Finite Group Databasebeta

← #15756817

Subgroups — #15756817

Order 3328.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123949C211yesmaximal, characteristic
2#13114988C211yesmaximal, 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⋊#1055—22no—
15C2×C4⋊#1055C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17C4×#6099C2211yescharacteristic
18#11718498—21no—
19#11718496—21no—
20#11718391—22no—
21#11718349—21no—
22#11718340—21no—
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—
65C4⋊#1055—44no—
66#88043—21no—
67C4×#1055—21no—
68#8841—131nomaximal, Sylow
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4111yescharacteristic
74C2×C22⋊D13—21no—
75#6127—21no—
76#6127—21no—
77#6127—21no—
78#6127—21no—
79C2×D52C4⋊C411yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×Dic26C4⋊C411yescharacteristic
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—41no—
87C42×C13—22no—
88C42×C13—22no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—42no—
93C42×C13M1612yescomplemented
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×Q811yescharacteristic
97C42×C13#4111yescharacteristic
98C22⋊Dic13—21no—
99#6103—21no—
100#6103—21no—
101C4⋊Dic13C4⋊C411yescharacteristic
102C4⋊Dic13C4⋊C411yescharacteristic
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108#6099—21no—
109#6099—21no—
110#6099—21no—
111#6099M1612yescomplemented
112C2×#1055—21no—
113C2×#1055—21no—
114C2×#1055—22no—
115C2×#1055—42no—
116C2×#1055—42no—
117C2×#1055—41no—
118#6094—82no—
119#2989—131no—
120#1842—131no—
121C4×#104—131no—
122#1565—131no—
123#1477—131no—
124#1283—131no—
125#1276D1311yescharacteristic, complemented
126C23×C13C4×D411yescharacteristic
127C22×D13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13C2×C4⋊C411yescharacteristic
138C2×C4×C13C4×D411yescharacteristic
139C2×C4×C13#12011yescharacteristic
140C2×C4×C13C22⋊Q811yescharacteristic
141C2×C4×C13C22⋊Q811yescharacteristic
142C2×C4×C13#12311yescharacteristic
143C2×C4×C13C2×M1611yescharacteristic
144C2×C4×C13C2×M1611yescharacteristic
145C2×C4×C13#13111yescharacteristic
146C2×C4×C13#13111yescharacteristic
147C22⋊D13—41no—
148C22⋊D13—41no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152D52—21no—
153D52—21no—
154C4×D13—41no—
155C4×D13—41no—
156C4×D13—41no—
157C4×D13—41no—
158C4×D13—81no—
159Dic26—21no—
160Dic26—21no—
161C8×C13—41no—
162C8×C13—41no—
163C8×C13—81no—
164#1055—22no—
165#1055—41no—
166#1055—42no—
167#1055—81no—
168C4×#41—131no—
169#446—261no—
170#436—261no—
171#435—262no—
172#432—261no—
173#431C2×D1311yescharacteristic
174#431C2×D1311yescharacteristic
175#423—261no—
176C2×C4⋊C8—131no—
177C2×C4⋊C8—131no—
178C2×C4⋊C8—262no—
179C2×#104—131no—
180C2×#104—131no—
181C4×M16—131no—
182C43C2×D1311yescharacteristic
183#339—131no—
184#339—131no—
185#335—261no—
186#334—261no—
187Q8⋊C8—261no—
188D4⋊C8—261no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13#38511yescharacteristic
192C22×C13#43511yescharacteristic
193C22×C13#43611yescharacteristic
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C4×C13—24no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—42no—
202C4×C13#42311yescharacteristic
203C4×C13#42411yescharacteristic
204C4×C13#43511yescharacteristic
205C4×C13#43611yescharacteristic
206C4×C13#45311yescharacteristic
207C4×C13#45611yescharacteristic
208Dic13—41no—
209Dic13—41no—
210Dic13—41no—
211C2×#41—131no—
212C2×M16—131no—
213C2×M16—131no—
214C2×M16—262no—
215C22×C8—132no—
216C22×C8—261no—
217C4×Q8—131no—
218C4×Q8—131no—
219C4×D4—131no—
220C4×D4—131no—
221C4×D4—261no—
222C4×D4—261no—
223#117—131no—
224#117—261no—
225C2×C42—21no—
226C2×C42—21no—
227C2×C42—261no—
228C2×C42C4×D1311yescharacteristic
229C2×C42C4×D1311yescharacteristic
230C2×C42C22×D1311yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—262no—
233C4⋊C8—261no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8—524no—
238C4⋊C8D5211yescharacteristic
239C4⋊C8D5211yescharacteristic
240#104—262no—
241#104—262no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—262no—
245#97—262no—
246#97—261no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8—261no—
250C2×C13—21no—
251C2×C13—21no—
252C2×C13#185111yescharacteristic
253C2×C13#185911yescharacteristic
254C2×C13#186111yescharacteristic
255D13—81no—
256#41—261no—
257#41—261no—
258#41—261no—
259#41—261no—
260C2×Q8—131no—
261C2×D4—131no—
262C2×D4—261no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4C2×C4×D1311yescharacteristic
269C22×C4D4×D1311yescharacteristic
270C22×C4#612911yescharacteristic
271M16—132no—
272M16—261no—
273M16—261no—
274M16—261no—
275M16—1042no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—262no—
282C2×C8—522no—
283C2×C8—522no—
284C2×C8—521no—
285C4⋊C4—131no—
286C4⋊C4—131no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—22no—
293C42—22no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—42no—
298C42—261no—
299C42—261no—
300C42—261no—
301C42#609412yescomplemented
302C42C2×D5211yescharacteristic
303C42#612711yescharacteristic
304C42D4×D1311yescharacteristic
305C42Q8×D1311yescharacteristic
306C13#884111yescharacteristic, complemented, Sylow
307C23—261no—
308C23#8813511yescharacteristic
309Q8—261no—
310Q8—261no—
311D4—261no—
312D4—261no—
313D4—521no—
314D4—521no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—1041no—
332C2×C4C4×D5211yescharacteristic
333C2×C4#8813611yescharacteristic
334C2×C4#8813711yescharacteristic
335C2×C4C4⋊C4×D1311yescharacteristic
336C2×C4#8815011yescharacteristic
337C2×C4#8815111yescharacteristic
338C2×C4C2×#609411yescharacteristic
339C2×C4#8815511yescharacteristic
340C2×C4M16×D1311yescharacteristic
341C2×C4#8816111yescharacteristic
342C8—41no—
343C8—41no—
344C8—81no—
345C8—262no—
346C8—522no—
347C8—521no—
348C8—1041no—
349C22—21no—
350C22—21no—
351C22—521no—
352C22—521no—
353C22—521no—
354C22#1171832911yescharacteristic
355C22#1171839011yescharacteristic
356C22#1171839111yescharacteristic
357C4—24no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—521no—
363C4—521no—
364C4—521no—
365C4#1171834911yescharacteristic
366C4#1171836711yescharacteristic
367C4#1171848311yescharacteristic
368C4#1171848711yescharacteristic
369C4#1171849811yescharacteristic
370C4#1171850011yescharacteristic
371C2—21no—
372C2—21no—
373C2—1041no—
374C2#1311502011yescharacteristic
375C2#1311506311yescharacteristic
376C2#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#8841
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. #13114988C2semidirect
4. #13113589C2semidirect
6. #13112685C2semidirect
7. C13×#1276C2semidirect
93. C42×C13M16semidirect
111. #6099M16semidirect
125. #1276D13semidirect
301. C42#6094semidirect
306. C13#8841semidirect

Maximal subgroups

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

subgroupindex
#131239492
#131149882
C4×#880452
#131135892
#131132242
#131126852
C13×#12762
#884113