Finite Group Databasebeta

← C2×C107×#1660 #41044947

Subgroups — C2×C107×#1660 #41044947

Order 27392.

958 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#563×C107C211yesmaximal, characteristic
2C2×#501×C107C212yesmaximal, complemented
3C2×#497×C107C211yesmaximal, characteristic
4C107×#1660C218yesmaximal, direct product factor
5C2×#330×C107C212yesmaximal, complemented
6C2×#329×C107C211yesmaximal, characteristic
7C22×Q16×C107—21no—
8C22×SD16×C107—21no—
9#563×C107—24no—
10#563×C107—22no—
11#563×C107C2214yes—
12C2×C4⋊Q8×C107—21no—
13C2×C4⋊Q8×C107C2211yescharacteristic
14C2×#126×C107—22no—
15C2×#125×C107C2212yes—
16C2×#124×C107C2211yescharacteristic
17C2×#123×C107—21no—
18C2×C22⋊Q8×C107—22no—
19#501×C107—24no—
20#501×C107C2218yescomplemented
21#497×C107—22no—
22#497×C107C2214yes—
23C2×#107×C107—22no—
24C2×#106×C107—22no—
25C2×#97×C107C2211yescharacteristic
26C2×#97×C107C2212yes—
27#330×C107C2218yescomplemented
28#329×C107C2214yes—
29C22×Q8×C107—21no—
30C22×Q8×C107—21no—
31C22×Q8×C107D411yescharacteristic
32C22×D4×C107D411yescharacteristic
33C23×C4×C107—21no—
34C2×Q16×C107—24no—
35C2×Q16×C107—44no—
36C2×SD16×C107—24no—
37C2×SD16×C107—44no—
38C22×C8×C107—22no—
39C22×C8×C107—21no—
40C4⋊Q8×C107—24no—
41C4⋊Q8×C107—24no—
42C4⋊Q8×C107—22no—
43C4⋊Q8×C107—21no—
44C4⋊Q8×C107C2312yes—
45#126×C107—28no—
46#126×C107—28no—
47#125×C107—22no—
48#125×C107—22no—
49#125×C107D414yes—
50#125×C107C2314yes—
51#124×C107—22no—
52#124×C107D412yes—
53#124×C107C2312yes—
54#123×C107—24no—
55#123×C107—24no—
56C22⋊Q8×C107—28no—
57C22⋊Q8×C107—28no—
58C2×C4⋊C4×C107—22no—
59C2×C4⋊C4×C107—22no—
60C2×C4⋊C4×C107—22no—
61C2×C4⋊C4×C107—22no—
62C2×C4⋊C4×C107D412yes—
63C2×C4⋊C4×C107D412yes—
64C2×C22⋊C4×C107—22no—
65C2×C22⋊C4×C107—21no—
66C2×C22⋊C4×C107—22no—
67C2×C42×C107—21no—
68C2×C42×C107C2311yescharacteristic
69#107×C107—28no—
70#106×C107—28no—
71#97×C107—21no—
72#97×C107—22no—
73#97×C107C2312yes—
74#97×C107C2314yes—
75C24×C107—21no—
76C2×Q8×C107—24no—
77C2×Q8×C107—21no—
78C2×Q8×C107—22no—
79C2×Q8×C107—42no—
80C2×Q8×C107—42no—
81C2×Q8×C107—42no—
82C2×Q8×C107—41no—
83C2×Q8×C107—82no—
84C2×Q8×C107C2×D412yes—
85C2×D4×C107—21no—
86C2×D4×C107—42no—
87C2×D4×C107C2×D412yes—
88C22×C4×C107—22no—
89C22×C4×C107—21no—
90C22×C4×C107—22no—
91C22×C4×C107—24no—
92C22×C4×C107—41no—
93C22×C4×C107—82no—
94C22×C4×C107C2×D412yes—
95C22×C4×C107C2×D411yescharacteristic
96Q16×C107—48no—
97SD16×C107—48no—
98C2×C8×C107—28no—
99C2×C8×C107—24no—
100C2×C8×C107—24no—
101C2×C8×C107—22no—
102C4⋊C4×C107—28no—
103C4⋊C4×C107—24no—
104C4⋊C4×C107—24no—
105C4⋊C4×C107—22no—
106C4⋊C4×C107—22no—
107C4⋊C4×C107—24no—
108C4⋊C4×C107—24no—
109C4⋊C4×C107—24no—
110C4⋊C4×C107—42no—
111C4⋊C4×C107C2×D414yes—
112C4⋊C4×C107C2×D414yes—
113C22⋊C4×C107—28no—
114C22⋊C4×C107—24no—
115C22⋊C4×C107—24no—
116C22⋊C4×C107—24no—
117C42×C107—24no—
118C42×C107C2×D412yes—
119C42×C107C2×D411yescharacteristic
120C42×C107C2411yescharacteristic
121C23×C107—22no—
122C23×C107—42no—
123C23×C107—44no—
124C23×C107#12011yescharacteristic
125Q8×C107—42no—
126Q8×C107—42no—
127Q8×C107—42no—
128Q8×C107—81no—
129Q8×C107—82no—
130Q8×C107—84no—
131D4×C107—42no—
132D4×C107—81no—
133C2×C4×C107—22no—
134C2×C4×C107—24no—
135C2×C4×C107—24no—
136C2×C4×C107—22no—
137C2×C4×C107—24no—
138C2×C4×C107—44no—
139C2×C4×C107—42no—
140C2×C4×C107—44no—
141C2×C4×C107—42no—
142C2×C4×C107—84no—
143C2×C4×C107—82no—
144C2×C4×C107#12012yes—
145C2×C4×C107#12011yescharacteristic
146C2×C4×C107C22×D412yes—
147C2×C4×C107C22×D411yescharacteristic
148C8×C107—28no—
149C8×C107—24no—
150C22×C107—42no—
151C22×C107—44no—
152C22×C107—84no—
153C22×C107#45312yes—
154C22×C107#45614yes—
155C22×C107C2×#12011yescharacteristic
156C4×C107—21no—
157C4×C107—21no—
158C4×C107—22no—
159C4×C107—22no—
160C4×C107—44no—
161C4×C107—42no—
162C4×C107—44no—
163C4×C107—82no—
164C2×#1660C10711yesmaximal, characteristic, direct product factor, Sylow
165C2×C107—82no—
166C2×C107#166014yesdirect product factor
167C2×C107C2×#45311yescharacteristic
168C2×C107C2×#45612yes—
169C2×#563C2×C10711yescharacteristic
170C2×#501C2×C10712yescomplemented
171C2×#497C2×C10711yescharacteristic
172#1660C2×C10718yesdirect product factor
173C2×#330C2×C10712yescomplemented
174C2×#329C2×C10711yescharacteristic
175C107C2×#166011yescharacteristic, direct product factor, Sylow
176C22×Q16—21no—
177C22×SD16—21no—
178#563—24no—
179#563—22no—
180#563C22×C10714yes—
181C2×C4⋊Q8—21no—
182C2×C4⋊Q8C22×C10711yescharacteristic
183C2×#126—22no—
184C2×#125C22×C10712yes—
185C2×#124C22×C10711yescharacteristic
186C2×#123—21no—
187C2×C22⋊Q8—22no—
188#501—24no—
189#501C22×C10718yescomplemented
190#497—22no—
191#497C22×C10714yes—
192C2×#107—22no—
193C2×#106—22no—
194C2×#97C22×C10711yescharacteristic
195C2×#97C22×C10712yes—
196#330C22×C10718yescomplemented
197#329C22×C10714yes—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8D4×C10711yescharacteristic
201C22×D4D4×C10711yescharacteristic
202C23×C4—21no—
203C2×Q16—24no—
204C2×Q16—44no—
205C2×SD16—24no—
206C2×SD16—44no—
207C22×C8—21no—
208C22×C8—22no—
209C4⋊Q8—24no—
210C4⋊Q8—24no—
211C4⋊Q8—22no—
212C4⋊Q8—21no—
213C4⋊Q8C23×C10712yes—
214#126—28no—
215#126—28no—
216#125—22no—
217#125—22no—
218#125D4×C10714yes—
219#125C23×C10714yes—
220#124—22no—
221#124D4×C10712yes—
222#124C23×C10712yes—
223#123—24no—
224#123—24no—
225C22⋊Q8—28no—
226C22⋊Q8—28no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4D4×C10712yes—
232C2×C4⋊C4D4×C10712yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—22no—
236C2×C42—21no—
237C2×C42C23×C10711yescharacteristic
238#107—28no—
239#106—28no—
240#97—21no—
241#97—22no—
242#97C23×C10714yes—
243#97C23×C10712yes—
244C24—21no—
245C2×Q8—24no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×Q8C2×D4×C10712yes—
254C2×D4—21no—
255C2×D4—42no—
256C2×D4C2×D4×C10712yes—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—41no—
262C22×C4—82no—
263C22×C4C2×D4×C10712yes—
264C22×C4C2×D4×C10711yescharacteristic
265Q16—48no—
266SD16—48no—
267C2×C8—24no—
268C2×C8—28no—
269C2×C8—24no—
270C2×C8—22no—
271C4⋊C4—28no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—42no—
280C4⋊C4C2×D4×C10714yes—
281C4⋊C4C2×D4×C10714yes—
282C22⋊C4—28no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C22⋊C4—24no—
286C42—24no—
287C42C2×D4×C10712yes—
288C42C2×D4×C10711yescharacteristic
289C42C24×C10711yescharacteristic
290C23—22no—
291C23—42no—
292C23—44no—
293C23#120×C10711yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—42no—
297Q8—81no—
298Q8—82no—
299Q8—84no—
300D4—42no—
301D4—81no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—84no—
312C2×C4—82no—
313C2×C4#120×C10712yes—
314C2×C4#120×C10711yescharacteristic
315C2×C4C22×D4×C10712yes—
316C2×C4C22×D4×C10711yescharacteristic
317C8—24no—
318C8—28no—
319C22—42no—
320C22—44no—
321C22—84no—
322C22#453×C10712yes—
323C22#456×C10714yes—
324C22C2×#120×C10711yescharacteristic
325C4—21no—
326C4—21no—
327C4—22no—
328C4—22no—
329C4—44no—
330C4—42no—
331C4—44no—
332C4—82no—
333C2—82no—
334C2C107×#166014yesdirect product factor
335C2C2×#453×C10711yescharacteristic
336C2C2×#456×C10712yes—
subgroupG/H
center, socleC23×C107#120
commutator, Frattini, cosocleC42C24×C107
prime radicalC22×D4×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#501×C107C2semidirect
4. C107×#1660C2direct (N × H)
5. C2×#330×C107C2semidirect
20. #501×C107C22semidirect
27. #330×C107C22semidirect
164. C2×#1660C107direct (N × H)
166. C2×C107#1660direct (N × H)
170. C2×#501C2×C107semidirect
172. #1660C2×C107direct (N × H)
173. C2×#330C2×C107semidirect
175. C107C2×#1660direct (N × H)
189. #501C22×C107semidirect
196. #330C22×C107semidirect
334. C2C107×#1660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#563×C1072
C2×#501×C1072
C2×#497×C1072
C107×#16602
C2×#330×C1072
C2×#329×C1072
C2×#1660107