Finite Group Databasebeta

← #16019165

Subgroups — #16019165

Order 3328.

442 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125495C211yesmaximal, characteristic
2#13117119C211yesmaximal, characteristic, complemented
3#13117112C211yesmaximal, characteristic, complemented
4#13117083C211yesmaximal, characteristic, complemented
5#13117065C211yesmaximal, characteristic, complemented
6#13117044C211yesmaximal, characteristic
7#13117044C211yesmaximal, characteristic
8#13117038C211yesmaximal, characteristic
9#13117033C211yesmaximal, characteristic
10#13116997C211yesmaximal, characteristic, complemented
11#13116997C211yesmaximal, characteristic, complemented
12#13116985C211yesmaximal, characteristic, complemented
13#13116975C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic
15C13×#3164C211yesmaximal, characteristic
16C13×#544—21no—
17#11719223—21no—
18C13×#501—21no—
19C13×#501—21no—
20C13×#500C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#428—21no—
25C13×#427C2211yescharacteristic
26C2×C13×#107C2211yescharacteristic
27C13×#405C2211yescharacteristic
28#11718798—21no—
29#11718777C2211yescharacteristic
30#11718777C2211yescharacteristic
31#11718377—21no—
32#11718364—21no—
33#11718360C2211yescharacteristic
34C4×Dic52C2211yescharacteristic
35C4×Dic52C2211yescharacteristic
36#11718344C2211yescharacteristic
37C22⋊#6090C2211yescharacteristic
38C22⋊#6090C2211yescharacteristic
39#11718084C2211yescharacteristic
40#11718084C2211yescharacteristic
41#11718084C2211yescharacteristic
42#11718084C2211yescharacteristic
43#11718084C2211yescharacteristic
44#11718084C2211yescharacteristic
45#11718084C2211yescharacteristic
46#11718084C2211yescharacteristic
47#11718082C2211yescharacteristic
48#11718082C2211yescharacteristic
49#11718082C2211yescharacteristic
50#11718082C2211yescharacteristic
51#11718081C2211yescharacteristic
52#11718081C2211yescharacteristic
53#11718081C2211yescharacteristic
54#11718081C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56C4⋊#6090C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×M16D411yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—41no—
64C13×#125—21no—
65C13×#125—21no—
66C13×#125—41no—
67C13×C22⋊Q8—41no—
68C13×C22⋊Q8—41no—
69C13×#117—21no—
70C13×#117D411yescharacteristic
71C2×C13×C4⋊C4—21no—
72#88178—21no—
73#88178—21no—
74C2×Dic52—21no—
75C2×Dic52C2311yescharacteristic
76C2×Dic52C2311yescharacteristic
77#88143—41no—
78#88143—41no—
79#88133—41no—
80#88133—41no—
81#88124—21no—
82#88123—21no—
83C4×Dic26—21no—
84C4×Dic26—21no—
85C13×#107—21no—
86C13×#107—21no—
87C13×#107—21no—
88C13×#107C2311yescharacteristic
89C13×#107C2311yescharacteristic
90C13×#107C2311yescharacteristic
91C13×#107C2311yescharacteristic
92C13×#106—21no—
93C13×#106—21no—
94C13×#106—21no—
95C13×#97D411yescharacteristic
96C13×#97D411yescharacteristic
97C4×C8×C13C2311yescharacteristic
98C4×C8×C13C2311yescharacteristic
99#88058C2311yescharacteristic
100#88058C2311yescharacteristic
101#88057—21no—
102#88056—21no—
103#88056—21no—
104#88056—21no—
105#88056—21no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108C2×#6090C2311yescharacteristic
109C2×#6090C2311yescharacteristic
110#33808—131nomaximal, Sylow
111C2×Q8×C13—41no—
112C2×Q8×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13C2×D411yescharacteristic
115C2×Dic26—21no—
116C2×Dic26—21no—
117C13×M16—22no—
118C2×C8×C13—21no—
119C2×C8×C13—21no—
120C2×C8×C13C2×D411yescharacteristic
121C2×C8×C13C2×D411yescharacteristic
122C2×C8×C13C2×D411yescharacteristic
123C2×C8×C13C2411yescharacteristic
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—41no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C4⋊C4—41no—
135C13×C4⋊C4D811yescharacteristic
136C13×C4⋊C4D811yescharacteristic
137C13×C22⋊C4—41no—
138C13×C22⋊C4D811yescharacteristic
139C13×C22⋊C4D811yescharacteristic
140C42×C13—41no—
141C42×C13C2×D411yescharacteristic
142C42×C13C2×D411yescharacteristic
143C22⋊Dic13—41no—
144C22⋊Dic13—41no—
145C4⋊Dic13—21no—
146C4⋊Dic13—21no—
147C4⋊Dic13—41no—
148C4⋊Dic13—41no—
149#6101—41no—
150#6101—41no—
151#6101—41no—
152#6101—41no—
153#6101—41no—
154#6101—41no—
155C4×Dic13—41no—
156C4×Dic13—41no—
157Dic52—21no—
158Dic52—21no—
159Dic52—21no—
160Dic52—21no—
161Dic52—42no—
162#6090—21no—
163#6090—21no—
164#6090—21no—
165#6090—21no—
166#3177—131no—
167#3164D1311yescharacteristic
168#2255—131no—
169#2253—131no—
170#2245—131no—
171#2241—131no—
172#2237—131no—
173#2237—131no—
174#2236—131no—
175#2235—131no—
176#2229—131no—
177#2229—131no—
178#2227—131no—
179#2225—131no—
180#2164—131no—
181C23×C13C2×D811yescharacteristic
182Q8×C13—161no—
183Q8×C13—161no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—161no—
191C2×C4×C13C2×D811yescharacteristic
192C2×C4×C13C2×D811yescharacteristic
193C2×C4×C13C2×D811yescharacteristic
194C2×C4×C13C2×D811yescharacteristic
195C2×C4×C13C2×D811yescharacteristic
196C2×C4×C13C22×D411yescharacteristic
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201Dic26—41no—
202Dic26—41no—
203Dic26—41no—
204Dic26—41no—
205C8×C13—21no—
206C8×C13—21no—
207C8×C13#13712yes—
208C8×C132−1+411yescharacteristic
209C8×C132−1+411yescharacteristic
210#544—21no—
211#541—261no—
212#501—21no—
213#501—21no—
214#500C2×D1311yescharacteristic
215#500C2×D1311yescharacteristic
216#499—131no—
217#499C2×D1311yescharacteristic
218#499C2×D1311yescharacteristic
219#494—131no—
220#491—261no—
221#470—261no—
222#467—131no—
223#467—131no—
224#441—261no—
225C4×Q16—131no—
226C4×Q16—131no—
227#428—21no—
228#427C2×D1311yescharacteristic
229C2×#107C2×D1311yescharacteristic
230#405C2×D1311yescharacteristic
231#367—131no—
232#367—131no—
233#367—131no—
234#367—131no—
235#366—131no—
236#366—131no—
237#366—131no—
238#366—131no—
239C4⋊C16—131no—
240C4⋊C16—131no—
241#358—131no—
242#358—131no—
243#358—131no—
244#358—131no—
245#358—131no—
246#358—131no—
247#358—131no—
248#358—131no—
249C22⋊C16—131no—
250C22⋊C16—131no—
251#346—131no—
252C4×C16—131no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13C22×D811yescharacteristic
257C4×C13—21no—
258C4×C13—21no—
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—21no—
262C4×C13—81no—
263C4×C13—81no—
264C4×C13—81no—
265C4×C13—81no—
266C4×C13#53611yescharacteristic
267C4×C13C2×#13711yescharacteristic
268Dic13—81no—
269Dic13—81no—
270Dic13—81no—
271Dic13—81no—
272C2×Q16—131no—
273C2×Q16—131no—
274C2×Q16—261no—
275C2×M16C22⋊D1311yescharacteristic
276C22×C8C22×D1311yescharacteristic
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—41no—
280C4⋊Q8—261no—
281#126—521no—
282#126—521no—
283#125—21no—
284#125—21no—
285#125—41no—
286#125—261no—
287#125—521no—
288#125—521no—
289C22⋊Q8—41no—
290C22⋊Q8—41no—
291C22⋊Q8—261no—
292C22⋊Q8—261no—
293C4×Q8—261no—
294C4×Q8—261no—
295#117—21no—
296#117C22⋊D1311yescharacteristic
297C2×C4⋊C4—21no—
298C2×C16—131no—
299C2×C16—131no—
300C2×C16—131no—
301C2×C16—131no—
302#107—21no—
303#107—21no—
304#107—21no—
305#107—131no—
306#107—131no—
307#107C22×D1311yescharacteristic
308#107C22×D1311yescharacteristic
309#107C22×D1311yescharacteristic
310#107C22×D1311yescharacteristic
311#106—21no—
312#106—21no—
313#106—21no—
314#106—261no—
315#103—261no—
316#103—261no—
317#103—261no—
318#103—261no—
319#97C22⋊D1311yescharacteristic
320#97C22⋊D1311yescharacteristic
321C4×C8C22×D1311yescharacteristic
322C4×C8C22×D1311yescharacteristic
323C2×C13—41no—
324C2×C13#322611yescharacteristic
325C2×C13#341611yescharacteristic
326C2×C13#341711yescharacteristic
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—261no—
330C2×Q8—261no—
331C22×C4—41no—
332C22×C4C2×C22⋊D1311yescharacteristic
333Q16—261no—
334Q16—261no—
335Q16—261no—
336Q16—261no—
337Q16—522no—
338M16—22no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8C2×C22⋊D1311yescharacteristic
342C2×C8C2×C22⋊D1311yescharacteristic
343C2×C8C2×C22⋊D1311yescharacteristic
344C2×C8C23×D1311yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—261no—
357C4⋊C4—261no—
358C4⋊C4—521no—
359C4⋊C4—521no—
360C4⋊C4—521no—
361C4⋊C4—521no—
362C4⋊C4—521no—
363C4⋊C4—521no—
364C4⋊C4—521no—
365C4⋊C4—521no—
366C4⋊C4#610411yescharacteristic
367C4⋊C4#610411yescharacteristic
368C22⋊C4—41no—
369C22⋊C4—521no—
370C22⋊C4—521no—
371C22⋊C4#610411yescharacteristic
372C22⋊C4#610411yescharacteristic
373C42—41no—
374C42—521no—
375C42—521no—
376C42C2×C22⋊D1311yescharacteristic
377C42C2×C22⋊D1311yescharacteristic
378C16—261no—
379C16—261no—
380C16—261no—
381C16—261no—
382C13#3380811yescharacteristic, complemented, Sylow
383C23C2×#610411yescharacteristic
384Q8—161no—
385Q8—161no—
386Q8—521no—
387Q8—521no—
388Q8—521no—
389Q8—521no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—161no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—521no—
401C2×C4C2×#610411yescharacteristic
402C2×C4C2×#610411yescharacteristic
403C2×C4C2×#610411yescharacteristic
404C2×C4C2×#610411yescharacteristic
405C2×C4C2×#610411yescharacteristic
406C2×C4C22×C22⋊D1311yescharacteristic
407C8—21no—
408C8—21no—
409C8#8819612yes—
410C8#8825411yescharacteristic
411C8#8825411yescharacteristic
412C22—21no—
413C22—21no—
414C22—21no—
415C22C22×#610411yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—1041no—
426C4—1041no—
427C4—1041no—
428C4—1041no—
429C4C2×#8819611yescharacteristic
430C4#1171952111yescharacteristic
431C2—41no—
432C2#1312595711yescharacteristic
433C2#1312798311yescharacteristic
434C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3164C2
socleC22×C13C22×D8
prime radicalC23×C13C2×D8
hypercenter#3164D13
hypocenterC13#33808
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3164

Complements

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

NH ≅ G/Ntype
2. #13117119C2semidirect
3. #13117112C2semidirect
4. #13117083C2semidirect
5. #13117065C2semidirect
10. #13116997C2semidirect
11. #13116997C2semidirect
12. #13116985C2semidirect
13. #13116975C2semidirect
382. C13#33808semidirect

Maximal subgroups

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

subgroupindex
#131254952
#131171192
#131171122
#131170832
#131170652
#131170442
#131170382
#131170332
#131169972
#131169852
#131169752
#131166432
C13×#31642
#3380813