Finite Group Databasebeta

← C107×#11905 #41037869

Subgroups — C107×#11905 #41037869

Order 27392.

372 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2581C211yesmaximal, characteristic
2C107×#1801C211yesmaximal, characteristic
3C107×#1461C211yesmaximal, characteristic
4C107×#1354C212yesmaximal
5C107×#1353C212yesmaximal
6C2×C4×Q8×C107C411yescharacteristic
7C2×C4×Q8×C107C2211yescharacteristic
8#431×C107—21no—
9#423×C107—21no—
10C2×#101×C107—21no—
11#400×C107C411yescharacteristic
12#400×C107C2211yescharacteristic
13#395×C107C411yescharacteristic
14#395×C107C2211yescharacteristic
15#391×C107—21no—
16#389×C107—21no—
17#387×C107—21no—
18#387×C107—21no—
19#382×C107C411yescharacteristic
20#343×C107C2212yes—
21#324×C107—21no—
22#324×C107C2212yes—
23C22×Q8×C107C2×C411yescharacteristic
24C22×Q8×C107D411yescharacteristic
25C2×M16×C107—22no—
26C4×Q8×C107—41no—
27C4×Q8×C107—41no—
28C4×Q8×C107—41no—
29C4×Q8×C107—41no—
30C2×C4⋊C4×C107—21no—
31C2×C4⋊C4×C107—21no—
32C2×C4⋊C4×C107—21no—
33C2×C4⋊C4×C107—21no—
34C2×C4⋊C4×C107C2×C411yescharacteristic
35C2×C4⋊C4×C107C2×C411yescharacteristic
36C2×C4⋊C4×C107D411yescharacteristic
37C2×C4⋊C4×C107C2311yescharacteristic
38C2×C42×C107—21no—
39C2×C42×C107C2×C411yescharacteristic
40C2×C42×C107D411yescharacteristic
41C2×C42×C107D411yescharacteristic
42C4⋊C8×C107—41no—
43C4⋊C8×C107—41no—
44C4⋊C8×C107—41no—
45#101×C107—42no—
46C22⋊C8×C107—22no—
47C4×C8×C107—41no—
48#95×C107—21no—
49#95×C107—21no—
50#95×C107—21no—
51#95×C107—21no—
52#95×C107—21no—
53#95×C107—21no—
54#95×C107—21no—
55#95×C107C2×C411yescharacteristic
56#95×C107C2×C411yescharacteristic
57C2×Q8×C107—41no—
58C2×Q8×C107—41no—
59C2×Q8×C107—42no—
60C2×Q8×C107—41no—
61C2×Q8×C107SD1612yes—
62C2×Q8×C107Q1612yes—
63C22×C4×C107—21no—
64C22×C4×C107—21no—
65C22×C4×C107—21no—
66C22×C4×C107—21no—
67C22×C4×C107C22⋊C411yescharacteristic
68C22×C4×C107C22⋊C411yescharacteristic
69C22×C4×C107C22⋊C411yescharacteristic
70C22×C4×C107C22⋊C411yescharacteristic
71C22×C4×C107C22×C411yescharacteristic
72C22×C4×C107C2×D411yescharacteristic
73C22×C4×C107C2×D411yescharacteristic
74M16×C107—42no—
75M16×C107—42no—
76C2×C8×C107—42no—
77C2×C8×C107—42no—
78C4⋊C4×C107—41no—
79C4⋊C4×C107—41no—
80C4⋊C4×C107—41no—
81C4⋊C4×C107—41no—
82C4⋊C4×C107—42no—
83C4⋊C4×C107—42no—
84C4⋊C4×C107—42no—
85C4⋊C4×C107—41no—
86C4⋊C4×C107—41no—
87C42×C107—21no—
88C42×C107—21no—
89C42×C107—21no—
90C42×C107—21no—
91C42×C107—21no—
92C42×C107—21no—
93C42×C107—42no—
94C23×C107C2×C22⋊C411yescharacteristic
95Q8×C107—42no—
96Q8×C107—42no—
97Q8×C107—42no—
98Q8×C107—42no—
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—22no—
106C2×C4×C107—21no—
107C2×C4×C107—21no—
108C2×C4×C107—21no—
109C2×C4×C107—41no—
110C2×C4×C107—41no—
111C2×C4×C107—41no—
112C2×C4×C107—41no—
113C2×C4×C107—41no—
114C2×C4×C107—41no—
115C2×C4×C107—41no—
116C2×C4×C107—41no—
117C2×C4×C107—41no—
118C2×C4×C107—41no—
119C2×C4×C107—42no—
120C2×C4×C107—41no—
121C2×C4×C107—41no—
122C2×C4×C107—41no—
123C2×C4×C107#9911yescharacteristic
124C2×C4×C107#9911yescharacteristic
125C2×C4×C107#10312yes—
126C2×C4×C107#10312yes—
127C2×C4×C107C2×SD1611yescharacteristic
128C2×C4×C107C2×Q1611yescharacteristic
129C8×C107—82no—
130C8×C107—82no—
131C22×C107—21no—
132C22×C107—21no—
133C22×C107C2×#9911yescharacteristic
134C22×C107C2×#10311yescharacteristic
135C22×C107#42111yescharacteristic
136C4×C107—21no—
137C4×C107—21no—
138C4×C107—21no—
139C4×C107—22no—
140C4×C107—22no—
141C4×C107—21no—
142C4×C107—41no—
143C4×C107—41no—
144C4×C107—42no—
145C4×C107—41no—
146C4×C107—81no—
147C4×C107—81no—
148C4×C107—81no—
149#11905C10711yesmaximal, characteristic, direct product factor, Sylow
150C2×C107—21no—
151C2×C107—21no—
152C2×C107#152011yescharacteristic
153C2×C107#212011yescharacteristic
154C2×C107#213311yescharacteristic
155#2581C2×C10711yescharacteristic
156#1801C2×C10711yescharacteristic
157#1461C2×C10711yescharacteristic
158#1354C2×C10712yes—
159#1353C2×C10712yes—
160C107#1190511yescharacteristic, direct product factor, Sylow
161C2×C4×Q8C4×C10711yescharacteristic
162C2×C4×Q8C22×C10711yescharacteristic
163#431—21no—
164#423—21no—
165C2×#101—21no—
166#400C4×C10711yescharacteristic
167#400C22×C10711yescharacteristic
168#395C4×C10711yescharacteristic
169#395C22×C10711yescharacteristic
170#391—21no—
171#389—21no—
172#387—21no—
173#387—21no—
174#382C4×C10711yescharacteristic
175#343C22×C10712yes—
176#324—21no—
177#324C22×C10712yes—
178C22×Q8C2×C4×C10711yescharacteristic
179C22×Q8D4×C10711yescharacteristic
180C2×M16—22no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—41no—
184C4×Q8—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×C4×C10711yescharacteristic
190C2×C4⋊C4C2×C4×C10711yescharacteristic
191C2×C4⋊C4D4×C10711yescharacteristic
192C2×C4⋊C4C23×C10711yescharacteristic
193C2×C42—21no—
194C2×C42C2×C4×C10711yescharacteristic
195C2×C42D4×C10711yescharacteristic
196C2×C42D4×C10711yescharacteristic
197C4⋊C8—41no—
198C4⋊C8—41no—
199C4⋊C8—41no—
200#101—42no—
201C22⋊C8—22no—
202C4×C8—41no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95C2×C4×C10711yescharacteristic
211#95C2×C4×C10711yescharacteristic
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C2×Q8SD16×C10712yes—
217C2×Q8Q16×C10712yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊C4×C10711yescharacteristic
223C22×C4C22⋊C4×C10711yescharacteristic
224C22×C4C22⋊C4×C10711yescharacteristic
225C22×C4C22⋊C4×C10711yescharacteristic
226C22×C4C22×C4×C10711yescharacteristic
227C22×C4C2×D4×C10711yescharacteristic
228C22×C4C2×D4×C10711yescharacteristic
229M16—42no—
230M16—42no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—42no—
249C23C2×C22⋊C4×C10711yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4#99×C10711yescharacteristic
279C2×C4#99×C10711yescharacteristic
280C2×C4#103×C10712yes—
281C2×C4#103×C10712yes—
282C2×C4C2×SD16×C10711yescharacteristic
283C2×C4C2×Q16×C10711yescharacteristic
284C8—82no—
285C8—82no—
286C22—21no—
287C22—21no—
288C22C2×#99×C10711yescharacteristic
289C22C2×#103×C10711yescharacteristic
290C22#421×C10711yescharacteristic
291C4—21no—
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—21no—
297C4—41no—
298C4—42no—
299C4—41no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2C107×#152011yescharacteristic
307C2C107×#212011yescharacteristic
308C2C107×#213311yescharacteristic
subgroupG/H
center, socleC22×C107C2×#99
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C4⋊C4C23×C107
prime radicalC23×C107C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C22×C4×C107 ◁ C2×C4×Q8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
149. #11905C107direct (N × H)
160. C107#11905direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#25812
C107×#18012
C107×#14612
C107×#13542
C107×#13532
#11905107