Finite Group Databasebeta

← #28339719

Subgroups — #28339719

Order 13696.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D107)⋊C4C211yesmaximal, characteristic
2C2×#16812065C211yesmaximal, characteristic, complemented
3#20292568C211yesmaximal, characteristic, complemented
4#20292562C211yesmaximal, characteristic, complemented
5#20292561C211yesmaximal, characteristic, complemented
6#20292556C211yesmaximal, characteristic, complemented
7#20292555C211yesmaximal, characteristic, complemented
8#20292543C211yesmaximal, characteristic
9#20292542C211yesmaximal, characteristic
10C4⋊C4×Dic107C211yesmaximal, characteristic, complemented
11#20292478C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic107C211yesmaximal, characteristic, complemented
13#20292474C211yesmaximal, characteristic, complemented
14#20292474C211yesmaximal, characteristic, complemented
15#397×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C23×Dic107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19(C22⋊D107)⋊C4—24no—
20#16812065—24no—
21C2×C4⋊Dic107C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×C4×Dic107C2211yescharacteristic
35C2×C4×Dic107C2211yescharacteristic
36C2×C4×Dic107C2211yescharacteristic
37C2×C4×Dic107C2211yescharacteristic
38C2×C4×Dic107C2211yescharacteristic
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
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C2×C22⋊D107—22no—
55C2×C22⋊D107—22no—
56C2×C22⋊D107—22no—
57C22×Dic107—22no—
58C22×Dic107—22no—
59C22×Dic107D414yes—
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C2×C4×D107—22no—
68C2×C4×D107—22no—
69C2×C4×D107—22no—
70C4⋊Dic107—22no—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—22no—
75Dic107⋊C4—22no—
76C22⋊Dic107—22no—
77C22⋊Dic107—22no—
78(C2×D107)⋊C4—22no—
79(C2×D107)⋊C4—22no—
80(C2×D107)⋊C4—22no—
81(C2×D107)⋊C4—22no—
82(C2×D107)⋊C4—22no—
83C4×Dic107—22no—
84C4×Dic107—22no—
85C4×Dic107—22no—
86C4×Dic107—22no—
87C4×Dic107—22no—
88C24×C107C2311yescharacteristic
89C22×C4×C107C2311yescharacteristic
90C22×C4×C107C2311yescharacteristic
91C22×C4×C107C2311yescharacteristic
92C22×C4×C107C2311yescharacteristic
93C22×C4×C107C2311yescharacteristic
94C22×C4×C107C2311yescharacteristic
95C4⋊C4×C107—22no—
96C22⋊C4×C107—22no—
97C22⋊C4×C107—22no—
98C22⋊C4×C107—22no—
99C23×C107—21no—
100C23×C107—21no—
101C23×C107—21no—
102C23×C107—21no—
103C23×C107—21no—
104C23×C107—21no—
105C23×C107C2×D412yes—
106C23×C107C2411yescharacteristic
107C22×D107—21no—
108C22×D107—21no—
109C22×D107—21no—
110C22×D107—21no—
111C22×D107—21no—
112C22×D107—21no—
113C22×D107#4112yes—
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—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107—21no—
129C2×C4×C107—21no—
130C2×C4×C107—21no—
131C2×C4×C107#4112yes—
132C22⋊D107—28no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107—21no—
138C2×Dic107—21no—
139C2×Dic107—28no—
140C2×Dic107—21no—
141C2×Dic107—21no—
142C2×Dic107—21no—
143C2×Dic107—21no—
144C2×Dic107—21no—
145C2×Dic107—21no—
146C2×Dic107—21no—
147C2×Dic107—21no—
148C2×Dic107—21no—
149C2×Dic107C2×D412yes—
150C2×Dic107C2×D412yes—
151C2×Dic107#4112yes—
152C2×Dic107#4112yes—
153C2×Dic107#4112yes—
154C2×Dic107#4112yes—
155C4×D107—44no—
156C22×C107—22no—
157C22×C107—22no—
158C22×C107—22no—
159C22×C107—41no—
160C22×C107—41no—
161C22×C107—41no—
162C22×C107—41no—
163C22×C107C22×D411yescharacteristic
164C22×C107C2×#4111yescharacteristic
165C22×C107C2×#4111yescharacteristic
166C22×C107C2×#4111yescharacteristic
167C22×C107C2×#4111yescharacteristic
168C22×C107C2×#4111yescharacteristic
169C22×C107C2×#4111yescharacteristic
170C2×D107—22no—
171C2×D107—22no—
172C2×D107—22no—
173C2×D107—41no—
174C2×D107—41no—
175C2×D107—41no—
176C2×D107—41no—
177C4×C107—22no—
178C4×C107—41no—
179C4×C107—41no—
180C4×C107—41no—
181C4×C107—41no—
182C4×C107—41no—
183Dic107—22no—
184Dic107—22no—
185Dic107—22no—
186Dic107—41no—
187Dic107—41no—
188Dic107—41no—
189Dic107#12314yes—
190C2×C107—42no—
191C2×C107C2×#12311yescharacteristic
192C2×C107#52511yescharacteristic
193C2×C107#52911yescharacteristic
194C2×C107#52911yescharacteristic
195C2×C107#52911yescharacteristic
196C2×C107#52911yescharacteristic
197C2×C107#53211yescharacteristic
198D107—42no—
199#2395—1071nomaximal, Sylow
200C107#239511yescharacteristic, complemented, Sylow
201C2×C4×D4—1071no—
202C2×#117—1071no—
203#400—1071no—
204#399—1071no—
205#398—1071no—
206#397—1071no—
207#397—1071no—
208#397D10711yescharacteristic, complemented
209#394—1071no—
210#394—1071no—
211C4×C4⋊C4—1071no—
212C4×C4⋊C4—1071no—
213C4×C22⋊C4—1071no—
214C4×C22⋊C4—1071no—
215C4×C22⋊C4—1071no—
216C22×D4—1071no—
217C23×C4—1071no—
218C23×C4—1071no—
219C4×D4—2144no—
220#117—2144no—
221C2×C4⋊C4—1071no—
222C2×C4⋊C4—1071no—
223C2×C4⋊C4—1071no—
224C2×C4⋊C4—1071no—
225C2×C4⋊C4—1071no—
226C2×C4⋊C4—1071no—
227C2×C4⋊C4C2×D10711yescharacteristic
228C2×C22⋊C4—1071no—
229C2×C22⋊C4—1071no—
230C2×C22⋊C4—1071no—
231C2×C22⋊C4—1071no—
232C2×C22⋊C4—1071no—
233C2×C22⋊C4—1071no—
234C2×C22⋊C4—1071no—
235C2×C22⋊C4C2×D10711yescharacteristic
236C2×C22⋊C4C2×D10711yescharacteristic
237C2×C22⋊C4C2×D10711yescharacteristic
238C2×C42—1071no—
239C2×C42—1071no—
240C2×C42—1071no—
241C2×C42—1071no—
242C2×C42—1071no—
243#95—1071no—
244#95—1071no—
245#95—1071no—
246#95—1071no—
247#95—1071no—
248#95—1071no—
249#95—1071no—
250#95C2×D10711yescharacteristic
251#95C2×D10711yescharacteristic
252#95C2×D10711yescharacteristic
253C24—1071no—
254C24C22×D10711yescharacteristic
255C2×D4—2142no—
256C2×D4—2142no—
257C2×D4—2142no—
258C22×C4—1071no—
259C22×C4—1074no—
260C22×C4—1071no—
261C22×C4—1071no—
262C22×C4—1071no—
263C22×C4—1071no—
264C22×C4—1071no—
265C22×C4—1071no—
266C22×C4—2142no—
267C22×C4—2142no—
268C22×C4—2142no—
269C22×C4—2142no—
270C22×C4—2142no—
271C22×C4C22×D10711yescharacteristic
272C22×C4C22×D10711yescharacteristic
273C22×C4C22×D10711yescharacteristic
274C22×C4C22×D10711yescharacteristic
275C22×C4C22×D10711yescharacteristic
276C22×C4C22×D10711yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—2142no—
279C4⋊C4—2142no—
280C4⋊C4—2142no—
281C4⋊C4—2142no—
282C4⋊C4—2142no—
283C4⋊C4—2142no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—2142no—
288C22⋊C4—2142no—
289C22⋊C4—2142no—
290C22⋊C4—2142no—
291C22⋊C4—2142no—
292C22⋊C4—2142no—
293C22⋊C4—2142no—
294C42—2142no—
295C42—2142no—
296C42—2142no—
297C42—2142no—
298C42—2142no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—1072no—
306C23—2141no—
307C23—2141no—
308C23—2141no—
309C23—2141no—
310C23—2141no—
311C23—2141no—
312C23D4×D10712yes—
313C23C23×D10711yescharacteristic
314D4—2148no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1072no—
333C2×C4—1072no—
334C2×C4—1072no—
335C2×C4—1072no—
336C2×C4—1072no—
337C2×C4—1072no—
338C2×C4—4284no—
339C2×C4—2148no—
340C2×C4—2141no—
341C2×C4—2141no—
342C2×C4—2141no—
343C2×C4—2141no—
344C2×C4—2141no—
345C2×C4—2141no—
346C2×C4—2141no—
347C2×C4—2141no—
348C2×C4—2141no—
349C2×C4—2141no—
350C2×C4—2141no—
351C2×C4—2141no—
352C2×C4—2141no—
353C2×C4—2141no—
354C2×C4—2141no—
355C2×C4#1313381712yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—4281no—
364C22—4281no—
365C22—4281no—
366C22—4281no—
367C22—2142no—
368C22—2142no—
369C22—2142no—
370C22C2×D4×D10711yescharacteristic
371C22#41×D10711yescharacteristic
372C22#41×D10711yescharacteristic
373C22#41×D10711yescharacteristic
374C22#41×D10711yescharacteristic
375C22#41×D10711yescharacteristic
376C22C2×#1313381711yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—1074no—
384C4—4281no—
385C4—4281no—
386C4—4281no—
387C4—2142no—
388C4—2142no—
389C4—2142no—
390C2—42no—
391C2—4282no—
392C2#123×D10711yescharacteristic
393C2#2029313511yescharacteristic
394C2#2029315411yescharacteristic
395C2#2029315611yescharacteristic
396C2#2029316011yescharacteristic
397C2#2029316011yescharacteristic
398C2#2029317211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#397×C107C2
prime radicalC22×C22⋊D107C22
hypercenter#397D107
hypocenterC107#2395
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#16812065C2semidirect
3. #20292568C2semidirect
4. #20292562C2semidirect
5. #20292561C2semidirect
6. #20292556C2semidirect
7. #20292555C2semidirect
10. C4⋊C4×Dic107C2semidirect
11. #20292478C2semidirect
12. C22⋊C4×Dic107C2semidirect
13. #20292474C2semidirect
14. #20292474C2semidirect
15. #397×C107C2semidirect
200. C107#2395semidirect
208. #397D107semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D107)⋊C42
C2×#168120652
#202925682
#202925622
#202925612
#202925562
#202925552
#202925432
#202925422
C4⋊C4×Dic1072
#202924782
C22⋊C4×Dic1072
#202924742
#397×C1072
#2395107