Finite Group Databasebeta

← C107×#13396 #41039360

Subgroups — C107×#13396 #41039360

Order 27392.

422 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3058C211yesmaximal, characteristic
2C107×#2155C211yesmaximal, characteristic, complemented
3C2×#361×C107C211yesmaximal, characteristic, complemented
4C107×#2140C211yesmaximal, characteristic, complemented
5C107×#2117C211yesmaximal, characteristic, complemented
6C107×#1814C211yesmaximal, characteristic, complemented
7C107×#1384C211yesmaximal, characteristic, complemented
8C22×D8×C107C2211yescharacteristic
9C2×#131×C107C2211yescharacteristic
10#535×C107—21no—
11C2×M32×C107C2211yescharacteristic
12C2×M32×C107C2211yescharacteristic
13#469×C107—22no—
14#466×C107—22no—
15C2×#108×C107C2211yescharacteristic
16#427×C107C2211yescharacteristic
17#427×C107C2211yescharacteristic
18#421×C107—21no—
19#418×C107—21no—
20#365×C107—22no—
21#361×C107—22no—
22#357×C107—22no—
23#350×C107—22no—
24#344×C107—21no—
25C2×#41×C107D411yescharacteristic
26C22×D4×C107—21no—
27C2×D8×C107—21no—
28C2×D8×C107—21no—
29C2×D8×C107—21no—
30C2×D8×C107—21no—
31C2×D8×C107—21no—
32C2×D8×C107D412yes—
33#131×C107—21no—
34#131×C107—21no—
35#131×C107—21no—
36#131×C107—21no—
37C2×M16×C107—21no—
38C2×M16×C107—21no—
39C2×M16×C107D411yescharacteristic
40C22×C8×C107—21no—
41C22×C8×C107C2311yescharacteristic
42#127×C107—41no—
43#124×C107—41no—
44#121×C107—24no—
45#120×C107—42no—
46#117×C107—21no—
47#117×C107—21no—
48M32×C107—21no—
49M32×C107—21no—
50M32×C107—21no—
51M32×C107—21no—
52C2×C16×C107—21no—
53C2×C16×C107D412yescomplemented
54#108×C107—21no—
55#108×C107—21no—
56#107×C107—21no—
57#107×C107—21no—
58#106×C107—21no—
59#106×C107D412yes—
60#104×C107—42no—
61#102×C107—24no—
62C24×C107—41no—
63#41×C107—21no—
64#41×C107—21no—
65#41×C107—21no—
66#41×C107—21no—
67C2×Q8×C107SD1611yescharacteristic
68C2×D4×C107—21no—
69C2×D4×C107—22no—
70C2×D4×C107—44no—
71C2×D4×C107—41no—
72C2×D4×C107—41no—
73C2×D4×C107—41no—
74C2×D4×C107—41no—
75C2×D4×C107—41no—
76C2×D4×C107SD1611yescharacteristic
77C22×C4×C107—21no—
78C22×C4×C107C2×D411yescharacteristic
79D8×C107—22no—
80D8×C107—22no—
81D8×C107—41no—
82D8×C107—41no—
83M16×C107—21no—
84M16×C107—21no—
85M16×C107—41no—
86M16×C107—41no—
87M16×C107—41no—
88M16×C107—41no—
89C2×C8×C107—21no—
90C2×C8×C107—41no—
91C2×C8×C107—41no—
92C2×C8×C107—41no—
93C2×C8×C107C2×D411yescharacteristic
94C2×C8×C107C2×D411yescharacteristic
95C2×C8×C107C2×D411yescharacteristic
96C2×C8×C107#4111yescharacteristic
97C2×C8×C107#4111yescharacteristic
98C2×C8×C107#4111yescharacteristic
99C4⋊C4×C107—22no—
100C4⋊C4×C107—41no—
101C22⋊C4×C107—44no—
102C22⋊C4×C107—41no—
103C22⋊C4×C107—41no—
104C42×C107—41no—
105C42×C107—41no—
106C16×C107—22no—
107C16×C107—41no—
108C23×C107—21no—
109C23×C107—42no—
110C23×C107—81no—
111C23×C107—81no—
112C23×C107—162no—
113C23×C107AGL(1,ℤ/8)11yescharacteristic
114Q8×C107—21no—
115Q8×C107—21no—
116D4×C107—21no—
117D4×C107—21no—
118D4×C107—41no—
119D4×C107—41no—
120D4×C107—42no—
121D4×C107—42no—
122D4×C107—81no—
123D4×C107—81no—
124D4×C107—164no—
125C2×C4×C107—21no—
126C2×C4×C107—41no—
127C2×C4×C107—41no—
128C2×C4×C107—42no—
129C2×C4×C107—81no—
130C2×C4×C107#12011yescharacteristic
131C2×C4×C107#12111yescharacteristic
132C2×C4×C107#12311yescharacteristic
133C2×C4×C107C2×SD1611yescharacteristic
134C2×C4×C107#13511yescharacteristic
135C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
136C8×C107—41no—
137C8×C107—81no—
138C8×C107#12111yescharacteristic
139C8×C107#12111yescharacteristic
140C8×C107#12311yescharacteristic
141C8×C107#12411yescharacteristic
142C22×C107—41no—
143C22×C107—42no—
144C22×C107—41no—
145C22×C107—84no—
146C22×C107—82no—
147C22×C107—162no—
148C22×C107—162no—
149C22×C107#45011yescharacteristic
150C22×C107#46911yescharacteristic
151C22×C107#48211yescharacteristic
152C4×C107—41no—
153C4×C107—82no—
154C4×C107—161no—
155C4×C107#39411yescharacteristic
156C4×C107#44911yescharacteristic
157C4×C107#46511yescharacteristic
158C4×C107#48111yescharacteristic
159#13396C10711yesmaximal, characteristic, direct product factor, Sylow
160C2×C107—21no—
161C2×C107—21no—
162C2×C107—21no—
163C2×C107—81no—
164C2×C107—162no—
165C2×C107#203411yescharacteristic
166#3058C2×C10711yescharacteristic
167#2155C2×C10711yescharacteristic, complemented
168C2×#361C2×C10711yescharacteristic, complemented
169#2140C2×C10711yescharacteristic, complemented
170#2117C2×C10711yescharacteristic, complemented
171#1814C2×C10711yescharacteristic, complemented
172#1384C2×C10711yescharacteristic, complemented
173C107#1339611yescharacteristic, direct product factor, Sylow
174C22×D8C22×C10711yescharacteristic
175C2×#131C22×C10711yescharacteristic
176#535—21no—
177C2×M32C22×C10711yescharacteristic
178C2×M32C22×C10711yescharacteristic
179#469—22no—
180#466—22no—
181C2×#108C22×C10711yescharacteristic
182#427C22×C10711yescharacteristic
183#427C22×C10711yescharacteristic
184#421—21no—
185#418—21no—
186#365—22no—
187#361—22no—
188#357—22no—
189#350—22no—
190#344—21no—
191C2×#41D4×C10711yescharacteristic
192C22×D4—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8D4×C10712yes—
199#131—21no—
200#131—21no—
201#131—21no—
202#131—21no—
203C2×M16—21no—
204C2×M16—21no—
205C2×M16D4×C10711yescharacteristic
206C22×C8—21no—
207C22×C8C23×C10711yescharacteristic
208#127—41no—
209#124—41no—
210#121—24no—
211#120—42no—
212#117—21no—
213#117—21no—
214M32—21no—
215M32—21no—
216M32—21no—
217M32—21no—
218C2×C16—21no—
219C2×C16D4×C10712yescomplemented
220#108—21no—
221#108—21no—
222#107—21no—
223#107—21no—
224#106—21no—
225#106D4×C10712yes—
226#104—42no—
227#102—24no—
228C24—41no—
229#41—21no—
230#41—21no—
231#41—21no—
232#41—21no—
233C2×Q8SD16×C10711yescharacteristic
234C2×D4—21no—
235C2×D4—22no—
236C2×D4—44no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4SD16×C10711yescharacteristic
243C22×C4—21no—
244C22×C4C2×D4×C10711yescharacteristic
245D8—22no—
246D8—22no—
247D8—41no—
248D8—41no—
249M16—21no—
250M16—21no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8C2×D4×C10711yescharacteristic
260C2×C8C2×D4×C10711yescharacteristic
261C2×C8C2×D4×C10711yescharacteristic
262C2×C8#41×C10711yescharacteristic
263C2×C8#41×C10711yescharacteristic
264C2×C8#41×C10711yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—41no—
267C22⋊C4—44no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42—41no—
271C42—41no—
272C16—22no—
273C16—41no—
274C23—21no—
275C23—42no—
276C23—81no—
277C23—81no—
278C23—162no—
279C23AGL(1,ℤ/8)×C10711yescharacteristic
280Q8—21no—
281Q8—21no—
282D4—21no—
283D4—21no—
284D4—41no—
285D4—41no—
286D4—42no—
287D4—42no—
288D4—81no—
289D4—81no—
290D4—164no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4#120×C10711yescharacteristic
297C2×C4#121×C10711yescharacteristic
298C2×C4#123×C10711yescharacteristic
299C2×C4C2×SD16×C10711yescharacteristic
300C2×C4#135×C10711yescharacteristic
301C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
302C8—41no—
303C8—81no—
304C8#121×C10711yescharacteristic
305C8#121×C10711yescharacteristic
306C8#123×C10711yescharacteristic
307C8#124×C10711yescharacteristic
308C22—41no—
309C22—42no—
310C22—41no—
311C22—84no—
312C22—82no—
313C22—162no—
314C22—162no—
315C22#450×C10711yescharacteristic
316C22#469×C10711yescharacteristic
317C22#482×C10711yescharacteristic
318C4—41no—
319C4—82no—
320C4—161no—
321C4#394×C10711yescharacteristic
322C4#449×C10711yescharacteristic
323C4#465×C10711yescharacteristic
324C4#481×C10711yescharacteristic
325C2—21no—
326C2—21no—
327C2—21no—
328C2—81no—
329C2—162no—
330C2C107×#203411yescharacteristic
subgroupG/H
center, socleC2×C107#2034
commutator, Frattini, cosocleC22×C8C23×C107
prime radicalC107×#3058C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C22×C4×C107 ◁ C2×#131×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2155C2semidirect
3. C2×#361×C107C2semidirect
4. C107×#2140C2semidirect
5. C107×#2117C2semidirect
6. C107×#1814C2semidirect
7. C107×#1384C2semidirect
53. C2×C16×C107D4semidirect
159. #13396C107direct (N × H)
167. #2155C2×C107semidirect
168. C2×#361C2×C107semidirect
169. #2140C2×C107semidirect
170. #2117C2×C107semidirect
171. #1814C2×C107semidirect
172. #1384C2×C107semidirect
173. C107#13396direct (N × H)
219. C2×C16D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30582
C107×#21552
C2×#361×C1072
C107×#21402
C107×#21172
C107×#18142
C107×#13842
#13396107