Finite Group Databasebeta

← #28339459

Subgroups — #28339459

Order 13696.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812090C211yesmaximal, characteristic
2C2×D4×Dic107C211yesmaximal, characteristic
3C2×#16812065C211yesmaximal, characteristic, complemented
4#20292524C211yesmaximal, characteristic, complemented
5#20292521C211yesmaximal, characteristic, complemented
6#20292515C211yesmaximal, characteristic, complemented
7#20292514C211yesmaximal, characteristic, complemented
8#20292509C211yesmaximal, characteristic, complemented
9#20292499C211yesmaximal, characteristic, complemented
10#20292499C211yesmaximal, characteristic, complemented
11#20292478C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic107C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic107C211yesmaximal, characteristic, complemented
14C2×C107⋊#95C211yesmaximal, characteristic, complemented
15#386×C107C211yesmaximal, characteristic
16C23×Dic107C2211yescharacteristic
17C23×Dic107C2211yescharacteristic
18C23×Dic107C2211yescharacteristic
19#16812090C418yescomplemented
20D4×Dic107—24no—
21#16812065—24no—
22C2×C4⋊Dic107C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×Dic107⋊C4C2211yescharacteristic
28C2×Dic107⋊C4C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×C22⋊Dic107C2211yescharacteristic
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
46C107⋊#95C2211yescharacteristic
47C22×D4×C107C2211yescharacteristic
48C23×C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50C2×C22⋊C4×C107C2211yescharacteristic
51C2×C22⋊C4×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53#95×C107C2211yescharacteristic
54C22×Dic107—22no—
55C22×Dic107—22no—
56C22×Dic107—22no—
57C22×Dic107—22no—
58C22×Dic107—22no—
59C22×Dic107—22no—
60C22×Dic107—41no—
61C22×Dic107—41no—
62C22×Dic107C2×C414yescomplemented
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C22×Dic107C2311yescharacteristic
68C22×Dic107C2311yescharacteristic
69C22×Dic107C2311yescharacteristic
70C22×Dic107C2311yescharacteristic
71C4⋊Dic107—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—22no—
75Dic107⋊C4—41no—
76Dic107⋊C4C2×C414yescomplemented
77Dic107⋊C4C2×C414yescomplemented
78C22⋊Dic107—22no—
79C22⋊Dic107C2×C414yescomplemented
80C22⋊Dic107C2×C414yescomplemented
81C22⋊Dic107C2×C414yescomplemented
82C22⋊Dic107D414yes—
83C4×Dic107—22no—
84C4×Dic107—22no—
85C4×Dic107—22no—
86C4×Dic107—22no—
87C4×Dic107—41no—
88C24×C107C2311yescharacteristic
89C24×C107C2311yescharacteristic
90C2×D4×C107—22no—
91C2×D4×C107—22no—
92C2×D4×C107C2×C414yes—
93C22×C4×C107—22no—
94C22×C4×C107—22no—
95C22×C4×C107—41no—
96C22×C4×C107C2311yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C22⋊C4×C107—22no—
102C22⋊C4×C107—22no—
103C22⋊C4×C107—41no—
104C23×C107—21no—
105C23×C107—21no—
106C23×C107—21no—
107C23×C107—21no—
108C23×C107—21no—
109C23×C107—21no—
110C23×C107—21no—
111C23×C107—21no—
112C23×C107—21no—
113C23×C107—21no—
114C23×C107C22×C412yes—
115C23×C107C22×C412yes—
116C23×C107C2×D412yes—
117C23×C107#4112yes—
118C23×C107C2411yescharacteristic
119D4×C107—28no—
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—21no—
132C2×C4×C107—21no—
133C2×C4×C107—44no—
134C2×C4×C107C22×C412yes—
135C2×C4×C107#4112yes—
136C2×Dic107—28no—
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—44no—
155C2×Dic107—44no—
156C2×Dic107C22×C412yes—
157C2×Dic107C22×C412yes—
158C2×Dic107C22×C412yes—
159C2×Dic107C22×C412yes—
160C2×Dic107C2×D412yes—
161C2×Dic107C2×D412yes—
162C2×Dic107#4112yes—
163C22×C107—22no—
164C22×C107—22no—
165C22×C107—22no—
166C22×C107—22no—
167C22×C107—22no—
168C22×C107—22no—
169C22×C107—22no—
170C22×C107—22no—
171C22×C107—22no—
172C22×C107—41no—
173C22×C107—41no—
174C22×C107—41no—
175C22×C107—41no—
176C22×C107C4×D414yes—
177C22×C107C23×C411yescharacteristic
178C22×C107C22×D411yescharacteristic
179C22×C107C2×#4111yescharacteristic
180C22×C107C2×#4111yescharacteristic
181C22×C107C2×#4111yescharacteristic
182C22×C107H(5,𝔽2)11yescharacteristic
183C22×C1072−1+411yescharacteristic
184C4×C107—22no—
185C4×C107—22no—
186C4×C107—41no—
187C4×C107—41no—
188C4×C107—41no—
189Dic107—22no—
190Dic107—22no—
191Dic107—22no—
192Dic107—22no—
193Dic107—22no—
194Dic107—22no—
195Dic107—22no—
196Dic107—41no—
197C2×C107—24no—
198C2×C107—42no—
199C2×C107C2×C4×D411yescharacteristic
200C2×C107C4×#4111yescharacteristic
201C2×C107#52011yescharacteristic
202C2×C107#54611yescharacteristic
203C2×C107#54711yescharacteristic
204C2×C107#55111yescharacteristic
205C2×C107#55211yescharacteristic
206#2359—1071nomaximal, Sylow
207C107#235911yescharacteristic, complemented, Sylow
208C2×#123—1071no—
209C2×C4×D4—1071no—
210C2×#117—1071no—
211#389—1071no—
212#388—1071no—
213#388—1071no—
214#387—1071no—
215#387—1071no—
216#386D10711yescharacteristic
217#385—1071no—
218#385—1071no—
219C4×C4⋊C4—1071no—
220C4×C22⋊C4—1071no—
221C4×C22⋊C4—1071no—
222C2×#95—1071no—
223C22×D4C2×D10711yescharacteristic
224C23×C4—1071no—
225C23×C4—1071no—
226C23×C4—1071no—
227C23×C4C2×D10711yescharacteristic
228#123—1078no—
229C4×D4—2144no—
230#117—2144no—
231C2×C4⋊C4—1071no—
232C2×C4⋊C4—1071no—
233C2×C4⋊C4—1071no—
234C2×C4⋊C4—1071no—
235C2×C4⋊C4—1071no—
236C2×C4⋊C4—1071no—
237C2×C4⋊C4—1071no—
238C2×C22⋊C4—1071no—
239C2×C22⋊C4—1071no—
240C2×C22⋊C4—1071no—
241C2×C22⋊C4—1071no—
242C2×C22⋊C4—1071no—
243C2×C22⋊C4C2×D10711yescharacteristic
244C2×C22⋊C4C2×D10711yescharacteristic
245C2×C22⋊C4C2×D10711yescharacteristic
246C2×C42—1071no—
247C2×C42—1071no—
248C2×C42—1071no—
249C2×C42—1071no—
250C2×C42—1071no—
251#95—1071no—
252#95—1071no—
253#95—1071no—
254#95—1071no—
255#95—1071no—
256#95—1071no—
257#95—1071no—
258#95—1071no—
259#95C2×D10711yescharacteristic
260#95C2×D10711yescharacteristic
261C24C22×D10711yescharacteristic
262C24C22×D10711yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4C4×D10714yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—1074no—
270C22×C4—1071no—
271C22×C4—1071no—
272C22×C4—1071no—
273C22×C4—1071no—
274C22×C4—1071no—
275C22×C4—1071no—
276C22×C4—1071no—
277C22×C4—1071no—
278C22×C4—4281no—
279C22×C4—4281no—
280C22×C4—2142no—
281C22×C4—2142no—
282C22×C4—2142no—
283C22×C4—2142no—
284C22×C4—2142no—
285C22×C4—2142no—
286C22×C4C22×D10711yescharacteristic
287C22×C4C22×D10711yescharacteristic
288C22×C4C22×D10711yescharacteristic
289C22×C4C22×D10711yescharacteristic
290C22×C4C22×D10711yescharacteristic
291C4⋊C4—1074no—
292C4⋊C4—1074no—
293C4⋊C4—4281no—
294C4⋊C4—2142no—
295C4⋊C4—2142no—
296C4⋊C4—2142no—
297C4⋊C4—2142no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—1074no—
302C22⋊C4—1074no—
303C22⋊C4—1074no—
304C22⋊C4—1074no—
305C22⋊C4—2142no—
306C42—4281no—
307C42—2142no—
308C42—2142no—
309C42—2142no—
310C42—2142no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4×D10712yes—
322C23C2×C4×D10712yes—
323C23D4×D10712yes—
324C23#1313381712yes—
325C23C23×D10711yescharacteristic
326D4—28no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—1072no—
342C2×C4—1072no—
343C2×C4—1072no—
344C2×C4—1072no—
345C2×C4—1072no—
346C2×C4—1072no—
347C2×C4—1072no—
348C2×C4—4284no—
349C2×C4—4284no—
350C2×C4—2141no—
351C2×C4—2141no—
352C2×C4—2141no—
353C2×C4—2148no—
354C2×C4—2141no—
355C2×C4—2141no—
356C2×C4—2141no—
357C2×C4—2141no—
358C2×C4—2141no—
359C2×C4—2141no—
360C2×C4—2141no—
361C2×C4—2141no—
362C2×C4—2141no—
363C2×C4—2141no—
364C2×C4—2141no—
365C2×C4—2141no—
366C2×C4—2141no—
367C2×C4—2141no—
368C2×C4C2×C4×D10712yes—
369C2×C4#1313381712yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22(C22⋊D107)⋊C414yes—
384C22C22×C4×D10711yescharacteristic
385C22C2×D4×D10711yescharacteristic
386C22#41×D10711yescharacteristic
387C22C2×#1313381711yescharacteristic
388C22C2×#1313381711yescharacteristic
389C22#1681215411yescharacteristic
390C22#1681215611yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—4281no—
397C4—2142no—
398C4—2142no—
399C4—2142no—
400C4—2142no—
401C4—2142no—
402C4—2142no—
403C4—2142no—
404C2—24no—
405C2—42no—
406C2C2×(C22⋊D107)⋊C411yescharacteristic
407C2C4×#1313381711yescharacteristic
408C2#2029310611yescharacteristic
409C2#2029326611yescharacteristic
410C2#2029327711yescharacteristic
411C2#2029330811yescharacteristic
412C2#2029331411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#386×C107C2
socle, cosocleC23×C107C24
prime radicalC22×D4×C107C22
hypercenter#386D107
hypocenterC107#2359
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. C2×#16812065C2semidirect
4. #20292524C2semidirect
5. #20292521C2semidirect
6. #20292515C2semidirect
7. #20292514C2semidirect
8. #20292509C2semidirect
9. #20292499C2semidirect
10. #20292499C2semidirect
11. #20292478C2semidirect
12. C22⋊C4×Dic107C2semidirect
13. C4×C22⋊Dic107C2semidirect
14. C2×C107⋊#95C2semidirect
19. #16812090C4semidirect
62. C22×Dic107C2×C4semidirect
76. Dic107⋊C4C2×C4semidirect
77. Dic107⋊C4C2×C4semidirect
79. C22⋊Dic107C2×C4semidirect
80. C22⋊Dic107C2×C4semidirect
81. C22⋊Dic107C2×C4semidirect
207. C107#2359semidirect

Maximal subgroups

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

subgroupindex
C2×#168120902
C2×D4×Dic1072
C2×#168120652
#202925242
#202925212
#202925152
#202925142
#202925092
#202924992
#202924782
C22⋊C4×Dic1072
C4×C22⋊Dic1072
C2×C107⋊#952
#386×C1072
#2359107