Finite Group Databasebeta

← C107×#12939 #41038903

Subgroups — C107×#12939 #41038903

Order 27392.

398 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#443×C107C211yesmaximal, characteristic
2C2×#368×C107C211yesmaximal, characteristic, complemented
3C2×#359×C107C211yesmaximal, characteristic
4C107×#2138C211yesmaximal, characteristic
5C107×#1945C211yesmaximal, characteristic, complemented
6C107×#1382C211yesmaximal, characteristic, complemented
7C107×#1374C211yesmaximal, characteristic, complemented
8C2×#135×C107C2211yescharacteristic
9C2×#131×C107—21no—
10C22×C16×C107C2211yescharacteristic
11C22×C16×C107C2211yescharacteristic
12#443×C107—22no—
13#443×C107—22no—
14C2×#108×C107C2211yescharacteristic
15C2×#108×C107C2211yescharacteristic
16#427×C107C2211yescharacteristic
17#424×C107—21no—
18C2×#104×C107—21no—
19C2×C4×C8×C107C2211yescharacteristic
20#368×C107—22no—
21#359×C107—22no—
22#358×C107C411yescharacteristic, complemented
23#358×C107C411yescharacteristic, complemented
24#357×C107C411yescharacteristic, complemented
25#357×C107C411yescharacteristic, complemented
26#339×C107—21no—
27C2×#41×C107—21no—
28#135×C107—21no—
29#135×C107—21no—
30#135×C107D412yes—
31#135×C107Q812yes—
32C2×Q16×C107C2×C411yescharacteristic
33C2×SD16×C107—21no—
34C2×D8×C107C2×C411yescharacteristic
35#131×C107—24no—
36#131×C107—42no—
37C2×M16×C107—21no—
38C2×M16×C107—21no—
39C2×M16×C107—41no—
40C22×C8×C107—41no—
41C22×C8×C107D411yescharacteristic
42C22×C8×C107C2311yescharacteristic
43#117×C107—21no—
44C2×C42×C107D411yescharacteristic
45C2×C16×C107—21no—
46C2×C16×C107—21no—
47C2×C16×C107—21no—
48C2×C16×C107—21no—
49C2×C16×C107—21no—
50C2×C16×C107C2×C411yescharacteristic
51C2×C16×C107C2×C411yescharacteristic
52#108×C107—21no—
53#108×C107—21no—
54#108×C107—21no—
55#108×C107D412yes—
56#107×C107C2×C411yescharacteristic
57#107×C107C2×C411yescharacteristic
58#106×C107—21no—
59C4⋊C8×C107—41no—
60C4⋊C8×C107—41no—
61#104×C107—24no—
62C4×C8×C107—21no—
63C4×C8×C107—21no—
64#41×C107—22no—
65#41×C107—22no—
66#41×C107—41no—
67#41×C107—41no—
68C2×Q8×C107—21no—
69C2×D4×C107—21no—
70C2×D4×C107—41no—
71C22×C4×C107—21no—
72C22×C4×C107—41no—
73C22×C4×C107C2×D411yescharacteristic
74Q16×C107—21no—
75Q16×C107C4⋊C412yes—
76SD16×C107—22no—
77SD16×C107—22no—
78D8×C107—21no—
79D8×C107C4⋊C412yes—
80M16×C107—22no—
81M16×C107—44no—
82M16×C107—41no—
83M16×C107—41no—
84M16×C107—41no—
85C2×C8×C107—21no—
86C2×C8×C107—21no—
87C2×C8×C107—44no—
88C2×C8×C107—41no—
89C2×C8×C107—41no—
90C2×C8×C107D811yescharacteristic
91C2×C8×C107D811yescharacteristic
92C2×C8×C107C22×C411yescharacteristic
93C2×C8×C107C2×D411yescharacteristic
94C2×C8×C107C2×D411yescharacteristic
95C2×C8×C107C2×Q811yescharacteristic
96C2×C8×C107#4111yescharacteristic
97C2×C8×C107#4111yescharacteristic
98C4⋊C4×C107—21no—
99C4⋊C4×C107—21no—
100C22⋊C4×C107—41no—
101C42×C107—21no—
102C42×C107—21no—
103C42×C107—41no—
104C16×C107—21no—
105C16×C107—21no—
106C16×C107—41no—
107C23×C107—41no—
108C23×C107#13511yescharacteristic
109Q8×C107—22no—
110Q8×C107—41no—
111D4×C107—22no—
112D4×C107—42no—
113D4×C107—42no—
114D4×C107—41no—
115C2×C4×C107—22no—
116C2×C4×C107—41no—
117C2×C4×C107—41no—
118C2×C4×C107—41no—
119C2×C4×C107—42no—
120C2×C4×C107—42no—
121C2×C4×C107—41no—
122C2×C4×C107—41no—
123C2×C4×C107C4×D411yescharacteristic
124C2×C4×C107#12011yescharacteristic
125C2×C4×C107C22⋊Q811yescharacteristic
126C2×C4×C107C2×D811yescharacteristic
127C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C107#13711yescharacteristic
129C8×C107—21no—
130C8×C107—21no—
131C8×C107—42no—
132C8×C107—81no—
133C8×C107C2×C4⋊C411yescharacteristic
134C8×C107C4×D411yescharacteristic
135C8×C107C22⋊Q811yescharacteristic
136C8×C107#12311yescharacteristic
137C22×C107—21no—
138C22×C107—21no—
139C22×C107—42no—
140C22×C107—81no—
141C22×C107—81no—
142C22×C107C4×D811yescharacteristic
143C22×C107#45211yescharacteristic
144C22×C107#47811yescharacteristic
145C4×C107—42no—
146C4×C107—42no—
147C4×C107—81no—
148C4×C107—81no—
149C4×C107#38511yescharacteristic
150C4×C107#44011yescharacteristic
151C4×C107#44711yescharacteristic
152C4×C107#47411yescharacteristic
153#12939C10711yesmaximal, characteristic, direct product factor, Sylow
154C2×C107—21no—
155C2×C107—21no—
156C2×C107—82no—
157C2×C107#186211yescharacteristic
158C2×C107#217811yescharacteristic
159C2×C107#217911yescharacteristic
160C2×#443C2×C10711yescharacteristic
161C2×#368C2×C10711yescharacteristic, complemented
162C2×#359C2×C10711yescharacteristic
163#2138C2×C10711yescharacteristic
164#1945C2×C10711yescharacteristic, complemented
165#1382C2×C10711yescharacteristic, complemented
166#1374C2×C10711yescharacteristic, complemented
167C107#1293911yescharacteristic, direct product factor, Sylow
168C2×#135C22×C10711yescharacteristic
169C2×#131—21no—
170C22×C16C22×C10711yescharacteristic
171C22×C16C22×C10711yescharacteristic
172#443—22no—
173#443—22no—
174C2×#108C22×C10711yescharacteristic
175C2×#108C22×C10711yescharacteristic
176#427C22×C10711yescharacteristic
177#424—21no—
178C2×#104—21no—
179C2×C4×C8C22×C10711yescharacteristic
180#368—22no—
181#359—22no—
182#358C4×C10711yescharacteristic, complemented
183#358C4×C10711yescharacteristic, complemented
184#357C4×C10711yescharacteristic, complemented
185#357C4×C10711yescharacteristic, complemented
186#339—21no—
187C2×#41—21no—
188#135—21no—
189#135—21no—
190#135D4×C10712yes—
191#135Q8×C10712yes—
192C2×Q16C2×C4×C10711yescharacteristic
193C2×SD16—21no—
194C2×D8C2×C4×C10711yescharacteristic
195#131—24no—
196#131—42no—
197C2×M16—21no—
198C2×M16—21no—
199C2×M16—41no—
200C22×C8—41no—
201C22×C8D4×C10711yescharacteristic
202C22×C8C23×C10711yescharacteristic
203#117—21no—
204C2×C42D4×C10711yescharacteristic
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—21no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16C2×C4×C10711yescharacteristic
211C2×C16C2×C4×C10711yescharacteristic
212#108—21no—
213#108—21no—
214#108—21no—
215#108D4×C10712yes—
216#107C2×C4×C10711yescharacteristic
217#107C2×C4×C10711yescharacteristic
218#106—21no—
219C4⋊C8—41no—
220C4⋊C8—41no—
221#104—24no—
222C4×C8—21no—
223C4×C8—21no—
224#41—22no—
225#41—22no—
226#41—41no—
227#41—41no—
228C2×Q8—21no—
229C2×D4—21no—
230C2×D4—41no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4C2×D4×C10711yescharacteristic
234Q16—21no—
235Q16C4⋊C4×C10712yes—
236SD16—22no—
237SD16—22no—
238D8—21no—
239D8C4⋊C4×C10712yes—
240M16—22no—
241M16—44no—
242M16—41no—
243M16—41no—
244M16—41no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—44no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8D8×C10711yescharacteristic
251C2×C8D8×C10711yescharacteristic
252C2×C8C22×C4×C10711yescharacteristic
253C2×C8C2×D4×C10711yescharacteristic
254C2×C8C2×D4×C10711yescharacteristic
255C2×C8C2×Q8×C10711yescharacteristic
256C2×C8#41×C10711yescharacteristic
257C2×C8#41×C10711yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C22⋊C4—41no—
261C42—21no—
262C42—21no—
263C42—41no—
264C16—21no—
265C16—21no—
266C16—41no—
267C23—41no—
268C23#135×C10711yescharacteristic
269Q8—22no—
270Q8—41no—
271D4—22no—
272D4—42no—
273D4—42no—
274D4—41no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4C4×D4×C10711yescharacteristic
284C2×C4#120×C10711yescharacteristic
285C2×C4C22⋊Q8×C10711yescharacteristic
286C2×C4C2×D8×C10711yescharacteristic
287C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
288C2×C4#137×C10711yescharacteristic
289C8—21no—
290C8—21no—
291C8—42no—
292C8—81no—
293C8C2×C4⋊C4×C10711yescharacteristic
294C8C4×D4×C10711yescharacteristic
295C8C22⋊Q8×C10711yescharacteristic
296C8#123×C10711yescharacteristic
297C22—21no—
298C22—21no—
299C22—42no—
300C22—81no—
301C22—81no—
302C22C4×D8×C10711yescharacteristic
303C22#452×C10711yescharacteristic
304C22#478×C10711yescharacteristic
305C4—42no—
306C4—42no—
307C4—81no—
308C4—81no—
309C4#385×C10711yescharacteristic
310C4#440×C10711yescharacteristic
311C4#447×C10711yescharacteristic
312C4#474×C10711yescharacteristic
313C2—21no—
314C2—21no—
315C2—82no—
316C2C107×#186211yescharacteristic
317C2C107×#217811yescharacteristic
318C2C107×#217911yescharacteristic
subgroupG/H
centerC2×C4×C107C2×D8
commutatorC2×C8C22×C4×C107
Frattini, cosocleC22×C8C23×C107
socleC22×C107C4×D8
prime radicalC2×#135×C107C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C22×C8×C107 ◁ C2×C4×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#368×C107C2semidirect
5. C107×#1945C2semidirect
6. C107×#1382C2semidirect
7. C107×#1374C2semidirect
22. #358×C107C4semidirect
23. #358×C107C4semidirect
24. #357×C107C4semidirect
25. #357×C107C4semidirect
153. #12939C107direct (N × H)
161. C2×#368C2×C107semidirect
164. #1945C2×C107semidirect
165. #1382C2×C107semidirect
166. #1374C2×C107semidirect
167. C107#12939direct (N × H)
182. #358C4×C107semidirect
183. #358C4×C107semidirect
184. #357C4×C107semidirect
185. #357C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#443×C1072
C2×#368×C1072
C2×#359×C1072
C107×#21382
C107×#19452
C107×#13822
C107×#13742
#12939107