Finite Group Databasebeta

← #11808005

Subgroups — #11808005

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 715 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64098C211yesmaximal, characteristic
2C3×#4984C211yesmaximal, characteristic
3C3×#4980C211yesmaximal, characteristic
4#10591360C211yesmaximal, characteristic
5#10591271C211yesmaximal, characteristic
6#10591264C211yesmaximal, characteristic
7#10591264C211yesmaximal, characteristic
8#10591263C211yesmaximal, characteristic
9#10591263C211yesmaximal, characteristic
10#10591263C211yesmaximal, characteristic
11#10591230C211yesmaximal, characteristic
12#10591212C211yesmaximal, characteristic
13#10591197C211yesmaximal, characteristic
14#10591197C211yesmaximal, characteristic
15#10591197C211yesmaximal, characteristic
16#75993—31nomaximal
17#74979—31nomaximal
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64098C418yescomplemented
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
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×#889—31no—
55C2×#889—31no—
56C2×#889—61no—
57C3×#389—31no—
58C3×#387—31no—
59#4984D311yescharacteristic
60#4980D311yescharacteristic
61#4978—31no—
62#4978—31no—
63#4978—31no—
64#4977—31no—
65#4977—31no—
66#4976—31no—
67#4976—31no—
68#4972—31no—
69#4933—31no—
70#4933—31no—
71#4933—31no—
72#4928—31no—
73#4655—31no—
74#4655—31no—
75#4655—31no—
76#4654—31no—
77#4653—31no—
78#4652—31no—
79#4652—31no—
80#4652—31no—
81#4650—31no—
82#4650—31no—
83#4647—31no—
84#4647—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)C2×C414yes—
102#3750C2×C414yes—
103#3750C2×C414yes—
104#3750C2×C414yes—
105#3750C2×C414yes—
106C4×C3⋊Dic3C2×C414yes—
107C3×C4⋊Dic3—41no—
108C3×C4⋊Dic3—41no—
109C3×C4⋊Dic3—41no—
110C3×C4⋊Dic3—41no—
111C3×C4×Dic3—41no—
112C3×C4×Dic3—41no—
113#3724—41no—
114#3724—41no—
115#3724—41no—
116#3724—41no—
117Dic32—41no—
118Dic32—41no—
119#2382—91noSylow
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4C2×D311yescharacteristic
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C42—31no—
128C2×C3×C42—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—61no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133C2×C4⋊Dic3C2×D311yescharacteristic
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×C4⋊Dic3C2×D311yescharacteristic
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—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—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—61no—
153C2×Dic3⋊C4—61no—
154C2×Dic3⋊C4—61no—
155C2×Dic3⋊C4—61no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—61no—
163C2×C4×Dic3C2×D311yescharacteristic
164C2×C4×Dic3C2×D311yescharacteristic
165#889—38no—
166#889—38no—
167#889—68no—
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—31no—
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C3⋊#95C2×D311yescharacteristic
199C3⋊#95C2×D311yescharacteristic
200C23×C32C2411yescharacteristic
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4C22×C412yes—
208C2×C32×C4C22×C412yes—
209C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
219C2×C3⋊Dic3C22×C412yes—
220C2×C3⋊Dic3C22×C412yes—
221C2×C3⋊Dic3C22×C412yes—
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×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×#125—91no—
247#389—31no—
248#389—91no—
249#389—91no—
250#389—91no—
251#387—31no—
252#387—91no—
253#387—91no—
254#387—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#387—91no—
259#382—91no—
260#382—91no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
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×C4—31no—
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C22×Dic3—61no—
289C22×Dic3—61no—
290C22×Dic3C22×D311yescharacteristic
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C3×C4⋊C4—24no—
299C3×C4⋊C4—121no—
300C3×C4⋊C4—121no—
301C3×C4⋊C4—121no—
302C3×C4⋊C4—121no—
303C3×C4⋊C4C4×D314yes—
304C3×C4⋊C4C4×D314yes—
305C3×C42—121no—
306C3×C42—121no—
307C4⋊Dic3—34no—
308C4⋊Dic3—34no—
309C4⋊Dic3—41no—
310C4⋊Dic3—41no—
311C4⋊Dic3—41no—
312C4⋊Dic3—41no—
313C4⋊Dic3—64no—
314Dic3⋊C4—34no—
315Dic3⋊C4—34no—
316Dic3⋊C4—34no—
317Dic3⋊C4—34no—
318Dic3⋊C4—34no—
319Dic3⋊C4—34no—
320Dic3⋊C4—34no—
321Dic3⋊C4—34no—
322Dic3⋊C4—64no—
323Dic3⋊C4—64no—
324Dic3⋊C4—64no—
325Dic3⋊C4—64no—
326Dic3⋊C4—121no—
327Dic3⋊C4—121no—
328Dic3⋊C4—121no—
329Dic3⋊C4—121no—
330Dic3⋊C4—121no—
331Dic3⋊C4—121no—
332Dic3⋊C4—121no—
333Dic3⋊C4—121no—
334C4×Dic3—34no—
335C4×Dic3—34no—
336C4×Dic3—41no—
337C4×Dic3—41no—
338C4×Dic3—64no—
339C4×Dic3—121no—
340C4×Dic3—121no—
341C4×Dic3—121no—
342C4×Dic3—121no—
343C22×C32C23×C411yescharacteristic
344C22×C32H(5,𝔽2)11yescharacteristic
345C22×C32H(5,𝔽2)11yescharacteristic
346C22×C322−1+411yescharacteristic
347C22×C322−1+411yescharacteristic
348C22×C322−1+411yescharacteristic
349C22×C322−1+411yescharacteristic
350C32×C4—22no—
351C32×C4—22no—
352C32×C4—22no—
353C3⋊Dic3—22no—
354C3⋊Dic3—22no—
355C3⋊Dic3—22no—
356C3⋊Dic3—22no—
357C3×Dic3—41no—
358C3×Dic3—41no—
359C3×Dic3—41no—
360C3×Dic3—41no—
361C3×Dic3—41no—
362C3×Dic3—41no—
363C3×Dic3—41no—
364C3×Dic3—41no—
365#125—98no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—91no—
371C2×C4⋊C4—91no—
372C2×C4⋊C4—91no—
373C2×C4⋊C4—91no—
374C2×C4⋊C4—91no—
375C2×C4⋊C4—91no—
376C2×C4⋊C4—91no—
377C2×C4⋊C4—91no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4D3211yescharacteristic
380C2×C42—31no—
381C2×C42—31no—
382C2×C42—91no—
383C2×C42—91no—
384C2×C42—91no—
385#95—31no—
386#95—31no—
387#95—31no—
388#95—31no—
389#95—31no—
390#95—31no—
391#95—91no—
392#95—91no—
393#95—91no—
394#95—91no—
395#95—91no—
396#95—91no—
397#95—91no—
398#95—91no—
399#95—91no—
400#95—91no—
401C23×C3—21no—
402C23×C3C23×D311yescharacteristic
403C23×C3C23×D311yescharacteristic
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—21no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
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—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×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4C2×C4×D312yes—
450C2×C3×C4C2×C4×D312yes—
451C2×C3×C4C2×C4×D312yes—
452C2×C3×C4C2×C4×D312yes—
453C2×C3×C4C2×C4×D312yes—
454C2×C3×C4C2×C4×D312yes—
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—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—32no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—121no—
510C2×Dic3—121no—
511C2×Dic3—121no—
512C2×Dic3—121no—
513C2×Dic3—121no—
514C2×Dic3—121no—
515C2×C32#51911yescharacteristic
516C2×C32#52011yescharacteristic
517C2×C32#52011yescharacteristic
518C2×C32#56211yescharacteristic
519C2×C32#56311yescharacteristic
520C2×C32#56311yescharacteristic
521C2×C32#56411yescharacteristic
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—91no—
531C22×C4—91no—
532C22×C4—91no—
533C22×C4—91no—
534C22×C4C2×D3211yescharacteristic
535C22×C4C2×D3211yescharacteristic
536C22×C4C2×D3211yescharacteristic
537C4⋊C4—94no—
538C4⋊C4—94no—
539C4⋊C4—94no—
540C4⋊C4—94no—
541C4⋊C4—94no—
542C4⋊C4—121no—
543C4⋊C4—121no—
544C4⋊C4—121no—
545C4⋊C4—121no—
546C4⋊C4—361no—
547C4⋊C4—361no—
548C4⋊C4—361no—
549C4⋊C4—361no—
550C4⋊C4#62414yes—
551C42—94no—
552C42—121no—
553C42—121no—
554C42—361no—
555C42—361no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3C22×C4×D311yescharacteristic
564C22×C3C22×C4×D311yescharacteristic
565C22×C3#100411yescharacteristic
566C22×C3#100411yescharacteristic
567C22×C3#100411yescharacteristic
568C22×C3#100711yescharacteristic
569C22×C3#100711yescharacteristic
570C22×C3#100711yescharacteristic
571C22×C3#100911yescharacteristic
572C22×C3#101011yescharacteristic
573C22×C3#101011yescharacteristic
574C22×C3#101011yescharacteristic
575C22×C3#101011yescharacteristic
576C22×C3#101011yescharacteristic
577C3×C4—22no—
578C3×C4—22no—
579C3×C4—22no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—42no—
584C3×C4—42no—
585C3×C4—42no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4—121no—
589C3×C4—121no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4—121no—
594Dic3—41no—
595Dic3—41no—
596Dic3—41no—
597Dic3—41no—
598Dic3—41no—
599Dic3—41no—
600Dic3—41no—
601Dic3—41no—
602Dic3—64no—
603Dic3—62no—
604Dic3—62no—
605Dic3—62no—
606Dic3—62no—
607Dic3—62no—
608Dic3—62no—
609Dic3—62no—
610Dic3—62no—
611Dic3—122no—
612Dic3—122no—
613Dic3—122no—
614C32#238211yescharacteristic, complemented, Sylow
615C23C22×D3211yescharacteristic
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
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—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—92no—
647C2×C4—92no—
648C2×C4—92no—
649C2×C4—92no—
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×C4C2×#62412yes—
659C2×C4C2×#62412yes—
660C2×C4C2×#62412yes—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3#550411yescharacteristic
669C2×C3#552311yescharacteristic
670C2×C3#554611yescharacteristic
671C2×C3#554611yescharacteristic
672C2×C3#557211yescharacteristic
673C2×C3#557211yescharacteristic
674C2×C3#562111yescharacteristic
675C2×C3#564611yescharacteristic
676C2×C3#564711yescharacteristic
677C2×C3#565111yescharacteristic
678C2×C3C3⋊#56411yescharacteristic
679C2×C3C3⋊#56411yescharacteristic
680C2×C3#571211yescharacteristic
681C2×C3#573511yescharacteristic
682C22#6429711yescharacteristic
683C22#6430711yescharacteristic
684C22#6430911yescharacteristic
685C22#6431311yescharacteristic
686C22#6431511yescharacteristic
687C22#6431511yescharacteristic
688C22C22×#62411yescharacteristic
689C4—22no—
690C4—22no—
691C4—22no—
692C4—121no—
693C4—121no—
694C4—121no—
695C4—121no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—121no—
700C4—182no—
701C4—182no—
702C4—182no—
703C4—182no—
704C3—21no—
705C3#7497911yescharacteristic, complemented
706C3#7599311yescharacteristic, complemented
707C2#1059432611yescharacteristic
708C2#1059449211yescharacteristic
709C2#1059449511yescharacteristic
710C2#1059458611yescharacteristic
711C2#1059499011yescharacteristic
712C2#1059521911yescharacteristic
713C2#1059533911yescharacteristic
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
25. #64098C4semidirect
614. C32#2382semidirect
705. C3#74979semidirect
706. C3#75993semidirect

Maximal subgroups

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

subgroupindex
C2×#640982
C3×#49842
C3×#49802
#105913602
#105912712
#105912642
#105912632
#105912302
#105912122
#105911972
#759933
#749793