Finite Group Databasebeta

← #16807897

Subgroups — #16807897

Order 3328.

1974 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131382C212yesmaximal, complemented
2#13131378C212yesmaximal
3#13131371C212yesmaximal, complemented
4#13131370C211yesmaximal, characteristic, complemented
5#13131370C211yesmaximal, characteristic, complemented
6#13131369C211yesmaximal, characteristic, complemented
7#13131365C211yesmaximal, characteristic, complemented
8#13131362C212yesmaximal
9#13131346C211yesmaximal, characteristic
10#13131346C211yesmaximal, characteristic
11#13131345C211yesmaximal, characteristic
12#13131344C211yesmaximal, characteristic
13#13131332C212yesmaximal
14#13131331C211yesmaximal, characteristic, complemented
15#13131331C212yesmaximal, complemented
16#13131330C211yesmaximal, characteristic, complemented
17#13131327C212yesmaximal, complemented
18#13131323C212yesmaximal
19#13131314C211yesmaximal, characteristic
20C4⋊Q8×#261C211yesmaximal, characteristic, complemented
21#125×#261C211yesmaximal, characteristic, complemented
22#13131298C211yesmaximal, characteristic
23D13×#544C211yesmaximal, characteristic
24C2×Q8×#261C2212yes—
25C2×Q8×#261C2212yes—
26C2×#88237C2212yes—
27C13×#544C411yescharacteristic, complemented
28#11719434C411yescharacteristic, complemented
29#11719434C411yescharacteristic, complemented
30#11719434C412yescomplemented
31D13×C4⋊Q8C2211yescharacteristic
32D13×C4⋊Q8C2212yes—
33D13×C4⋊Q8C2211yescharacteristic
34#11719394C411yescharacteristic, complemented
35#11719394C412yescomplemented
36#11719394C411yescharacteristic, complemented
37D13×#125C2211yescharacteristic
38D13×#125C2211yescharacteristic
39D13×#125C2212yes—
40D13×C22⋊Q8C2212yes—
41D13×C22⋊Q8C2212yes—
42#11719328C412yescomplemented
43#11719328C412yescomplemented
44D13×#117C2211yescharacteristic
45D13×#117C2211yescharacteristic
46#11719224C411yescharacteristic, complemented
47#11719224C411yescharacteristic, complemented
48C2×C4⋊C4×D13C2211yescharacteristic
49#11719205C411yescharacteristic, complemented
50(C2×#261)⋊Q8C2212yes—
51(C2×#261)⋊Q8C2212yes—
52(C2×#261)⋊Q8C2212yes—
53(C2×#261)⋊Q8C2212yes—
54(C2×#261)⋊Q8C2212yes—
55(C2×#261)⋊Q8C2212yes—
56#11719136C2211yescharacteristic
57#11719136C2211yescharacteristic
58#11719136C2212yes—
59#11719135C2212yes—
60C4×C22⋊#261C2211yescharacteristic
61C4×C22⋊#261C2211yescharacteristic
62C4×C22⋊#261C2212yes—
63#11719083C2211yescharacteristic
64#11719083C2211yescharacteristic
65#11719083C2211yescharacteristic
66#11719083C2211yescharacteristic
67#11719083C2212yes—
68#11719083C2212yes—
69#11719083C2212yes—
70#11719083C2212yes—
71#11719083C2211yescharacteristic
72#11719083C2211yescharacteristic
73#11719083C2212yes—
74#11719083C2211yescharacteristic
75#11719083C2211yescharacteristic
76#11719083C2212yes—
77#11719082C2211yescharacteristic
78#11719082C2211yescharacteristic
79#11719082C2211yescharacteristic
80#11719082C2211yescharacteristic
81#11719082C2212yes—
82#11719082C2212yes—
83#11719082C2212yes—
84#11719082C2212yes—
85#11719082C2212yes—
86#11719082C2212yes—
87#11719082C2212yes—
88#11719082C2212yes—
89#11719082C2212yes—
90#11719082C2212yes—
91#11719082C2212yes—
92#11719082C2212yes—
93#11719082C2212yes—
94#11719082C2212yes—
95#11719082C2212yes—
96#11719082C2212yes—
97#11719082C2212yes—
98#11719082C2212yes—
99C4⋊C4×#261C2212yes—
100C4⋊C4×#261C2211yescharacteristic
101C4⋊C4×#261C2211yescharacteristic
102C4⋊C4×#261C2212yes—
103C4⋊C4×#261C2211yescharacteristic
104C4⋊C4×#261C2211yescharacteristic
105C4⋊C4×#261C2212yes—
106C4⋊C4×#261C2212yes—
107C4⋊C4×#261C2211yescharacteristic
108C4⋊C4×#261C2211yescharacteristic
109C4⋊C4×#261C2211yescharacteristic
110C4⋊C4×#261C2211yescharacteristic
111C4⋊C4×#261C2212yes—
112C4⋊C4×#261C2212yes—
113#11719071C2211yescharacteristic
114#11719071C2211yescharacteristic
115#11719071C2211yescharacteristic
116#11719071C2211yescharacteristic
117#11719071C2212yes—
118#11719071C2212yes—
119#11719071C2212yes—
120#11719071C2212yes—
121#11719071C2212yes—
122#11719071C2212yes—
123#11719060C2211yescharacteristic
124#11719060C2212yes—
125#11719060C2212yes—
126#11719059C2211yescharacteristic
127C4×C4⋊#261C2211yescharacteristic
128C4×C4⋊#261C2211yescharacteristic
129C4×C4⋊#261C2211yescharacteristic
130C4×C4⋊#261C2211yescharacteristic
131#11719057C2211yescharacteristic
132#11719057C2212yes—
133#11719057C2212yes—
134C42×#261C2211yescharacteristic
135C2×Q8×D13C2312yes—
136C2×Q8×D13C2312yes—
137C22×C4×D13C2311yescharacteristic
138C22×C4×D13C2312yes—
139C2×C22⋊#261C2311yescharacteristic
140C2×C22⋊#261C2311yescharacteristic
141C2×C22⋊#261C2312yes—
142C2×C22⋊#261C2311yescharacteristic
143C2×C22⋊#261C2311yescharacteristic
144C2×C22⋊#261C2312yes—
145Q8×#261—44no—
146Q8×#261—44no—
147#88237—44no—
148C2×C4⋊#261C2311yescharacteristic
149C2×C4⋊#261C2311yescharacteristic
150C2×C4⋊#261C2311yescharacteristic
151C2×C4⋊#261C2311yescharacteristic
152C2×C4⋊#261C2311yescharacteristic
153C2×C4⋊#261C2311yescharacteristic
154C2×C4⋊#261C2312yes—
155C2×C4⋊#261C2311yescharacteristic
156C2×C4⋊#261C2311yescharacteristic
157C2×C4⋊#261C2312yes—
158C2×C4⋊#261C2312yes—
159C2×C4⋊#261C2312yes—
160C2×C4⋊#261C2312yes—
161C2×C4⋊#261C2312yes—
162C2×C4⋊#261C2312yes—
163C2×C4⋊#261C2312yes—
164C2×C4⋊#261C2312yes—
165C2×C4⋊#261C2312yes—
166C2×C4×#261C2311yescharacteristic
167C2×C4×#261C2311yescharacteristic
168C2×C4×#261C2311yescharacteristic
169C2×C4×#261C2311yescharacteristic
170C2×C4×#261C2311yescharacteristic
171C2×C4×#261C2311yescharacteristic
172C2×C4×#261C2312yes—
173C2×C4×#261C2312yes—
174C2×C4×#261C2312yes—
175C2×C4×#261C2311yescharacteristic
176C2×C4×#261C2311yescharacteristic
177C2×C4×#261C2312yes—
178C2×C4×#261C2312yes—
179C2×C4×#261C2312yes—
180C2×C4×#261C2312yes—
181C2×C4×#261C2312yes—
182C2×C4×#261C2312yes—
183C2×C4×#261C2312yes—
184C13×C4⋊Q8C2×C411yescharacteristic
185C13×C4⋊Q8C2×C412yes—
186C13×C4⋊Q8C2×C411yescharacteristic
187C13×#125C2×C411yescharacteristic
188C13×#125C2×C411yescharacteristic
189C13×#125C2×C412yes—
190C13×C22⋊Q8C2×C412yes—
191C13×C22⋊Q8C2×C412yes—
192C13×#117C2×C411yescharacteristic
193C13×#117C2×C411yescharacteristic
194C2×C13×C4⋊C4C2×C411yescharacteristic
195#88200C2×C412yes—
196#88200C2×C412yes—
197#88198C2×C412yes—
198#88198C2×C412yes—
199#88198C2×C412yes—
200#88198C2×C412yes—
201#88180C2×C411yescharacteristic
202#88180C2×C411yescharacteristic
203C2×C4⋊Dic13C2×C411yescharacteristic
204#88178C2×C412yes—
205#88178C2×C412yes—
206C2×#6101C2×C412yes—
207#88151C2×C412yes—
208#88151C2×C412yes—
209#88150C2×C412yes—
210#88150C2×C412yes—
211#88150C2×C412yes—
212#88150C2×C412yes—
213#88146C2×C411yescharacteristic
214#88146C2×C411yescharacteristic
215#88146C2×C411yescharacteristic
216#88146C2×C411yescharacteristic
217C4⋊C4×D13C2×C411yescharacteristic
218C4⋊C4×D13C2×C411yescharacteristic
219C4⋊C4×D13C2×C412yes—
220C4⋊C4×D13C2311yescharacteristic
221C4⋊C4×D13C2311yescharacteristic
222C4⋊C4×D13C2311yescharacteristic
223C4⋊C4×D13C2311yescharacteristic
224C4⋊C4×D13C2312yes—
225C4⋊C4×D13C2312yes—
226C4⋊C4×D13C2312yes—
227C4⋊C4×D13C2312yes—
228C4⋊C4×D13C2312yes—
229C4⋊C4×D13C2311yescharacteristic
230C4⋊C4×D13C2311yescharacteristic
231C4⋊C4×D13C2312yes—
232C4⋊C4×D13C2312yes—
233#88144C2×C411yescharacteristic
234#88144C2×C411yescharacteristic
235#88144C2×C412yes—
236#88144C2×C411yescharacteristic
237#88144C2×C411yescharacteristic
238#88144C2×C412yes—
239#88143C2×C412yes—
240#88143C2×C412yes—
241#88143C2×C412yes—
242#88143C2×C412yes—
243#88143C2×C412yes—
244#88143C2×C412yes—
245#88143C2×C412yes—
246#88143C2×C412yes—
247#88142C2×C411yescharacteristic
248#88142C2×C412yes—
249#88142C2×C411yescharacteristic
250#88142C2×C411yescharacteristic
251#88142C2×C412yes—
252#88142C2×C411yescharacteristic
253#88142C2×C412yes—
254#88142C2×C412yes—
255#88142C2×C412yes—
256#88142C2×C412yes—
257C22⋊C4×D13C2311yescharacteristic
258C22⋊C4×D13C2311yescharacteristic
259C22⋊C4×D13C2312yes—
260#88132C2×C412yes—
261#88132C2×C412yes—
262#88132C2×C412yes—
263#88132C2×C412yes—
264#88131C2×C411yescharacteristic
265#88131C2×C411yescharacteristic
266#88131C2×C412yes—
267#88126C2×C411yescharacteristic
268#88126C2×C411yescharacteristic
269#88126C2×C412yes—
270C42×D13C2311yescharacteristic
271C42×D13C2312yes—
272C42×D13C2311yescharacteristic
273#88124C2×C411yescharacteristic
274#88124C2×C411yescharacteristic
275#88124C2×C412yes—
276#88123C2×C411yescharacteristic
277#88123C2×C412yes—
278#88123C2×C411yescharacteristic
279(C2×#261)⋊C4C2311yescharacteristic
280(C2×#261)⋊C4C2311yescharacteristic
281(C2×#261)⋊C4C2312yes—
282(C2×#261)⋊C4C2312yes—
283(C2×#261)⋊C4C2312yes—
284(C2×#261)⋊C4C2312yes—
285(C2×#261)⋊C4C2311yescharacteristic
286(C2×#261)⋊C4C2312yes—
287(C2×#261)⋊C4C2311yescharacteristic
288(C2×#261)⋊C4C2311yescharacteristic
289(C2×#261)⋊C4C2312yes—
290(C2×#261)⋊C4C2311yescharacteristic
291(C2×#261)⋊C4C2311yescharacteristic
292(C2×#261)⋊C4C2311yescharacteristic
293(C2×#261)⋊C4C2311yescharacteristic
294(C2×#261)⋊C4C2312yes—
295(C2×#261)⋊C4C2311yescharacteristic
296(C2×#261)⋊C4C2312yes—
297(C2×#261)⋊C4C2311yescharacteristic
298(C2×#261)⋊C4C2311yescharacteristic
299(C2×#261)⋊C4C2312yes—
300(C2×#261)⋊C4C2312yes—
301(C2×#261)⋊C4C2312yes—
302(C2×#261)⋊C4C2312yes—
303(C2×#261)⋊C4C2312yes—
304(C2×#261)⋊C4C2312yes—
305(C2×#261)⋊C4C2312yes—
306(C2×#261)⋊C4C2312yes—
307(C2×#261)⋊C4C2312yes—
308(C2×#261)⋊C4C2312yes—
309(C2×#261)⋊C4C2312yes—
310(C2×#261)⋊C4C2312yes—
311(C2×#261)⋊C4C2312yes—
312(C2×#261)⋊C4C2312yes—
313#34435—131nomaximal, Sylow
314C23×D13C2411yescharacteristic
315C22×#261C2411yescharacteristic
316C22×#261C2411yescharacteristic
317C22×#261C2412yes—
318C22×#261C2411yescharacteristic
319C22×#261C2411yescharacteristic
320C22×#261C2412yes—
321C22×#261C2412yes—
322C22×#261C2411yescharacteristic
323C22×#261C2412yes—
324C22×#261C2411yescharacteristic
325C22×#261C2411yescharacteristic
326C22×#261C2411yescharacteristic
327C2×Q8×C13C22×C412yes—
328C2×Q8×C13C22×C412yes—
329C22×C4×C13C22×C411yescharacteristic
330C22×C4×C13C22×C412yes—
331C22×Dic13C22×C411yescharacteristic
332C22×Dic13C22×C412yes—
333Q8×D13—42no—
334Q8×D13—42no—
335Q8×D13—42no—
336Q8×D13—42no—
337C2×C4×D13—22no—
338C2×C4×D13—22no—
339C2×C4×D13—42no—
340C2×C4×D13—42no—
341C2×C4×D13C22×C411yescharacteristic
342C2×C4×D13C22×C411yescharacteristic
343C2×C4×D13C22×C412yes—
344C2×C4×D13C22×C412yes—
345C2×C4×D13C2411yescharacteristic
346C2×C4×D13C2412yes—
347C2×C4×D13C2411yescharacteristic
348C2×C4×D13C2411yescharacteristic
349C2×C4×D13C2412yes—
350C2×C4×D13C2411yescharacteristic
351C2×C4×D13C2411yescharacteristic
352C2×C4×D13C2412yes—
353C2×C4×D13C2412yes—
354C2×C4×D13C2411yescharacteristic
355C2×Dic26C22×C412yes—
356C2×Dic26C22×C412yes—
357C2×Dic26C22×C412yes—
358C2×Dic26C22×C412yes—
359C2×Dic26C22×C412yes—
360C2×Dic26C22×C412yes—
361C22⋊#261—22no—
362C22⋊#261—22no—
363C22⋊#261—42no—
364C22⋊#261—41no—
365C22⋊#261—41no—
366C22⋊#261—42no—
367C4⋊#261—24no—
368C4⋊#261—22no—
369C4⋊#261—22no—
370C4⋊#261—22no—
371C4⋊#261—22no—
372C4⋊#261—22no—
373C4⋊#261—22no—
374C4⋊#261—41no—
375C4⋊#261—42no—
376C4⋊#261—42no—
377C4⋊#261—42no—
378C4⋊#261—42no—
379C4⋊#261—41no—
380C4⋊#261—42no—
381C4⋊#261—42no—
382C4⋊#261—42no—
383C4⋊#261—42no—
384C4⋊#261—42no—
385C4×#261—24no—
386C4×#261—24no—
387C4×#261—22no—
388C4×#261—22no—
389C4×#261—24no—
390C4×#261—22no—
391C4×#261—22no—
392C4×#261—22no—
393C4×#261—22no—
394C4×#261—42no—
395C4×#261—42no—
396C4×#261—41no—
397C4×#261—42no—
398C4×#261—41no—
399C4×#261—42no—
400C4×#261—42no—
401C4×#261—42no—
402C4×#261—42no—
403C13×C4⋊C4C22×C411yescharacteristic
404C13×C4⋊C4C22×C411yescharacteristic
405C13×C4⋊C4C22×C412yes—
406C13×C4⋊C4C22×C412yes—
407C13×C4⋊C4C22×C412yes—
408C13×C4⋊C4C22×C412yes—
409C13×C4⋊C4C22×C412yes—
410C13×C4⋊C4C22×C411yescharacteristic
411C13×C4⋊C4C22×C411yescharacteristic
412C13×C4⋊C4C22×C412yes—
413C13×C4⋊C4C22×C412yes—
414C13×C4⋊C4C22×C411yescharacteristic
415C13×C4⋊C4C22×C411yescharacteristic
416C13×C22⋊C4C22×C411yescharacteristic
417C13×C22⋊C4C22×C411yescharacteristic
418C13×C22⋊C4C22×C412yes—
419C42×C13C22×C412yes—
420C42×C13C22×C411yescharacteristic
421C42×C13C22×C411yescharacteristic
422C22⋊Dic13C22×C411yescharacteristic
423C22⋊Dic13C22×C411yescharacteristic
424C22⋊Dic13C22×C412yes—
425#6103C22×C411yescharacteristic
426#6103C22×C411yescharacteristic
427#6103C22×C412yes—
428#6103C22×C411yescharacteristic
429#6103C22×C411yescharacteristic
430#6103C22×C412yes—
431C4⋊Dic13C22×C411yescharacteristic
432C4⋊Dic13C22×C411yescharacteristic
433C4⋊Dic13C22×C412yes—
434C4⋊Dic13C22×C411yescharacteristic
435C4⋊Dic13C22×C411yescharacteristic
436C4⋊Dic13C22×C412yes—
437C4⋊Dic13C22×C412yes—
438C4⋊Dic13C22×C412yes—
439C4⋊Dic13C22×C412yes—
440C4⋊Dic13C22×C411yescharacteristic
441C4⋊Dic13C22×C411yescharacteristic
442C4⋊Dic13C22×C412yes—
443C4⋊Dic13C22×C412yes—
444#6101C22×C412yes—
445#6101C22×C412yes—
446#6101C22×C412yes—
447#6101C22×C412yes—
448#6101C22×C412yes—
449#6101C22×C412yes—
450#6101C22×C412yes—
451#6101C22×C412yes—
452#6101C22×C411yescharacteristic
453#6101C22×C411yescharacteristic
454#6101C22×C412yes—
455#6101C22×C411yescharacteristic
456#6101C22×C411yescharacteristic
457#6101C22×C412yes—
458#6101C22×C412yes—
459#6101C22×C412yes—
460#6101C22×C412yes—
461#6101C22×C412yes—
462#6101C22×C412yes—
463#6101C22×C412yes—
464#6101C22×C412yes—
465#6101C22×C412yes—
466C4×Dic13C22×C412yes—
467C4×Dic13C22×C411yescharacteristic
468C4×Dic13C22×C411yescharacteristic
469C4×Dic13C22×C412yes—
470C4×Dic13C22×C411yescharacteristic
471C4×Dic13C22×C411yescharacteristic
472C4×Dic13C22×C412yes—
473C4×Dic13C22×C411yescharacteristic
474C4×Dic13C22×C411yescharacteristic
475C2×#544—131no—
476#2382—132no—
477#2378—132no—
478#2371—132no—
479#2370—131no—
480#2370—131no—
481#2369—131no—
482#2365—131no—
483#2362—132no—
484#2346—131no—
485#2346—131no—
486#2345—131no—
487#2344—131no—
488#2332—132no—
489#2331—131no—
490#2331—132no—
491#2330—131no—
492#2327—132no—
493#2323—132no—
494#2314—131no—
495C4×C4⋊Q8—131no—
496C4×#125—131no—
497#2298—131no—
498C23×C13C23×C411yescharacteristic
499C22×D13—21no—
500C22×D13—21no—
501C22×D13—21no—
502C22×D13—21no—
503C22×D13—21no—
504C22×D13—21no—
505C22×D13C23×C411yescharacteristic
506C22×D13C2511yescharacteristic
507C2×#261—21no—
508C2×#261—21no—
509C2×#261—21no—
510C2×#261—21no—
511C2×#261—22no—
512C2×#261—21no—
513C2×#261—22no—
514C2×#261—21no—
515C2×#261—22no—
516C2×#261—21no—
517C2×#261—22no—
518C2×#261—21no—
519C2×#261—21no—
520C2×#261—21no—
521C2×#261—21no—
522C2×#261—21no—
523C2×#261—21no—
524C2×#261—22no—
525C2×#261—22no—
526C2×#261—22no—
527C2×#261—21no—
528C2×#261—22no—
529C2×#261—21no—
530C2×#261—22no—
531C2×#261—22no—
532C2×#261—21no—
533C2×#261—21no—
534C2×#261—21no—
535C2×#261—21no—
536C2×#261—22no—
537C2×#261—21no—
538C2×#261—21no—
539C2×#261—21no—
540C2×#261—22no—
541C2×#261H(5,𝔽2)12yes—
542C2×#2612−1+412yes—
543Q8×C13—42no—
544Q8×C13—42no—
545C2×C4×C13—22no—
546C2×C4×C13—42no—
547C2×C4×C13C23×C411yescharacteristic
548C2×C4×C13C23×C412yes—
549C2×C4×C13C23×C411yescharacteristic
550C2×C4×C13C23×C411yescharacteristic
551C2×C4×C13C23×C412yes—
552C2×C4×C13C23×C411yescharacteristic
553C2×C4×C13C23×C411yescharacteristic
554C2×C4×C13C23×C412yes—
555C2×C4×C13C23×C412yes—
556C2×C4×C13C23×C411yescharacteristic
557C2×Dic13—22no—
558C2×Dic13—42no—
559C2×Dic13C23×C411yescharacteristic
560C2×Dic13C23×C412yes—
561C2×Dic13C23×C411yescharacteristic
562C2×Dic13C23×C411yescharacteristic
563C2×Dic13C23×C412yes—
564C2×Dic13C23×C411yescharacteristic
565C2×Dic13C23×C411yescharacteristic
566C2×Dic13C23×C412yes—
567C2×Dic13C23×C412yes—
568C2×Dic13C23×C411yescharacteristic
569C4×D13—22no—
570C4×D13—22no—
571C4×D13—21no—
572C4×D13—21no—
573C4×D13—22no—
574C4×D13—21no—
575C4×D13—22no—
576C4×D13—21no—
577C4×D13—21no—
578C4×D13—21no—
579C4×D13—21no—
580C4×D13—22no—
581C4×D13—21no—
582C4×D13—22no—
583C4×D13—21no—
584C4×D13—22no—
585C4×D13—22no—
586C4×D13—21no—
587C4×D13—22no—
588C4×D13—22no—
589C4×D13—42no—
590C4×D13—42no—
591C4×D132−1+412yes—
592C4×D132−1+412yes—
593Dic26—42no—
594Dic26—42no—
595Dic26—42no—
596Dic26—42no—
597Dic26—42no—
598Dic26—42no—
599#544—132no—
600#544—131no—
601#544—131no—
602#544—132no—
603#544—131no—
604#544—131no—
605#544—132no—
606#544—132no—
607#544—131no—
608#544—131no—
609#544—131no—
610#544#26111yescharacteristic, complemented
611C2×C4⋊Q8—131no—
612C2×C4⋊Q8—132no—
613C2×C4⋊Q8—131no—
614C2×#125—131no—
615C2×#125—131no—
616C2×#125—132no—
617C2×C22⋊Q8—132no—
618C2×C22⋊Q8—132no—
619C2×C4×Q8—132no—
620C2×C4×Q8—132no—
621C2×#117—131no—
622C2×#117—131no—
623C2×#117—132no—
624C22×C4⋊C4—131no—
625#391—132no—
626#391—132no—
627#391—132no—
628#391—132no—
629#391—132no—
630#391—132no—
631#389—131no—
632#389—131no—
633#389—131no—
634#389—131no—
635#389—132no—
636#389—132no—
637#389—132no—
638#389—132no—
639#389—131no—
640#389—131no—
641#389—132no—
642#389—131no—
643#389—131no—
644#389—132no—
645#388—132no—
646#388—132no—
647#388—131no—
648#388—132no—
649#388—132no—
650#388—131no—
651#388—132no—
652#388—132no—
653#388—131no—
654#388—131no—
655#387—132no—
656#387—132no—
657#387—132no—
658#387—132no—
659#387—132no—
660#387—131no—
661#387—132no—
662#387—132no—
663#387—132no—
664#387—132no—
665#387—132no—
666#387—132no—
667#387—131no—
668#387—132no—
669#387—132no—
670#387—132no—
671#387—132no—
672#387—132no—
673#387—132no—
674#387—132no—
675#387—131no—
676#387—131no—
677#384—131no—
678#382—131no—
679#382—132no—
680#382—132no—
681#381—132no—
682#380—131no—
683#380—131no—
684#380—132no—
685C4×C4⋊C4—132no—
686C4×C4⋊C4—131no—
687C4×C4⋊C4—131no—
688C4×C4⋊C4—132no—
689C4×C4⋊C4—131no—
690C4×C4⋊C4—131no—
691C4×C4⋊C4—132no—
692C4×C4⋊C4—131no—
693C4×C4⋊C4—131no—
694C4×C4⋊C4—132no—
695C4×C4⋊C4—131no—
696C4×C4⋊C4—131no—
697C4×C4⋊C4—131no—
698C4×C4⋊C4—131no—
699C4×C4⋊C4—132no—
700C4×C4⋊C4—132no—
701C4×C4⋊C4—131no—
702C4×C4⋊C4—131no—
703C4×C22⋊C4—132no—
704C4×C22⋊C4—131no—
705C4×C22⋊C4—131no—
706#376—132no—
707#376—131no—
708#376—132no—
709C43—131no—
710C22×C13—21no—
711C22×C13—21no—
712C22×C13—21no—
713C22×C13C24×C411yescharacteristic
714C2×D13—21no—
715C2×D13—21no—
716C2×D13—21no—
717C2×D13—41no—
718C2×D13—41no—
719C2×D13—41no—
720C2×D13—41no—
721C2×D13C2×H(5,𝔽2)11yescharacteristic
722C2×D13C2×2−1+411yescharacteristic
723C2×D13C2×2−1+411yescharacteristic
724C2×D13C2×2−1+411yescharacteristic
725C2×D13#58511yescharacteristic
726C2×D13#58511yescharacteristic
727#261—22no—
728#261—22no—
729#261—41no—
730#261—42no—
731#261—42no—
732#261—41no—
733#261—42no—
734#261—41no—
735#261—41no—
736#261—41no—
737#261—41no—
738#261—42no—
739C4×C13—21no—
740C4×C13—21no—
741C4×C13—22no—
742C4×C13—21no—
743C4×C13—22no—
744C4×C13—22no—
745C4×C13—21no—
746C4×C13—22no—
747C4×C13—21no—
748C4×C13#51912yes—
749Dic13—21no—
750Dic13—21no—
751Dic13—22no—
752Dic13—21no—
753Dic13—22no—
754Dic13—22no—
755Dic13—21no—
756Dic13—22no—
757Dic13—21no—
758Dic13#51912yes—
759C22×Q8—132no—
760C22×Q8—132no—
761C23×C4—131no—
762C23×C4—132no—
763C4⋊Q8—132no—
764C4⋊Q8—132no—
765C4⋊Q8—132no—
766C4⋊Q8—132no—
767C4⋊Q8—132no—
768C4⋊Q8—132no—
769C4⋊Q8—132no—
770C4⋊Q8—132no—
771C4⋊Q8—131no—
772C4⋊Q8—132no—
773C4⋊Q8—131no—
774C4⋊Q8—131no—
775C4⋊Q8—132no—
776C4⋊Q8—131no—
777C4⋊Q8—131no—
778C4⋊Q8—132no—
779C4⋊Q8—131no—
780C4⋊Q8C2×#26111yescharacteristic
781C4⋊Q8C2×#26112yes—
782C4⋊Q8C2×#26111yescharacteristic
783#125—132no—
784#125—132no—
785#125—132no—
786#125—132no—
787#125—132no—
788#125—132no—
789#125—132no—
790#125—132no—
791#125—131no—
792#125—131no—
793#125—132no—
794#125—131no—
795#125—131no—
796#125—132no—
797#125—131no—
798#125—131no—
799#125—132no—
800#125C2×#26111yescharacteristic
801#125C2×#26111yescharacteristic
802#125C2×#26112yes—
803C22⋊Q8—132no—
804C22⋊Q8—132no—
805C22⋊Q8—132no—
806C22⋊Q8—132no—
807C22⋊Q8—132no—
808C22⋊Q8—132no—
809C22⋊Q8—132no—
810C22⋊Q8—132no—
811C22⋊Q8—132no—
812C22⋊Q8—132no—
813C22⋊Q8—132no—
814C22⋊Q8—132no—
815C22⋊Q8—132no—
816C22⋊Q8—132no—
817C22⋊Q8C2×#26112yes—
818C22⋊Q8C2×#26112yes—
819C4×Q8—524no—
820C4×Q8—524no—
821#117—131no—
822#117—131no—
823#117—131no—
824#117—131no—
825#117—131no—
826#117—131no—
827#117—131no—
828#117—131no—
829#117—132no—
830#117—131no—
831#117—131no—
832#117—132no—
833#117—524no—
834#117C2×#26111yescharacteristic
835#117C2×#26111yescharacteristic
836C2×C4⋊C4—132no—
837C2×C4⋊C4—131no—
838C2×C4⋊C4—131no—
839C2×C4⋊C4—131no—
840C2×C4⋊C4—132no—
841C2×C4⋊C4—132no—
842C2×C4⋊C4—131no—
843C2×C4⋊C4—131no—
844C2×C4⋊C4—131no—
845C2×C4⋊C4—131no—
846C2×C4⋊C4—131no—
847C2×C4⋊C4—131no—
848C2×C4⋊C4—132no—
849C2×C4⋊C4—132no—
850C2×C4⋊C4—132no—
851C2×C4⋊C4—132no—
852C2×C4⋊C4—132no—
853C2×C4⋊C4—132no—
854C2×C4⋊C4—132no—
855C2×C4⋊C4—131no—
856C2×C4⋊C4—131no—
857C2×C4⋊C4—131no—
858C2×C4⋊C4—131no—
859C2×C4⋊C4—131no—
860C2×C4⋊C4—131no—
861C2×C4⋊C4—132no—
862C2×C4⋊C4—132no—
863C2×C4⋊C4—132no—
864C2×C4⋊C4—132no—
865C2×C4⋊C4—132no—
866C2×C4⋊C4—132no—
867C2×C4⋊C4—132no—
868C2×C4⋊C4—132no—
869C2×C4⋊C4—132no—
870C2×C4⋊C4—131no—
871C2×C4⋊C4—131no—
872C2×C4⋊C4C2×#26111yescharacteristic
873C2×C22⋊C4—131no—
874C2×C22⋊C4—131no—
875C2×C22⋊C4—132no—
876C2×C22⋊C4—131no—
877C2×C22⋊C4—131no—
878C2×C22⋊C4—132no—
879C2×C22⋊C4—132no—
880C2×C22⋊C4—131no—
881C2×C22⋊C4—131no—
882C2×C42—131no—
883C2×C42—132no—
884C2×C42—131no—
885C2×C42—132no—
886C2×C42—131no—
887C2×C42—132no—
888C2×C42—131no—
889C2×C42—131no—
890C2×C42—131no—
891C2×C42—131no—
892C2×C42—131no—
893C2×C42—132no—
894C2×C42—132no—
895C2×C42—132no—
896C2×C42—132no—
897C2×C42—131no—
898C2×C42—131no—
899C2×C42—132no—
900C2×C42—132no—
901C2×C42—132no—
902C2×C42—132no—
903#95—131no—
904#95—131no—
905#95—132no—
906#95—132no—
907#95—132no—
908#95—132no—
909#95—131no—
910#95—132no—
911#95—131no—
912#95—131no—
913#95—132no—
914#95—131no—
915#95—132no—
916#95—131no—
917#95—131no—
918#95—132no—
919#95—131no—
920#95—131no—
921#95—132no—
922#95—132no—
923#95—132no—
924#95—132no—
925#95—132no—
926#95—132no—
927#95—132no—
928#95—132no—
929#95—132no—
930#95—132no—
931#95—132no—
932#95—132no—
933#95—131no—
934#95—132no—
935#95—131no—
936#95—132no—
937C2×C13—41no—
938C2×C13C2×#51911yescharacteristic
939C2×C13C4×H(5,𝔽2)11yescharacteristic
940C2×C13C4×2−1+411yescharacteristic
941D13—41no—
942D13#354411yescharacteristic
943D13#354711yescharacteristic
944D13#356311yescharacteristic
945D13#356511yescharacteristic
946C24—131no—
947C2×Q8—132no—
948C2×Q8—132no—
949C2×Q8—132no—
950C2×Q8—132no—
951C2×Q8—132no—
952C2×Q8—132no—
953C2×Q8—522no—
954C2×Q8—522no—
955C2×Q8—522no—
956C2×Q8—522no—
957C2×Q8C22×#26112yes—
958C2×Q8C22×#26112yes—
959C22×C4—131no—
960C22×C4—131no—
961C22×C4—131no—
962C22×C4—131no—
963C22×C4—132no—
964C22×C4—131no—
965C22×C4—132no—
966C22×C4—131no—
967C22×C4—131no—
968C22×C4—132no—
969C22×C4—131no—
970C22×C4—131no—
971C22×C4—132no—
972C22×C4—132no—
973C22×C4—131no—
974C22×C4—131no—
975C22×C4—132no—
976C22×C4—132no—
977C22×C4—131no—
978C22×C4—132no—
979C22×C4—131no—
980C22×C4—131no—
981C22×C4—131no—
982C22×C4—132no—
983C22×C4—132no—
984C22×C4—132no—
985C22×C4—131no—
986C22×C4—131no—
987C22×C4—262no—
988C22×C4—262no—
989C22×C4—522no—
990C22×C4—522no—
991C22×C4C22×#26111yescharacteristic
992C22×C4C22×#26112yes—
993C4⋊C4—132no—
994C4⋊C4—132no—
995C4⋊C4—132no—
996C4⋊C4—132no—
997C4⋊C4—132no—
998C4⋊C4—131no—
999C4⋊C4—131no—
1000C4⋊C4—132no—
1001C4⋊C4—131no—
1002C4⋊C4—131no—
1003C4⋊C4—131no—
1004C4⋊C4—131no—
1005C4⋊C4—132no—
1006C4⋊C4—131no—
1007C4⋊C4—131no—
1008C4⋊C4—131no—
1009C4⋊C4—131no—
1010C4⋊C4—132no—
1011C4⋊C4—132no—
1012C4⋊C4—132no—
1013C4⋊C4—132no—
1014C4⋊C4—132no—
1015C4⋊C4—132no—
1016C4⋊C4—132no—
1017C4⋊C4—132no—
1018C4⋊C4—132no—
1019C4⋊C4—132no—
1020C4⋊C4—132no—
1021C4⋊C4—132no—
1022C4⋊C4—132no—
1023C4⋊C4—132no—
1024C4⋊C4—132no—
1025C4⋊C4—132no—
1026C4⋊C4—132no—
1027C4⋊C4—132no—
1028C4⋊C4—264no—
1029C4⋊C4—262no—
1030C4⋊C4—262no—
1031C4⋊C4—262no—
1032C4⋊C4—262no—
1033C4⋊C4—262no—
1034C4⋊C4—262no—
1035C4⋊C4—522no—
1036C4⋊C4—522no—
1037C4⋊C4—522no—
1038C4⋊C4—522no—
1039C4⋊C4—522no—
1040C4⋊C4—521no—
1041C4⋊C4—522no—
1042C4⋊C4—522no—
1043C4⋊C4—522no—
1044C4⋊C4—522no—
1045C4⋊C4—521no—
1046C4⋊C4C22×#26112yes—
1047C4⋊C4C22×#26111yescharacteristic
1048C4⋊C4C22×#26111yescharacteristic
1049C4⋊C4C22×#26111yescharacteristic
1050C4⋊C4C22×#26111yescharacteristic
1051C4⋊C4C22×#26111yescharacteristic
1052C4⋊C4C22×#26111yescharacteristic
1053C4⋊C4C22×#26112yes—
1054C4⋊C4C22×#26112yes—
1055C4⋊C4C22×#26112yes—
1056C4⋊C4C22×#26112yes—
1057C4⋊C4C22×#26112yes—
1058C4⋊C4C22×#26112yes—
1059C22⋊C4—131no—
1060C22⋊C4—131no—
1061C22⋊C4—132no—
1062C22⋊C4—131no—
1063C22⋊C4—131no—
1064C22⋊C4—132no—
1065C22⋊C4—131no—
1066C22⋊C4—131no—
1067C22⋊C4—132no—
1068C22⋊C4—262no—
1069C22⋊C4—262no—
1070C22⋊C4—522no—
1071C22⋊C4—521no—
1072C22⋊C4—521no—
1073C22⋊C4—522no—
1074C22⋊C4C22×#26111yescharacteristic
1075C22⋊C4C22×#26111yescharacteristic
1076C22⋊C4C22×#26112yes—
1077C42—131no—
1078C42—131no—
1079C42—131no—
1080C42—131no—
1081C42—132no—
1082C42—132no—
1083C42—132no—
1084C42—131no—
1085C42—131no—
1086C42—264no—
1087C42—264no—
1088C42—262no—
1089C42—262no—
1090C42—262no—
1091C42—262no—
1092C42—262no—
1093C42—262no—
1094C42—264no—
1095C42—522no—
1096C42—522no—
1097C42—522no—
1098C42—522no—
1099C42—522no—
1100C42—521no—
1101C42—522no—
1102C42—521no—
1103C42—522no—
1104C42C22×#26112yes—
1105C42C22×#26111yescharacteristic
1106C42C22×#26111yescharacteristic
1107C13#3443511yescharacteristic, complemented, Sylow
1108C23—131no—
1109C23—131no—
1110C23—261no—
1111C23—261no—
1112C23—261no—
1113C23—261no—
1114C23—261no—
1115C23—261no—
1116C23C23×#26111yescharacteristic
1117Q8—42no—
1118Q8—42no—
1119Q8—522no—
1120Q8—522no—
1121Q8—522no—
1122Q8—522no—
1123Q8—522no—
1124Q8—522no—
1125C2×C4—22no—
1126C2×C4—42no—
1127C2×C4—131no—
1128C2×C4—132no—
1129C2×C4—132no—
1130C2×C4—132no—
1131C2×C4—132no—
1132C2×C4—131no—
1133C2×C4—131no—
1134C2×C4—132no—
1135C2×C4—131no—
1136C2×C4—131no—
1137C2×C4—132no—
1138C2×C4—131no—
1139C2×C4—132no—
1140C2×C4—132no—
1141C2×C4—262no—
1142C2×C4—262no—
1143C2×C4—262no—
1144C2×C4—261no—
1145C2×C4—261no—
1146C2×C4—262no—
1147C2×C4—261no—
1148C2×C4—261no—
1149C2×C4—262no—
1150C2×C4—262no—
1151C2×C4—261no—
1152C2×C4—262no—
1153C2×C4—261no—
1154C2×C4—262no—
1155C2×C4—261no—
1156C2×C4—262no—
1157C2×C4—261no—
1158C2×C4—261no—
1159C2×C4—261no—
1160C2×C4—262no—
1161C2×C4—261no—
1162C2×C4—261no—
1163C2×C4—261no—
1164C2×C4—261no—
1165C2×C4—262no—
1166C2×C4—262no—
1167C2×C4—262no—
1168C2×C4—261no—
1169C2×C4—261no—
1170C2×C4—261no—
1171C2×C4—261no—
1172C2×C4—261no—
1173C2×C4—261no—
1174C2×C4—261no—
1175C2×C4—262no—
1176C2×C4—261no—
1177C2×C4—262no—
1178C2×C4—261no—
1179C2×C4—261no—
1180C2×C4—261no—
1181C2×C4—262no—
1182C2×C4—262no—
1183C2×C4—261no—
1184C2×C4—262no—
1185C2×C4—261no—
1186C2×C4—261no—
1187C2×C4—261no—
1188C2×C4—262no—
1189C2×C4—262no—
1190C2×C4—262no—
1191C2×C4—262no—
1192C2×C4—262no—
1193C2×C4—261no—
1194C2×C4—261no—
1195C2×C4—261no—
1196C2×C4—522no—
1197C2×C4—522no—
1198C2×C4—522no—
1199C2×C4C23×#26111yescharacteristic
1200C2×C4C23×#26111yescharacteristic
1201C2×C4C23×#26112yes—
1202C2×C4C23×#26111yescharacteristic
1203C2×C4C23×#26111yescharacteristic
1204C2×C4C23×#26112yes—
1205C2×C4C23×#26111yescharacteristic
1206C2×C4C23×#26112yes—
1207C2×C4C23×#26112yes—
1208C2×C4C23×#26111yescharacteristic
1209C22—21no—
1210C22—21no—
1211C22—21no—
1212C22—131no—
1213C22—131no—
1214C22—131no—
1215C22—131no—
1216C22—131no—
1217C22—131no—
1218C22—261no—
1219C22—261no—
1220C22—261no—
1221C22—521no—
1222C22—521no—
1223C22—521no—
1224C22—521no—
1225C22C24×#26111yescharacteristic
1226C4—21no—
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—21no—
1231C4—21no—
1232C4—21no—
1233C4—22no—
1234C4—21no—
1235C4—132no—
1236C4—262no—
1237C4—262no—
1238C4—261no—
1239C4—262no—
1240C4—262no—
1241C4—261no—
1242C4—262no—
1243C4—261no—
1244C4—261no—
1245C4—262no—
1246C4—261no—
1247C4—522no—
1248C4—521no—
1249C4—521no—
1250C4—522no—
1251C4—522no—
1252C4—521no—
1253C4—521no—
1254C4—521no—
1255C4—521no—
1256C4—522no—
1257C4#1171962712yes—
1258C2—41no—
1259C2—131no—
1260C2—131no—
1261C2—131no—
1262C2—131no—
1263C2—521no—
1264C2C2×#1171962711yescharacteristic
1265C2H(5,𝔽2)×#26111yescharacteristic
1266C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#544C4
prime radicalC23×D13C24
cosocleC22×D13C25
hypercenter#544#261
hypocenterC13#34435
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #544

Complements

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

NH ≅ G/Ntype
1. #13131382C2semidirect
3. #13131371C2semidirect
4. #13131370C2semidirect
5. #13131370C2semidirect
6. #13131369C2semidirect
7. #13131365C2semidirect
14. #13131331C2semidirect
15. #13131331C2semidirect
16. #13131330C2semidirect
17. #13131327C2semidirect
20. C4⋊Q8×#261C2semidirect
21. #125×#261C2semidirect
27. C13×#544C4semidirect
28. #11719434C4semidirect
29. #11719434C4semidirect
30. #11719434C4semidirect
34. #11719394C4semidirect
35. #11719394C4semidirect
36. #11719394C4semidirect
42. #11719328C4semidirect
43. #11719328C4semidirect
46. #11719224C4semidirect
47. #11719224C4semidirect
49. #11719205C4semidirect
610. #544#261semidirect
1107. C13#34435semidirect

Maximal subgroups

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

subgroupindex
#131313822
#131313782
#131313712
#131313702
#131313692
#131313652
#131313622
#131313462
#131313452
#131313442
#131313322
#131313312
#131313302
#131313272
#131313232
#131313142
C4⋊Q8×#2612
#125×#2612
#131312982
D13×#5442
#3443513