Finite Group Databasebeta

← #15756824

Subgroups — #15756824

Order 3328.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123949C211yesmaximal, characteristic
2#13114953C211yesmaximal, characteristic, complemented
3C4×#88045C211yesmaximal, characteristic
4#13113589C211yesmaximal, characteristic, complemented
5#13113224C211yesmaximal, characteristic
6#13112685C211yesmaximal, characteristic, complemented
7C13×#1276C211yesmaximal, characteristic, complemented
8C4×#6127C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C43×C13C2211yescharacteristic
12C2×#88045C411yescharacteristic
13C2×#88045C411yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16C4×#6099C2211yescharacteristic
17#11718498—21no—
18#11718496—21no—
19#11718391—22no—
20#11718349—21no—
21#11718340—21no—
22#11718116—22no—
23#11718115C411yescharacteristic
24#11718115C411yescharacteristic
25#11718072—21no—
26#11718071—21no—
27#11718051—21no—
28#11718048—21no—
29C2×#6127C2×C411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13—21no—
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C4×C22⋊D13—21no—
36C4×C22⋊D13—21no—
37#88180C2×C411yescharacteristic
38C2×#6099C2×C411yescharacteristic
39C2×#6099C2×C411yescharacteristic
40C22×#1055—21no—
41C22×#1055D412yes—
42C2×#6094—22no—
43C4×D52D411yescharacteristic
44C4×D52Q811yescharacteristic
45#88126—21no—
46C42×D13—21no—
47C4×Dic26D411yescharacteristic
48C4×Dic26Q811yescharacteristic
49C13×C4⋊C8—21no—
50C13×C4⋊C8D411yescharacteristic
51C13×C4⋊C8D411yescharacteristic
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C4×C8×C13—21no—
55C4×C8×C13—21no—
56#88060—22no—
57#88055—22no—
58#88054—22no—
59#88045—22no—
60#88045—22no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65#88043—21no—
66C4×#1055—21no—
67#8842—131nomaximal, Sylow
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C2×C22⋊D13—21no—
74#6127—21no—
75#6127—21no—
76#6127—21no—
77#6127—21no—
78C2×D52C4⋊C411yescharacteristic
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×Dic26C4⋊C411yescharacteristic
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—41no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—41no—
90C42×C13—41no—
91C42×C13—42no—
92C42×C13M1612yescomplemented
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13C2×Q811yescharacteristic
96C42×C13#4111yescharacteristic
97C22⋊Dic13—21no—
98#6103—21no—
99#6103—21no—
100C4⋊Dic13C4⋊C411yescharacteristic
101C4⋊Dic13C4⋊C411yescharacteristic
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107#6099—21no—
108#6099—21no—
109#6099—21no—
110#6099M1612yescomplemented
111C2×#1055—21no—
112C2×#1055—21no—
113C2×#1055—22no—
114C2×#1055—42no—
115C2×#1055—42no—
116C2×#1055—41no—
117#6094—82no—
118#2989—131no—
119#1831—131no—
120C4×#104—131no—
121#1565—131no—
122#1477—131no—
123#1283—131no—
124#1276D1311yescharacteristic, complemented
125C23×C13C4×D411yescharacteristic
126C22×D13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13C2×C4⋊C411yescharacteristic
137C2×C4×C13C4×D411yescharacteristic
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13C22⋊Q811yescharacteristic
140C2×C4×C13C22⋊Q811yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13C2×M1611yescharacteristic
143C2×C4×C13C2×M1611yescharacteristic
144C2×C4×C13#13111yescharacteristic
145C2×C4×C13#13111yescharacteristic
146C22⋊D13—41no—
147C22⋊D13—41no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151D52—21no—
152D52—21no—
153C4×D13—41no—
154C4×D13—41no—
155C4×D13—41no—
156C4×D13—41no—
157C4×D13—81no—
158Dic26—21no—
159Dic26—21no—
160C8×C13—41no—
161C8×C13—41no—
162C8×C13—81no—
163#1055—22no—
164#1055—41no—
165#1055—42no—
166#1055—81no—
167C4×#41—131no—
168#446—261no—
169#436—261no—
170#435—262no—
171#432—261no—
172#431C2×D1311yescharacteristic
173#431C2×D1311yescharacteristic
174#423—261no—
175C2×C4⋊C8—131no—
176C2×C4⋊C8—131no—
177C2×#104—131no—
178C2×#104—131no—
179C4×M16—131no—
180C43C2×D1311yescharacteristic
181#339—131no—
182#339—131no—
183#336—262no—
184#335—261no—
185#334—261no—
186Q8⋊C8—261no—
187D4⋊C8—261no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13#38511yescharacteristic
191C22×C13#43511yescharacteristic
192C22×C13#43611yescharacteristic
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—42no—
200C4×C13—42no—
201C4×C13#42311yescharacteristic
202C4×C13#42411yescharacteristic
203C4×C13#43511yescharacteristic
204C4×C13#43611yescharacteristic
205C4×C13#45411yescharacteristic
206C4×C13#45511yescharacteristic
207Dic13—41no—
208Dic13—41no—
209Dic13—41no—
210C2×#41—131no—
211C2×M16—131no—
212C2×M16—131no—
213C2×M16—262no—
214C22×C8—132no—
215C22×C8—261no—
216C4×Q8—131no—
217C4×Q8—131no—
218C4×D4—131no—
219C4×D4—131no—
220C4×D4—261no—
221C4×D4—261no—
222#117—131no—
223#117—261no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—261no—
227C2×C42C4×D1311yescharacteristic
228C2×C42C4×D1311yescharacteristic
229C2×C42C22×D1311yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—262no—
232C4⋊C8—261no—
233C4⋊C8—261no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C4⋊C8D5211yescharacteristic
237C4⋊C8D5211yescharacteristic
238#104—262no—
239#104—262no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—262no—
243#97—262no—
244#97—261no—
245C4×C8—21no—
246C4×C8—21no—
247C4×C8—261no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13#185111yescharacteristic
251C2×C13#186011yescharacteristic
252C2×C13#186111yescharacteristic
253D13—81no—
254#41—261no—
255#41—261no—
256#41—261no—
257#41—261no—
258C2×Q8—131no—
259C2×D4—131no—
260C2×D4—261no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4C2×C4×D1311yescharacteristic
267C22×C4D4×D1311yescharacteristic
268C22×C4#612911yescharacteristic
269M16—132no—
270M16—261no—
271M16—261no—
272M16—261no—
273M16—1042no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—41no—
277C2×C8—261no—
278C2×C8—261no—
279C2×C8—262no—
280C2×C8—522no—
281C2×C8—522no—
282C2×C8—521no—
283C4⋊C4—131no—
284C4⋊C4—131no—
285C4⋊C4—261no—
286C4⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—41no—
294C42—41no—
295C42—42no—
296C42—261no—
297C42—261no—
298C42—261no—
299C42#609412yescomplemented
300C42C2×D5211yescharacteristic
301C42#612711yescharacteristic
302C42D4×D1311yescharacteristic
303C42Q8×D1311yescharacteristic
304C13#884211yescharacteristic, complemented, Sylow
305C23—261no—
306C23#8813511yescharacteristic
307Q8—261no—
308Q8—261no—
309D4—261no—
310D4—261no—
311D4—521no—
312D4—521no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—1041no—
330C2×C4C4×D5211yescharacteristic
331C2×C4#8813611yescharacteristic
332C2×C4#8813711yescharacteristic
333C2×C4C4⋊C4×D1311yescharacteristic
334C2×C4#8815011yescharacteristic
335C2×C4#8815111yescharacteristic
336C2×C4C2×#609411yescharacteristic
337C2×C4#8815511yescharacteristic
338C2×C4M16×D1311yescharacteristic
339C2×C4#8816111yescharacteristic
340C8—41no—
341C8—41no—
342C8—81no—
343C8—262no—
344C8—522no—
345C8—521no—
346C8—1041no—
347C22—21no—
348C22—21no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22#1171832911yescharacteristic
353C22#1171839011yescharacteristic
354C22#1171839111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—521no—
361C4—521no—
362C4—521no—
363C4#1171834911yescharacteristic
364C4#1171836711yescharacteristic
365C4#1171848611yescharacteristic
366C4#1171848811yescharacteristic
367C4#1171849811yescharacteristic
368C4#1171850011yescharacteristic
369C2—21no—
370C2—21no—
371C2—1041no—
372C2#1311502011yescharacteristic
373C2#1311507011yescharacteristic
374C2#1311507711yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#385
prime radicalC2×#6127C2×C4
cosocleC2×C42×C13C23
hypercenter#1276D13
hypocenterC13#8842
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #13114953C2semidirect
4. #13113589C2semidirect
6. #13112685C2semidirect
7. C13×#1276C2semidirect
92. C42×C13M16semidirect
110. #6099M16semidirect
124. #1276D13semidirect
299. C42#6094semidirect
304. C13#8842semidirect

Maximal subgroups

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

subgroupindex
#131239492
#131149532
C4×#880452
#131135892
#131132242
#131126852
C13×#12762
#884213