dic3—41no—
595Dic3—41no—
596Dic3—41no—
597Dic3—122no—
598Dic3—122no—
599Dic3—121no—
600Dic3—121no—
601Dic3—121no—
602Dic3—121no—
603Dic3—121no—
604Dic3—121no—
605Dic3—121no—
606Dic3—121no—
607Dic3—241no—
608Dic3—241no—
609C32#238211yescharacteristic, complemented, Sylow
610C23C22×D3211yescharacteristic
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—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—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4C2×D3×Dic312yes—
654C2×C4C2×D3×Dic312yes—
655C2×C4C2×D3×Dic312yes—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3#550411yescharacteristic
664C2×C3#554611yescharacteristic
665C2×C3#557211yescharacteristic
666C2×C3#562111yescharacteristic
667C2×C3#564611yescharacteristic
668C2×C3C3⋊#56411yescharacteristic
669C2×C3C3⋊#56411yescharacteristic
670C2×C3#569911yescharacteristic
671C2×C3#569911yescharacteristic
672C2×C3#570011yescharacteristic
673C2×C3#573511yescharacteristic
674C2×C3#581211yescharacteristic
675C2×C3#582711yescharacteristic
676C2×C3#582711yescharacteristic
677C22#6429711yescharacteristic
678C22#6430711yescharacteristic
679C22#6430911yescharacteristic
680C22#6431411yescharacteristic
681C22#6431511yescharacteristic
682C22#6431611yescharacteristic
683C22C22×D3×Dic311yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—62no—
688C4—62no—
689C4—62no—
690C4—62no—
691C4—121no—
692C4—121no—
693C4—121no—
694C4—121no—
695C4—361no—
696C4—361no—
697C4—361no—
698C4—361no—
699C3—21no—
700C3#7599311yescharacteristic, complemented
701C3#8302711yescharacteristic, complemented
702C2#1059432611yescharacteristic
703C2#1059435311yescharacteristic
704C2#1059449311yescharacteristic
705C2#1059458711yescharacteristic
706C2#1059498611yescharacteristic
707C2#1059522211yescharacteristic
708C2#1059534711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. C3×#889C4semidirect
162. #889Dic3semidirect
609. C32#2382semidirect
700. C3#75993semidirect
701. C3#83027semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8892
#105926792
C3×#49842
#105913572
#105912722
#105912702
#105912652
#105912622
#105912242
#105912062
#105912012
#105911922
#830273
#759933