Finite Group Databasebeta

← C107×#9285 #41035249

Subgroups — C107×#9285 #41035249

Order 27392.

426 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3210C211yesmaximal, characteristic
2C107×#2981C211yesmaximal, characteristic
3C107×#1531C211yesmaximal, characteristic, complemented
4C107×#1530C211yesmaximal, characteristic
5C107×#1497C211yesmaximal, characteristic, complemented
6C107×#1287C211yesmaximal, characteristic, complemented
7C107×#1275C211yesmaximal, characteristic, complemented
8#533×C107C2211yescharacteristic
9#532×C107C2211yescharacteristic
10#494×C107C411yescharacteristic
11#492×C107C411yescharacteristic
12#487×C107C411yescharacteristic
13#486×C107C411yescharacteristic
14#464×C107—22no—
15#452×C107—22no—
16#436×C107—21no—
17#435×C107—22no—
18C8×D4×C107—21no—
19#432×C107C2211yescharacteristic
20#432×C107C2211yescharacteristic
21#431×C107C2211yescharacteristic
22#431×C107C2211yescharacteristic
23#408×C107—22no—
24C2×#97×C107C2211yescharacteristic
25#330×C107—22no—
26#329×C107—22no—
27Q8⋊C8×C107—21no—
28Q8⋊C8×C107—21no—
29C2×#41×C107D412yes—
30C2×Q16×C107—22no—
31C2×SD16×C107—22no—
32C2×M16×C107—22no—
33C22×C8×C107—21no—
34C22×C8×C107—22no—
35C4⋊Q8×C107C2×C411yescharacteristic
36C4⋊Q8×C107C2×C411yescharacteristic
37C4⋊Q8×C107C2×C411yescharacteristic
38#127×C107C2×C411yescharacteristic
39#125×C107—21no—
40#124×C107D412yes—
41C22⋊Q8×C107—21no—
42C22⋊Q8×C107—21no—
43#121×C107—21no—
44#121×C107—21no—
45C4×Q8×C107—21no—
46C4×Q8×C107—21no—
47C4×D4×C107—21no—
48C4×D4×C107—21no—
49#117×C107—21no—
50C2×C42×C107C2311yescharacteristic
51C4⋊C8×C107—21no—
52C4⋊C8×C107—21no—
53C4⋊C8×C107—21no—
54C4⋊C8×C107—21no—
55#103×C107—22no—
56#102×C107—22no—
57C22⋊C8×C107—22no—
58C22⋊C8×C107—22no—
59C22⋊C8×C107—21no—
60C22⋊C8×C107—21no—
61C22⋊C8×C107—21no—
62C22⋊C8×C107—21no—
63#97×C107—21no—
64#97×C107—21no—
65#97×C107—21no—
66#97×C107D412yes—
67C4×C8×C107C2×C411yescharacteristic
68C4×C8×C107C2×C411yescharacteristic
69C4×C8×C107D411yescharacteristic
70C4×C8×C107D411yescharacteristic
71#41×C107—82no—
72C2×Q8×C107—21no—
73C2×Q8×C107—21no—
74C2×Q8×C107C22⋊C412yes—
75C2×D4×C107—22no—
76C2×D4×C107—21no—
77C2×D4×C107—21no—
78C2×D4×C107C22⋊C412yes—
79C22×C4×C107—22no—
80C22×C4×C107C2×D411yescharacteristic
81C22×C4×C107#4111yescharacteristic
82C22×C4×C107#4111yescharacteristic
83Q16×C107—82no—
84SD16×C107—82no—
85M16×C107—82no—
86C2×C8×C107—22no—
87C2×C8×C107—21no—
88C2×C8×C107—21no—
89C2×C8×C107—21no—
90C2×C8×C107—21no—
91C2×C8×C107—22no—
92C2×C8×C107—41no—
93C2×C8×C107—41no—
94C2×C8×C107—41no—
95C2×C8×C107—82no—
96C4⋊C4×C107—21no—
97C4⋊C4×C107—21no—
98C4⋊C4×C107—21no—
99C4⋊C4×C107—21no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107—21no—
102C4⋊C4×C107—41no—
103C4⋊C4×C107—41no—
104C22⋊C4×C107—22no—
105C22⋊C4×C107—22no—
106C22⋊C4×C107—41no—
107C42×C107—41no—
108C42×C107C22×C411yescharacteristic
109C42×C107C2×D411yescharacteristic
110C42×C107C2×D411yescharacteristic
111C42×C107C2×D411yescharacteristic
112C23×C107—22no—
113C23×C107#12311yescharacteristic
114Q8×C107—42no—
115Q8×C107—42no—
116Q8×C107—41no—
117Q8×C107—41no—
118D4×C107—42no—
119D4×C107—41no—
120D4×C107—41no—
121D4×C107—81no—
122D4×C107—82no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—22no—
126C2×C4×C107—41no—
127C2×C4×C107—41no—
128C2×C4×C107—42no—
129C2×C4×C107—42no—
130C2×C4×C107—41no—
131C2×C4×C107—41no—
132C2×C4×C107C2×C22⋊C411yescharacteristic
133C2×C4×C107C4×D411yescharacteristic
134C2×C4×C107C4×D411yescharacteristic
135C2×C4×C107#12011yescharacteristic
136C2×C4×C107#12111yescharacteristic
137C2×C4×C107#12111yescharacteristic
138C8×C107—42no—
139C8×C107—41no—
140C8×C107—42no—
141C8×C107—41no—
142C8×C107—41no—
143C8×C107—41no—
144C8×C107—81no—
145C22×C107—21no—
146C22×C107—21no—
147C22×C107—21no—
148C22×C107—42no—
149C22×C107—42no—
150C22×C107—42no—
151C22×C107#38611yescharacteristic
152C4×C107—21no—
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—21no—
156C4×C107—21no—
157C4×C107—42no—
158C4×C107—81no—
159C4×C107—81no—
160C4×C107#44311yescharacteristic
161C4×C107#44411yescharacteristic
162#9285C10711yesmaximal, characteristic, direct product factor, Sylow
163C2×C107—41no—
164C2×C107—82no—
165C2×C107#187611yescharacteristic
166C2×C107#190211yescharacteristic
167C2×C107#191111yescharacteristic
168#3210C2×C10711yescharacteristic
169#2981C2×C10711yescharacteristic
170#1531C2×C10711yescharacteristic, complemented
171#1530C2×C10711yescharacteristic
172#1497C2×C10711yescharacteristic, complemented
173#1287C2×C10711yescharacteristic, complemented
174#1275C2×C10711yescharacteristic, complemented
175C107#928511yescharacteristic, direct product factor, Sylow
176#533C22×C10711yescharacteristic
177#532C22×C10711yescharacteristic
178#494C4×C10711yescharacteristic
179#492C4×C10711yescharacteristic
180#487C4×C10711yescharacteristic
181#486C4×C10711yescharacteristic
182#464—22no—
183#452—22no—
184#436—21no—
185#435—22no—
186C8×D4—21no—
187#432C22×C10711yescharacteristic
188#432C22×C10711yescharacteristic
189#431C22×C10711yescharacteristic
190#431C22×C10711yescharacteristic
191#408—22no—
192C2×#97C22×C10711yescharacteristic
193#330—22no—
194#329—22no—
195Q8⋊C8—21no—
196Q8⋊C8—21no—
197C2×#41D4×C10712yes—
198C2×Q16—22no—
199C2×SD16—22no—
200C2×M16—22no—
201C22×C8—21no—
202C22×C8—22no—
203C4⋊Q8C2×C4×C10711yescharacteristic
204C4⋊Q8C2×C4×C10711yescharacteristic
205C4⋊Q8C2×C4×C10711yescharacteristic
206#127C2×C4×C10711yescharacteristic
207#125—21no—
208#124D4×C10712yes—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×D4—21no—
216C4×D4—21no—
217#117—21no—
218C2×C42C23×C10711yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223#103—22no—
224#102—22no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231#97—21no—
232#97—21no—
233#97—21no—
234#97D4×C10712yes—
235C4×C8C2×C4×C10711yescharacteristic
236C4×C8C2×C4×C10711yescharacteristic
237C4×C8D4×C10711yescharacteristic
238C4×C8D4×C10711yescharacteristic
239#41—82no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8C22⋊C4×C10712yes—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4C22⋊C4×C10712yes—
247C22×C4—22no—
248C22×C4C2×D4×C10711yescharacteristic
249C22×C4#41×C10711yescharacteristic
250C22×C4#41×C10711yescharacteristic
251Q16—82no—
252SD16—82no—
253M16—82no—
254C2×C8—22no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—82no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C42—41no—
276C42C22×C4×C10711yescharacteristic
277C42C2×D4×C10711yescharacteristic
278C42C2×D4×C10711yescharacteristic
279C42C2×D4×C10711yescharacteristic
280C23—22no—
281C23#123×C10711yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—41no—
285Q8—41no—
286D4—42no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—82no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4C2×C22⋊C4×C10711yescharacteristic
301C2×C4C4×D4×C10711yescharacteristic
302C2×C4C4×D4×C10711yescharacteristic
303C2×C4#120×C10711yescharacteristic
304C2×C4#121×C10711yescharacteristic
305C2×C4#121×C10711yescharacteristic
306C8—42no—
307C8—41no—
308C8—42no—
309C8—41no—
310C8—41no—
311C8—41no—
312C8—81no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22#386×C10711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—81no—
327C4—81no—
328C4#443×C10711yescharacteristic
329C4#444×C10711yescharacteristic
330C2—41no—
331C2—82no—
332C2C107×#187611yescharacteristic
333C2C107×#190211yescharacteristic
334C2C107×#191111yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radical#532×C107C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1531C2semidirect
5. C107×#1497C2semidirect
6. C107×#1287C2semidirect
7. C107×#1275C2semidirect
162. #9285C107direct (N × H)
170. #1531C2×C107semidirect
172. #1497C2×C107semidirect
173. #1287C2×C107semidirect
174. #1275C2×C107semidirect
175. C107#9285direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32102
C107×#29812
C107×#15312
C107×#15302
C107×#14972
C107×#12872
C107×#12752
#9285107