Finite Group Databasebeta

← C107×#10028 #41035992

Subgroups — C107×#10028 #41035992

Order 27392.

512 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3245C211yesmaximal, characteristic
2C107×#3112C212yesmaximal, complemented
3C107×#1985C211yesmaximal, characteristic, complemented
4C107×#1530C212yesmaximal, complemented
5C107×#1290C211yesmaximal, characteristic, complemented
6#532×C107C2212yes—
7C2×C4×Q8×C107C2211yescharacteristic
8#480×C107—22no—
9#477×C107—22no—
10#474×C107—22no—
11#466×C107—22no—
12#460×C107—22no—
13#459×C107—22no—
14#448×C107—22no—
15#440×C107—24no—
16#432×C107C2212yes—
17C2×C4⋊C8×C107C2211yescharacteristic
18C2×#97×C107C2211yescharacteristic
19#336×C107—22no—
20#329×C107—24no—
21C2×#41×C107—22no—
22C22×Q8×C107D411yescharacteristic
23C2×SD16×C107—24no—
24C2×D8×C107—22no—
25C22×C8×C107—21no—
26C22×C8×C107D412yes—
27C4⋊Q8×C107D412yes—
28#127×C107D412yes—
29#124×C107—22no—
30#121×C107—22no—
31#121×C107—22no—
32C4×Q8×C107—22no—
33C4×Q8×C107—22no—
34C4×D4×C107—22no—
35C4×D4×C107—22no—
36C2×C4⋊C4×C107—21no—
37C2×C4⋊C4×C107D411yescharacteristic
38C2×C42×C107—21no—
39C2×C42×C107C2311yescharacteristic
40#107×C107—24no—
41#107×C107—22no—
42C4⋊C8×C107—22no—
43C4⋊C8×C107—22no—
44#103×C107—24no—
45#102×C107—24no—
46#102×C107—24no—
47C22⋊C8×C107—22no—
48#97×C107—22no—
49#97×C107D414yes—
50#41×C107—84no—
51C2×Q8×C107—22no—
52C2×Q8×C107—22no—
53C2×Q8×C107—42no—
54C2×D4×C107—22no—
55C2×D4×C107—22no—
56C2×D4×C107—22no—
57C2×D4×C107—42no—
58C22×C4×C107—21no—
59C22×C4×C107—21no—
60C22×C4×C107—42no—
61C22×C4×C107C2×D411yescharacteristic
62C22×C4×C107C2×D411yescharacteristic
63C22×C4×C107#4111yescharacteristic
64SD16×C107—48no—
65D8×C107—82no—
66C2×C8×C107—22no—
67C2×C8×C107—24no—
68C2×C8×C107—22no—
69C2×C8×C107—41no—
70C2×C8×C107—41no—
71C2×C8×C107—42no—
72C4⋊C4×C107—22no—
73C4⋊C4×C107—22no—
74C4⋊C4×C107—22no—
75C4⋊C4×C107—42no—
76C22⋊C4×C107—42no—
77C22⋊C4×C107—42no—
78C42×C107—41no—
79C42×C107—41no—
80C42×C107C2×D412yes—
81C42×C107C2×D412yes—
82C23×C107—42no—
83C23×C107#12111yescharacteristic
84Q8×C107—24no—
85Q8×C107—42no—
86Q8×C107—82no—
87D4×C107—44no—
88D4×C107—42no—
89D4×C107—42no—
90D4×C107—82no—
91D4×C107—84no—
92C2×C4×C107—22no—
93C2×C4×C107—21no—
94C2×C4×C107—21no—
95C2×C4×C107—22no—
96C2×C4×C107—41no—
97C2×C4×C107—41no—
98C2×C4×C107—41no—
99C2×C4×C107—41no—
100C2×C4×C107—42no—
101C2×C4×C107—42no—
102C2×C4×C107—84no—
103C2×C4×C107#12012yes—
104C2×C4×C107#12011yescharacteristic
105C2×C4×C107#12112yes—
106C2×C4×C107#12711yescharacteristic
107C8×C107—42no—
108C8×C107—44no—
109C8×C107—42no—
110C22×C107—21no—
111C22×C107—21no—
112C22×C107—82no—
113C22×C107—82no—
114C22×C107—82no—
115C22×C107#39211yescharacteristic
116C22×C107#47212yes—
117C4×C107—21no—
118C4×C107—22no—
119C4×C107—22no—
120C4×C107—42no—
121C4×C107—81no—
122C4×C107—82no—
123C4×C107#45511yescharacteristic
124C4×C107#45611yescharacteristic
125#10028C10711yesmaximal, characteristic, direct product factor, Sylow
126C2×C107—22no—
127C2×C107—162no—
128C2×C107#200711yescharacteristic
129C2×C107#201011yescharacteristic
130C2×C107#201811yescharacteristic
131#3245C2×C10711yescharacteristic
132#3112C2×C10712yescomplemented
133#1985C2×C10711yescharacteristic, complemented
134#1530C2×C10712yescomplemented
135#1290C2×C10711yescharacteristic, complemented
136C107#1002811yescharacteristic, direct product factor, Sylow
137#532C22×C10712yes—
138C2×C4×Q8C22×C10711yescharacteristic
139#480—22no—
140#477—22no—
141#474—22no—
142#466—22no—
143#460—22no—
144#459—22no—
145#448—22no—
146#440—24no—
147#432C22×C10712yes—
148C2×C4⋊C8C22×C10711yescharacteristic
149C2×#97C22×C10711yescharacteristic
150#336—22no—
151#329—24no—
152C2×#41—22no—
153C22×Q8D4×C10711yescharacteristic
154C2×SD16—24no—
155C2×D8—22no—
156C22×C8—21no—
157C22×C8D4×C10712yes—
158C4⋊Q8D4×C10712yes—
159#127D4×C10712yes—
160#124—22no—
161#121—22no—
162#121—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×D4—22no—
166C4×D4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4D4×C10711yescharacteristic
169C2×C42—21no—
170C2×C42C23×C10711yescharacteristic
171#107—24no—
172#107—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175#103—24no—
176#102—24no—
177#102—24no—
178C22⋊C8—22no—
179#97—22no—
180#97D4×C10714yes—
181#41—84no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—42no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—42no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—42no—
192C22×C4C2×D4×C10711yescharacteristic
193C22×C4C2×D4×C10711yescharacteristic
194C22×C4#41×C10711yescharacteristic
195SD16—48no—
196D8—82no—
197C2×C8—22no—
198C2×C8—24no—
199C2×C8—22no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—42no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—41no—
210C42—41no—
211C42C2×D4×C10712yes—
212C42C2×D4×C10712yes—
213C23—42no—
214C23#121×C10711yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—82no—
218D4—44no—
219D4—42no—
220D4—42no—
221D4—82no—
222D4—84no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—84no—
234C2×C4#120×C10712yes—
235C2×C4#120×C10711yescharacteristic
236C2×C4#121×C10712yes—
237C2×C4#127×C10711yescharacteristic
238C8—42no—
239C8—44no—
240C8—42no—
241C22—21no—
242C22—21no—
243C22—82no—
244C22—82no—
245C22—82no—
246C22#392×C10711yescharacteristic
247C22#472×C10712yes—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—42no—
252C4—81no—
253C4—82no—
254C4#455×C10711yescharacteristic
255C4#456×C10711yescharacteristic
256C2—22no—
257C2—162no—
258C2C107×#200711yescharacteristic
259C2C107×#201011yescharacteristic
260C2C107×#201811yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC107×#3245C2
LCSG ▷ C2×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×#3112C2semidirect
3. C107×#1985C2semidirect
4. C107×#1530C2semidirect
5. C107×#1290C2semidirect
125. #10028C107direct (N × H)
132. #3112C2×C107semidirect
133. #1985C2×C107semidirect
134. #1530C2×C107semidirect
135. #1290C2×C107semidirect
136. C107#10028direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32452
C107×#31122
C107×#19852
C107×#15302
C107×#12902
#10028107