Finite Group Databasebeta

← #28344781

Subgroups — #28344781

Order 13696.

582 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812091C211yesmaximal, characteristic
2C2×C42×D107C211yesmaximal, characteristic, complemented
3#20292521C211yesmaximal, characteristic, complemented
4#20292520C211yesmaximal, characteristic, complemented
5#20292515C211yesmaximal, characteristic, complemented
6#20292514C211yesmaximal, characteristic, complemented
7#20292513C211yesmaximal, characteristic, complemented
8#20292512C211yesmaximal, characteristic, complemented
9#20292511C211yesmaximal, characteristic, complemented
10#20292503C211yesmaximal, characteristic
11#20292503C211yesmaximal, characteristic
12#20292501C211yesmaximal, characteristic, complemented
13#20292498C211yesmaximal, characteristic, complemented
14#20292489C211yesmaximal, characteristic, complemented
15#388×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C22×C4×D107C2211yescharacteristic
20#16812091—24no—
21C2×C4⋊Dic107C2211yescharacteristic
22C2×C4⋊Dic107C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×C22⋊Dic107C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C2×C4×Dic107C2211yescharacteristic
34C2×C4×Dic107C2211yescharacteristic
35C42×D107—24no—
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
53C23×D107C2311yescharacteristic
54C2×C22⋊D107—22no—
55C2×C22⋊D107—22no—
56C2×C22⋊D107—22no—
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C2×C4×D107—22no—
65C2×C4×D107—22no—
66C2×C4×D107—22no—
67C2×C4×D107—22no—
68C2×C4×D107—22no—
69C2×C4×D107—22no—
70C2×C4×D107—22no—
71C2×C4×D107—22no—
72C2×C4×D107D414yes—
73C4⋊Dic107—22no—
74C4⋊Dic107—22no—
75Dic107⋊C4—22no—
76Dic107⋊C4—22no—
77Dic107⋊C4—22no—
78C22⋊Dic107—22no—
79C22⋊Dic107—22no—
80C22⋊Dic107—22no—
81(C2×D107)⋊C4—22no—
82(C2×D107)⋊C4—22no—
83(C2×D107)⋊C4—22no—
84C4×Dic107—22no—
85C4×Dic107—22no—
86C4×Dic107—22no—
87C24×C107C2311yescharacteristic
88C22×C4×C107C2311yescharacteristic
89C22×C4×C107C2311yescharacteristic
90C22×C4×C107C2311yescharacteristic
91C22×C4×C107C2311yescharacteristic
92C22×C4×C107C2311yescharacteristic
93C22×C4×C107C2311yescharacteristic
94C4⋊C4×C107—22no—
95C22⋊C4×C107—22no—
96C22⋊C4×C107—22no—
97C22⋊C4×C107—22no—
98C42×C107—22no—
99C23×C107—21no—
100C23×C107—21no—
101C23×C107—21no—
102C23×C107—21no—
103C23×C107—21no—
104C23×C107—21no—
105C23×C107—21no—
106C23×C107C2411yescharacteristic
107C22×D107—21no—
108C22×D107—21no—
109C22×D107—21no—
110C22×D107—21no—
111C22×D107C2×D412yes—
112C22×D107#4112yes—
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×C107C2×D412yes—
130C2×C4×C107#4112yes—
131C2×C4×C107#4112yes—
132C22⋊D107—44no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107—21no—
138C2×Dic107—21no—
139C2×Dic107—21no—
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×Dic107—21no—
150C2×Dic107—21no—
151C2×Dic107C2×D412yes—
152C2×Dic107#4112yes—
153C2×Dic107#4112yes—
154C4×D107—28no—
155C4×D107—28no—
156C4×D107—28no—
157C22×C107—41no—
158C22×C107—41no—
159C22×C107—41no—
160C22×C107—41no—
161C22×C107—41no—
162C22×C107—41no—
163C22×C107—41no—
164C22×C107C22×D411yescharacteristic
165C22×C107C2×#4111yescharacteristic
166C22×C107C2×#4111yescharacteristic
167C22×C107C2×#4111yescharacteristic
168C22×C107C2×#4111yescharacteristic
169C22×C107C2×#4111yescharacteristic
170C22×C107C2×#4111yescharacteristic
171C2×D107—22no—
172C2×D107—22no—
173C2×D107—22no—
174C2×D107—22no—
175C2×D107—22no—
176C2×D107—22no—
177C2×D107#12314yes—
178C4×C107—22no—
179C4×C107—22no—
180C4×C107—22no—
181C4×C107—41no—
182C4×C107—41no—
183C4×C107—41no—
184Dic107—22no—
185Dic107—22no—
186Dic107—22no—
187Dic107—41no—
188Dic107—41no—
189Dic107—41no—
190Dic107—41no—
191C2×C107—81no—
192C2×C107C2×#12311yescharacteristic
193C2×C107#52511yescharacteristic
194C2×C107#52511yescharacteristic
195C2×C107#52911yescharacteristic
196C2×C107#52911yescharacteristic
197C2×C107#52911yescharacteristic
198C2×C107#52911yescharacteristic
199D107—24no—
200#2853—1071nomaximal, Sylow
201C107#285311yescharacteristic, complemented, Sylow
202C2×#123—1071no—
203C22×C42—1071no—
204#388—1071no—
205#388—1071no—
206#388—1071no—
207#388D10711yescharacteristic, complemented
208#387—1071no—
209#387—1071no—
210#387—1071no—
211#387—1071no—
212#386—1071no—
213#386—1071no—
214#385—1071no—
215#385—1071no—
216#381—1071no—
217C22×D4—1071no—
218C23×C4—1071no—
219C23×C4—1071no—
220C23×C4—1071no—
221#123—2144no—
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⋊C4C2×D10711yescharacteristic
235C2×C22⋊C4C2×D10711yescharacteristic
236C2×C22⋊C4C2×D10711yescharacteristic
237C2×C42—1071no—
238C2×C42—1071no—
239C2×C42—1071no—
240C2×C42—2144no—
241C2×C42C2×D10711yescharacteristic
242#95—1071no—
243#95—1071no—
244#95—1071no—
245#95—1071no—
246#95—1071no—
247#95—1071no—
248#95—1071no—
249#95—1071no—
250#95—1071no—
251#95—1071no—
252#95C2×D10711yescharacteristic
253#95C2×D10711yescharacteristic
254C24—1071no—
255C24C22×D10711yescharacteristic
256C2×D4—2142no—
257C2×D4—2142no—
258C2×D4—2142no—
259C22×C4—1071no—
260C22×C4—1071no—
261C22×C4—1071no—
262C22×C4—1074no—
263C22×C4—1071no—
264C22×C4—1071no—
265C22×C4—1071no—
266C22×C4—1071no—
267C22×C4—2142no—
268C22×C4—2142no—
269C22×C4—2142no—
270C22×C4—2142no—
271C22×C4—2142no—
272C22×C4—2142no—
273C22×C4—2142no—
274C22×C4—2142no—
275C22×C4C22×D10711yescharacteristic
276C22×C4C22×D10711yescharacteristic
277C22×C4C22×D10711yescharacteristic
278C22×C4C22×D10711yescharacteristic
279C22×C4C22×D10711yescharacteristic
280C22×C4C22×D10711yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—2142no—
283C4⋊C4—2142no—
284C4⋊C4—2142no—
285C4⋊C4—2142no—
286C4⋊C4—2142no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—2142no—
291C22⋊C4—2142no—
292C22⋊C4—2142no—
293C22⋊C4—2142no—
294C22⋊C4—2142no—
295C22⋊C4—2142no—
296C42—22no—
297C42—2142no—
298C42—2142no—
299C42—2142no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—1072no—
308C23—1072no—
309C23—1072no—
310C23—2141no—
311C23—2141no—
312C23—2141no—
313C23—2141no—
314C23C23×D10711yescharacteristic
315D4—4284no—
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—1072no—
332C2×C4—1072no—
333C2×C4—1072no—
334C2×C4—2148no—
335C2×C4—2148no—
336C2×C4—2148no—
337C2×C4—2141no—
338C2×C4—2141no—
339C2×C4—2141no—
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×C4D4×D10712yes—
356C2×C4#1313381712yes—
357C2×C4#1313381812yes—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—1074no—
366C22—2142no—
367C22—2142no—
368C22—2142no—
369C22—2142no—
370C22—2142no—
371C22—2142no—
372C22C2×D4×D10711yescharacteristic
373C22#41×D10711yescharacteristic
374C22#41×D10711yescharacteristic
375C22#41×D10711yescharacteristic
376C22#41×D10711yescharacteristic
377C22C2×#1313381711yescharacteristic
378C22C2×#1313381811yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—4281no—
386C4—4281no—
387C4—4281no—
388C4—4281no—
389C4—2142no—
390C4—2142no—
391C4—2142no—
392C2—81no—
393C2—2144no—
394C2#123×D10711yescharacteristic
395C2#2029313611yescharacteristic
396C2#2029313711yescharacteristic
397C2#2029315511yescharacteristic
398C2#2029315611yescharacteristic
399C2#2029315911yescharacteristic
400C2#2029316011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#388×C107C2
prime radicalC22×C22⋊D107C22
hypercenter#388D107
hypocenterC107#2853
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C42×D107C2semidirect
3. #20292521C2semidirect
4. #20292520C2semidirect
5. #20292515C2semidirect
6. #20292514C2semidirect
7. #20292513C2semidirect
8. #20292512C2semidirect
9. #20292511C2semidirect
12. #20292501C2semidirect
13. #20292498C2semidirect
14. #20292489C2semidirect
15. #388×C107C2semidirect
201. C107#2853semidirect
207. #388D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120912
C2×C42×D1072
#202925212
#202925202
#202925152
#202925142
#202925132
#202925122
#202925112
#202925032
#202925012
#202924982
#202924892
#388×C1072
#2853107