Finite Group Databasebeta

← C107×#8916 #41034880

Subgroups — C107×#8916 #41034880

Order 27392.

354 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
1C107×#2995C211yesmaximal, characteristic
2C107×#1849C211yesmaximal, characteristic, complemented
3C107×#1569C211yesmaximal, characteristic, complemented
4C107×#1524C211yesmaximal, characteristic
5C107×#1495C211yesmaximal, characteristic
6C107×#1302C211yesmaximal, characteristic, complemented
7C107×#1299C211yesmaximal, characteristic, complemented
8#529×C107C2211yescharacteristic
9#446×C107—21no—
10#436×C107—21no—
11#435×C107—21no—
12#435×C107—21no—
13#433×C107—21no—
14#432×C107C2211yescharacteristic
15#431×C107C2211yescharacteristic
16C2×#108×C107—21no—
17C2×#108×C107—21no—
18#424×C107—21no—
19#423×C107C2211yescharacteristic
20#423×C107C2211yescharacteristic
21C4×M16×C107C2211yescharacteristic
22C2×#97×C107C2211yescharacteristic
23#335×C107—21no—
24#334×C107—21no—
25#330×C107C411yescharacteristic
26#330×C107C411yescharacteristic
27#329×C107C411yescharacteristic
28#329×C107C411yescharacteristic
29Q8⋊C8×C107—21no—
30D4⋊C8×C107—21no—
31C2×M16×C107—21no—
32C2×M16×C107—21no—
33C2×M16×C107—21no—
34C2×M16×C107D411yescharacteristic
35C2×M16×C107D411yescharacteristic
36C22×C8×C107—21no—
37C22×C8×C107—21no—
38#126×C107—21no—
39#125×C107C2×C411yescharacteristic
40#124×C107C2×C411yescharacteristic
41#123×C107—21no—
42C22⋊Q8×C107Q811yescharacteristic
43#121×C107Q811yescharacteristic
44C4×Q8×C107D411yescharacteristic
45C4×D4×C107—21no—
46C4×D4×C107D411yescharacteristic
47#117×C107—21no—
48C2×C42×C107C2311yescharacteristic
49#108×C107—42no—
50#108×C107—42no—
51C4⋊C8×C107—21no—
52C4⋊C8×C107—21no—
53C4⋊C8×C107—21no—
54C4⋊C8×C107—21no—
55C4⋊C8×C107—21no—
56C4⋊C8×C107—21no—
57C4⋊C8×C107—21no—
58C4⋊C8×C107D411yescharacteristic
59C4⋊C8×C107D411yescharacteristic
60C22⋊C8×C107—21no—
61C22⋊C8×C107—21no—
62C22⋊C8×C107—21no—
63C22⋊C8×C107—21no—
64#97×C107—21no—
65#97×C107—21no—
66#97×C107—21no—
67#97×C107C2×C411yescharacteristic
68#97×C107C2×C411yescharacteristic
69#97×C107C2×C411yescharacteristic
70#97×C107C2×C411yescharacteristic
71C4×C8×C107—21no—
72C4×C8×C107—21no—
73C4×C8×C107—21no—
74C2×Q8×C107C4⋊C411yescharacteristic
75C2×D4×C107—21no—
76C2×D4×C107C4⋊C411yescharacteristic
77C22×C4×C107—21no—
78C22×C4×C107C2×D411yescharacteristic
79C22×C4×C107C2×Q811yescharacteristic
80C22×C4×C107#4111yescharacteristic
81M16×C107—42no—
82M16×C107—41no—
83M16×C107—41no—
84M16×C107—41no—
85M16×C107—41no—
86M16×C107—81no—
87C2×C8×C107—22no—
88C2×C8×C107—22no—
89C2×C8×C107—21no—
90C2×C8×C107—21no—
91C2×C8×C107—21no—
92C2×C8×C107—21no—
93C2×C8×C107—21no—
94C2×C8×C107—21no—
95C2×C8×C107—21no—
96C2×C8×C107—21no—
97C2×C8×C107—41no—
98C2×C8×C107—41no—
99C2×C8×C107—81no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107—21no—
102C4⋊C4×C107—21no—
103C4⋊C4×C107—21no—
104C4⋊C4×C107C4⋊C411yescharacteristic
105C4⋊C4×C107C4⋊C411yescharacteristic
106C22⋊C4×C107—21no—
107C22⋊C4×C107—21no—
108C22⋊C4×C107—21no—
109C22⋊C4×C107—21no—
110C22⋊C4×C107—21no—
111C42×C107—21no—
112C42×C107C22×C411yescharacteristic
113C42×C107C2×D411yescharacteristic
114C42×C107C2×D411yescharacteristic
115C42×C107#4111yescharacteristic
116C23×C107—21no—
117C23×C107C22⋊Q811yescharacteristic
118Q8×C107—41no—
119D4×C107—41no—
120D4×C107—81no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—41no—
127C2×C4×C107—41no—
128C2×C4×C107—41no—
129C2×C4×C107—41no—
130C2×C4×C107C2×C4⋊C411yescharacteristic
131C2×C4×C107C4×D411yescharacteristic
132C2×C4×C107C4×D411yescharacteristic
133C2×C4×C107#12011yescharacteristic
134C2×C4×C107C22⋊Q811yescharacteristic
135C2×C4×C107#12311yescharacteristic
136C8×C107—22no—
137C8×C107—22no—
138C8×C107—22no—
139C8×C107—41no—
140C8×C107—41no—
141C8×C107—41no—
142C8×C107—41no—
143C8×C107—41no—
144C8×C107—81no—
145C8×C107—81no—
146C22×C107—21no—
147C22×C107—21no—
148C22×C107—21no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107—41no—
152C22×C107#38511yescharacteristic
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—21no—
156C4×C107—21no—
157C4×C107—21no—
158C4×C107—41no—
159C4×C107—41no—
160C4×C107—41no—
161C4×C107#45311yescharacteristic
162C4×C107#45611yescharacteristic
163#8916C10711yesmaximal, characteristic, direct product factor, Sylow
164C2×C107—41no—
165C2×C107—81no—
166C2×C107#185811yescharacteristic
167C2×C107#185911yescharacteristic
168C2×C107#186111yescharacteristic
169#2995C2×C10711yescharacteristic
170#1849C2×C10711yescharacteristic, complemented
171#1569C2×C10711yescharacteristic, complemented
172#1524C2×C10711yescharacteristic
173#1495C2×C10711yescharacteristic
174#1302C2×C10711yescharacteristic, complemented
175#1299C2×C10711yescharacteristic, complemented
176C107#891611yescharacteristic, direct product factor, Sylow
177#529C22×C10711yescharacteristic
178#446—21no—
179#436—21no—
180#435—21no—
181#435—21no—
182#433—21no—
183#432C22×C10711yescharacteristic
184#431C22×C10711yescharacteristic
185C2×#108—21no—
186C2×#108—21no—
187#424—21no—
188#423C22×C10711yescharacteristic
189#423C22×C10711yescharacteristic
190C4×M16C22×C10711yescharacteristic
191C2×#97C22×C10711yescharacteristic
192#335—21no—
193#334—21no—
194#330C4×C10711yescharacteristic
195#330C4×C10711yescharacteristic
196#329C4×C10711yescharacteristic
197#329C4×C10711yescharacteristic
198Q8⋊C8—21no—
199D4⋊C8—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16D4×C10711yescharacteristic
204C2×M16D4×C10711yescharacteristic
205C22×C8—21no—
206C22×C8—21no—
207#126—21no—
208#125C2×C4×C10711yescharacteristic
209#124C2×C4×C10711yescharacteristic
210#123—21no—
211C22⋊Q8Q8×C10711yescharacteristic
212#121Q8×C10711yescharacteristic
213C4×Q8D4×C10711yescharacteristic
214C4×D4—21no—
215C4×D4D4×C10711yescharacteristic
216#117—21no—
217C2×C42C23×C10711yescharacteristic
218#108—42no—
219#108—42no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C10711yescharacteristic
228C4⋊C8D4×C10711yescharacteristic
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233#97—21no—
234#97—21no—
235#97—21no—
236#97C2×C4×C10711yescharacteristic
237#97C2×C4×C10711yescharacteristic
238#97C2×C4×C10711yescharacteristic
239#97C2×C4×C10711yescharacteristic
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C2×Q8C4⋊C4×C10711yescharacteristic
244C2×D4—21no—
245C2×D4C4⋊C4×C10711yescharacteristic
246C22×C4—21no—
247C22×C4C2×D4×C10711yescharacteristic
248C22×C4C2×Q8×C10711yescharacteristic
249C22×C4#41×C10711yescharacteristic
250M16—42no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—81no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—81no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4C4⋊C4×C10711yescharacteristic
274C4⋊C4C4⋊C4×C10711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C42—21no—
281C42C22×C4×C10711yescharacteristic
282C42C2×D4×C10711yescharacteristic
283C42C2×D4×C10711yescharacteristic
284C42#41×C10711yescharacteristic
285C23—21no—
286C23C22⋊Q8×C10711yescharacteristic
287Q8—41no—
288D4—41no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4C2×C4⋊C4×C10711yescharacteristic
300C2×C4C4×D4×C10711yescharacteristic
301C2×C4C4×D4×C10711yescharacteristic
302C2×C4#120×C10711yescharacteristic
303C2×C4C22⋊Q8×C10711yescharacteristic
304C2×C4#123×C10711yescharacteristic
305C8—22no—
306C8—22no—
307C8—22no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—81no—
314C8—81no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22#385×C10711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4#453×C10711yescharacteristic
331C4#456×C10711yescharacteristic
332C2—41no—
333C2—81no—
334C2C107×#185811yescharacteristic
335C2C107×#185911yescharacteristic
336C2C107×#186111yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#385
prime radical#121×C107Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1849C2semidirect
3. C107×#1569C2semidirect
6. C107×#1302C2semidirect
7. C107×#1299C2semidirect
163. #8916C107direct (N × H)
170. #1849C2×C107semidirect
171. #1569C2×C107semidirect
174. #1302C2×C107semidirect
175. #1299C2×C107semidirect
176. C107#8916direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#29952
C107×#18492
C107×#15692
C107×#15242
C107×#14952
C107×#13022
C107×#12992
#8916107