Finite Group Databasebeta

← C107×#36600 #41062564

Subgroups — C107×#36600 #41062564

Order 27392.

1574 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2859C211yesmaximal, characteristic
2C107×#2859C212yesmaximal
3C107×#2585C218yesmaximal
4C107×#2570C214yesmaximal
5C107×#2552C212yesmaximal
6C107×#2453C214yesmaximal
7C107×#2370C214yesmaximal
8C107×#2355C212yesmaximal
9C4×#125×C107C211yesmaximal, characteristic
10C4×#125×C107C212yesmaximal
11C42×Q8×C107C211yesmaximal, characteristic
12C2×#125×C107C2214yes—
13C2×#125×C107C2211yescharacteristic
14C2×#125×C107C2212yes—
15C2×C4×Q8×C107C2212yes—
16C2×C4×Q8×C107C2211yescharacteristic
17#400×C107C2218yes—
18#398×C107C2218yes—
19#398×C107C2218yes—
20#391×C107C2214yes—
21#389×C107C2214yes—
22#389×C107C2218yes—
23#389×C107C2214yes—
24#389×C107C2214yes—
25#389×C107C2212yes—
26#389×C107C2214yes—
27#389×C107C2218yes—
28#387×C107C2218yes—
29#387×C107C2214yes—
30#387×C107C2218yes—
31#387×C107C2218yes—
32#387×C107C2218yes—
33#384×C107C2214yes—
34#384×C107C2212yes—
35#382×C107C2211yescharacteristic
36#382×C107C2212yes—
37#382×C107C2214yes—
38C4×C4⋊C4×C107C2214yes—
39C4×C4⋊C4×C107C2211yescharacteristic
40C4×C4⋊C4×C107C2212yes—
41C4×C4⋊C4×C107C2214yes—
42C4×C4⋊C4×C107C2212yes—
43C4×C4⋊C4×C107C2212yes—
44C4×C4⋊C4×C107C2214yes—
45C4×C4⋊C4×C107C2218yes—
46C4×C4⋊C4×C107C2214yes—
47C43×C107C2211yescharacteristic
48C43×C107C2212yes—
49C22×Q8×C107C2311yescharacteristic
50#125×C107—216no—
51#125×C107—24no—
52#125×C107—28no—
53C4×Q8×C107—28no—
54C4×Q8×C107Q818yes—
55C2×C4⋊C4×C107C2312yes—
56C2×C4⋊C4×C107C2314yes—
57C2×C4⋊C4×C107C2312yes—
58C2×C4⋊C4×C107C2314yes—
59C2×C4⋊C4×C107C2314yes—
60C2×C4⋊C4×C107C2318yes—
61C2×C4⋊C4×C107C2314yes—
62C2×C4⋊C4×C107C2318yes—
63C2×C4⋊C4×C107C2318yes—
64C2×C4⋊C4×C107C2314yes—
65C2×C4⋊C4×C107C2314yes—
66C2×C4⋊C4×C107C2318yes—
67C2×C4⋊C4×C107C2311yescharacteristic
68C2×C4⋊C4×C107C2312yes—
69C2×C4⋊C4×C107C2312yes—
70C2×C42×C107C2312yes—
71C2×C42×C107C2311yescharacteristic
72C2×C42×C107C2312yes—
73C2×C42×C107C2314yes—
74C2×C42×C107C2314yes—
75C2×C42×C107C2314yes—
76C2×C42×C107C2312yes—
77C2×C42×C107C2318yes—
78C2×C42×C107C2312yes—
79C2×C42×C107C2311yescharacteristic
80C2×C42×C107C2311yescharacteristic
81#95×C107C2314yes—
82#95×C107C2314yes—
83#95×C107C2312yes—
84#95×C107C2318yes—
85#95×C107C2314yes—
86#95×C107C2314yes—
87#95×C107C2318yes—
88#95×C107C2318yes—
89#95×C107C2318yes—
90#95×C107C2318yes—
91C2×Q8×C107—24no—
92C2×Q8×C107C2×Q814yes—
93C22×C4×C107C2412yes—
94C22×C4×C107C2414yes—
95C22×C4×C107C2414yes—
96C22×C4×C107C2418yes—
97C22×C4×C107C2412yes—
98C22×C4×C107C2412yes—
99C22×C4×C107C2411yescharacteristic
100C22×C4×C107C2414yes—
101C22×C4×C107C2412yes—
102C22×C4×C107C2411yescharacteristic
103C22×C4×C107C2411yescharacteristic
104C4⋊C4×C107—28no—
105C4⋊C4×C107—216no—
106C4⋊C4×C107—216no—
107C4⋊C4×C107—28no—
108C4⋊C4×C107—216no—
109C4⋊C4×C107—28no—
110C4⋊C4×C107—24no—
111C4⋊C4×C107—28no—
112C4⋊C4×C107—24no—
113C4⋊C4×C107—44no—
114C4⋊C4×C107—48no—
115C4⋊C4×C107—44no—
116C4⋊C4×C107C2×Q818yes—
117C4⋊C4×C107C2×Q814yes—
118C4⋊C4×C107#4118yes—
119C42×C107—28no—
120C42×C107—24no—
121C42×C107—28no—
122C42×C107—24no—
123C42×C107—22no—
124C42×C107—44no—
125C42×C107—42no—
126C42×C107—48no—
127C42×C107C2×Q818yes—
128C42×C107C2×Q814yes—
129C42×C107#4114yes—
130C23×C107C2511yescharacteristic
131Q8×C107—28no—
132C2×C4×C107—22no—
133C2×C4×C107—24no—
134C2×C4×C107—24no—
135C2×C4×C107—22no—
136C2×C4×C107—24no—
137C2×C4×C107—22no—
138C2×C4×C107—24no—
139C2×C4×C107—24no—
140C2×C4×C107—22no—
141C2×C4×C107—24no—
142C2×C4×C107—28no—
143C2×C4×C107—24no—
144C2×C4×C107—28no—
145C2×C4×C107—22no—
146C2×C4×C107—24no—
147C2×C4×C107—24no—
148C2×C4×C107—28no—
149C2×C4×C107—22no—
150C2×C4×C107—24no—
151C2×C4×C107C22×Q814yes—
152C2×C4×C107C22×Q812yes—
153C2×C4×C107C22×Q814yes—
154C2×C4×C107C22×Q812yes—
155C2×C4×C107C22×Q812yes—
156C2×C4×C107C2×#4118yes—
157C2×C4×C107C2×#4114yes—
158C2×C4×C107C2×#4114yes—
159C2×C4×C107C2×#4112yes—
160C2×C4×C1072−1+412yes—
161C22×C107C23×Q811yescharacteristic
162C22×C107C22×#4112yes—
163C22×C107C22×#4111yescharacteristic
164C22×C107C2×2−1+411yescharacteristic
165C22×C107#58512yes—
166C4×C107—24no—
167C4×C107—24no—
168C4×C107—24no—
169C4×C107—22no—
170C4×C107—28no—
171C4×C107—44no—
172C4×C107—48no—
173C4×C107—42no—
174C4×C107—44no—
175C4×C107#53314yes—
176C4×C107#55714yes—
177#36600C10711yesmaximal, characteristic, direct product factor, Sylow
178C2×C107C2×#53311yescharacteristic
179C2×C107C2×#55711yescharacteristic
180C2×C107#348012yes—
181C2×C107#350411yescharacteristic
182C2×C107#351512yes—
183#2859C2×C10711yescharacteristic
184#2859C2×C10712yes—
185#2585C2×C10718yes—
186#2570C2×C10714yes—
187#2552C2×C10712yes—
188#2453C2×C10714yes—
189#2370C2×C10714yes—
190#2355C2×C10712yes—
191C4×#125C2×C10712yes—
192C4×#125C2×C10711yescharacteristic
193C42×Q8C2×C10711yescharacteristic
194C107#3660011yescharacteristic, direct product factor, Sylow
195C2×#125C22×C10712yes—
196C2×#125C22×C10711yescharacteristic
197C2×#125C22×C10714yes—
198C2×C4×Q8C22×C10712yes—
199C2×C4×Q8C22×C10711yescharacteristic
200#400C22×C10718yes—
201#398C22×C10718yes—
202#398C22×C10718yes—
203#391C22×C10714yes—
204#389C22×C10712yes—
205#389C22×C10714yes—
206#389C22×C10714yes—
207#389C22×C10718yes—
208#389C22×C10718yes—
209#389C22×C10714yes—
210#389C22×C10714yes—
211#387C22×C10714yes—
212#387C22×C10718yes—
213#387C22×C10718yes—
214#387C22×C10718yes—
215#387C22×C10718yes—
216#384C22×C10714yes—
217#384C22×C10712yes—
218#382C22×C10711yescharacteristic
219#382C22×C10712yes—
220#382C22×C10714yes—
221C4×C4⋊C4C22×C10714yes—
222C4×C4⋊C4C22×C10718yes—
223C4×C4⋊C4C22×C10712yes—
224C4×C4⋊C4C22×C10714yes—
225C4×C4⋊C4C22×C10712yes—
226C4×C4⋊C4C22×C10714yes—
227C4×C4⋊C4C22×C10714yes—
228C4×C4⋊C4C22×C10712yes—
229C4×C4⋊C4C22×C10711yescharacteristic
230C43C22×C10711yescharacteristic
231C43C22×C10712yes—
232C22×Q8C23×C10711yescharacteristic
233#125—216no—
234#125—28no—
235#125—24no—
236C4×Q8—28no—
237C4×Q8Q8×C10718yes—
238C2×C4⋊C4C23×C10714yes—
239C2×C4⋊C4C23×C10714yes—
240C2×C4⋊C4C23×C10712yes—
241C2×C4⋊C4C23×C10714yes—
242C2×C4⋊C4C23×C10718yes—
243C2×C4⋊C4C23×C10718yes—
244C2×C4⋊C4C23×C10714yes—
245C2×C4⋊C4C23×C10718yes—
246C2×C4⋊C4C23×C10712yes—
247C2×C4⋊C4C23×C10714yes—
248C2×C4⋊C4C23×C10714yes—
249C2×C4⋊C4C23×C10718yes—
250C2×C4⋊C4C23×C10711yescharacteristic
251C2×C4⋊C4C23×C10712yes—
252C2×C4⋊C4C23×C10712yes—
253C2×C42C23×C10712yes—
254C2×C42C23×C10714yes—
255C2×C42C23×C10714yes—
256C2×C42C23×C10711yescharacteristic
257C2×C42C23×C10712yes—
258C2×C42C23×C10714yes—
259C2×C42C23×C10712yes—
260C2×C42C23×C10718yes—
261C2×C42C23×C10712yes—
262C2×C42C23×C10711yescharacteristic
263C2×C42C23×C10711yescharacteristic
264#95C23×C10714yes—
265#95C23×C10714yes—
266#95C23×C10712yes—
267#95C23×C10718yes—
268#95C23×C10714yes—
269#95C23×C10714yes—
270#95C23×C10718yes—
271#95C23×C10718yes—
272#95C23×C10718yes—
273#95C23×C10718yes—
274C2×Q8—24no—
275C2×Q8C2×Q8×C10714yes—
276C22×C4C24×C10712yes—
277C22×C4C24×C10714yes—
278C22×C4C24×C10714yes—
279C22×C4C24×C10718yes—
280C22×C4C24×C10712yes—
281C22×C4C24×C10712yes—
282C22×C4C24×C10711yescharacteristic
283C22×C4C24×C10714yes—
284C22×C4C24×C10712yes—
285C22×C4C24×C10711yescharacteristic
286C22×C4C24×C10711yescharacteristic
287C4⋊C4—28no—
288C4⋊C4—216no—
289C4⋊C4—216no—
290C4⋊C4—216no—
291C4⋊C4—28no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C4⋊C4—24no—
295C4⋊C4—24no—
296C4⋊C4—44no—
297C4⋊C4—48no—
298C4⋊C4—44no—
299C4⋊C4C2×Q8×C10718yes—
300C4⋊C4C2×Q8×C10714yes—
301C4⋊C4#41×C10718yes—
302C42—28no—
303C42—24no—
304C42—28no—
305C42—24no—
306C42—22no—
307C42—44no—
308C42—42no—
309C42—48no—
310C42C2×Q8×C10718yes—
311C42C2×Q8×C10714yes—
312C42#41×C10714yes—
313C23C25×C10711yescharacteristic
314Q8—28no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—28no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4C22×Q8×C10714yes—
335C2×C4C22×Q8×C10712yes—
336C2×C4C22×Q8×C10714yes—
337C2×C4C22×Q8×C10712yes—
338C2×C4C22×Q8×C10712yes—
339C2×C4C2×#41×C10718yes—
340C2×C4C2×#41×C10714yes—
341C2×C4C2×#41×C10714yes—
342C2×C4C2×#41×C10712yes—
343C2×C42−1+4×C10712yes—
344C22C23×Q8×C10711yescharacteristic
345C22C22×#41×C10712yes—
346C22C22×#41×C10711yescharacteristic
347C22C2×2−1+4×C10711yescharacteristic
348C22#585×C10712yes—
349C4—24no—
350C4—24no—
351C4—24no—
352C4—22no—
353C4—28no—
354C4—44no—
355C4—48no—
356C4—42no—
357C4—44no—
358C4#533×C10714yes—
359C4#557×C10714yes—
360C2C2×#533×C10711yescharacteristic
361C2C2×#557×C10711yescharacteristic
362C2C107×#348012yes—
363C2C107×#350411yescharacteristic
364C2C107×#351512yes—
subgroupG/H
center, socle, prime radicalC23×C107C25
commutator, Frattini, cosocleC23C25×C107
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C107 ◁ G

Complements

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

NH ≅ G/Ntype
177. #36600C107direct (N × H)
194. C107#36600direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#28592
C107×#25852
C107×#25702
C107×#25522
C107×#24532
C107×#23702
C107×#23552
C4×#125×C1072
C42×Q8×C1072
#36600107