Finite Group Databasebeta

← C107×#13476 #41039440

Subgroups — C107×#13476 #41039440

Order 27392.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#367×C107C211yesmaximal, characteristic, complemented
2C2×C4⋊C16×C107C211yesmaximal, characteristic, complemented
3C2×#357×C107C211yesmaximal, characteristic
4C2×#357×C107C211yesmaximal, characteristic
5C107×#1970C211yesmaximal, characteristic
6C107×#1942C211yesmaximal, characteristic, complemented
7C107×#1380C211yesmaximal, characteristic, complemented
8C22×D8×C107C2211yescharacteristic
9C22×C16×C107C2211yescharacteristic
10C22×C16×C107C2211yescharacteristic
11C2×#107×C107C2211yescharacteristic
12C2×#107×C107C2211yescharacteristic
13C2×#107×C107C2211yescharacteristic
14C2×#102×C107—21no—
15C2×C4×C8×C107C2211yescharacteristic
16#390×C107—21no—
17#389×C107—21no—
18#367×C107—22no—
19C4⋊C16×C107—22no—
20#357×C107—22no—
21#357×C107—22no—
22#340×C107—21no—
23C22×D4×C107—21no—
24C2×D8×C107—21no—
25C2×D8×C107—21no—
26C2×D8×C107—21no—
27C2×D8×C107—21no—
28C2×D8×C107—21no—
29C2×D8×C107Q812yes—
30C22×C8×C107D411yescharacteristic
31C22×C8×C107C2311yescharacteristic
32C2×C4⋊C4×C107—21no—
33C2×C4⋊C4×C107—21no—
34C2×C4⋊C4×C107—21no—
35C2×C4⋊C4×C107—41no—
36C2×C22⋊C4×C107—41no—
37C2×C22⋊C4×C107—41no—
38C2×C42×C107D411yescharacteristic
39C2×C16×C107—21no—
40C2×C16×C107—21no—
41C2×C16×C107—21no—
42C2×C16×C107—21no—
43C2×C16×C107—21no—
44C2×C16×C107D412yes—
45#107×C107—21no—
46#107×C107—21no—
47#107×C107—21no—
48#107×C107—21no—
49#107×C107—21no—
50#107×C107D412yes—
51#102×C107—42no—
52C4×C8×C107—21no—
53C4×C8×C107—21no—
54#95×C107—41no—
55C24×C107—41no—
56C2×D4×C107—22no—
57C2×D4×C107—41no—
58C2×D4×C107—41no—
59C2×D4×C107—41no—
60C2×D4×C107—41no—
61C2×D4×C107—41no—
62C22×C4×C107—41no—
63C22×C4×C107—41no—
64C22×C4×C107—41no—
65C22×C4×C107D811yescharacteristic
66C22×C4×C107D811yescharacteristic
67C22×C4×C107C2×D411yescharacteristic
68D8×C107—22no—
69D8×C107—22no—
70D8×C107—41no—
71D8×C107—41no—
72C2×C8×C107—21no—
73C2×C8×C107—21no—
74C2×C8×C107—21no—
75C2×C8×C107C2×D411yescharacteristic
76C2×C8×C107C2×D411yescharacteristic
77C2×C8×C107C2×Q811yescharacteristic
78C2×C8×C107#4111yescharacteristic
79C2×C8×C107#4111yescharacteristic
80C2×C8×C107#4111yescharacteristic
81C4⋊C4×C107—22no—
82C4⋊C4×C107—41no—
83C4⋊C4×C107—41no—
84C4⋊C4×C107—41no—
85C4⋊C4×C107—41no—
86C4⋊C4×C107—41no—
87C4⋊C4×C107—82no—
88C22⋊C4×C107—82no—
89C22⋊C4×C107—82no—
90C42×C107—21no—
91C42×C107—21no—
92C16×C107—22no—
93C16×C107—41no—
94C23×C107—42no—
95C23×C107—81no—
96C23×C107—81no—
97C23×C107—81no—
98C23×C107—81no—
99C23×C107—81no—
100C23×C107—81no—
101C23×C107C2×D811yescharacteristic
102D4×C107—42no—
103D4×C107—42no—
104D4×C107—81no—
105D4×C107—81no—
106C2×C4×C107—21no—
107C2×C4×C107—21no—
108C2×C4×C107—21no—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—42no—
112C2×C4×C107—81no—
113C2×C4×C107—81no—
114C2×C4×C107—81no—
115C2×C4×C107—81no—
116C2×C4×C107—81no—
117C2×C4×C107—81no—
118C2×C4×C107—81no—
119C2×C4×C107—81no—
120C2×C4×C107SD3212yes—
121C2×C4×C107#12111yescharacteristic
122C2×C4×C107#12111yescharacteristic
123C2×C4×C107C22⋊Q811yescharacteristic
124C2×C4×C107#13511yescharacteristic
125C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C107#13711yescharacteristic
127C8×C107—41no—
128C8×C107#12111yescharacteristic
129C8×C107C22⋊Q811yescharacteristic
130C8×C107C22⋊Q811yescharacteristic
131C8×C107#12611yescharacteristic
132C22×C107—82no—
133C22×C107—82no—
134C22×C107—82no—
135C22×C107—161no—
136C22×C107—161no—
137C22×C107—161no—
138C22×C107—161no—
139C22×C107#45911yescharacteristic
140C22×C107#46611yescharacteristic
141C22×C107#47411yescharacteristic
142C22×C107C2×SD3211yescharacteristic
143C22×C107#50811yescharacteristic
144C22×C107#50911yescharacteristic
145C22×C107#50911yescharacteristic
146C4×C107—22no—
147C4×C107—41no—
148C4×C107—82no—
149C4×C107—161no—
150C4×C107—161no—
151C4×C107#39611yescharacteristic
152C4×C107#46411yescharacteristic
153C4×C107#46811yescharacteristic
154C4×C107#47811yescharacteristic
155#13476C10711yesmaximal, characteristic, direct product factor, Sylow
156C2×C107—162no—
157C2×C107#206711yescharacteristic
158C2×C107#220711yescharacteristic
159C2×C107#221011yescharacteristic
160C2×C107#221711yescharacteristic
161C2×C107#221811yescharacteristic
162C2×C107#222611yescharacteristic
163C2×C107#222811yescharacteristic
164C2×#367C2×C10711yescharacteristic, complemented
165C2×C4⋊C16C2×C10711yescharacteristic, complemented
166C2×#357C2×C10711yescharacteristic
167C2×#357C2×C10711yescharacteristic
168#1970C2×C10711yescharacteristic
169#1942C2×C10711yescharacteristic, complemented
170#1380C2×C10711yescharacteristic, complemented
171C107#1347611yescharacteristic, direct product factor, Sylow
172C22×D8C22×C10711yescharacteristic
173C22×C16C22×C10711yescharacteristic
174C22×C16C22×C10711yescharacteristic
175C2×#107C22×C10711yescharacteristic
176C2×#107C22×C10711yescharacteristic
177C2×#107C22×C10711yescharacteristic
178C2×#102—21no—
179C2×C4×C8C22×C10711yescharacteristic
180#390—21no—
181#389—21no—
182#367—22no—
183C4⋊C16—22no—
184#357—22no—
185#357—22no—
186#340—21no—
187C22×D4—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8—21no—
193C2×D8Q8×C10712yes—
194C22×C8D4×C10711yescharacteristic
195C22×C8C23×C10711yescharacteristic
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—41no—
200C2×C22⋊C4—41no—
201C2×C22⋊C4—41no—
202C2×C42D4×C10711yescharacteristic
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—21no—
208C2×C16D4×C10712yes—
209#107—21no—
210#107—21no—
211#107—21no—
212#107—21no—
213#107—21no—
214#107D4×C10712yes—
215#102—42no—
216C4×C8—21no—
217C4×C8—21no—
218#95—41no—
219C24—41no—
220C2×D4—22no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4D8×C10711yescharacteristic
230C22×C4D8×C10711yescharacteristic
231C22×C4C2×D4×C10711yescharacteristic
232D8—22no—
233D8—22no—
234D8—41no—
235D8—41no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8C2×D4×C10711yescharacteristic
240C2×C8C2×D4×C10711yescharacteristic
241C2×C8C2×Q8×C10711yescharacteristic
242C2×C8#41×C10711yescharacteristic
243C2×C8#41×C10711yescharacteristic
244C2×C8#41×C10711yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—82no—
252C22⋊C4—82no—
253C22⋊C4—82no—
254C42—21no—
255C42—21no—
256C16—22no—
257C16—41no—
258C23—42no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23—81no—
263C23—81no—
264C23—81no—
265C23C2×D8×C10711yescharacteristic
266D4—42no—
267D4—42no—
268D4—81no—
269D4—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4SD32×C10712yes—
285C2×C4#121×C10711yescharacteristic
286C2×C4#121×C10711yescharacteristic
287C2×C4C22⋊Q8×C10711yescharacteristic
288C2×C4#135×C10711yescharacteristic
289C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
290C2×C4#137×C10711yescharacteristic
291C8—41no—
292C8#121×C10711yescharacteristic
293C8C22⋊Q8×C10711yescharacteristic
294C8C22⋊Q8×C10711yescharacteristic
295C8#126×C10711yescharacteristic
296C22—82no—
297C22—82no—
298C22—82no—
299C22—161no—
300C22—161no—
301C22—161no—
302C22—161no—
303C22#459×C10711yescharacteristic
304C22#466×C10711yescharacteristic
305C22#474×C10711yescharacteristic
306C22C2×SD32×C10711yescharacteristic
307C22#508×C10711yescharacteristic
308C22#509×C10711yescharacteristic
309C22#509×C10711yescharacteristic
310C4—22no—
311C4—41no—
312C4—82no—
313C4—161no—
314C4—161no—
315C4#396×C10711yescharacteristic
316C4#464×C10711yescharacteristic
317C4#468×C10711yescharacteristic
318C4#478×C10711yescharacteristic
319C2—162no—
320C2C107×#206711yescharacteristic
321C2C107×#220711yescharacteristic
322C2C107×#221011yescharacteristic
323C2C107×#221711yescharacteristic
324C2C107×#221811yescharacteristic
325C2C107×#222611yescharacteristic
326C2C107×#222811yescharacteristic
subgroupG/H
center, socleC23×C107C2×D8
commutator, Frattini, cosocleC22×C8C23×C107
prime radicalC22×D8×C107C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ C2×C4×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#367×C107C2semidirect
2. C2×C4⋊C16×C107C2semidirect
6. C107×#1942C2semidirect
7. C107×#1380C2semidirect
155. #13476C107direct (N × H)
164. C2×#367C2×C107semidirect
165. C2×C4⋊C16C2×C107semidirect
169. #1942C2×C107semidirect
170. #1380C2×C107semidirect
171. C107#13476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#367×C1072
C2×C4⋊C16×C1072
C2×#357×C1072
C107×#19702
C107×#19422
C107×#13802
#13476107