Finite Group Databasebeta

← C107×#22691 #41048655

Subgroups — C107×#22691 #41048655

Order 27392.

846 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#443×C107C211yesmaximal, characteristic
2C107×#2952C212yesmaximal
3C107×#2913C212yesmaximal, complemented
4C107×#1951C212yesmaximal, complemented
5C107×#1860C214yesmaximal, complemented
6C107×#1846C211yesmaximal, characteristic, complemented
7C107×#1816C212yesmaximal, complemented
8C107×#1772C211yesmaximal, characteristic, complemented
9C2×#135×C107C2211yescharacteristic
10C2×#131×C107C2212yes—
11#520×C107C2214yes—
12#443×C107C418yescomplemented
13#442×C107—22no—
14#441×C107—22no—
15C4×SD16×C107—24no—
16C2×#108×C107C2211yescharacteristic
17C2×#108×C107C2211yescharacteristic
18#428×C107—24no—
19#428×C107C2214yes—
20#427×C107—22no—
21#427×C107C2211yescharacteristic
22C2×#107×C107—22no—
23C2×#107×C107C2212yes—
24C2×#106×C107C2212yes—
25C2×#104×C107C2212yes—
26#417×C107C2214yes—
27#405×C107C2212yes—
28C2×C4×C8×C107C2211yescharacteristic
29#382×C107C2212yes—
30#343×C107C2214yes—
31#339×C107C2212yes—
32C2×#41×C107C2312yes—
33#135×C107C2×C414yes—
34#135×C107Q814yes—
35C2×Q16×C107D411yescharacteristic
36C2×SD16×C107D412yes—
37C2×D8×C107D411yescharacteristic
38#131×C107—24no—
39#131×C107C2×C418yescomplemented
40C2×M16×C107—22no—
41C2×M16×C107C2312yes—
42C2×M16×C107C2312yes—
43C22×C8×C107—22no—
44C22×C8×C107C2311yescharacteristic
45C22×C8×C107C2311yescharacteristic
46C4×Q8×C107—24no—
47C4×D4×C107—24no—
48C4×D4×C107—44no—
49#117×C107—24no—
50#117×C107C2312yes—
51C2×C4⋊C4×C107—24no—
52C2×C4⋊C4×C107C2314yes—
53C2×C42×C107C2311yescharacteristic
54#108×C107—22no—
55#108×C107C2×C414yescomplemented
56#107×C107—22no—
57#107×C107—22no—
58#107×C107—24no—
59#107×C107D412yes—
60#106×C107—22no—
61#106×C107—22no—
62#106×C107—24no—
63#106×C107D412yes—
64#104×C107C2×C418yescomplemented
65#103×C107—24no—
66#102×C107—24no—
67#97×C107—22no—
68C4×C8×C107—22no—
69C4×C8×C107C2×C414yescomplemented
70#95×C107—42no—
71#41×C107—22no—
72#41×C107—22no—
73#41×C107C22×C414yes—
74#41×C107C2×Q814yes—
75C2×Q8×C107C2×D412yes—
76C2×D4×C107—22no—
77C2×D4×C107C2×D412yes—
78C22×C4×C107—22no—
79C22×C4×C107—21no—
80C22×C4×C107—24no—
81C22×C4×C107—44no—
82C22×C4×C107C2411yescharacteristic
83Q16×C107C4⋊C414yes—
84SD16×C107C4⋊C418yes—
85D8×C107C4⋊C414yes—
86M16×C107—22no—
87M16×C107—28no—
88M16×C107—22no—
89M16×C107—22no—
90M16×C107C22×C414yes—
91C2×C8×C107—22no—
92C2×C8×C107—28no—
93C2×C8×C107—22no—
94C2×C8×C107C22×C412yes—
95C2×C8×C107C22×C412yes—
96C2×C8×C107C2×D411yescharacteristic
97C2×C8×C107C2×D411yescharacteristic
98C2×C8×C107C2×D411yescharacteristic
99C2×C8×C107C2×D411yescharacteristic
100C2×C8×C107C2×Q812yes—
101C2×C8×C107#4112yes—
102C4⋊C4×C107—24no—
103C4⋊C4×C107—24no—
104C4⋊C4×C107—44no—
105C4⋊C4×C107C2×D414yes—
106C22⋊C4×C107—22no—
107C22⋊C4×C107—44no—
108C42×C107—22no—
109C42×C107—21no—
110C42×C107—44no—
111C42×C107C22×C412yes—
112C23×C107—22no—
113C23×C107H(5,𝔽2)11yescharacteristic
114Q8×C107—22no—
115Q8×C107C2×C4⋊C414yes—
116D4×C107—24no—
117D4×C107—24no—
118D4×C107—22no—
119D4×C107C2×C4⋊C414yes—
120C2×C4×C107—22no—
121C2×C4×C107—24no—
122C2×C4×C107—24no—
123C2×C4×C107—22no—
124C2×C4×C107—24no—
125C2×C4×C107—42no—
126C2×C4×C107—44no—
127C2×C4×C107—84no—
128C2×C4×C107—164no—
129C2×C4×C107C23×C411yescharacteristic
130C2×C4×C107C22×D411yescharacteristic
131C2×C4×C107C22×D411yescharacteristic
132C2×C4×C107C22×Q811yescharacteristic
133C2×C4×C107C2×#4111yescharacteristic
134C2×C4×C1072−1+411yescharacteristic
135C8×C107—24no—
136C8×C107—42no—
137C8×C107C2×C4⋊C412yes—
138C8×C107C2×C4⋊C412yes—
139C8×C107C4×D412yes—
140C8×C107C4×D412yes—
141C22×C107—22no—
142C22×C107—24no—
143C22×C107—42no—
144C22×C107—42no—
145C22×C107#52011yescharacteristic
146C22×C107D4211yescharacteristic
147C22×C107#55411yescharacteristic
148C4×C107—24no—
149C4×C107—42no—
150C4×C107—44no—
151C4×C107—84no—
152C4×C107C22×C4⋊C411yescharacteristic
153C4×C107C2×C4×D411yescharacteristic
154C4×C107#54711yescharacteristic
155C4×C107D4×Q811yescharacteristic
156#22691C10711yesmaximal, characteristic, direct product factor, Sylow
157C2×C107—21no—
158C2×C107—21no—
159C2×C107—44no—
160C2×C107D4×C4⋊C411yescharacteristic
161C2×C107#329012yes—
162C2×#443C2×C10711yescharacteristic
163#2952C2×C10712yes—
164#2913C2×C10712yescomplemented
165#1951C2×C10712yescomplemented
166#1860C2×C10714yescomplemented
167#1846C2×C10711yescharacteristic, complemented
168#1816C2×C10712yescomplemented
169#1772C2×C10711yescharacteristic, complemented
170C107#2269111yescharacteristic, direct product factor, Sylow
171C2×#135C22×C10711yescharacteristic
172C2×#131C22×C10712yes—
173#520C22×C10714yes—
174#443C4×C10718yescomplemented
175#442—22no—
176#441—22no—
177C4×SD16—24no—
178C2×#108C22×C10711yescharacteristic
179C2×#108C22×C10711yescharacteristic
180#428—24no—
181#428C22×C10714yes—
182#427—22no—
183#427C22×C10711yescharacteristic
184C2×#107—22no—
185C2×#107C22×C10712yes—
186C2×#106C22×C10712yes—
187C2×#104C22×C10712yes—
188#417C22×C10714yes—
189#405C22×C10712yes—
190C2×C4×C8C22×C10711yescharacteristic
191#382C22×C10712yes—
192#343C22×C10714yes—
193#339C22×C10712yes—
194C2×#41C23×C10712yes—
195#135C2×C4×C10714yes—
196#135Q8×C10714yes—
197C2×Q16D4×C10711yescharacteristic
198C2×SD16D4×C10712yes—
199C2×D8D4×C10711yescharacteristic
200#131—24no—
201#131C2×C4×C10718yescomplemented
202C2×M16—22no—
203C2×M16C23×C10712yes—
204C2×M16C23×C10712yes—
205C22×C8—22no—
206C22×C8C23×C10711yescharacteristic
207C22×C8C23×C10711yescharacteristic
208C4×Q8—24no—
209C4×D4—24no—
210C4×D4—44no—
211#117—24no—
212#117C23×C10712yes—
213C2×C4⋊C4—24no—
214C2×C4⋊C4C23×C10714yes—
215C2×C42C23×C10711yescharacteristic
216#108—22no—
217#108C2×C4×C10714yescomplemented
218#107—22no—
219#107—22no—
220#107—24no—
221#107D4×C10712yes—
222#106—22no—
223#106—22no—
224#106—24no—
225#106D4×C10712yes—
226#104C2×C4×C10718yescomplemented
227#103—24no—
228#102—24no—
229#97—22no—
230C4×C8—22no—
231C4×C8C2×C4×C10714yescomplemented
232#95—42no—
233#41—22no—
234#41—22no—
235#41C22×C4×C10714yes—
236#41C2×Q8×C10714yes—
237C2×Q8C2×D4×C10712yes—
238C2×D4—22no—
239C2×D4C2×D4×C10712yes—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—24no—
243C22×C4—44no—
244C22×C4C24×C10711yescharacteristic
245Q16C4⋊C4×C10714yes—
246SD16C4⋊C4×C10718yes—
247D8C4⋊C4×C10714yes—
248M16—22no—
249M16—28no—
250M16—22no—
251M16—22no—
252M16C22×C4×C10714yes—
253C2×C8—22no—
254C2×C8—28no—
255C2×C8—22no—
256C2×C8C22×C4×C10712yes—
257C2×C8C22×C4×C10712yes—
258C2×C8C2×D4×C10711yescharacteristic
259C2×C8C2×D4×C10711yescharacteristic
260C2×C8C2×D4×C10711yescharacteristic
261C2×C8C2×D4×C10711yescharacteristic
262C2×C8C2×Q8×C10712yes—
263C2×C8#41×C10712yes—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—44no—
267C4⋊C4C2×D4×C10714yes—
268C22⋊C4—22no—
269C22⋊C4—44no—
270C42—22no—
271C42—21no—
272C42—44no—
273C42C22×C4×C10712yes—
274C23—22no—
275C23H(5,𝔽2)×C10711yescharacteristic
276Q8—22no—
277Q8C2×C4⋊C4×C10714yes—
278D4—24no—
279D4—24no—
280D4—22no—
281D4C2×C4⋊C4×C10714yes—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—84no—
290C2×C4—164no—
291C2×C4C23×C4×C10711yescharacteristic
292C2×C4C22×D4×C10711yescharacteristic
293C2×C4C22×D4×C10711yescharacteristic
294C2×C4C22×Q8×C10711yescharacteristic
295C2×C4C2×#41×C10711yescharacteristic
296C2×C42−1+4×C10711yescharacteristic
297C8—24no—
298C8—42no—
299C8C2×C4⋊C4×C10712yes—
300C8C2×C4⋊C4×C10712yes—
301C8C4×D4×C10712yes—
302C8C4×D4×C10712yes—
303C22—22no—
304C22—24no—
305C22—42no—
306C22—42no—
307C22#520×C10711yescharacteristic
308C22D42×C10711yescharacteristic
309C22#554×C10711yescharacteristic
310C4—24no—
311C4—42no—
312C4—44no—
313C4—84no—
314C4C22×C4⋊C4×C10711yescharacteristic
315C4C2×C4×D4×C10711yescharacteristic
316C4#547×C10711yescharacteristic
317C4D4×Q8×C10711yescharacteristic
318C2—21no—
319C2—21no—
320C2—44no—
321C2D4×C4⋊C4×C10711yescharacteristic
322C2C107×#329012yes—
subgroupG/H
center, socleC22×C107D42
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC2×#135×C107C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#2913C2semidirect
4. C107×#1951C2semidirect
5. C107×#1860C2semidirect
6. C107×#1846C2semidirect
7. C107×#1816C2semidirect
8. C107×#1772C2semidirect
12. #443×C107C4semidirect
39. #131×C107C2×C4semidirect
55. #108×C107C2×C4semidirect
64. #104×C107C2×C4semidirect
69. C4×C8×C107C2×C4semidirect
156. #22691C107direct (N × H)
164. #2913C2×C107semidirect
165. #1951C2×C107semidirect
166. #1860C2×C107semidirect
167. #1846C2×C107semidirect
168. #1816C2×C107semidirect
169. #1772C2×C107semidirect
170. C107#22691direct (N × H)
174. #443C4×C107semidirect
201. #131C2×C4×C107semidirect
217. #108C2×C4×C107semidirect
226. #104C2×C4×C107semidirect
231. C4×C8C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#443×C1072
C107×#29522
C107×#29132
C107×#19512
C107×#18602
C107×#18462
C107×#18162
C107×#17722
#22691107