Finite Group Databasebeta

← #28339897

Subgroups — #28339897

Order 13696.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812080C212yesmaximal, complemented
2C2×#16812080C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D107C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D107C211yesmaximal, characteristic, complemented
5#20292550C212yesmaximal, complemented
6#20292541C212yesmaximal, complemented
7#20292530C211yesmaximal, characteristic, complemented
8#20292526C211yesmaximal, characteristic, complemented
9#20292503C212yesmaximal, complemented
10#20292487C211yesmaximal, characteristic, complemented
11C2×#121×C107C211yesmaximal, characteristic, complemented
12C22×C22⋊D107C2212yes—
13C22×C22⋊D107C2211yescharacteristic
14C22×C4×D107C2212yes—
15C22×C4×D107C2211yescharacteristic
16#16812080—28no—
17#16812080—24no—
18C4×C22⋊D107—24no—
19C2×C4⋊Dic107C2211yescharacteristic
20C2×C4⋊Dic107C2211yescharacteristic
21C2×C4⋊Dic107C2212yes—
22C2×Dic107⋊C4C2212yes—
23C2×Dic107⋊C4C2211yescharacteristic
24C4⋊C4×D107—24no—
25C2×C22⋊Dic107C2212yes—
26C2×C22⋊Dic107C2212yes—
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2212yes—
29C2×C22⋊Dic107C2212yes—
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×C4×Dic107C2211yescharacteristic
32C107⋊#95C2212yes—
33C107⋊#95C2212yes—
34C22×D4×C107C2211yescharacteristic
35C22×D4×C107C2212yes—
36C23×C4×C107C2211yescharacteristic
37#121×C107—24no—
38C2×C4⋊C4×C107C2211yescharacteristic
39C2×C22⋊C4×C107C2212yes—
40C23×D107C2311yescharacteristic
41C2×C22⋊D107—22no—
42C2×C22⋊D107—22no—
43C2×C22⋊D107—24no—
44C2×C22⋊D107—24no—
45C2×C22⋊D107—24no—
46C2×C22⋊D107D414yescomplemented
47C22×Dic107C2311yescharacteristic
48C22×Dic107C2312yes—
49C22×Dic107C2312yes—
50C22×Dic107C2311yescharacteristic
51C22×Dic107C2311yescharacteristic
52C2×C4×D107—22no—
53C2×C4×D107—22no—
54C2×C4×D107—24no—
55C2×C4×D107—24no—
56C2×C4×D107—42no—
57C2×C4×D107D414yescomplemented
58C4⋊Dic107—22no—
59C4⋊Dic107—22no—
60C4⋊Dic107—24no—
61Dic107⋊C4—24no—
62Dic107⋊C4—22no—
63C22⋊Dic107—24no—
64C22⋊Dic107—22no—
65C22⋊Dic107—24no—
66C22⋊Dic107—24no—
67C22⋊Dic107—42no—
68(C2×D107)⋊C4—22no—
69C4×Dic107—22no—
70C24×C107C2312yes—
71C24×C107C2311yescharacteristic
72C2×D4×C107—24no—
73C2×D4×C107—22no—
74C2×D4×C107—24no—
75C2×D4×C107—22no—
76C2×D4×C107—22no—
77C2×D4×C107—42no—
78C22×C4×C107—22no—
79C22×C4×C107—22no—
80C22×C4×C107—22no—
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2312yes—
83C22×C4×C107C2311yescharacteristic
84C4⋊C4×C107D414yescomplemented
85C22⋊C4×C107—24no—
86C23×C107—21no—
87C23×C107—21no—
88C23×C107—21no—
89C23×C107—21no—
90C23×C107—21no—
91C23×C107—21no—
92C23×C107—22no—
93C23×C107—22no—
94C23×C107—22no—
95C23×C107—22no—
96C23×C107—22no—
97C23×C107—22no—
98C23×C107—22no—
99C23×C107C2×D412yes—
100C23×C107C2411yescharacteristic
101C22×D107—21no—
102C22×D107—21no—
103C22×D107—21no—
104C22×D107—21no—
105C22×D107C2×D412yes—
106C22×D107C2×D412yes—
107C22×D107#4112yes—
108D4×C107—48no—
109D4×C107—44no—
110C2×C4×C107—22no—
111C2×C4×C107—22no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—44no—
116C2×C4×C107C2×D412yes—
117C2×C4×C107C2×D414yes—
118C2×C4×C107C2×D412yes—
119C2×C4×C107#4112yes—
120C22⋊D107—28no—
121C22⋊D107—48no—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—22no—
128C2×Dic107—22no—
129C2×Dic107—22no—
130C2×Dic107—22no—
131C2×Dic107—22no—
132C2×Dic107—21no—
133C2×Dic107—22no—
134C2×Dic107—21no—
135C2×Dic107C2×D412yes—
136C2×Dic107C2×D412yes—
137C4×D107—28no—
138C4×D107—48no—
139C22×C107—22no—
140C22×C107—22no—
141C22×C107—22no—
142C22×C107—41no—
143C22×C107—41no—
144C22×C107—41no—
145C22×C107—41no—
146C22×C107—42no—
147C22×C107—42no—
148C22×C107—42no—
149C22×C107—42no—
150C22×C107—42no—
151C22×C107—42no—
152C22×C107—42no—
153C22×C107C22×D411yescharacteristic
154C22×C107C22×D411yescharacteristic
155C22×C107C22×D411yescharacteristic
156C22×C107C2×#4111yescharacteristic
157C22×C107C2×#4111yescharacteristic
158C22×C107H(5,𝔽2)11yescharacteristic
159C22×C1072−1+411yescharacteristic
160C2×D107—22no—
161C2×D107—22no—
162C2×D107—22no—
163C2×D107—22no—
164C2×D107—22no—
165C2×D107—22no—
166C2×D107#12114yescomplemented
167C4×C107—24no—
168C4×C107—41no—
169C4×C107#12114yescomplemented
170Dic107—22no—
171Dic107—22no—
172Dic107—42no—
173Dic107—41no—
174Dic107—42no—
175C2×C107—42no—
176C2×C107—82no—
177C2×C107C2×#12111yescharacteristic
178C2×C107C2×#12111yescharacteristic
179C2×C107#53711yescharacteristic
180C2×C107D4211yescharacteristic
181C2×C107#54711yescharacteristic
182C2×C107#54811yescharacteristic
183C2×C107#55311yescharacteristic
184D107—24no—
185#2416—1071nomaximal, Sylow
186C107#241611yescharacteristic, complemented, Sylow
187C2×#121—1072no—
188C2×#121—1071no—
189C2×#121D10711yescharacteristic, complemented
190C2×C4×D4—1071no—
191C22×C4⋊C4—1071no—
192#396—1072no—
193#394—1072no—
194#390—1071no—
195#389—1071no—
196#386—1072no—
197#380—1071no—
198C22×D4—1071no—
199C22×D4—1072no—
200C22×D4C2×D10711yescharacteristic
201C22×D4C2×D10712yes—
202C23×C4—1071no—
203C23×C4—1072no—
204C23×C4C2×D10711yescharacteristic
205#121—24no—
206#121—2144no—
207#121—2148no—
208C4×D4—2144no—
209C2×C4⋊C4—1072no—
210C2×C4⋊C4—1071no—
211C2×C4⋊C4—1071no—
212C2×C4⋊C4—1071no—
213C2×C4⋊C4—1072no—
214C2×C4⋊C4—2144no—
215C2×C4⋊C4C2×D10711yescharacteristic
216C2×C22⋊C4—1072no—
217C2×C22⋊C4—1071no—
218C2×C22⋊C4—1072no—
219C2×C22⋊C4—1072no—
220C2×C22⋊C4—1072no—
221C2×C22⋊C4—1071no—
222C2×C22⋊C4C2×D10712yes—
223C2×C42—1071no—
224#95—1072no—
225#95—1072no—
226C24—1071no—
227C24C22×D10712yes—
228C24C22×D10711yescharacteristic
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—24no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—42no—
235C2×D4—1074no—
236C2×D4—2144no—
237C2×D4—2144no—
238C2×D4—2144no—
239C2×D4—2142no—
240C2×D4—2142no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—1071no—
245C22×C4—1071no—
246C22×C4—1074no—
247C22×C4—1071no—
248C22×C4—1072no—
249C22×C4—1072no—
250C22×C4—4282no—
251C22×C4—2144no—
252C22×C4—2144no—
253C22×C4—2142no—
254C22×C4—2142no—
255C22×C4C22×D10711yescharacteristic
256C22×C4C22×D10712yes—
257C22×C4C22×D10711yescharacteristic
258C4⋊C4—2142no—
259C4⋊C4—2144no—
260C4⋊C4—2142no—
261C4⋊C4—2144no—
262C4⋊C4—2142no—
263C4⋊C4C22⋊D10714yescomplemented
264C22⋊C4—24no—
265C22⋊C4—4282no—
266C22⋊C4—2142no—
267C22⋊C4—2142no—
268C22⋊C4—2144no—
269C22⋊C4—2144no—
270C22⋊C4—2144no—
271C42—2142no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—22no—
279C23—22no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—1072no—
286C23—1072no—
287C23—1072no—
288C23—2141no—
289C23—2141no—
290C23—2141no—
291C23—2141no—
292C23D4×D10712yes—
293C23C23×D10711yescharacteristic
294D4—48no—
295D4—44no—
296D4—4288no—
297D4—2148no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—44no—
304C2×C4—1072no—
305C2×C4—1072no—
306C2×C4—4288no—
307C2×C4—2141no—
308C2×C4—2142no—
309C2×C4—2142no—
310C2×C4—2142no—
311C2×C4—2142no—
312C2×C4—2142no—
313C2×C4—2141no—
314C2×C4—2142no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4—2148no—
321C2×C4D4×D10712yes—
322C2×C4C2×C22⋊D10714yes—
323C2×C4C2×C22⋊D10712yes—
324C2×C4#1313381712yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—1074no—
340C22—2142no—
341C22—2142no—
342C22—2142no—
343C22—2142no—
344C22—2142no—
345C22—2142no—
346C22C2×D4×D10711yescharacteristic
347C22C2×D4×D10711yescharacteristic
348C22C22×C22⋊D10711yescharacteristic
349C22#41×D10711yescharacteristic
350C22C2×#1313381711yescharacteristic
351C22#1681215411yescharacteristic
352C22#1681215611yescharacteristic
353C4—24no—
354C4—41no—
355C4—4281no—
356C4—4282no—
357C4—4282no—
358C4—2142no—
359C4—2142no—
360C4#1681208014yescomplemented
361C2—42no—
362C2—82no—
363C2—2144no—
364C2#121×D10711yescharacteristic
365C2C2×#1681208011yescharacteristic
366C2#2029320611yescharacteristic
367C2D4×C22⋊D10711yescharacteristic
368C2#2029327711yescharacteristic
369C2#2029328411yescharacteristic
370C2#2029332411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
FittingC2×#121×C107C2
hypercenterC2×#121D107
hypocenterC107#2416
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16812080C2semidirect
2. C2×#16812080C2semidirect
3. C2×C4×C22⋊D107C2semidirect
4. C2×C4⋊C4×D107C2semidirect
5. #20292550C2semidirect
6. #20292541C2semidirect
7. #20292530C2semidirect
8. #20292526C2semidirect
9. #20292503C2semidirect
10. #20292487C2semidirect
11. C2×#121×C107C2semidirect
46. C2×C22⋊D107D4semidirect
57. C2×C4×D107D4semidirect
84. C4⋊C4×C107D4semidirect
166. C2×D107#121semidirect
169. C4×C107#121semidirect
186. C107#2416semidirect
189. C2×#121D107semidirect
263. C4⋊C4C22⋊D107semidirect
360. C4#16812080semidirect

Maximal subgroups

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

subgroupindex
C2×#168120802
C2×C4×C22⋊D1072
C2×C4⋊C4×D1072
#202925502
#202925412
#202925302
#202925262
#202925032
#202924872
C2×#121×C1072
#2416107