Finite Group Databasebeta

← #28339932

Subgroups — #28339932

Order 13696.

560 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812090C211yesmaximal, characteristic
2#20292565C211yesmaximal, characteristic, complemented
3#20292558C211yesmaximal, characteristic, complemented
4#20292555C211yesmaximal, characteristic, complemented
5#20292555C211yesmaximal, characteristic, complemented
6#20292511C211yesmaximal, characteristic, complemented
7#20292511C211yesmaximal, characteristic, complemented
8#20292507C211yesmaximal, characteristic
9#20292500C211yesmaximal, characteristic, complemented
10#20292500C211yesmaximal, characteristic, complemented
11#20292490C211yesmaximal, characteristic, complemented
12#20292488C211yesmaximal, characteristic, complemented
13#20292485C211yesmaximal, characteristic, complemented
14C2×C107⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×D4×C107C211yesmaximal, characteristic
16C23×Dic107C2211yescharacteristic
17C23×Dic107C2211yescharacteristic
18#16812090—24no—
19C2×Dic107⋊C4C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×C22⋊Dic107C2211yescharacteristic
26C2×C22⋊Dic107C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C107⋊#95C2211yescharacteristic
32C107⋊#95C2211yescharacteristic
33C107⋊#95C2211yescharacteristic
34C107⋊#95C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C22×D4×C107C2211yescharacteristic
46C23×C4×C107C2211yescharacteristic
47C23×C4×C107C2211yescharacteristic
48C4×D4×C107—24no—
49C2×C4⋊C4×C107C2211yescharacteristic
50C2×C22⋊C4×C107C2211yescharacteristic
51C2×C22⋊C4×C107C2211yescharacteristic
52C2×C42×C107C2211yescharacteristic
53C22×Dic107—22no—
54C22×Dic107—22no—
55C22×Dic107—22no—
56C22×Dic107—22no—
57C22×Dic107—22no—
58C22×Dic107—41no—
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67Dic107⋊C4—22no—
68Dic107⋊C4—22no—
69Dic107⋊C4—22no—
70Dic107⋊C4—22no—
71Dic107⋊C4—41no—
72Dic107⋊C4—41no—
73C22⋊Dic107—22no—
74C22⋊Dic107—22no—
75C22⋊Dic107—22no—
76C22⋊Dic107—22no—
77C22⋊Dic107—22no—
78C22⋊Dic107—41no—
79C24×C107C2311yescharacteristic
80C24×C107C2311yescharacteristic
81C2×D4×C107—22no—
82C2×D4×C107—22no—
83C2×D4×C107D414yes—
84C22×C4×C107—22no—
85C22×C4×C107—22no—
86C22×C4×C107—22no—
87C22×C4×C107—22no—
88C22×C4×C107—41no—
89C22×C4×C107—41no—
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—
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×C107—21no—
107C23×C107—21no—
108C23×C107—21no—
109C23×C107C2×D412yes—
110C23×C107C2×D412yes—
111C23×C107#4112yes—
112C23×C107#4112yes—
113C23×C107C2411yescharacteristic
114D4×C107—28no—
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—44no—
129C2×C4×C107—44no—
130C2×C4×C107C2×D412yes—
131C2×C4×C107#4112yes—
132C2×Dic107—21no—
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×Dic107—21no—
152C2×Dic107—21no—
153C2×Dic107—21no—
154C2×Dic107—21no—
155C2×Dic107—44no—
156C2×Dic107—44no—
157C2×Dic107#4112yes—
158C22×C107—22no—
159C22×C107—22no—
160C22×C107—22no—
161C22×C107—22no—
162C22×C107—22no—
163C22×C107—22no—
164C22×C107—22no—
165C22×C107—22no—
166C22×C107—22no—
167C22×C107—41no—
168C22×C107—41no—
169C22×C107—41no—
170C22×C107—41no—
171C22×C107#12314yes—
172C22×C107C22×D411yescharacteristic
173C22×C107C2×#4111yescharacteristic
174C22×C107C2×#4111yescharacteristic
175C22×C107C2×#4111yescharacteristic
176C22×C107C2×#4111yescharacteristic
177C22×C107H(5,𝔽2)11yescharacteristic
178C22×C1072−1+411yescharacteristic
179C4×C107—22no—
180C4×C107—22no—
181C4×C107—41no—
182C4×C107—41no—
183C4×C107—41no—
184Dic107—22no—
185Dic107—41no—
186Dic107—41no—
187Dic107—41no—
188Dic107—41no—
189Dic107—41no—
190Dic107—41no—
191Dic107—41no—
192C2×C107—24no—
193C2×C107—42no—
194C2×C107C2×#12311yescharacteristic
195C2×C107#52911yescharacteristic
196C2×C107#53911yescharacteristic
197C2×C107#54611yescharacteristic
198C2×C107#54711yescharacteristic
199C2×C107#55111yescharacteristic
200C2×C107#55211yescharacteristic
201#2419—1071nomaximal, Sylow
202C107#241911yescharacteristic, complemented, Sylow
203C2×#123—1071no—
204C2×C4×D4D10711yescharacteristic
205#400—1071no—
206#398—1071no—
207#397—1071no—
208#397—1071no—
209#387—1071no—
210#387—1071no—
211#386—1071no—
212#385—1071no—
213#385—1071no—
214#381—1071no—
215#381—1071no—
216#380—1071no—
217C2×#95—1071no—
218C22×D4C2×D10711yescharacteristic
219C23×C4—1071no—
220C23×C4—1071no—
221C23×C4C2×D10711yescharacteristic
222C23×C4C2×D10711yescharacteristic
223#123—2144no—
224C4×D4—24no—
225C2×C4⋊C4—1071no—
226C2×C4⋊C4—1071no—
227C2×C4⋊C4—1071no—
228C2×C4⋊C4—1071no—
229C2×C4⋊C4—1071no—
230C2×C4⋊C4—1071no—
231C2×C4⋊C4C2×D10711yescharacteristic
232C2×C22⋊C4—1071no—
233C2×C22⋊C4—1071no—
234C2×C22⋊C4—1071no—
235C2×C22⋊C4—1071no—
236C2×C22⋊C4—1071no—
237C2×C22⋊C4—1071no—
238C2×C22⋊C4C2×D10711yescharacteristic
239C2×C22⋊C4C2×D10711yescharacteristic
240C2×C42C2×D10711yescharacteristic
241#95—1071no—
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#95—1071no—
253#95—1071no—
254#95—1071no—
255C24C22×D10711yescharacteristic
256C24C22×D10711yescharacteristic
257C2×D4—22no—
258C2×D4—22no—
259C2×D4C22⋊D10714yes—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—1071no—
267C22×C4—1071no—
268C22×C4—1071no—
269C22×C4—1071no—
270C22×C4—1071no—
271C22×C4—1071no—
272C22×C4—1071no—
273C22×C4—1071no—
274C22×C4—4281no—
275C22×C4—2142no—
276C22×C4—2142no—
277C22×C4—2142no—
278C22×C4—2142no—
279C22×C4—2142no—
280C22×C4C22×D10711yescharacteristic
281C22×C4C22×D10711yescharacteristic
282C22×C4C22×D10711yescharacteristic
283C22×C4C22×D10711yescharacteristic
284C22×C4C22×D10711yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—4281no—
287C4⋊C4—4281no—
288C4⋊C4—2142no—
289C4⋊C4—2142no—
290C4⋊C4—2142no—
291C4⋊C4—2142no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—4281no—
295C22⋊C4—2142no—
296C22⋊C4—2142no—
297C22⋊C4—2142no—
298C22⋊C4—2142no—
299C22⋊C4—2142no—
300C42—22no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23C2×C22⋊D10712yes—
312C23C2×C22⋊D10712yes—
313C23#1313381812yes—
314C23#1313381812yes—
315C23C23×D10711yescharacteristic
316D4—28no—
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—44no—
331C2×C4—44no—
332C2×C4—1072no—
333C2×C4—4284no—
334C2×C4—4284no—
335C2×C4—2141no—
336C2×C4—2141no—
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×C4—2141no—
356C2×C4—2141no—
357C2×C4—2141no—
358C2×C4C2×C22⋊D10712yes—
359C2×C4#1313381712yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22#1681209214yes—
374C22C22×C22⋊D10711yescharacteristic
375C22#41×D10711yescharacteristic
376C22C2×#1313381711yescharacteristic
377C22C2×#1313381811yescharacteristic
378C22C2×#1313381811yescharacteristic
379C22#1681215411yescharacteristic
380C22#1681215611yescharacteristic
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—4281no—
387C4—4281no—
388C4—4281no—
389C4—4281no—
390C4—4281no—
391C4—4281no—
392C4—4281no—
393C4—2142no—
394C2—24no—
395C2—42no—
396C2C2×#1681209211yescharacteristic
397C2#2029315711yescharacteristic
398C2#2029321911yescharacteristic
399C2#2029327111yescharacteristic
400C2#2029327611yescharacteristic
401C2#2029330611yescharacteristic
402C2#2029331711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
FittingC2×C4×D4×C107C2
prime radicalC22×D4×C107C22
hypercenterC2×C4×D4D107
hypocenterC107#2419
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #20292565C2semidirect
3. #20292558C2semidirect
4. #20292555C2semidirect
5. #20292555C2semidirect
6. #20292511C2semidirect
7. #20292511C2semidirect
9. #20292500C2semidirect
10. #20292500C2semidirect
11. #20292490C2semidirect
12. #20292488C2semidirect
13. #20292485C2semidirect
14. C2×C107⋊#95C2semidirect
202. C107#2419semidirect

Maximal subgroups

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

subgroupindex
C2×#168120902
#202925652
#202925582
#202925552
#202925112
#202925072
#202925002
#202924902
#202924882
#202924852
C2×C107⋊#952
C2×C4×D4×C1072
#2419107