Finite Group Databasebeta

← C107×#10030 #41035994

Subgroups — C107×#10030 #41035994

Order 27392.

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

normal subgroups only

This group has 520 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×#3249C211yesmaximal, characteristic, complemented
2C107×#3110C212yesmaximal
3C107×#1955C211yesmaximal, characteristic
4C107×#1531C212yesmaximal, complemented
5C107×#1290C211yesmaximal, characteristic, complemented
6#533×C107C2212yes—
7C2×C4×D4×C107C2211yescharacteristic
8#484×C107—22no—
9#477×C107—22no—
10#474×C107—22no—
11#467×C107—22no—
12#462×C107—22no—
13#461×C107—22no—
14#450×C107—22no—
15#440×C107—24no—
16#432×C107C2212yes—
17C2×C4⋊C8×C107C2211yescharacteristic
18C2×C22⋊C8×C107—22no—
19C2×#97×C107C2211yescharacteristic
20#330×C107—24no—
21C22×D4×C107D411yescharacteristic
22C23×C4×C107—21no—
23C2×Q16×C107—22no—
24C2×SD16×C107—24no—
25C22×C8×C107—21no—
26C22×C8×C107D412yes—
27C4⋊Q8×C107D412yes—
28C4⋊Q8×C107D412yes—
29#125×C107—22no—
30C22⋊Q8×C107—22no—
31C22⋊Q8×C107—22no—
32C4×Q8×C107—22no—
33C4×Q8×C107—22no—
34C4×D4×C107—22no—
35C4×D4×C107—22no—
36#117×C107—22no—
37C2×C4⋊C4×C107D411yescharacteristic
38C2×C22⋊C4×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#103×C107—24no—
46#102×C107—24no—
47C22⋊C8×C107—22no—
48C22⋊C8×C107—44no—
49#97×C107—22no—
50#97×C107D414yes—
51C24×C107—21no—
52C2×Q8×C107—22no—
53C2×Q8×C107—22no—
54C2×D4×C107—22no—
55C2×D4×C107—42no—
56C22×C4×C107—21no—
57C22×C4×C107—42no—
58C22×C4×C107—42no—
59C22×C4×C107—41no—
60C22×C4×C107—41no—
61C22×C4×C107C2×D411yescharacteristic
62C22×C4×C107C2×D411yescharacteristic
63C22×C4×C107#4111yescharacteristic
64Q16×C107—82no—
65SD16×C107—48no—
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—22no—
76C4⋊C4×C107—22no—
77C4⋊C4×C107—42no—
78C4⋊C4×C107—42no—
79C22⋊C4×C107—42no—
80C22⋊C4×C107—42no—
81C42×C107—42no—
82C42×C107C2×D412yes—
83C42×C107C2×D412yes—
84C23×C107—22no—
85C23×C107—42no—
86C23×C107—41no—
87C23×C107—41no—
88C23×C107—42no—
89C23×C107#12111yescharacteristic
90Q8×C107—44no—
91Q8×C107—42no—
92Q8×C107—42no—
93D4×C107—24no—
94D4×C107—42no—
95C2×C4×C107—22no—
96C2×C4×C107—21no—
97C2×C4×C107—21no—
98C2×C4×C107—41no—
99C2×C4×C107—42no—
100C2×C4×C107—42no—
101C2×C4×C107—42no—
102C2×C4×C107—41no—
103C2×C4×C107—82no—
104C2×C4×C107—81no—
105C2×C4×C107—81no—
106C2×C4×C107#12012yes—
107C2×C4×C107#12011yescharacteristic
108C2×C4×C107#12112yes—
109C2×C4×C107#12711yescharacteristic
110C8×C107—42no—
111C8×C107—44no—
112C8×C107—42no—
113C22×C107—21no—
114C22×C107—21no—
115C22×C107—44no—
116C22×C107—42no—
117C22×C107—82no—
118C22×C107—81no—
119C22×C107—81no—
120C22×C107#39211yescharacteristic
121C22×C107#47312yes—
122C4×C107—21no—
123C4×C107—22no—
124C4×C107—22no—
125C4×C107—81no—
126C4×C107—82no—
127C4×C107—82no—
128C4×C107#45311yescharacteristic
129C4×C107#45411yescharacteristic
130#10030C10711yesmaximal, characteristic, direct product factor, Sylow
131C2×C107—22no—
132C2×C107—82no—
133C2×C107#200611yescharacteristic
134C2×C107#201011yescharacteristic
135C2×C107#202011yescharacteristic
136#3249C2×C10711yescharacteristic, complemented
137#3110C2×C10712yes—
138#1955C2×C10711yescharacteristic
139#1531C2×C10712yescomplemented
140#1290C2×C10711yescharacteristic, complemented
141C107#1003011yescharacteristic, direct product factor, Sylow
142#533C22×C10712yes—
143C2×C4×D4C22×C10711yescharacteristic
144#484—22no—
145#477—22no—
146#474—22no—
147#467—22no—
148#462—22no—
149#461—22no—
150#450—22no—
151#440—24no—
152#432C22×C10712yes—
153C2×C4⋊C8C22×C10711yescharacteristic
154C2×C22⋊C8—22no—
155C2×#97C22×C10711yescharacteristic
156#330—24no—
157C22×D4D4×C10711yescharacteristic
158C23×C4—21no—
159C2×Q16—22no—
160C2×SD16—24no—
161C22×C8—21no—
162C22×C8D4×C10712yes—
163C4⋊Q8D4×C10712yes—
164C4⋊Q8D4×C10712yes—
165#125—22no—
166C22⋊Q8—22no—
167C22⋊Q8—22no—
168C4×Q8—22no—
169C4×Q8—22no—
170C4×D4—22no—
171C4×D4—22no—
172#117—22no—
173C2×C4⋊C4D4×C10711yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42C23×C10711yescharacteristic
176#107—24no—
177#107—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180#103—24no—
181#103—24no—
182#102—24no—
183C22⋊C8—22no—
184C22⋊C8—44no—
185#97—22no—
186#97D4×C10714yes—
187C24—21no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×D4—22no—
191C2×D4—42no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4C2×D4×C10711yescharacteristic
198C22×C4C2×D4×C10711yescharacteristic
199C22×C4#41×C10711yescharacteristic
200Q16—82no—
201SD16—48no—
202C2×C8—22no—
203C2×C8—24no—
204C2×C8—22no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—42no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C42—42no—
218C42C2×D4×C10712yes—
219C42C2×D4×C10712yes—
220C23—22no—
221C23—42no—
222C23—41no—
223C23—41no—
224C23—42no—
225C23#121×C10711yescharacteristic
226Q8—44no—
227Q8—42no—
228Q8—42no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4#120×C10712yes—
243C2×C4#120×C10711yescharacteristic
244C2×C4#121×C10712yes—
245C2×C4#127×C10711yescharacteristic
246C8—42no—
247C8—44no—
248C8—42no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#392×C10711yescharacteristic
257C22#473×C10712yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—81no—
262C4—82no—
263C4—82no—
264C4#453×C10711yescharacteristic
265C4#454×C10711yescharacteristic
266C2—22no—
267C2—82no—
268C2C107×#200611yescharacteristic
269C2C107×#201011yescharacteristic
270C2C107×#202011yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
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
1. C107×#3249C2semidirect
4. C107×#1531C2semidirect
5. C107×#1290C2semidirect
130. #10030C107direct (N × H)
136. #3249C2×C107semidirect
139. #1531C2×C107semidirect
140. #1290C2×C107semidirect
141. C107#10030direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32492
C107×#31102
C107×#19552
C107×#15312
C107×#12902
#10030107