Finite Group Databasebeta

← #28339961

Subgroups — #28339961

Order 13696.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812086C211yesmaximal, characteristic
2C2×C4×Dic214C211yesmaximal, characteristic, complemented
3#20292569C211yesmaximal, characteristic, complemented
4#20292567C211yesmaximal, characteristic, complemented
5#20292555C211yesmaximal, characteristic
6#20292552C211yesmaximal, characteristic
7#20292531C211yesmaximal, characteristic, complemented
8#20292522C211yesmaximal, characteristic, complemented
9#20292521C211yesmaximal, characteristic
10#20292513C211yesmaximal, characteristic, complemented
11#20292511C211yesmaximal, characteristic, complemented
12#20292491C211yesmaximal, characteristic, complemented
13#20292485C211yesmaximal, characteristic
14C22⋊C4×Dic107C211yesmaximal, characteristic
15#388×C107C211yesmaximal, characteristic
16C22×Dic214C2211yescharacteristic
17C23×Dic107C2211yescharacteristic
18#16812086—24no—
19C4×Dic214—24no—
20C2×C4⋊Dic107C2211yescharacteristic
21C2×C4⋊Dic107C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×Dic107⋊C4C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C4×Dic107C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C2×C4×Dic107C2211yescharacteristic
34C107⋊#95C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C22⋊C4×C107C2211yescharacteristic
48C2×C22⋊C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50C2×C42×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C2×Dic214—22no—
54C2×Dic214—22no—
55C2×Dic214D414yes—
56C22×Dic107—22no—
57C22×Dic107—22no—
58C22×Dic107—22no—
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C4⋊Dic107—22no—
68C4⋊Dic107—22no—
69Dic107⋊C4—22no—
70Dic107⋊C4—22no—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—22no—
75C22⋊Dic107—22no—
76C22⋊Dic107—22no—
77C22⋊Dic107—22no—
78C4×Dic107—22no—
79C4×Dic107—22no—
80C4×Dic107—22no—
81C24×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C4⋊C4×C107—22no—
89C22⋊C4×C107—22no—
90C22⋊C4×C107—22no—
91C22⋊C4×C107—22no—
92C42×C107—22no—
93C23×C107—21no—
94C23×C107—21no—
95C23×C107—21no—
96C23×C107—21no—
97C23×C107—21no—
98C23×C107—21no—
99C23×C107#4112yes—
100C23×C107C2411yescharacteristic
101C2×C4×C107—21no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
105C2×C4×C107—21no—
106C2×C4×C107—21no—
107C2×C4×C107—21no—
108C2×C4×C107—21no—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107C2×D412yes—
118C2×C4×C107#4112yes—
119C2×Dic107—21no—
120C2×Dic107—21no—
121C2×Dic107—21no—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107—21no—
138C2×Dic107—21no—
139C2×Dic107—44no—
140C2×Dic107C2×D412yes—
141C2×Dic107C2×D412yes—
142C2×Dic107#4112yes—
143C2×Dic107#4112yes—
144Dic214—28no—
145C22×C107—22no—
146C22×C107—22no—
147C22×C107—22no—
148C22×C107—41no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107—41no—
152C22×C107C22×D411yescharacteristic
153C22×C107C2×#4111yescharacteristic
154C22×C107C2×#4111yescharacteristic
155C22×C107C2×#4111yescharacteristic
156C22×C107C2×#4111yescharacteristic
157C22×C1072−1+411yescharacteristic
158C22×C1072−1+411yescharacteristic
159C4×C107—22no—
160C4×C107—22no—
161C4×C107—41no—
162C4×C107—41no—
163C4×C107—41no—
164C4×C107—41no—
165Dic107—22no—
166Dic107—41no—
167Dic107—41no—
168Dic107—41no—
169Dic107—41no—
170Dic107—41no—
171Dic107—41no—
172Dic107#12314yes—
173C2×C107—42no—
174C2×C107C2×#12311yescharacteristic
175C2×C107#52911yescharacteristic
176C2×C107#54111yescharacteristic
177C2×C107#54811yescharacteristic
178C2×C107#54811yescharacteristic
179C2×C107#55211yescharacteristic
180C2×C107#55611yescharacteristic
181#2421—1071nomaximal, Sylow
182C107#242111yescharacteristic, complemented, Sylow
183C2×C22⋊Q8—1071no—
184C2×C4×Q8—1071no—
185#400—1071no—
186#400—1071no—
187#397—1071no—
188#397—1071no—
189#391—1071no—
190#389—1071no—
191#388—1071no—
192#388D10711yescharacteristic
193#387—1071no—
194#387—1071no—
195#382—1071no—
196#380—1071no—
197C4×C22⋊C4—1071no—
198C22×Q8—1071no—
199C23×C4—1071no—
200C22⋊Q8—2144no—
201C4×Q8—2144no—
202C2×C4⋊C4—1071no—
203C2×C4⋊C4—1071no—
204C2×C4⋊C4—1071no—
205C2×C4⋊C4—1071no—
206C2×C4⋊C4—1071no—
207C2×C4⋊C4—1071no—
208C2×C4⋊C4—1071no—
209C2×C4⋊C4—1071no—
210C2×C4⋊C4C2×D10711yescharacteristic
211C2×C22⋊C4—1071no—
212C2×C22⋊C4—1071no—
213C2×C22⋊C4—1071no—
214C2×C22⋊C4C2×D10711yescharacteristic
215C2×C22⋊C4C2×D10711yescharacteristic
216C2×C22⋊C4C2×D10711yescharacteristic
217C2×C42—1071no—
218C2×C42—1071no—
219C2×C42—1071no—
220C2×C42C2×D10711yescharacteristic
221#95—1071no—
222#95—1071no—
223#95—1071no—
224#95—1071no—
225#95—1071no—
226#95—1071no—
227#95—1071no—
228#95—1071no—
229#95—1071no—
230#95—1071no—
231#95—1071no—
232#95—1071no—
233#95C2×D10711yescharacteristic
234#95C2×D10711yescharacteristic
235C24C22×D10711yescharacteristic
236C2×Q8—1074no—
237C2×Q8—2142no—
238C2×Q8—2142no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—1071no—
242C22×C4—1071no—
243C22×C4—1071no—
244C22×C4—1071no—
245C22×C4—1071no—
246C22×C4—1071no—
247C22×C4—2142no—
248C22×C4—2142no—
249C22×C4—2142no—
250C22×C4C22×D10711yescharacteristic
251C22×C4C22×D10711yescharacteristic
252C22×C4C22×D10711yescharacteristic
253C22×C4C22×D10711yescharacteristic
254C22×C4C22×D10711yescharacteristic
255C22×C4C22×D10711yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—2142no—
258C4⋊C4—2142no—
259C4⋊C4—2142no—
260C4⋊C4—2142no—
261C4⋊C4—2142no—
262C4⋊C4—2142no—
263C4⋊C4—2142no—
264C4⋊C4—2142no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—2142no—
269C22⋊C4—2142no—
270C22⋊C4—2142no—
271C42—22no—
272C42—2142no—
273C42—2142no—
274C42—2142no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23#1313381812yes—
282C23C23×D10711yescharacteristic
283Q8—2148no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—1072no—
301C2×C4—1072no—
302C2×C4—1072no—
303C2×C4—1072no—
304C2×C4—4284no—
305C2×C4—2141no—
306C2×C4—2141no—
307C2×C4—2141no—
308C2×C4—2141no—
309C2×C4—2141no—
310C2×C4—2141no—
311C2×C4—2141no—
312C2×C4—2141no—
313C2×C4—2141no—
314C2×C4—2141no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4—2141no—
325C2×C4D4×D10712yes—
326C2×C4#1313381712yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C2×D4×D10711yescharacteristic
335C22#41×D10711yescharacteristic
336C22#41×D10711yescharacteristic
337C22C2×#1313381711yescharacteristic
338C22C2×#1313381811yescharacteristic
339C22#1681215611yescharacteristic
340C22#1681215611yescharacteristic
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1074no—
348C4—4281no—
349C4—4281no—
350C4—4281no—
351C4—4281no—
352C4—4281no—
353C4—4281no—
354C4—2142no—
355C2—42no—
356C2#123×D10711yescharacteristic
357C2#2029315711yescharacteristic
358C2#2029323411yescharacteristic
359C2#2029328311yescharacteristic
360C2#2029328611yescharacteristic
361C2#2029331011yescharacteristic
362C2#2029334611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#388×C107C2
prime radicalC24×C107C23
hypercenter#388D107
hypocenterC107#2421
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic214C2semidirect
3. #20292569C2semidirect
4. #20292567C2semidirect
7. #20292531C2semidirect
8. #20292522C2semidirect
10. #20292513C2semidirect
11. #20292511C2semidirect
12. #20292491C2semidirect
182. C107#2421semidirect

Maximal subgroups

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

subgroupindex
C2×#168120862
C2×C4×Dic2142
#202925692
#202925672
#202925552
#202925522
#202925312
#202925222
#202925212
#202925132
#202925112
#202924912
#202924852
C22⋊C4×Dic1072
#388×C1072
#2421107