Finite Group Databasebeta

← #15766643

Subgroups — #15766643

Order 3328.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114832C211yesmaximal, characteristic
2#13113594C211yesmaximal, characteristic
3#13113526C211yesmaximal, characteristic
4#13113291C211yesmaximal, characteristic
5C2×Q8⋊#1055C211yesmaximal, characteristic
6#13112710C211yesmaximal, characteristic
7C13×#3078C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C13×#479—22no—
11C13×#477—21no—
12C13×#475—21no—
13C13×#428—21no—
14C13×#423C2211yescharacteristic
15C13×#419—21no—
16C2×#88076—21no—
17#11718585C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718139—21no—
22#11718138—21no—
23Q8⋊#1055—21no—
24Q8⋊#1055—21no—
25Q8⋊#1055—21no—
26Q8⋊#1055—21no—
27#11718122—21no—
28#11718071—22no—
29C22×Q8×C13D411yescharacteristic
30C2×C13×M16—21no—
31C13×C4⋊Q8D411yescharacteristic
32C13×C4⋊Q8D411yescharacteristic
33C13×#125—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C13×#117—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C42×C13—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6099—21no—
48C2×#6099—21no—
49C22×#1055—21no—
50C22×#1055—21no—
51C13×#107—22no—
52C13×#106—22no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8D412yes—
55C13×#103—22no—
56C13×#103—22no—
57#88076—42no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4×#1055—21no—
65C4×#1055D411yescharacteristic
66C4×#1055D411yescharacteristic
67#10463—131nomaximal, Sylow
68C2×Q8×C13—21no—
69C2×Q8×C13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13Q1612yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C13×M16—41no—
82C13×M16—41no—
83C2×C8×C13—22no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C22⋊C4—41no—
95C42×C13—41no—
96C42×C13—41no—
97C42×C13—41no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13#4111yescharacteristic
102#6099—41no—
103#6099—41no—
104#6099—41no—
105#6099—41no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—42no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—81no—
113#3078D1311yescharacteristic
114#1801—131no—
115#1567—131no—
116#1550—131no—
117#1493—131no—
118C2×Q8⋊C8—131no—
119#1292—131no—
120C23×C13#12311yescharacteristic
121Q8×C13—22no—
122Q8×C13—22no—
123Q8×C13—41no—
124Q8×C13—41no—
125Q8×C13—41no—
126Q8×C13—41no—
127Q8×C13—81no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
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×C13—41no—
137C2×C4×C13—81no—
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12311yescharacteristic
143C2×C4×C13#12411yescharacteristic
144C2×C4×C13C2×Q1611yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C8×C13—42no—
149#1055—22no—
150#1055—41no—
151#1055—81no—
152#1055—81no—
153#1055—81no—
154#533C2×D1311yescharacteristic
155C2×C4×Q8C2×D1311yescharacteristic
156#479—22no—
157#477—21no—
158#475—21no—
159#428—21no—
160#423—131no—
161#423—131no—
162#423C2×D1311yescharacteristic
163C2×C4⋊C8—131no—
164#419—21no—
165C2×#101—261no—
166C2×C4×C8—131no—
167#343—261no—
168#335—262no—
169#333—261no—
170#332—261no—
171Q8⋊C8—261no—
172Q8⋊C8—261no—
173Q8⋊C8—261no—
174Q8⋊C8—261no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13#39411yescharacteristic
178C22×C13#48411yescharacteristic
179C22×C13#48511yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—42no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13—81no—
187C4×C13#44911yescharacteristic
188C4×C13#45111yescharacteristic
189C4×C13#46711yescharacteristic
190C4×C13#46811yescharacteristic
191C4×C13#47111yescharacteristic
192C4×C13#47311yescharacteristic
193C22×Q8C22⋊D1311yescharacteristic
194C2×M16—21no—
195C2×M16—261no—
196C2×M16—261no—
197C22×C8—261no—
198C22×C8—261no—
199C4⋊Q8C22⋊D1311yescharacteristic
200C4⋊Q8C22⋊D1311yescharacteristic
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210#117—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C42—21no—
214C2×C42C22×D1311yescharacteristic
215#107—22no—
216#106—22no—
217C4⋊C8—21no—
218C4⋊C8—261no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4⋊C8C22⋊D1312yes—
225#103—22no—
226#103—22no—
227#101—522no—
228C4×C8—131no—
229C4×C8—131no—
230C4×C8—261no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13#203611yescharacteristic
234C2×C13#205011yescharacteristic
235C2×C13#205211yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8#610712yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4#612911yescharacteristic
247C22×C4#612911yescharacteristic
248C22×C4C2×C22⋊D1311yescharacteristic
249M16—41no—
250M16—41no—
251M16—521no—
252M16—521no—
253M16—521no—
254M16—521no—
255C2×C8—22no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—522no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—1041no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—41no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42D4×D1311yescharacteristic
278C42#612911yescharacteristic
279C42C2×C22⋊D1311yescharacteristic
280C42C2×C22⋊D1311yescharacteristic
281C13#1046311yescharacteristic, complemented, Sylow
282C23#8818911yescharacteristic
283Q8—22no—
284Q8—22no—
285Q8—41no—
286Q8—41no—
287Q8—41no—
288Q8—41no—
289Q8—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4#8818911yescharacteristic
301C2×C4#8819011yescharacteristic
302C2×C4#8819211yescharacteristic
303C2×C4#8819311yescharacteristic
304C2×C4#8819311yescharacteristic
305C2×C4#8819611yescharacteristic
306C2×C4C2×#610711yescharacteristic
307C2×C4#8820311yescharacteristic
308C2×C4#8820411yescharacteristic
309C2×C4#8820711yescharacteristic
310C8—42no—
311C8—262no—
312C8—521no—
313C8—1041no—
314C8—1041no—
315C8—1041no—
316C22—21no—
317C22—21no—
318C22#1171870511yescharacteristic
319C22#1171870611yescharacteristic
320C22#1171888311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4#1171871011yescharacteristic
329C4#1171871211yescharacteristic
330C4#1171886411yescharacteristic
331C4#1171886511yescharacteristic
332C4#1171888911yescharacteristic
333C4#1171889911yescharacteristic
334C2—21no—
335C2—21no—
336C2#1311603611yescharacteristic
337C2#1311612011yescharacteristic
338C2#1311613211yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3078C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#3078D13
hypocenterC13#10463
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
281. C13#10463semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131135942
#131135262
#131132912
C2×Q8⋊#10552
#131127102
C13×#30782
#1046313