Finite Group Databasebeta

← C107×#7728 #41033692

Subgroups — C107×#7728 #41033692

Order 27392.

494 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2857C211yesmaximal, characteristic
2C107×#1817C211yesmaximal, characteristic
3C107×#1797C211yesmaximal, characteristic
4C107×#1271C214yesmaximal, complemented
5C2×C4⋊Q8×C107C411yescharacteristic
6C2×C22⋊Q8×C107—21no—
7C22×C42×C107C2211yescharacteristic
8C2×C4⋊C8×C107—21no—
9C2×C22⋊C8×C107—21no—
10C2×C22⋊C8×C107—21no—
11#391×C107—21no—
12#389×C107—21no—
13#389×C107C2212yes—
14#384×C107C411yescharacteristic
15#380×C107—21no—
16#380×C107C412yes—
17#336×C107—21no—
18#336×C107C2212yes—
19#336×C107C2212yes—
20C22×Q8×C107—21no—
21C23×C4×C107C2×C411yescharacteristic
22C23×C4×C107D411yescharacteristic
23C23×C4×C107D411yescharacteristic
24C22×C8×C107—22no—
25C22×C8×C107—22no—
26C4⋊Q8×C107—42no—
27C22⋊Q8×C107—42no—
28C22⋊Q8×C107—42no—
29C2×C4⋊C4×C107—21no—
30C2×C4⋊C4×C107—21no—
31C2×C4⋊C4×C107—21no—
32C2×C4⋊C4×C107—22no—
33C2×C4⋊C4×C107C2×C412yes—
34C2×C4⋊C4×C107C2×C412yes—
35C2×C22⋊C4×C107—22no—
36C2×C42×C107—42no—
37C2×C42×C107C2×C411yescharacteristic
38C2×C42×C107D411yescharacteristic
39C2×C42×C107D411yescharacteristic
40C2×C42×C107C2311yescharacteristic
41C4⋊C8×C107—42no—
42C22⋊C8×C107—42no—
43C22⋊C8×C107—42no—
44#95×C107—22no—
45#95×C107—22no—
46C24×C107C22⋊C411yescharacteristic
47C2×Q8×C107—42no—
48C2×Q8×C107—42no—
49C2×Q8×C107—42no—
50C22×C4×C107—22no—
51C22×C4×C107—22no—
52C22×C4×C107—22no—
53C22×C4×C107—22no—
54C22×C4×C107—22no—
55C22×C4×C107—22no—
56C22×C4×C107—41no—
57C22×C4×C107—41no—
58C22×C4×C107—41no—
59C22×C4×C107—41no—
60C22×C4×C107C22⋊C411yescharacteristic
61C22×C4×C107C22⋊C411yescharacteristic
62C22×C4×C107C22⋊C411yescharacteristic
63C22×C4×C107D812yes—
64C22×C4×C107SD1612yes—
65C22×C4×C107C22×C411yescharacteristic
66C22×C4×C107C2×D411yescharacteristic
67C22×C4×C107C2×D411yescharacteristic
68C2×C8×C107—42no—
69C2×C8×C107—42no—
70C2×C8×C107—42no—
71C2×C8×C107—42no—
72C2×C8×C107—42no—
73C2×C8×C107—42no—
74C4⋊C4×C107—24no—
75C4⋊C4×C107—42no—
76C4⋊C4×C107—42no—
77C4⋊C4×C107—42no—
78C4⋊C4×C107—42no—
79C4⋊C4×C107—42no—
80C4⋊C4×C107—42no—
81C22⋊C4×C107—44no—
82C42×C107—22no—
83C42×C107—22no—
84C42×C107—41no—
85C42×C107—41no—
86C23×C107—21no—
87C23×C107—21no—
88C23×C107—21no—
89C23×C107—21no—
90C23×C107—21no—
91C23×C107—21no—
92C23×C107#10212yes—
93C23×C107C2×C22⋊C411yescharacteristic
94Q8×C107—84no—
95C2×C4×C107—21no—
96C2×C4×C107—21no—
97C2×C4×C107—21no—
98C2×C4×C107—21no—
99C2×C4×C107—21no—
100C2×C4×C107—21no—
101C2×C4×C107—21no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
105C2×C4×C107—21no—
106C2×C4×C107—21no—
107C2×C4×C107—42no—
108C2×C4×C107—42no—
109C2×C4×C107—44no—
110C2×C4×C107—44no—
111C2×C4×C107—42no—
112C2×C4×C107—42no—
113C2×C4×C107—42no—
114C2×C4×C107—42no—
115C2×C4×C107—42no—
116C2×C4×C107—42no—
117C2×C4×C107#9912yes—
118C2×C4×C107#10112yes—
119C2×C4×C107#10212yes—
120C2×C4×C107#13112yes—
121C2×C4×C107C2×D811yescharacteristic
122C2×C4×C107C2×SD1611yescharacteristic
123C2×C4×C107#13712yes—
124C8×C107—82no—
125C8×C107—82no—
126C22×C107—22no—
127C22×C107—22no—
128C22×C107—22no—
129C22×C107—41no—
130C22×C107—41no—
131C22×C107—41no—
132C22×C107—41no—
133C22×C107#40811yescharacteristic
134C22×C107C2×#9911yescharacteristic
135C22×C107C2×#10111yescharacteristic
136C22×C107C2×#10211yescharacteristic
137C22×C107#41911yescharacteristic
138C22×C107#42111yescharacteristic
139C22×C107#42111yescharacteristic
140C4×C107—22no—
141C4×C107—22no—
142C4×C107—22no—
143C4×C107—22no—
144C4×C107—21no—
145C4×C107—22no—
146C4×C107—21no—
147C4×C107—82no—
148C4×C107—82no—
149#7728C10711yesmaximal, characteristic, direct product factor, Sylow
150C2×C107—42no—
151C2×C107#147211yescharacteristic
152C2×C107#148011yescharacteristic
153C2×C107#149711yescharacteristic
154C2×C107#151111yescharacteristic
155C2×C107#151911yescharacteristic
156C2×C107#153711yescharacteristic
157C2×C107#154611yescharacteristic
158#2857C2×C10711yescharacteristic
159#1817C2×C10711yescharacteristic
160#1797C2×C10711yescharacteristic
161#1271C2×C10714yescomplemented
162C107#772811yescharacteristic, direct product factor, Sylow
163C2×C4⋊Q8C4×C10711yescharacteristic
164C2×C22⋊Q8—21no—
165C22×C42C22×C10711yescharacteristic
166C2×C4⋊C8—21no—
167C2×C22⋊C8—21no—
168C2×C22⋊C8—21no—
169#391—21no—
170#389—21no—
171#389C22×C10712yes—
172#384C4×C10711yescharacteristic
173#380—21no—
174#380C4×C10712yes—
175#336—21no—
176#336C22×C10712yes—
177#336C22×C10712yes—
178C22×Q8—21no—
179C23×C4C2×C4×C10711yescharacteristic
180C23×C4D4×C10711yescharacteristic
181C23×C4D4×C10711yescharacteristic
182C22×C8—22no—
183C22×C8—22no—
184C4⋊Q8—42no—
185C22⋊Q8—42no—
186C22⋊Q8—42no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4C2×C4×C10712yes—
192C2×C4⋊C4C2×C4×C10712yes—
193C2×C22⋊C4—22no—
194C2×C42—42no—
195C2×C42C2×C4×C10711yescharacteristic
196C2×C42D4×C10711yescharacteristic
197C2×C42D4×C10711yescharacteristic
198C2×C42C23×C10711yescharacteristic
199C4⋊C8—42no—
200C22⋊C8—42no—
201C22⋊C8—42no—
202#95—22no—
203#95—22no—
204C24C22⋊C4×C10711yescharacteristic
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—42no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4C22⋊C4×C10711yescharacteristic
219C22×C4C22⋊C4×C10711yescharacteristic
220C22×C4C22⋊C4×C10711yescharacteristic
221C22×C4D8×C10712yes—
222C22×C4SD16×C10712yes—
223C22×C4C22×C4×C10711yescharacteristic
224C22×C4C2×D4×C10711yescharacteristic
225C22×C4C2×D4×C10711yescharacteristic
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C4⋊C4—24no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C22⋊C4—44no—
240C42—22no—
241C42—22no—
242C42—41no—
243C42—41no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#102×C10712yes—
251C23C2×C22⋊C4×C10711yescharacteristic
252Q8—84no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4#99×C10712yes—
276C2×C4#101×C10712yes—
277C2×C4#102×C10712yes—
278C2×C4#131×C10712yes—
279C2×C4C2×D8×C10711yescharacteristic
280C2×C4C2×SD16×C10711yescharacteristic
281C2×C4#137×C10712yes—
282C8—82no—
283C8—82no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22#408×C10711yescharacteristic
292C22C2×#99×C10711yescharacteristic
293C22C2×#101×C10711yescharacteristic
294C22C2×#102×C10711yescharacteristic
295C22#419×C10711yescharacteristic
296C22#421×C10711yescharacteristic
297C22#421×C10711yescharacteristic
298C4—22no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—21no—
303C4—22no—
304C4—21no—
305C4—82no—
306C4—82no—
307C2—42no—
308C2C107×#147211yescharacteristic
309C2C107×#148011yescharacteristic
310C2C107×#149711yescharacteristic
311C2C107×#151111yescharacteristic
312C2C107×#151911yescharacteristic
313C2C107×#153711yescharacteristic
314C2C107×#154611yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC24×C107C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C107×#1271C2semidirect
149. #7728C107direct (N × H)
161. #1271C2×C107semidirect
162. C107#7728direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#28572
C107×#18172
C107×#17972
C107×#12712
#7728107