Finite Group Databasebeta

← #15757252

Subgroups — #15757252

Order 3328.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#6099C211yesmaximal, characteristic
2#13115609C211yesmaximal, characteristic
3#13113594C211yesmaximal, characteristic
4C2×Q8⋊#1055C211yesmaximal, characteristic
5#13112732C211yesmaximal, characteristic
6#13112672C211yesmaximal, characteristic
7C13×#1487C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×#88062—21no—
12#11718685—22no—
13#11718685—21no—
14Q8×#1055—21no—
15#11718585—21no—
16#11718585C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C4×#6099—21no—
19C4×#6099C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21C13×Q8⋊C8—21no—
22C13×Q8⋊C8—21no—
23#11718150—21no—
24Q8⋊#1055C411yescharacteristic
25Q8⋊#1055C411yescharacteristic
26Q8⋊#1055C411yescharacteristic
27Q8⋊#1055C411yescharacteristic
28#11718071—22no—
29C22×Q8×C13Q811yescharacteristic
30C2×C13×M16—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13C2×C411yescharacteristic
34C4×Q8×C13C2×C411yescharacteristic
35C4×Q8×C13D411yescharacteristic
36C4×Q8×C13D411yescharacteristic
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4Q811yescharacteristic
39C2×C42×C13—21no—
40C2×C42×C13C2311yescharacteristic
41C2×#6099—21no—
42C2×#6099D411yescharacteristic
43C2×#6099D411yescharacteristic
44C22×#1055—21no—
45C22×#1055—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C22⋊C8—21no—
50C4×C8×C13—21no—
51#88062—42no—
52C4⋊#1055—22no—
53C4⋊#1055—22no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055C2×C411yescharacteristic
57C4⋊#1055C2×C411yescharacteristic
58C4⋊#1055D412yes—
59#88043—22no—
60#88043—21no—
61C4×#1055—22no—
62C4×#1055—21no—
63C4×#1055—21no—
64C4×#1055C2×C411yescharacteristic
65C4×#1055C2×C411yescharacteristic
66#8907—131nomaximal, Sylow
67C2×Q8×C13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13C4⋊C411yescharacteristic
71C2×Q8×C13C4⋊C411yescharacteristic
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×Q811yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C13×M16—41no—
78C13×M16—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4C4⋊C411yescharacteristic
87C13×C4⋊C4C4⋊C411yescharacteristic
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13C22×C411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13#4111yescharacteristic
96#6099—21no—
97#6099—21no—
98#6099—21no—
99#6099—41no—
100#6099—41no—
101#6099Q1612yes—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—22no—
108C2×#1055—21no—
109C2×#1055—42no—
110C2×#1055—41no—
111C2×#1055—41no—
112Q8×M16—131no—
113#1950—131no—
114#1567—131no—
115#1487D1311yescharacteristic
116C2×Q8⋊C8—131no—
117#1301—131no—
118#1278—131no—
119C23×C13C22⋊Q811yescharacteristic
120Q8×C13—21no—
121Q8×C13—21no—
122Q8×C13—21no—
123Q8×C13—42no—
124Q8×C13#10812yescomplemented
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13C2×C4⋊C411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13C22⋊Q811yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×Q1611yescharacteristic
141C2×C4×C13#13511yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C8×C13—81no—
145C8×C13—81no—
146#1055—22no—
147#1055—22no—
148#1055—41no—
149#1055—41no—
150#1055—41no—
151#1055—41no—
152#1055—42no—
153C2×C4×Q8C2×D1311yescharacteristic
154#446—262no—
155#446—261no—
156C8×Q8—261no—
157#431C2×D1311yescharacteristic
158C2×#108—261no—
159#423—131no—
160#423—261no—
161#423C2×D1311yescharacteristic
162C2×C4⋊C8—131no—
163C4×M16—131no—
164C4×M16—261no—
165C2×C4×C8—131no—
166#341—261no—
167#335—262no—
168Q8⋊C8—21no—
169Q8⋊C8—21no—
170Q8⋊C8—131no—
171Q8⋊C8—131no—
172Q8⋊C8—131no—
173Q8⋊C8—131no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13#38511yescharacteristic
177C22×C13#47711yescharacteristic
178C22×C13#47911yescharacteristic
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13C2×#10811yescharacteristic
187C4×C13#43011yescharacteristic
188C4×C13C4×Q1611yescharacteristic
189C4×C13#44011yescharacteristic
190C4×C13#44911yescharacteristic
191C4×C13#45111yescharacteristic
192C22×Q8Dic2611yescharacteristic
193C2×M16—21no—
194C2×M16—131no—
195C2×M16—131no—
196C2×M16—261no—
197C22×C8—261no—
198C22×C8—261no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8C4×D1311yescharacteristic
202C4×Q8C4×D1311yescharacteristic
203C4×Q8C22⋊D1311yescharacteristic
204C4×Q8C22⋊D1311yescharacteristic
205C2×C4⋊C4—21no—
206C2×C4⋊C4Dic2611yescharacteristic
207C2×C42—21no—
208C2×C42C22×D1311yescharacteristic
209#108—522no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215C4⋊C8—132no—
216C4⋊C8—262no—
217C4⋊C8—262no—
218C4⋊C8—261no—
219C4⋊C8—261no—
220C22⋊C8—21no—
221#97—262no—
222#97—261no—
223C4×C8—21no—
224C4×C8—131no—
225C4×C8—131no—
226C4×C8—262no—
227C4×C8—261no—
228C4×C8—261no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13#185511yescharacteristic
232C2×C13#186111yescharacteristic
233C2×C13#186311yescharacteristic
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8#610111yescharacteristic
238C2×Q8#610111yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C2×Dic2611yescharacteristic
242C22×C4D4×D1311yescharacteristic
243C22×C4#612911yescharacteristic
244M16—41no—
245M16—41no—
246M16—132no—
247M16—261no—
248M16—261no—
249M16—261no—
250M16—521no—
251M16—521no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—261no—
255C2×C8—261no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—261no—
259C2×C8—262no—
260C2×C8—261no—
261C2×C8—522no—
262C2×C8—521no—
263C2×C8—521no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4#610111yescharacteristic
270C4⋊C4#610111yescharacteristic
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42C2×C4×D1311yescharacteristic
276C42D4×D1311yescharacteristic
277C42#612911yescharacteristic
278C42C2×C22⋊D1311yescharacteristic
279C13#890711yescharacteristic, complemented, Sylow
280C23#8813211yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#8806212yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4#8813211yescharacteristic
296C2×C4#8813511yescharacteristic
297C2×C4#8813511yescharacteristic
298C2×C4#8816811yescharacteristic
299C2×C4#8817011yescharacteristic
300C2×C4Q16×D1311yescharacteristic
301C2×C4#8817211yescharacteristic
302C2×C4C2×#610111yescharacteristic
303C2×C4#8818911yescharacteristic
304C2×C4#8819111yescharacteristic
305C8—81no—
306C8—81no—
307C8—262no—
308C8—262no—
309C8—521no—
310C8—521no—
311C8—521no—
312C8—521no—
313C8—522no—
314C22—21no—
315C22—21no—
316C22#1171845511yescharacteristic
317C22#1171846011yescharacteristic
318C22#1171860711yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4#1171845111yescharacteristic
327C4#1171847811yescharacteristic
328C4C2×#8806211yescharacteristic
329C4#1171878511yescharacteristic
330C4#1171883311yescharacteristic
331C4#1171884711yescharacteristic
332C2—21no—
333C2—21no—
334C2#1311504011yescharacteristic
335C2#1311507411yescharacteristic
336C2#1311508811yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1487C2
socleC22×C13#385
prime radicalC23×C13C22⋊Q8
cosocleC2×C42×C13C23
hypercenter#1487D13
hypocenterC13#8907
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
124. Q8×C13#108semidirect
279. C13#8907semidirect
285. Q8#88062semidirect

Maximal subgroups

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

subgroupindex
Q8×#60992
#131156092
#131135942
C2×Q8⋊#10552
#131127322
#131126722
C13×#14872
#890713