Finite Group Databasebeta

← C107×#12975 #41038939

Subgroups — C107×#12975 #41038939

Order 27392.

416 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2979C211yesmaximal, characteristic
2C107×#2132C211yesmaximal, characteristic
3C107×#1884C211yesmaximal, characteristic
4C107×#1858C212yesmaximal, complemented
5C107×#1395C212yesmaximal, complemented
6#568×C107C2211yescharacteristic
7#532×C107C2211yescharacteristic
8#436×C107—22no—
9C8×D4×C107—22no—
10#431×C107—21no—
11#430×C107—22no—
12#421×C107—21no—
13#413×C107C2212yes—
14#410×C107C2211yescharacteristic
15#408×C107—21no—
16#408×C107C2212yes—
17#356×C107C412yescomplemented
18#355×C107C412yescomplemented
19#341×C107—22no—
20#339×C107—21no—
21C2×#41×C107D411yescharacteristic
22C2×#41×C107C2311yescharacteristic
23#131×C107—42no—
24C2×M16×C107—21no—
25C2×M16×C107—21no—
26C2×M16×C107—22no—
27C2×M16×C107—22no—
28C2×M16×C107D412yes—
29C22×C8×C107—21no—
30C22×C8×C107D412yes—
31C4⋊Q8×C107C2×C411yescharacteristic
32#127×C107Q811yescharacteristic
33#124×C107C2×C411yescharacteristic
34#124×C107Q811yescharacteristic
35#121×C107—22no—
36C4×D4×C107—22no—
37#117×C107—21no—
38C2×C42×C107D411yescharacteristic
39#108×C107—44no—
40C4⋊C8×C107—21no—
41C4⋊C8×C107—21no—
42#104×C107—42no—
43#101×C107C2×C414yes—
44#100×C107—22no—
45#99×C107—22no—
46C22⋊C8×C107—22no—
47C22⋊C8×C107—22no—
48C22⋊C8×C107—22no—
49C4×C8×C107—22no—
50#41×C107—41no—
51#41×C107—41no—
52#41×C107—41no—
53#41×C107—41no—
54C2×Q8×C107C4⋊C411yescharacteristic
55C2×Q8×C107C22×C411yescharacteristic
56C2×D4×C107—22no—
57C2×D4×C107—21no—
58C2×D4×C107C4⋊C411yescharacteristic
59C2×D4×C107C2×Q811yescharacteristic
60C2×D4×C107#4112yes—
61C22×C4×C107—21no—
62C22×C4×C107—21no—
63C22×C4×C107C2×D411yescharacteristic
64C22×C4×C107C2×D412yes—
65M16×C107—22no—
66M16×C107—24no—
67M16×C107—24no—
68M16×C107—42no—
69M16×C107—41no—
70M16×C107—42no—
71M16×C107—81no—
72C2×C8×C107—22no—
73C2×C8×C107—22no—
74C2×C8×C107—42no—
75C2×C8×C107—41no—
76C2×C8×C107—42no—
77C2×C8×C107—42no—
78C2×C8×C107—81no—
79C4⋊C4×C107—22no—
80C4⋊C4×C107—41no—
81C22⋊C4×C107—22no—
82C22⋊C4×C107—22no—
83C22⋊C4×C107—41no—
84C42×C107—21no—
85C42×C107—41no—
86C42×C107C4⋊C411yescharacteristic
87C42×C107C4⋊C411yescharacteristic
88C23×C107—21no—
89C23×C107C22⋊Q812yes—
90C23×C107#12311yescharacteristic
91Q8×C107—41no—
92Q8×C107—41no—
93D4×C107—41no—
94D4×C107—42no—
95D4×C107—41no—
96D4×C107—44no—
97D4×C107—81no—
98C2×C4×C107—21no—
99C2×C4×C107—21no—
100C2×C4×C107—22no—
101C2×C4×C107—21no—
102C2×C4×C107—22no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
105C2×C4×C107—42no—
106C2×C4×C107—41no—
107C2×C4×C107—41no—
108C2×C4×C107—81no—
109C2×C4×C107C2×C4⋊C411yescharacteristic
110C2×C4×C107C4×D412yes—
111C2×C4×C107#12011yescharacteristic
112C8×C107—44no—
113C8×C107—42no—
114C8×C107—42no—
115C8×C107—42no—
116C22×C107—21no—
117C22×C107—22no—
118C22×C107—41no—
119C22×C107—42no—
120C22×C107—42no—
121C22×C107—41no—
122C22×C107#38511yescharacteristic
123C4×C107—22no—
124C4×C107—22no—
125C4×C107—21no—
126C4×C107—41no—
127C4×C107—41no—
128C4×C107—161no—
129C4×C107B(4,𝔽2)11yescharacteristic
130C4×C107#45811yescharacteristic
131#12975C10711yesmaximal, characteristic, direct product factor, Sylow
132C2×C107—21no—
133C2×C107—41no—
134C2×C107—42no—
135C2×C107—81no—
136C2×C107#186711yescharacteristic
137#2979C2×C10711yescharacteristic
138#2132C2×C10711yescharacteristic
139#1884C2×C10711yescharacteristic
140#1858C2×C10712yescomplemented
141#1395C2×C10712yescomplemented
142C107#1297511yescharacteristic, direct product factor, Sylow
143#568C22×C10711yescharacteristic
144#532C22×C10711yescharacteristic
145#436—22no—
146C8×D4—22no—
147#431—21no—
148#430—22no—
149#421—21no—
150#413C22×C10712yes—
151#410C22×C10711yescharacteristic
152#408—21no—
153#408C22×C10712yes—
154#356C4×C10712yescomplemented
155#355C4×C10712yescomplemented
156#341—22no—
157#339—21no—
158C2×#41D4×C10711yescharacteristic
159C2×#41C23×C10711yescharacteristic
160#131—42no—
161C2×M16—21no—
162C2×M16—21no—
163C2×M16—22no—
164C2×M16—22no—
165C2×M16D4×C10712yes—
166C22×C8—21no—
167C22×C8D4×C10712yes—
168C4⋊Q8C2×C4×C10711yescharacteristic
169#127Q8×C10711yescharacteristic
170#124C2×C4×C10711yescharacteristic
171#124Q8×C10711yescharacteristic
172#121—22no—
173C4×D4—22no—
174#117—21no—
175C2×C42D4×C10711yescharacteristic
176#108—44no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179#104—42no—
180#101C2×C4×C10714yes—
181#100—22no—
182#99—22no—
183C22⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C4×C8—22no—
187#41—41no—
188#41—41no—
189#41—41no—
190#41—41no—
191C2×Q8C4⋊C4×C10711yescharacteristic
192C2×Q8C22×C4×C10711yescharacteristic
193C2×D4—22no—
194C2×D4—21no—
195C2×D4C4⋊C4×C10711yescharacteristic
196C2×D4C2×Q8×C10711yescharacteristic
197C2×D4#41×C10712yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4C2×D4×C10711yescharacteristic
201C22×C4C2×D4×C10712yes—
202M16—22no—
203M16—24no—
204M16—24no—
205M16—42no—
206M16—41no—
207M16—42no—
208M16—81no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—42no—
212C2×C8—41no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—81no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C22⋊C4—41no—
221C42—21no—
222C42—41no—
223C42C4⋊C4×C10711yescharacteristic
224C42C4⋊C4×C10711yescharacteristic
225C23—21no—
226C23C22⋊Q8×C10712yes—
227C23#123×C10711yescharacteristic
228Q8—41no—
229Q8—41no—
230D4—41no—
231D4—42no—
232D4—41no—
233D4—44no—
234D4—81no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4C2×C4⋊C4×C10711yescharacteristic
247C2×C4C4×D4×C10712yes—
248C2×C4#120×C10711yescharacteristic
249C8—44no—
250C8—42no—
251C8—42no—
252C8—42no—
253C22—21no—
254C22—22no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22#385×C10711yescharacteristic
260C4—22no—
261C4—22no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—161no—
266C4B(4,𝔽2)×C10711yescharacteristic
267C4#458×C10711yescharacteristic
268C2—21no—
269C2—41no—
270C2—42no—
271C2—81no—
272C2C107×#186711yescharacteristic
subgroupG/H
centerC4×C107B(4,𝔽2)
commutatorC2×Q8C22×C4×C107
Frattini, cosocleC2×#41C23×C107
socleC2×C107#1867
prime radical#532×C107C22
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C2×C4×C107 ◁ C2×#41×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C107×#1858C2semidirect
5. C107×#1395C2semidirect
17. #356×C107C4semidirect
18. #355×C107C4semidirect
131. #12975C107direct (N × H)
140. #1858C2×C107semidirect
141. #1395C2×C107semidirect
142. C107#12975direct (N × H)
154. #356C4×C107semidirect
155. #355C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#29792
C107×#21322
C107×#18842
C107×#18582
C107×#13952
#12975107