Finite Group Databasebeta

← #28340049

Subgroups — #28340049

Order 13696.

832 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
1C2×#16812106C211yesmaximal, characteristic, complemented
2C2×#16812083C211yesmaximal, characteristic, complemented
3C2×#16812083C211yesmaximal, characteristic, complemented
4C2×#16812082C212yesmaximal, complemented
5C2×C4×D428C211yesmaximal, characteristic, complemented
6#20292545C212yesmaximal, complemented
7#20292536C212yesmaximal, complemented
8#20292529C211yesmaximal, characteristic, complemented
9#20292525C211yesmaximal, characteristic, complemented
10#20292505C212yesmaximal, complemented
11C4×C22⋊C4×C107C211yesmaximal, characteristic, complemented
12C22×D428C2211yescharacteristic
13C22×D428C2212yes—
14C22×D428C2212yes—
15C22×D428C2211yescharacteristic
16C22×C22⋊D107C2212yes—
17C22×C22⋊D107C2212yes—
18C22×C4×D107C2212yes—
19#16812106—24no—
20#16812083—24no—
21#16812083—24no—
22#16812082—28no—
23C4×D428—24no—
24C2×C4⋊Dic107C2211yescharacteristic
25C2×C4⋊Dic107C2211yescharacteristic
26C2×Dic107⋊C4C2212yes—
27C2×(C2×D107)⋊C4C2212yes—
28C2×(C2×D107)⋊C4C2212yes—
29C2×(C2×D107)⋊C4C2212yes—
30C2×(C2×D107)⋊C4C2212yes—
31C2×(C2×D107)⋊C4C2212yes—
32C107⋊#95C2212yes—
33C23×C4×C107C2211yescharacteristic
34C2×C22⋊C4×C107C2211yescharacteristic
35C2×C22⋊C4×C107C2211yescharacteristic
36C2×C42×C107C2211yescharacteristic
37C2×C42×C107C2211yescharacteristic
38#95×C107C2211yescharacteristic
39#95×C107C2211yescharacteristic
40C23×D107C2312yes—
41C23×D107C2312yes—
42C2×D428—22no—
43C2×D428—22no—
44C2×D428—24no—
45C2×D428—24no—
46C2×D428—24no—
47C2×D428—22no—
48C2×D428—22no—
49C2×D428—24no—
50C2×D428—22no—
51C2×D428—42no—
52C2×D428—42no—
53C2×D428D414yescomplemented
54C2×C22⋊D107—24no—
55C2×C22⋊D107—24no—
56C2×C22⋊D107—24no—
57C2×C22⋊D107—24no—
58C2×C22⋊D107—42no—
59C2×C22⋊D107—42no—
60C22×Dic107C2312yes—
61C22×Dic107C2312yes—
62C2×C4×D107—24no—
63C2×C4×D107—24no—
64C2×C4×D107—42no—
65C4⋊Dic107—22no—
66C4⋊Dic107D414yescomplemented
67Dic107⋊C4—24no—
68(C2×D107)⋊C4—24no—
69(C2×D107)⋊C4—24no—
70(C2×D107)⋊C4—24no—
71(C2×D107)⋊C4—24no—
72(C2×D107)⋊C4—42no—
73C24×C107C2311yescharacteristic
74C22×C4×C107—22no—
75C22×C4×C107—22no—
76C22×C4×C107—22no—
77C22×C4×C107C2311yescharacteristic
78C22×C4×C107C2311yescharacteristic
79C22×C4×C107C2311yescharacteristic
80C22×C4×C107C2311yescharacteristic
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22⋊C4×C107—22no—
84C22⋊C4×C107D414yescomplemented
85C42×C107—22no—
86C42×C107—22no—
87C23×C107—21no—
88C23×C107—21no—
89C23×C107—21no—
90C23×C107—21no—
91C23×C107—21no—
92C23×C107—21no—
93C23×C107C2×D412yes—
94C23×C107C2411yescharacteristic
95C22×D107—22no—
96C22×D107—22no—
97C22×D107—22no—
98C22×D107—22no—
99C22×D107—22no—
100C22×D107—22no—
101C22×D107—22no—
102C22×D107—22no—
103C22×D107—22no—
104C22×D107—22no—
105C22×D107—22no—
106C22×D107—22no—
107C22×D107—22no—
108C22×D107C2×D414yes—
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×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—44no—
122C2×C4×C107C2×D412yes—
123C2×C4×C107C2×D412yes—
124C2×C4×C107C2×D412yes—
125C2×C4×C107C2×D412yes—
126C2×C4×C107#4112yes—
127C2×C4×C107#4112yes—
128C22⋊D107—48no—
129C22⋊D107—48no—
130C2×Dic107—22no—
131C2×Dic107—22no—
132C2×Dic107—22no—
133C2×Dic107—22no—
134C2×Dic107—22no—
135C2×Dic107C2×D414yes—
136D428—28no—
137D428—48no—
138D428—48no—
139D428—44no—
140C4×D107—48no—
141C22×C107—22no—
142C22×C107—22no—
143C22×C107—22no—
144C22×C107—41no—
145C22×C107—41no—
146C22×C107—41no—
147C22×C107—41no—
148C22×C107C22×D411yescharacteristic
149C22×C107C22×D411yescharacteristic
150C22×C107C22×D411yescharacteristic
151C22×C107C2×#4111yescharacteristic
152C22×C107C2×#4111yescharacteristic
153C22×C107H(5,𝔽2)11yescharacteristic
154C22×C107H(5,𝔽2)11yescharacteristic
155C2×D107—24no—
156C2×D107—24no—
157C2×D107—24no—
158C2×D107—42no—
159C2×D107—42no—
160C2×D107—42no—
161C2×D107—42no—
162C2×D107—42no—
163C2×D107—42no—
164C2×D107—42no—
165C2×D107—42no—
166C2×D107—42no—
167C2×D107—42no—
168C2×D107—42no—
169C4×C107—22no—
170C4×C107—22no—
171C4×C107—22no—
172C4×C107—41no—
173C4×C107—41no—
174C4×C107#12114yescomplemented
175Dic107—24no—
176Dic107—42no—
177C2×C107—42no—
178C2×C107C2×#12111yescharacteristic
179C2×C107#53211yescharacteristic
180C2×C107#54011yescharacteristic
181C2×C107D4211yescharacteristic
182C2×C107D4211yescharacteristic
183C2×C107#54611yescharacteristic
184C2×C107#55011yescharacteristic
185D107—44no—
186D107—82no—
187#2428—1071nomaximal, Sylow
188C107#242811yescharacteristic, complemented, Sylow
189C2×#127—1071no—
190C2×#121—1071no—
191C2×#121—1071no—
192C2×#121—1072no—
193C2×C4×D4—1071no—
194#394—1072no—
195#392—1072no—
196#390—1071no—
197#389—1071no—
198#386—1072no—
199C4×C22⋊C4D10711yescharacteristic, complemented
200C22×D4—1072no—
201C22×D4—1072no—
202C22×D4—1071no—
203C22×D4—1072no—
204C22×D4—1072no—
205C22×D4—1071no—
206C23×C4—1072no—
207C23×C4C2×D10711yescharacteristic
208#127—2144no—
209#121—2144no—
210#121—2144no—
211#121—2148no—
212C4×D4—2144no—
213C2×C4⋊C4—1071no—
214C2×C4⋊C4—1072no—
215C2×C4⋊C4—1071no—
216C2×C22⋊C4—1072no—
217C2×C22⋊C4—1072no—
218C2×C22⋊C4—1072no—
219C2×C22⋊C4—1072no—
220C2×C22⋊C4—1072no—
221C2×C22⋊C4C2×D10711yescharacteristic
222C2×C22⋊C4C2×D10711yescharacteristic
223C2×C42C2×D10711yescharacteristic
224C2×C42C2×D10711yescharacteristic
225#95—1072no—
226#95C2×D10711yescharacteristic
227#95C2×D10711yescharacteristic
228C24—1072no—
229C24—1072no—
230C24C22×D10711yescharacteristic
231C2×D4—1074no—
232C2×D4—4282no—
233C2×D4—4282no—
234C2×D4—4282no—
235C2×D4—4282no—
236C2×D4—2144no—
237C2×D4—2144no—
238C2×D4—2144no—
239C2×D4—2144no—
240C2×D4—2144no—
241C2×D4—2144no—
242C2×D4—2142no—
243C2×D4—2142no—
244C2×D4—2142no—
245C2×D4—2144no—
246C2×D4—2144no—
247C2×D4—2142no—
248C2×D4—2142no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—1072no—
253C22×C4—1072no—
254C22×C4—4282no—
255C22×C4—2144no—
256C22×C4—2144no—
257C22×C4C22×D10711yescharacteristic
258C22×C4C22×D10711yescharacteristic
259C22×C4C22×D10711yescharacteristic
260C22×C4C22×D10711yescharacteristic
261C22×C4C22×D10711yescharacteristic
262C22×C4C22×D10711yescharacteristic
263C4⋊C4—1074no—
264C4⋊C4—2142no—
265C4⋊C4—2144no—
266C22⋊C4—22no—
267C22⋊C4—4282no—
268C22⋊C4—2144no—
269C22⋊C4—2144no—
270C22⋊C4—2144no—
271C22⋊C4—2144no—
272C22⋊C4D42814yescomplemented
273C42—22no—
274C42—22no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—1074no—
282C23—2142no—
283C23—2142no—
284C23—2142no—
285C23—2142no—
286C23—2142no—
287C23—2142no—
288C23—2142no—
289C23—2142no—
290C23—2142no—
291C23—2142no—
292C23—2142no—
293C23—2142no—
294C23—2142no—
295C23C2×D42812yes—
296C23C23×D10711yescharacteristic
297D4—4288no—
298D4—4288no—
299D4—4288no—
300D4—4288no—
301D4—4284no—
302D4—2148no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—44no—
316C2×C4—1074no—
317C2×C4—4288no—
318C2×C4—2142no—
319C2×C4—2142no—
320C2×C4—2142no—
321C2×C4—2142no—
322C2×C4—2142no—
323C2×C4D4×D10712yes—
324C2×C4D4×D10712yes—
325C2×C4C2×D42812yes—
326C2×C4C2×D42812yes—
327C2×C4#1313381812yes—
328C2×C4#1313381812yes—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—4282no—
337C22—4282no—
338C22—4282no—
339C22—4282no—
340C22—4282no—
341C22—4282no—
342C22—4282no—
343C22—4282no—
344C22—4282no—
345C22—4282no—
346C22—4282no—
347C22—2144no—
348C22—2144no—
349C22—2144no—
350C22C2×D4×D10711yescharacteristic
351C22C2×D4×D10711yescharacteristic
352C22C22×D42811yescharacteristic
353C22C2×#1313381811yescharacteristic
354C22C2×#1313381811yescharacteristic
355C22#1681215511yescharacteristic
356C22#1681215511yescharacteristic
357C4—22no—
358C4—22no—
359C4—22no—
360C4—41no—
361C4—41no—
362C4—4282no—
363C4—2144no—
364C4#1681208214yescomplemented
365C2—42no—
366C2—8562no—
367C2—4284no—
368C2C2×#1681208211yescharacteristic
369C2#2029317711yescharacteristic
370C2#2029323211yescharacteristic
371C2D4×D42811yescharacteristic
372C2D4×D42811yescharacteristic
373C2#2029327311yescharacteristic
374C2#2029329811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
FittingC4×C22⋊C4×C107C2
hypercenterC4×C22⋊C4D107
hypocenterC107#2428
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16812106C2semidirect
2. C2×#16812083C2semidirect
3. C2×#16812083C2semidirect
4. C2×#16812082C2semidirect
5. C2×C4×D428C2semidirect
6. #20292545C2semidirect
7. #20292536C2semidirect
8. #20292529C2semidirect
9. #20292525C2semidirect
10. #20292505C2semidirect
11. C4×C22⋊C4×C107C2semidirect
53. C2×D428D4semidirect
66. C4⋊Dic107D4semidirect
84. C22⋊C4×C107D4semidirect
174. C4×C107#121semidirect
188. C107#2428semidirect
199. C4×C22⋊C4D107semidirect
272. C22⋊C4D428semidirect
364. C4#16812082semidirect

Maximal subgroups

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

subgroupindex
C2×#168121062
C2×#168120832
C2×#168120822
C2×C4×D4282
#202925452
#202925362
#202925292
#202925252
#202925052
C4×C22⋊C4×C1072
#2428107