Finite Group Databasebeta

← C107×#33656 #41059620

Subgroups — C107×#33656 #41059620

Order 27392.

556 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3054C211yesmaximal, characteristic
2C2×#430×C107C211yesmaximal, characteristic, complemented
3C107×#2239C214yesmaximal, complemented
4C107×#2238C214yesmaximal, complemented
5C107×#2155C212yesmaximal, complemented
6C107×#2148C212yesmaximal, complemented
7C2×#349×C107C211yesmaximal, characteristic, complemented
8C2×#135×C107C2211yescharacteristic
9C22×M16×C107—21no—
10C22×M16×C107C2211yescharacteristic
11#525×C107—21no—
12C2×M32×C107C2212yes—
13#470×C107C2212yes—
14#469×C107C2212yes—
15#468×C107—22no—
16#430×C107—22no—
17#430×C107C2214yes—
18C2×#108×C107—21no—
19C2×#108×C107C2212yes—
20#427×C107C2211yescharacteristic
21#416×C107—21no—
22#365×C107C2218yescomplemented
23#362×C107C2214yescomplemented
24#361×C107C2214yescomplemented
25#349×C107C2214yes—
26C2×#41×C107—21no—
27C23×C4×C107D411yescharacteristic
28#135×C107—22no—
29#135×C107—22no—
30C2×Q16×C107C2311yescharacteristic
31C2×SD16×C107—21no—
32C2×D8×C107C2311yescharacteristic
33C2×M16×C107—22no—
34C2×M16×C107—22no—
35C2×M16×C107—24no—
36C2×M16×C107—22no—
37C2×M16×C107—42no—
38C2×M16×C107—41no—
39C2×M16×C107D412yes—
40C2×M16×C107C2312yes—
41C22×C8×C107—41no—
42C22×C8×C107D411yescharacteristic
43C22×C8×C107C2311yescharacteristic
44#123×C107—41no—
45C22⋊Q8×C107—22no—
46#121×C107—22no—
47#120×C107—41no—
48C4×D4×C107—42no—
49#117×C107—21no—
50M32×C107—22no—
51M32×C107C2314yes—
52C2×C16×C107—22no—
53#108×C107—24no—
54#108×C107—22no—
55#108×C107C2314yes—
56#107×C107—21no—
57#106×C107C2312yes—
58#103×C107—22no—
59#102×C107—22no—
60C24×C107SD1611yescharacteristic
61#41×C107—41no—
62#41×C107—41no—
63#41×C107—41no—
64#41×C107—41no—
65C2×Q8×C107—21no—
66C2×D4×C107—21no—
67C2×D4×C107—42no—
68C2×D4×C107—41no—
69C22×C4×C107—21no—
70C22×C4×C107—21no—
71C22×C4×C107—21no—
72C22×C4×C107—21no—
73C22×C4×C107—41no—
74C22×C4×C107SD1612yes—
75C22×C4×C107SD1611yescharacteristic
76C22×C4×C107C2×D412yes—
77C22×C4×C107C2×D411yescharacteristic
78Q16×C107—22no—
79SD16×C107—42no—
80D8×C107—22no—
81M16×C107—24no—
82M16×C107—24no—
83M16×C107—24no—
84M16×C107—44no—
85M16×C107—42no—
86C2×C8×C107—21no—
87C2×C8×C107—21no—
88C2×C8×C107—44no—
89C2×C8×C107—42no—
90C2×C8×C107C2×D412yes—
91C2×C8×C107C2×D411yescharacteristic
92C2×C8×C107#4112yes—
93C2×C8×C107#4112yes—
94C2×C8×C107C2411yescharacteristic
95C4⋊C4×C107—22no—
96C4⋊C4×C107—42no—
97C22⋊C4×C107—41no—
98C22⋊C4×C107—42no—
99C22⋊C4×C107—42no—
100C42×C107—41no—
101C16×C107—24no—
102C23×C107—21no—
103C23×C107—21no—
104C23×C107—41no—
105C23×C107—81no—
106C23×C107C2×SD1612yes—
107C23×C107C2×SD1611yescharacteristic
108Q8×C107—41no—
109Q8×C107—41no—
110D4×C107—41no—
111D4×C107—41no—
112D4×C107—84no—
113D4×C107—81no—
114D4×C107—81no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—22no—
118C2×C4×C107—22no—
119C2×C4×C107—22no—
120C2×C4×C107—22no—
121C2×C4×C107—42no—
122C2×C4×C107—41no—
123C2×C4×C107—81no—
124C2×C4×C107—81no—
125C2×C4×C107#12311yescharacteristic
126C2×C4×C107#12311yescharacteristic
127C2×C4×C107C2×SD1612yes—
128C2×C4×C107C2×SD1611yescharacteristic
129C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C107C22×D411yescharacteristic
132C8×C107—22no—
133C8×C107—44no—
134C8×C107#12312yes—
135C8×C107C2×#4112yes—
136C22×C107—22no—
137C22×C107—41no—
138C22×C107—42no—
139C22×C107—42no—
140C22×C107—81no—
141C22×C107—82no—
142C22×C107—81no—
143C22×C107#48111yescharacteristic
144C22×C107#48111yescharacteristic
145C22×C107C22×SD1611yescharacteristic
146C4×C107—22no—
147C4×C107—82no—
148C4×C107—81no—
149C4×C107#48111yescharacteristic
150C4×C107#48111yescharacteristic
151C4×C107C2×#12311yescharacteristic
152C4×C107C2×AGL(1,ℤ/8)11yescharacteristic
153#33656C10711yesmaximal, characteristic, direct product factor, Sylow
154C2×C107—21no—
155C2×C107—21no—
156C2×C107—21no—
157C2×C107—42no—
158C2×C107—161no—
159C2×C107C2×#48111yescharacteristic
160#3054C2×C10711yescharacteristic
161C2×#430C2×C10711yescharacteristic, complemented
162#2239C2×C10714yescomplemented
163#2238C2×C10714yescomplemented
164#2155C2×C10712yescomplemented
165#2148C2×C10712yescomplemented
166C2×#349C2×C10711yescharacteristic, complemented
167C107#3365611yescharacteristic, direct product factor, Sylow
168C2×#135C22×C10711yescharacteristic
169C22×M16—21no—
170C22×M16C22×C10711yescharacteristic
171#525—21no—
172C2×M32C22×C10712yes—
173#470C22×C10712yes—
174#469C22×C10712yes—
175#468—22no—
176#430—22no—
177#430C22×C10714yes—
178C2×#108—21no—
179C2×#108C22×C10712yes—
180#427C22×C10711yescharacteristic
181#416—21no—
182#365C22×C10718yescomplemented
183#362C22×C10714yescomplemented
184#361C22×C10714yescomplemented
185#349C22×C10714yes—
186C2×#41—21no—
187C23×C4D4×C10711yescharacteristic
188#135—22no—
189#135—22no—
190C2×Q16C23×C10711yescharacteristic
191C2×SD16—21no—
192C2×D8C23×C10711yescharacteristic
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—24no—
197C2×M16—42no—
198C2×M16—41no—
199C2×M16D4×C10712yes—
200C2×M16C23×C10712yes—
201C22×C8—41no—
202C22×C8D4×C10711yescharacteristic
203C22×C8C23×C10711yescharacteristic
204#123—41no—
205C22⋊Q8—22no—
206#121—22no—
207#120—41no—
208C4×D4—42no—
209#117—21no—
210M32—22no—
211M32C23×C10714yes—
212C2×C16—22no—
213#108—24no—
214#108—22no—
215#108C23×C10714yes—
216#107—21no—
217#106C23×C10712yes—
218#103—22no—
219#102—22no—
220C24SD16×C10711yescharacteristic
221#41—41no—
222#41—41no—
223#41—41no—
224#41—41no—
225C2×Q8—21no—
226C2×D4—21no—
227C2×D4—42no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4SD16×C10712yes—
235C22×C4SD16×C10711yescharacteristic
236C22×C4C2×D4×C10712yes—
237C22×C4C2×D4×C10711yescharacteristic
238Q16—22no—
239SD16—42no—
240D8—22no—
241M16—24no—
242M16—24no—
243M16—24no—
244M16—44no—
245M16—42no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—44no—
249C2×C8—42no—
250C2×C8C2×D4×C10712yes—
251C2×C8C2×D4×C10711yescharacteristic
252C2×C8#41×C10712yes—
253C2×C8#41×C10712yes—
254C2×C8C24×C10711yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C42—41no—
261C16—24no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—81no—
266C23C2×SD16×C10712yes—
267C23C2×SD16×C10711yescharacteristic
268Q8—41no—
269Q8—41no—
270D4—41no—
271D4—41no—
272D4—84no—
273D4—81no—
274D4—81no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4#123×C10711yescharacteristic
286C2×C4#123×C10711yescharacteristic
287C2×C4C2×SD16×C10712yes—
288C2×C4C2×SD16×C10711yescharacteristic
289C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
290C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
291C2×C4C22×D4×C10711yescharacteristic
292C8—22no—
293C8—44no—
294C8#123×C10712yes—
295C8C2×#41×C10712yes—
296C22—22no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—81no—
301C22—82no—
302C22—81no—
303C22#481×C10711yescharacteristic
304C22#481×C10711yescharacteristic
305C22C22×SD16×C10711yescharacteristic
306C4—22no—
307C4—82no—
308C4—81no—
309C4#481×C10711yescharacteristic
310C4#481×C10711yescharacteristic
311C4C2×#123×C10711yescharacteristic
312C4C2×AGL(1,ℤ/8)×C10711yescharacteristic
313C2—21no—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—161no—
318C2C2×#481×C10711yescharacteristic
subgroupG/H
centerC4×C107#481
commutator, Frattini, cosocleC2×C8C24×C107
socleC2×C107C2×#481
prime radicalC107×#3054C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C22×C4×C107 ◁ C22×M16×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#430×C107C2semidirect
3. C107×#2239C2semidirect
4. C107×#2238C2semidirect
5. C107×#2155C2semidirect
6. C107×#2148C2semidirect
7. C2×#349×C107C2semidirect
22. #365×C107C22semidirect
23. #362×C107C22semidirect
24. #361×C107C22semidirect
153. #33656C107direct (N × H)
161. C2×#430C2×C107semidirect
162. #2239C2×C107semidirect
163. #2238C2×C107semidirect
164. #2155C2×C107semidirect
165. #2148C2×C107semidirect
166. C2×#349C2×C107semidirect
167. C107#33656direct (N × H)
182. #365C22×C107semidirect
183. #362C22×C107semidirect
184. #361C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30542
C2×#430×C1072
C107×#22392
C107×#22382
C107×#21552
C107×#21482
C2×#349×C1072
#33656107