Finite Group Databasebeta

← C107×#7751 #41033715

Subgroups — C107×#7751 #41033715

Order 27392.

492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2724C211yesmaximal, characteristic
2C107×#2057C212yesmaximal, complemented
3C107×#2013C211yesmaximal, characteristic
4C107×#1271C212yesmaximal, complemented
5C107×#1270C211yesmaximal, characteristic
6C22×SD16×C107—21no—
7C2×C4⋊Q8×C107C2211yescharacteristic
8C2×#123×C107—21no—
9C2×#107×C107—22no—
10C2×#103×C107—21no—
11#398×C107—21no—
12#397×C107—22no—
13#390×C107C2211yescharacteristic
14#389×C107C2212yes—
15#385×C107—22no—
16#340×C107—22no—
17#336×C107C2211yescharacteristic
18#336×C107C2212yes—
19C22×Q8×C107—21no—
20C22×D4×C107D411yescharacteristic
21C23×C4×C107—21no—
22C2×SD16×C107—42no—
23C2×SD16×C107—42no—
24C2×SD16×C107—42no—
25C22×C8×C107—22no—
26C22×C8×C107—21no—
27C4⋊Q8×C107—42no—
28#123×C107—42no—
29#123×C107—42no—
30C2×C4⋊C4×C107—22no—
31C2×C4⋊C4×C107—22no—
32C2×C4⋊C4×C107—21no—
33C2×C4⋊C4×C107D412yes—
34C2×C4⋊C4×C107D412yes—
35C2×C4⋊C4×C107D411yescharacteristic
36C2×C22⋊C4×C107—22no—
37C2×C22⋊C4×C107—21no—
38C2×C22⋊C4×C107—22no—
39C2×C42×C107C2311yescharacteristic
40#107×C107—44no—
41#103×C107—42no—
42#95×C107—22no—
43#95×C107—21no—
44#95×C107—22no—
45C24×C107—21no—
46C2×Q8×C107—22no—
47C2×Q8×C107—41no—
48C2×Q8×C107—41no—
49C2×Q8×C107—41no—
50C2×Q8×C107—41no—
51C2×Q8×C107—41no—
52C2×D4×C107—21no—
53C2×D4×C107—41no—
54C2×D4×C107—41no—
55C2×D4×C107D812yes—
56C22×C4×C107—22no—
57C22×C4×C107—21no—
58C22×C4×C107—22no—
59C22×C4×C107—42no—
60C22×C4×C107—41no—
61C22×C4×C107—81no—
62C22×C4×C107—81no—
63C22×C4×C107C2×D411yescharacteristic
64C22×C4×C107C2×D412yes—
65SD16×C107—48no—
66C2×C8×C107—22no—
67C2×C8×C107—24no—
68C2×C8×C107—42no—
69C2×C8×C107—41no—
70C2×C8×C107—41no—
71C2×C8×C107—42no—
72C4⋊C4×C107—24no—
73C4⋊C4×C107—22no—
74C4⋊C4×C107—22no—
75C4⋊C4×C107—41no—
76C4⋊C4×C107—42no—
77C4⋊C4×C107—42no—
78C4⋊C4×C107—42no—
79C4⋊C4×C107—42no—
80C4⋊C4×C107—81no—
81C22⋊C4×C107—42no—
82C22⋊C4×C107—44no—
83C22⋊C4×C107—42no—
84C22⋊C4×C107—42no—
85C42×C107—41no—
86C23×C107—22no—
87C23×C107—42no—
88C23×C107—41no—
89C23×C107—42no—
90C23×C107—41no—
91C23×C107#12011yescharacteristic
92Q8×C107—42no—
93Q8×C107—42no—
94Q8×C107—81no—
95Q8×C107—81no—
96D4×C107—42no—
97D4×C107—81no—
98C2×C4×C107—21no—
99C2×C4×C107—22no—
100C2×C4×C107—22no—
101C2×C4×C107—21no—
102C2×C4×C107—42no—
103C2×C4×C107—42no—
104C2×C4×C107—42no—
105C2×C4×C107—42no—
106C2×C4×C107—41no—
107C2×C4×C107—42no—
108C2×C4×C107—42no—
109C2×C4×C107—42no—
110C2×C4×C107—42no—
111C2×C4×C107—84no—
112C2×C4×C107—81no—
113C2×C4×C107—81no—
114C2×C4×C107C2×D811yescharacteristic
115C2×C4×C107#13512yes—
116C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C107#13712yes—
118C8×C107—44no—
119C8×C107—42no—
120C22×C107—42no—
121C22×C107—44no—
122C22×C107—82no—
123C22×C107—81no—
124C22×C107—81no—
125C22×C107#44711yescharacteristic
126C22×C107#45212yes—
127C22×C107#45311yescharacteristic
128C22×C107#45612yes—
129C22×C107B(4,𝔽2)11yescharacteristic
130C4×C107—21no—
131C4×C107—21no—
132C4×C107—22no—
133C4×C107—22no—
134C4×C107—82no—
135C4×C107—82no—
136C4×C107—81no—
137C4×C107—82no—
138#7751C10711yesmaximal, characteristic, direct product factor, Sylow
139C2×C107—82no—
140C2×C107#159511yescharacteristic
141C2×C107#160312yes—
142C2×C107#163011yescharacteristic
143C2×C107#164712yes—
144C2×C107#166011yescharacteristic
145#2724C2×C10711yescharacteristic
146#2057C2×C10712yescomplemented
147#2013C2×C10711yescharacteristic
148#1271C2×C10712yescomplemented
149#1270C2×C10711yescharacteristic
150C107#775111yescharacteristic, direct product factor, Sylow
151C22×SD16—21no—
152C2×C4⋊Q8C22×C10711yescharacteristic
153C2×#123—21no—
154C2×#107—22no—
155C2×#103—21no—
156#398—21no—
157#397—22no—
158#390C22×C10711yescharacteristic
159#389C22×C10712yes—
160#385—22no—
161#340—22no—
162#336C22×C10712yes—
163#336C22×C10711yescharacteristic
164C22×Q8—21no—
165C22×D4D4×C10711yescharacteristic
166C23×C4—21no—
167C2×SD16—42no—
168C2×SD16—42no—
169C2×SD16—42no—
170C22×C8—21no—
171C22×C8—22no—
172C4⋊Q8—42no—
173#123—42no—
174#123—42no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4D4×C10712yes—
179C2×C4⋊C4D4×C10712yes—
180C2×C4⋊C4D4×C10711yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—22no—
184C2×C42C23×C10711yescharacteristic
185#107—44no—
186#103—42no—
187#95—22no—
188#95—21no—
189#95—22no—
190C24—21no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4D8×C10712yes—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4C2×D4×C10711yescharacteristic
209C22×C4C2×D4×C10712yes—
210SD16—48no—
211C2×C8—22no—
212C2×C8—24no—
213C2×C8—42no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—42no—
217C4⋊C4—24no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—81no—
226C22⋊C4—42no—
227C22⋊C4—44no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C42—41no—
231C23—22no—
232C23—42no—
233C23—41no—
234C23—42no—
235C23—41no—
236C23#120×C10711yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—81no—
240Q8—81no—
241D4—42no—
242D4—81no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—84no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4C2×D8×C10711yescharacteristic
260C2×C4#135×C10712yes—
261C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
262C2×C4#137×C10712yes—
263C8—42no—
264C8—44no—
265C22—44no—
266C22—42no—
267C22—81no—
268C22—81no—
269C22—82no—
270C22#447×C10711yescharacteristic
271C22#452×C10712yes—
272C22#453×C10711yescharacteristic
273C22#456×C10712yes—
274C22B(4,𝔽2)×C10711yescharacteristic
275C4—21no—
276C4—21no—
277C4—22no—
278C4—22no—
279C4—81no—
280C4—82no—
281C4—82no—
282C4—82no—
283C2—82no—
284C2C107×#159511yescharacteristic
285C2C107×#160312yes—
286C2C107×#163011yescharacteristic
287C2C107×#164712yes—
288C2C107×#166011yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2057C2semidirect
4. C107×#1271C2semidirect
138. #7751C107direct (N × H)
146. #2057C2×C107semidirect
148. #1271C2×C107semidirect
150. C107#7751direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#27242
C107×#20572
C107×#20132
C107×#12712
C107×#12702
#7751107