Finite Group Databasebeta

← C107×#19058 #41045022

Subgroups — C107×#19058 #41045022

Order 27392.

840 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3550C211yesmaximal, characteristic
2C107×#3237C212yesmaximal, complemented
3C107×#3135C211yesmaximal, characteristic
4C107×#1664C218yesmaximal, complemented
5C107×#1536C211yesmaximal, characteristic
6C107×#1531C212yesmaximal, complemented
7#563×C107C2214yes—
8#559×C107—21no—
9Q82×C107—21no—
10#556×C107—22no—
11D4×Q8×C107—22no—
12#542×C107—24no—
13#536×C107—22no—
14#533×C107C2211yescharacteristic
15#533×C107C2212yes—
16#532×C107C2211yescharacteristic
17#501×C107C2214yes—
18#491×C107—21no—
19#491×C107C2214yes—
20#490×C107—21no—
21#489×C107C2214yes—
22#485×C107—24no—
23#477×C107—22no—
24#475×C107—22no—
25#432×C107C2212yes—
26#416×C107—22no—
27C2×#97×C107C2211yescharacteristic
28#330×C107C2218yes—
29#329×C107C2214yes—
30C2×#41×C107D412yes—
31C22×Q8×C107—22no—
32C22×C8×C107—21no—
33C4⋊Q8×C107—24no—
34C4⋊Q8×C107—24no—
35C4⋊Q8×C107D411yescharacteristic
36C4⋊Q8×C107D412yes—
37C4⋊Q8×C107D412yes—
38C4⋊Q8×C107C2312yes—
39#127×C107D411yescharacteristic
40#126×C107—28no—
41#125×C107—21no—
42#125×C107C2314yes—
43#124×C107—24no—
44#124×C107—24no—
45#124×C107C2312yes—
46#123×C107—24no—
47#123×C107—24no—
48C22⋊Q8×C107—24no—
49C22⋊Q8×C107—22no—
50C22⋊Q8×C107—22no—
51C22⋊Q8×C107—28no—
52C22⋊Q8×C107—22no—
53#121×C107—22no—
54C4×Q8×C107—24no—
55C4×Q8×C107—22no—
56C4×Q8×C107—22no—
57C4×Q8×C107—22no—
58C4×D4×C107—24no—
59C4×D4×C107—22no—
60#117×C107—22no—
61#117×C107—21no—
62#117×C107D414yes—
63C2×C42×C107C2311yescharacteristic
64#107×C107—24no—
65#106×C107—24no—
66C4⋊C8×C107—22no—
67#103×C107—24no—
68#103×C107—24no—
69#103×C107—24no—
70#102×C107—24no—
71C22⋊C8×C107—22no—
72#97×C107—21no—
73#97×C107C2312yes—
74#97×C107C2314yes—
75#41×C107—44no—
76C2×Q8×C107—24no—
77C2×Q8×C107—22no—
78C2×Q8×C107—22no—
79C2×Q8×C107—22no—
80C2×Q8×C107—84no—
81C2×Q8×C107C2×D412yes—
82C2×D4×C107—22no—
83C2×D4×C107—22no—
84C2×D4×C107C2×D412yes—
85C22×C4×C107—24no—
86C22×C4×C107—22no—
87C22×C4×C107C2×D411yescharacteristic
88C22×C4×C107C2×D412yes—
89C2×C8×C107—22no—
90C2×C8×C107—24no—
91C2×C8×C107—42no—
92C4⋊C4×C107—28no—
93C4⋊C4×C107—22no—
94C4⋊C4×C107—22no—
95C4⋊C4×C107—22no—
96C4⋊C4×C107—24no—
97C4⋊C4×C107—24no—
98C4⋊C4×C107—22no—
99C4⋊C4×C107—22no—
100C4⋊C4×C107—42no—
101C4⋊C4×C107C2×D414yes—
102C4⋊C4×C107C2×D414yes—
103C22⋊C4×C107—24no—
104C22⋊C4×C107—28no—
105C22⋊C4×C107—24no—
106C22⋊C4×C107—24no—
107C22⋊C4×C107—41no—
108C42×C107—24no—
109C42×C107—24no—
110C42×C107—41no—
111C42×C107C2×D411yescharacteristic
112C42×C107C2×D412yes—
113C42×C107C2411yescharacteristic
114C23×C107—22no—
115C23×C107#12011yescharacteristic
116Q8×C107—42no—
117Q8×C107—44no—
118Q8×C107—44no—
119Q8×C107—44no—
120Q8×C107—84no—
121D4×C107—42no—
122D4×C107—44no—
123D4×C107—82no—
124C2×C4×C107—22no—
125C2×C4×C107—24no—
126C2×C4×C107—22no—
127C2×C4×C107—24no—
128C2×C4×C107—42no—
129C2×C4×C107—44no—
130C2×C4×C107—42no—
131C2×C4×C107—84no—
132C2×C4×C107#12012yes—
133C2×C4×C107#12011yescharacteristic
134C2×C4×C107C22×D412yes—
135C2×C4×C107C22×D411yescharacteristic
136C8×C107—44no—
137C8×C107—42no—
138C22×C107—21no—
139C22×C107—22no—
140C22×C107—42no—
141C22×C107—44no—
142C22×C107C2×#12011yescharacteristic
143C4×C107—21no—
144C4×C107—22no—
145C4×C107—22no—
146C4×C107—42no—
147C4×C107—44no—
148C4×C107—44no—
149C4×C107—82no—
150C4×C107#45512yes—
151#19058C10711yesmaximal, characteristic, direct product factor, Sylow
152C2×C107—41no—
153C2×C107—82no—
154C2×C107C2×#45511yescharacteristic
155C2×C107#302012yes—
156#3550C2×C10711yescharacteristic
157#3237C2×C10712yescomplemented
158#3135C2×C10711yescharacteristic
159#1664C2×C10718yescomplemented
160#1536C2×C10711yescharacteristic
161#1531C2×C10712yescomplemented
162C107#1905811yescharacteristic, direct product factor, Sylow
163#563C22×C10714yes—
164#559—21no—
165Q82—21no—
166#556—22no—
167D4×Q8—22no—
168#542—24no—
169#536—22no—
170#533C22×C10711yescharacteristic
171#533C22×C10712yes—
172#532C22×C10711yescharacteristic
173#501C22×C10714yes—
174#491—21no—
175#491C22×C10714yes—
176#490—21no—
177#489C22×C10714yes—
178#485—24no—
179#477—22no—
180#475—22no—
181#432C22×C10712yes—
182#416—22no—
183C2×#97C22×C10711yescharacteristic
184#330C22×C10718yes—
185#329C22×C10714yes—
186C2×#41D4×C10712yes—
187C22×Q8—22no—
188C22×C8—21no—
189C4⋊Q8—24no—
190C4⋊Q8—24no—
191C4⋊Q8D4×C10711yescharacteristic
192C4⋊Q8D4×C10712yes—
193C4⋊Q8D4×C10712yes—
194C4⋊Q8C23×C10712yes—
195#127D4×C10711yescharacteristic
196#126—28no—
197#125—21no—
198#125C23×C10714yes—
199#124—24no—
200#124—24no—
201#124C23×C10712yes—
202#123—24no—
203#123—24no—
204C22⋊Q8—24no—
205C22⋊Q8—22no—
206C22⋊Q8—22no—
207C22⋊Q8—28no—
208C22⋊Q8—22no—
209#121—22no—
210C4×Q8—24no—
211C4×Q8—22no—
212C4×Q8—22no—
213C4×Q8—22no—
214C4×D4—24no—
215C4×D4—22no—
216#117—22no—
217#117—21no—
218#117D4×C10714yes—
219C2×C42C23×C10711yescharacteristic
220#107—24no—
221#106—24no—
222C4⋊C8—22no—
223#103—24no—
224#103—24no—
225#103—24no—
226#102—24no—
227C22⋊C8—22no—
228#97—21no—
229#97C23×C10714yes—
230#97C23×C10712yes—
231#41—44no—
232C2×Q8—24no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—84no—
237C2×Q8C2×D4×C10712yes—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4C2×D4×C10712yes—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4C2×D4×C10711yescharacteristic
244C22×C4C2×D4×C10712yes—
245C2×C8—22no—
246C2×C8—24no—
247C2×C8—42no—
248C4⋊C4—28no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—42no—
257C4⋊C4C2×D4×C10714yes—
258C4⋊C4C2×D4×C10714yes—
259C22⋊C4—24no—
260C22⋊C4—28no—
261C22⋊C4—24no—
262C22⋊C4—24no—
263C22⋊C4—41no—
264C42—24no—
265C42—24no—
266C42—41no—
267C42C2×D4×C10711yescharacteristic
268C42C2×D4×C10712yes—
269C42C24×C10711yescharacteristic
270C23—22no—
271C23#120×C10711yescharacteristic
272Q8—42no—
273Q8—44no—
274Q8—44no—
275Q8—44no—
276Q8—84no—
277D4—42no—
278D4—44no—
279D4—82no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—84no—
288C2×C4#120×C10712yes—
289C2×C4#120×C10711yescharacteristic
290C2×C4C22×D4×C10712yes—
291C2×C4C22×D4×C10711yescharacteristic
292C8—42no—
293C8—44no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—44no—
298C22C2×#120×C10711yescharacteristic
299C4—21no—
300C4—22no—
301C4—22no—
302C4—42no—
303C4—44no—
304C4—44no—
305C4—82no—
306C4#455×C10712yes—
307C2—41no—
308C2—82no—
309C2C2×#455×C10711yescharacteristic
310C2C107×#302012yes—
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
prime radical#532×C107C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3237C2semidirect
4. C107×#1664C2semidirect
6. C107×#1531C2semidirect
151. #19058C107direct (N × H)
157. #3237C2×C107semidirect
159. #1664C2×C107semidirect
161. #1531C2×C107semidirect
162. C107#19058direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35502
C107×#32372
C107×#31352
C107×#16642
C107×#15362
C107×#15312
#19058107