Finite Group Databasebeta

← #16019159

Subgroups — #16019159

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#13125375C211yesmaximal, characteristic
2#13117123C211yesmaximal, characteristic, complemented
3#13117112C211yesmaximal, characteristic, complemented
4#13117081C211yesmaximal, characteristic, complemented
5#13117063C211yesmaximal, characteristic, complemented
6#13117041C211yesmaximal, characteristic
7#13117041C211yesmaximal, characteristic
8#13117036C211yesmaximal, characteristic
9#13117031C211yesmaximal, characteristic
10#13117000C211yesmaximal, characteristic, complemented
11#13117000C211yesmaximal, characteristic, complemented
12#13116988C211yesmaximal, characteristic, complemented
13#13116978C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic
15C13×#3177C211yesmaximal, characteristic
16C13×#541—21no—
17#11719224—21no—
18C13×#499C2211yescharacteristic
19C13×#494C2211yescharacteristic
20C13×#491—21no—
21C13×#470—21no—
22C13×#467C2211yescharacteristic
23C13×#467C2211yescharacteristic
24C13×#441—21no—
25C4×C13×Q16C2211yescharacteristic
26C4×C13×Q16C2211yescharacteristic
27C13×#405C2211yescharacteristic
28#11718782—21no—
29#11718767C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31#11718363—21no—
32#11718363—21no—
33#11718344C2211yescharacteristic
34#11718344C2211yescharacteristic
35#11718343C2211yescharacteristic
36#11718343C2211yescharacteristic
37#11718156C2211yescharacteristic
38#11718156C2211yescharacteristic
39#11718156C2211yescharacteristic
40#11718156C2211yescharacteristic
41#11718156C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718156C2211yescharacteristic
44#11718156C2211yescharacteristic
45C22⋊#6090C2211yescharacteristic
46C22⋊#6090C2211yescharacteristic
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×Q16—21no—
60C2×C13×Q16C2311yescharacteristic
61C2×C13×Q16C2311yescharacteristic
62C2×C13×M16D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×C4⋊Q8—21no—
65C13×#126—41no—
66C13×#126—41no—
67C13×#125—21no—
68C13×#125—41no—
69C13×#125—41no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8—21no—
72C4×Q8×C13—21no—
73C4×Q8×C13—21no—
74C13×#117D411yescharacteristic
75#88180—21no—
76C2×C4⋊Dic13—21no—
77#88144—41no—
78#88142—41no—
79#88132—41no—
80#88132—41no—
81#88124—21no—
82#88124—21no—
83#88123—21no—
84#88123—21no—
85C13×#107C2311yescharacteristic
86C13×#107C2311yescharacteristic
87C13×#106—21no—
88C13×#103—21no—
89C13×#103—21no—
90C13×#103—21no—
91C13×#103—21no—
92C13×#97D411yescharacteristic
93C13×#97D411yescharacteristic
94C4×C8×C13C2311yescharacteristic
95C4×C8×C13C2311yescharacteristic
96#88058—21no—
97#88058—21no—
98#88058—21no—
99#88058C2311yescharacteristic
100#88058C2311yescharacteristic
101#88058C2311yescharacteristic
102#88058C2311yescharacteristic
103#88057—21no—
104#88057—21no—
105#88057—21no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108C2×#6090C2311yescharacteristic
109C2×#6090C2311yescharacteristic
110#33808—131nomaximal, Sylow
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C22×C4×C13C2×D411yescharacteristic
114C22×Dic13—41no—
115C2×Dic26—41no—
116C2×Dic26—41no—
117C13×Q16—21no—
118C13×Q16—21no—
119C13×Q16—21no—
120C13×Q16—21no—
121C13×Q16—42no—
122C13×M16—22no—
123C2×C8×C13—21no—
124C2×C8×C13—21no—
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2411yescharacteristic
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C4⋊C4—41no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4D811yescharacteristic
140C13×C4⋊C4D811yescharacteristic
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4D811yescharacteristic
144C13×C22⋊C4D811yescharacteristic
145C42×C13—41no—
146C42×C13—41no—
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C22⋊Dic13—41no—
150C4⋊Dic13—21no—
151C4⋊Dic13—21no—
152C4⋊Dic13—21no—
153C4⋊Dic13—21no—
154C4⋊Dic13—41no—
155C4⋊Dic13—41no—
156C4⋊Dic13—41no—
157#6101—41no—
158#6101—41no—
159#6101—41no—
160#6101—41no—
161C4×Dic13—41no—
162#6090—21no—
163#6090—21no—
164#6090—21no—
165#6090—21no—
166#3177D1311yescharacteristic
167#3164—131no—
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—41no—
183Q8×C13—41no—
184Q8×C13—41no—
185Q8×C13—41no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13C2×D811yescharacteristic
193C2×C4×C13C2×D811yescharacteristic
194C2×C4×C13C2×D811yescharacteristic
195C2×C4×C13C2×D811yescharacteristic
196C2×C4×C13C2×D811yescharacteristic
197C2×C4×C13C22×D411yescharacteristic
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202C2×Dic13—161no—
203Dic26—161no—
204Dic26—161no—
205C8×C13—21no—
206C8×C13—21no—
207C8×C13#13712yes—
208C8×C132−1+411yescharacteristic
209C8×C132−1+411yescharacteristic
210#544—261no—
211#541—21no—
212#501—261no—
213#501—261no—
214#500—131no—
215#500—131no—
216#499—131no—
217#499—131no—
218#499C2×D1311yescharacteristic
219#494C2×D1311yescharacteristic
220#491—21no—
221#470—21no—
222#467C2×D1311yescharacteristic
223#467C2×D1311yescharacteristic
224#441—21no—
225C4×Q16C2×D1311yescharacteristic
226C4×Q16C2×D1311yescharacteristic
227#428—261no—
228#427—131no—
229C2×#107—131no—
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—21no—
273C2×Q16C22×D1311yescharacteristic
274C2×Q16C22×D1311yescharacteristic
275C2×M16C22⋊D1311yescharacteristic
276C22×C8C22×D1311yescharacteristic
277C4⋊Q8—21no—
278C4⋊Q8—261no—
279C4⋊Q8—261no—
280C4⋊Q8—521no—
281#126—41no—
282#126—41no—
283#125—21no—
284#125—41no—
285#125—41no—
286#125—261no—
287#125—261no—
288#125—521no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—521no—
292C22⋊Q8—521no—
293C4×Q8—21no—
294C4×Q8—21no—
295#117—261no—
296#117C22⋊D1311yescharacteristic
297C2×C4⋊C4—261no—
298C2×C16—131no—
299C2×C16—131no—
300C2×C16—131no—
301C2×C16—131no—
302#107—131no—
303#107—131no—
304#107—131no—
305#107—131no—
306#107—261no—
307#107—261no—
308#107—261no—
309#107C22×D1311yescharacteristic
310#107C22×D1311yescharacteristic
311#106—21no—
312#106—261no—
313#106—261no—
314#106—261no—
315#103—21no—
316#103—21no—
317#103—21no—
318#103—21no—
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—21no—
328C2×Q8—21no—
329C2×Q8—521no—
330C2×Q8—521no—
331C22×C4—521no—
332C22×C4C2×C22⋊D1311yescharacteristic
333Q16—21no—
334Q16—21no—
335Q16—21no—
336Q16—21no—
337Q16—42no—
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—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—261no—
356C4⋊C4—261no—
357C4⋊C4—261no—
358C4⋊C4—261no—
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—41no—
370C22⋊C4—521no—
371C22⋊C4#610411yescharacteristic
372C22⋊C4#610411yescharacteristic
373C42—41no—
374C42—41no—
375C42—521no—
376C42C2×C22⋊D1311yescharacteristic
377C42C2×C22⋊D1311yescharacteristic
378C16—261no—
379C16—261no—
380C16—261no—
381C16—261no—
382C13#3380811yescharacteristic, complemented, Sylow
383C23C2×#610411yescharacteristic
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—41no—
388Q8—2081no—
389Q8—2081no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—2081no—
401C2×C4C2×#610411yescharacteristic
402C2×C4C2×#610411yescharacteristic
403C2×C4C2×#610411yescharacteristic
404C2×C4C2×#610411yescharacteristic
405C2×C4C2×#610411yescharacteristic
406C2×C4C22×C22⋊D1311yescharacteristic
407C8—21no—
408C8—21no—
409C8#8820512yes—
410C8#8825711yescharacteristic
411C8#8825711yescharacteristic
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×#8820511yescharacteristic
430C4#1171953011yescharacteristic
431C2—41no—
432C2#1312595411yescharacteristic
433C2#1312798011yescharacteristic
434C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3177C2
socleC22×C13C22×D8
prime radicalC23×C13C2×D8
hypercenter#3177D13
hypocenterC13#33808
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
2. #13117123C2semidirect
3. #13117112C2semidirect
4. #13117081C2semidirect
5. #13117063C2semidirect
10. #13117000C2semidirect
11. #13117000C2semidirect
12. #13116988C2semidirect
13. #13116978C2semidirect
382. C13#33808semidirect

Maximal subgroups

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

subgroupindex
#131253752
#131171232
#131171122
#131170812
#131170632
#131170412
#131170362
#131170312
#131170002
#131169882
#131169782
#131166432
C13×#31772
#3380813