Finite Group Databasebeta

← C107×#18189 #41044153

Subgroups — C107×#18189 #41044153

Order 27392.

902 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3502C211yesmaximal, characteristic
2C107×#3113C212yesmaximal
3C107×#2399C211yesmaximal, characteristic
4C107×#1611C214yesmaximal
5C107×#1605C214yesmaximal
6C107×#1506C212yesmaximal
7C107×#1467C211yesmaximal, characteristic
8Q82×C107—22no—
9#557×C107—22no—
10#557×C107—24no—
11#544×C107—21no—
12#544×C107C2214yes—
13#533×C107—22no—
14#533×C107C2212yes—
15#519×C107—21no—
16C2×C4×Q8×C107C2211yescharacteristic
17C2×C4×Q8×C107C2211yescharacteristic
18#483×C107C2214yes—
19#475×C107—22no—
20#462×C107—22no—
21#451×C107C2214yes—
22#441×C107—24no—
23#432×C107C2212yes—
24#398×C107—21no—
25#398×C107C2212yes—
26#395×C107—21no—
27#395×C107C2212yes—
28C4×C4⋊C4×C107—22no—
29#376×C107C2211yescharacteristic
30#328×C107C2218yes—
31#324×C107C2214yes—
32C22×Q8×C107D411yescharacteristic
33C22×Q8×C107C2311yescharacteristic
34C2×Q16×C107—24no—
35C4⋊Q8×C107—22no—
36C4⋊Q8×C107—22no—
37C4⋊Q8×C107—24no—
38C4⋊Q8×C107—28no—
39C4⋊Q8×C107D412yes—
40C4⋊Q8×C107D412yes—
41#125×C107—24no—
42#125×C107—24no—
43#125×C107—28no—
44#125×C107—22no—
45C22⋊Q8×C107—22no—
46C22⋊Q8×C107—24no—
47C22⋊Q8×C107C2314yes—
48C4×Q8×C107—24no—
49C4×Q8×C107—24no—
50C4×Q8×C107—24no—
51C4×Q8×C107—24no—
52C4×Q8×C107—22no—
53C4×Q8×C107—22no—
54C4×Q8×C107—22no—
55C4×Q8×C107—22no—
56C4×Q8×C107—22no—
57C4×Q8×C107D414yes—
58#117×C107—24no—
59#117×C107—22no—
60C2×C4⋊C4×C107—22no—
61C2×C4⋊C4×C107—22no—
62C2×C4⋊C4×C107—21no—
63C2×C4⋊C4×C107D411yescharacteristic
64C2×C4⋊C4×C107C2311yescharacteristic
65C2×C4⋊C4×C107C2312yes—
66C2×C42×C107—21no—
67C2×C42×C107—21no—
68C2×C42×C107D412yes—
69C2×C42×C107C2311yescharacteristic
70#106×C107—24no—
71C4⋊C8×C107—22no—
72#103×C107—24no—
73#103×C107—24no—
74C22⋊C8×C107C2314yes—
75#97×C107—22no—
76#95×C107—21no—
77#95×C107—22no—
78#95×C107—22no—
79#95×C107C2312yes—
80C2×Q8×C107—24no—
81C2×Q8×C107—22no—
82C2×Q8×C107—22no—
83C2×Q8×C107—24no—
84C2×Q8×C107—22no—
85C2×Q8×C107—42no—
86C2×Q8×C107C2×D414yes—
87C22×C4×C107—22no—
88C22×C4×C107—21no—
89C22×C4×C107—21no—
90C22×C4×C107C2×D411yescharacteristic
91C22×C4×C107C2×D411yescharacteristic
92C22×C4×C107C2×D412yes—
93C22×C4×C107C2×D412yes—
94C22×C4×C107C2411yescharacteristic
95Q16×C107—48no—
96C2×C8×C107—24no—
97C4⋊C4×C107—24no—
98C4⋊C4×C107—24no—
99C4⋊C4×C107—24no—
100C4⋊C4×C107—28no—
101C4⋊C4×C107—22no—
102C4⋊C4×C107—22no—
103C4⋊C4×C107—22no—
104C4⋊C4×C107—22no—
105C4⋊C4×C107—24no—
106C4⋊C4×C107—24no—
107C4⋊C4×C107—24no—
108C4⋊C4×C107—22no—
109C4⋊C4×C107—44no—
110C4⋊C4×C107—42no—
111C4⋊C4×C107—44no—
112C4⋊C4×C107C2×D414yes—
113C22⋊C4×C107—24no—
114C42×C107—24no—
115C42×C107—28no—
116C42×C107—22no—
117C42×C107—22no—
118C42×C107—24no—
119C42×C107—41no—
120C42×C107—41no—
121C42×C107C2×D412yes—
122C42×C107C2×D412yes—
123C23×C107C22×D411yescharacteristic
124Q8×C107—28no—
125Q8×C107—24no—
126Q8×C107—44no—
127Q8×C107—42no—
128Q8×C107—44no—
129Q8×C107—84no—
130C2×C4×C107—22no—
131C2×C4×C107—22no—
132C2×C4×C107—22no—
133C2×C4×C107—22no—
134C2×C4×C107—24no—
135C2×C4×C107—22no—
136C2×C4×C107—24no—
137C2×C4×C107—24no—
138C2×C4×C107—22no—
139C2×C4×C107—41no—
140C2×C4×C107—42no—
141C2×C4×C107—41no—
142C2×C4×C107—41no—
143C2×C4×C107—42no—
144C2×C4×C107—42no—
145C2×C4×C107—41no—
146C2×C4×C107—42no—
147C2×C4×C107#12011yescharacteristic
148C2×C4×C107#12012yes—
149C2×C4×C107#12011yescharacteristic
150C2×C4×C107#13714yes—
151C2×C4×C107C22×D412yes—
152C8×C107—44no—
153C22×C107—21no—
154C22×C107—21no—
155C22×C107C2×#12011yescharacteristic
156C22×C107C2×#13712yes—
157C4×C107—22no—
158C4×C107—24no—
159C4×C107—21no—
160C4×C107—22no—
161C4×C107—44no—
162C4×C107—44no—
163C4×C107—42no—
164C4×C107—42no—
165C4×C107—44no—
166C4×C107—81no—
167C4×C107#45612yes—
168#18189C10711yesmaximal, characteristic, direct product factor, Sylow
169C2×C107—22no—
170C2×C107#300411yescharacteristic
171C2×C107C2×#45611yescharacteristic
172C2×C107#302511yescharacteristic
173#3502C2×C10711yescharacteristic
174#3113C2×C10712yes—
175#2399C2×C10711yescharacteristic
176#1611C2×C10714yes—
177#1605C2×C10714yes—
178#1506C2×C10712yes—
179#1467C2×C10711yescharacteristic
180C107#1818911yescharacteristic, direct product factor, Sylow
181Q82—22no—
182#557—22no—
183#557—24no—
184#544—21no—
185#544C22×C10714yes—
186#533—22no—
187#533C22×C10712yes—
188#519—21no—
189C2×C4×Q8C22×C10711yescharacteristic
190C2×C4×Q8C22×C10711yescharacteristic
191#483C22×C10714yes—
192#475—22no—
193#462—22no—
194#451C22×C10714yes—
195#441—24no—
196#432C22×C10712yes—
197#398—21no—
198#398C22×C10712yes—
199#395—21no—
200#395C22×C10712yes—
201C4×C4⋊C4—22no—
202#376C22×C10711yescharacteristic
203#328C22×C10718yes—
204#324C22×C10714yes—
205C22×Q8D4×C10711yescharacteristic
206C22×Q8C23×C10711yescharacteristic
207C2×Q16—24no—
208C4⋊Q8—22no—
209C4⋊Q8—22no—
210C4⋊Q8—24no—
211C4⋊Q8—28no—
212C4⋊Q8D4×C10712yes—
213C4⋊Q8D4×C10712yes—
214#125—24no—
215#125—24no—
216#125—28no—
217#125—22no—
218C22⋊Q8—22no—
219C22⋊Q8—24no—
220C22⋊Q8C23×C10714yes—
221C4×Q8—24no—
222C4×Q8—24no—
223C4×Q8—24no—
224C4×Q8—24no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×Q8D4×C10714yes—
231#117—24no—
232#117—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4D4×C10711yescharacteristic
237C2×C4⋊C4C23×C10711yescharacteristic
238C2×C4⋊C4C23×C10712yes—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42D4×C10712yes—
242C2×C42C23×C10711yescharacteristic
243#106—24no—
244C4⋊C8—22no—
245#103—24no—
246#103—24no—
247C22⋊C8C23×C10714yes—
248#97—22no—
249#95—21no—
250#95—22no—
251#95—22no—
252#95C23×C10712yes—
253C2×Q8—24no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—24no—
257C2×Q8—22no—
258C2×Q8—42no—
259C2×Q8C2×D4×C10714yes—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4C2×D4×C10711yescharacteristic
264C22×C4C2×D4×C10711yescharacteristic
265C22×C4C2×D4×C10712yes—
266C22×C4C2×D4×C10712yes—
267C22×C4C24×C10711yescharacteristic
268Q16—48no—
269C2×C8—24no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—28no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—22no—
282C4⋊C4—44no—
283C4⋊C4—42no—
284C4⋊C4—44no—
285C4⋊C4C2×D4×C10714yes—
286C22⋊C4—24no—
287C42—24no—
288C42—28no—
289C42—22no—
290C42—22no—
291C42—24no—
292C42—41no—
293C42—41no—
294C42C2×D4×C10712yes—
295C42C2×D4×C10712yes—
296C23C22×D4×C10711yescharacteristic
297Q8—28no—
298Q8—24no—
299Q8—44no—
300Q8—42no—
301Q8—44no—
302Q8—84no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4#120×C10711yescharacteristic
321C2×C4#120×C10712yes—
322C2×C4#120×C10711yescharacteristic
323C2×C4#137×C10714yes—
324C2×C4C22×D4×C10712yes—
325C8—44no—
326C22—21no—
327C22—21no—
328C22C2×#120×C10711yescharacteristic
329C22C2×#137×C10712yes—
330C4—22no—
331C4—24no—
332C4—21no—
333C4—22no—
334C4—44no—
335C4—44no—
336C4—42no—
337C4—42no—
338C4—44no—
339C4—81no—
340C4#456×C10712yes—
341C2—22no—
342C2C107×#300411yescharacteristic
343C2C2×#456×C10711yescharacteristic
344C2C107×#302511yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC23×C107C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
168. #18189C107direct (N × H)
180. C107#18189direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35022
C107×#31132
C107×#23992
C107×#16112
C107×#16052
C107×#15062
C107×#14672
#18189107