Finite Group Databasebeta

← C107×#12979 #41038943

Subgroups — C107×#12979 #41038943

Order 27392.

456 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3407C211yesmaximal, characteristic, complemented
2C107×#2955C211yesmaximal, characteristic
3C107×#2117C211yesmaximal, characteristic, complemented
4C2×#350×C107C211yesmaximal, characteristic, complemented
5C107×#2113C211yesmaximal, characteristic, complemented
6C107×#1379C211yesmaximal, characteristic, complemented
7C107×#1378C211yesmaximal, characteristic, complemented
8#575×C107C411yescharacteristic
9C2×#131×C107C2211yescharacteristic
10C2×#131×C107C2211yescharacteristic
11#504×C107—22no—
12#504×C107—22no—
13C2×M32×C107—22no—
14C2×M32×C107C2211yescharacteristic
15C2×M32×C107C2211yescharacteristic
16C2×M32×C107C2211yescharacteristic
17C22×C16×C107C2211yescharacteristic
18#444×C107—22no—
19#443×C107—22no—
20#430×C107C411yescharacteristic
21#421×C107C411yescharacteristic
22#421×C107C411yescharacteristic
23#405×C107C2211yescharacteristic
24#350×C107—22no—
25#350×C107—22no—
26C22⋊C16×C107—22no—
27C2×#41×C107C2×C411yescharacteristic
28C2×#41×C107C2×C411yescharacteristic
29#137×C107—21no—
30#137×C107C812yes—
31AGL(1,ℤ/8)×C107—21no—
32AGL(1,ℤ/8)×C107C812yes—
33#135×C107—22no—
34#131×C107—21no—
35#131×C107—21no—
36#131×C107—21no—
37#131×C107—21no—
38#131×C107—21no—
39#131×C107—21no—
40#131×C107D412yes—
41#131×C107D412yes—
42C2×M16×C107—21no—
43C2×M16×C107—21no—
44C2×M16×C107C2×C411yescharacteristic
45C2×M16×C107C2×C411yescharacteristic
46C2×M16×C107C2×C411yescharacteristic
47C22×C8×C107—21no—
48C22×C8×C107—21no—
49C22×C8×C107C2311yescharacteristic
50#117×C107C2×C411yescharacteristic
51M32×C107—24no—
52M32×C107—21no—
53M32×C107—21no—
54M32×C107—21no—
55M32×C107—21no—
56M32×C107—21no—
57M32×C107D412yes—
58C2×C16×C107—24no—
59C2×C16×C107—21no—
60C2×C16×C107—21no—
61C2×C16×C107—21no—
62C2×C16×C107—21no—
63C2×C16×C107—21no—
64C2×C16×C107D412yes—
65#108×C107—22no—
66#104×C107—22no—
67#104×C107—22no—
68#97×C107—21no—
69C4×C8×C107—21no—
70#41×C107—21no—
71#41×C107—21no—
72#41×C107—21no—
73#41×C107—21no—
74#41×C107—21no—
75#41×C107—21no—
76#41×C107C22⋊C412yes—
77#41×C107C2×C812yes—
78C2×Q8×C107C2×C811yescharacteristic
79C2×Q8×C107M1611yescharacteristic
80C2×D4×C107—21no—
81C2×D4×C107—21no—
82C2×D4×C107C2×C811yescharacteristic
83C2×D4×C107M1611yescharacteristic
84C22×C4×C107—21no—
85C22×C4×C107—21no—
86C22×C4×C107C22×C411yescharacteristic
87Q16×C107—22no—
88SD16×C107—22no—
89SD16×C107—22no—
90D8×C107—22no—
91M16×C107—21no—
92M16×C107—21no—
93M16×C107—22no—
94M16×C107—22no—
95M16×C107—21no—
96M16×C107—21no—
97M16×C107—41no—
98M16×C107—41no—
99M16×C107C22⋊C412yes—
100M16×C107C2×C812yes—
101C2×C8×C107—21no—
102C2×C8×C107—21no—
103C2×C8×C107—22no—
104C2×C8×C107—22no—
105C2×C8×C107—21no—
106C2×C8×C107—41no—
107C2×C8×C107—41no—
108C2×C8×C107C2×D411yescharacteristic
109C2×C8×C107C2×D411yescharacteristic
110C2×C8×C107C2×D411yescharacteristic
111C2×C8×C107C2×D411yescharacteristic
112C2×C8×C107#4111yescharacteristic
113C2×C8×C107#4111yescharacteristic
114C4⋊C4×C107—21no—
115C22⋊C4×C107—21no—
116C42×C107—21no—
117C16×C107—22no—
118C16×C107—22no—
119C16×C107—41no—
120C16×C107—41no—
121C23×C107—21no—
122C23×C107—21no—
123C23×C107#13111yescharacteristic
124Q8×C107—21no—
125Q8×C107—21no—
126Q8×C107—21no—
127Q8×C107C22⋊C812yes—
128D4×C107—22no—
129D4×C107—22no—
130D4×C107—21no—
131D4×C107—21no—
132D4×C107—21no—
133D4×C107—41no—
134D4×C107—41no—
135D4×C107C22⋊C812yes—
136C2×C4×C107—21no—
137C2×C4×C107—22no—
138C2×C4×C107—22no—
139C2×C4×C107—21no—
140C2×C4×C107—41no—
141C2×C4×C107—41no—
142C2×C4×C107—41no—
143C2×C4×C107C2×C22⋊C411yescharacteristic
144C2×C4×C107C4×D411yescharacteristic
145C2×C4×C107C4×D411yescharacteristic
146C2×C4×C107C22×C811yescharacteristic
147C2×C4×C107C2×M1611yescharacteristic
148C2×C4×C107#13111yescharacteristic
149C8×C107—22no—
150C8×C107—22no—
151C8×C107—41no—
152C8×C107#12011yescharacteristic
153C8×C107#12111yescharacteristic
154C8×C107#12111yescharacteristic
155C8×C107#12311yescharacteristic
156C22×C107—22no—
157C22×C107—41no—
158C22×C107—42no—
159C22×C107—41no—
160C22×C107—81no—
161C22×C107#40811yescharacteristic
162C22×C107C8×D411yescharacteristic
163C22×C107#43511yescharacteristic
164C4×C107—22no—
165C4×C107—41no—
166C4×C107—81no—
167C4×C107#38611yescharacteristic
168C4×C107C2×C22⋊C811yescharacteristic
169C4×C107C8×D411yescharacteristic
170C4×C107#43511yescharacteristic
171#12979C10711yesmaximal, characteristic, direct product factor, Sylow
172C2×C107—21no—
173C2×C107—21no—
174C2×C107—21no—
175C2×C107—42no—
176C2×C107—81no—
177C2×C107#186911yescharacteristic
178#3407C2×C10711yescharacteristic, complemented
179#2955C2×C10711yescharacteristic
180#2117C2×C10711yescharacteristic, complemented
181C2×#350C2×C10711yescharacteristic, complemented
182#2113C2×C10711yescharacteristic, complemented
183#1379C2×C10711yescharacteristic, complemented
184#1378C2×C10711yescharacteristic, complemented
185C107#1297911yescharacteristic, direct product factor, Sylow
186#575C4×C10711yescharacteristic
187C2×#131C22×C10711yescharacteristic
188C2×#131C22×C10711yescharacteristic
189#504—22no—
190#504—22no—
191C2×M32—22no—
192C2×M32C22×C10711yescharacteristic
193C2×M32C22×C10711yescharacteristic
194C2×M32C22×C10711yescharacteristic
195C22×C16C22×C10711yescharacteristic
196#444—22no—
197#443—22no—
198#430C4×C10711yescharacteristic
199#421C4×C10711yescharacteristic
200#421C4×C10711yescharacteristic
201#405C22×C10711yescharacteristic
202#350—22no—
203#350—22no—
204C22⋊C16—22no—
205C2×#41C2×C4×C10711yescharacteristic
206C2×#41C2×C4×C10711yescharacteristic
207#137—21no—
208#137C8×C10712yes—
209AGL(1,ℤ/8)—21no—
210AGL(1,ℤ/8)C8×C10712yes—
211#135—22no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—21no—
216#131—21no—
217#131—21no—
218#131D4×C10712yes—
219#131D4×C10712yes—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16C2×C4×C10711yescharacteristic
223C2×M16C2×C4×C10711yescharacteristic
224C2×M16C2×C4×C10711yescharacteristic
225C22×C8—21no—
226C22×C8—21no—
227C22×C8C23×C10711yescharacteristic
228#117C2×C4×C10711yescharacteristic
229M32—24no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32D4×C10712yes—
236C2×C16—24no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16D4×C10712yes—
243#108—22no—
244#104—22no—
245#104—22no—
246#97—21no—
247C4×C8—21no—
248#41—21no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—21no—
254#41C22⋊C4×C10712yes—
255#41C2×C8×C10712yes—
256C2×Q8C2×C8×C10711yescharacteristic
257C2×Q8M16×C10711yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4C2×C8×C10711yescharacteristic
261C2×D4M16×C10711yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4C22×C4×C10711yescharacteristic
265Q16—22no—
266SD16—22no—
267SD16—22no—
268D8—22no—
269M16—21no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—21no—
274M16—21no—
275M16—41no—
276M16—41no—
277M16C22⋊C4×C10712yes—
278M16C2×C8×C10712yes—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C10711yescharacteristic
287C2×C8C2×D4×C10711yescharacteristic
288C2×C8C2×D4×C10711yescharacteristic
289C2×C8C2×D4×C10711yescharacteristic
290C2×C8#41×C10711yescharacteristic
291C2×C8#41×C10711yescharacteristic
292C4⋊C4—21no—
293C22⋊C4—21no—
294C42—21no—
295C16—22no—
296C16—22no—
297C16—41no—
298C16—41no—
299C23—21no—
300C23—21no—
301C23#131×C10711yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8C22⋊C8×C10712yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—41no—
313D4C22⋊C8×C10712yes—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4C2×C22⋊C4×C10711yescharacteristic
322C2×C4C4×D4×C10711yescharacteristic
323C2×C4C4×D4×C10711yescharacteristic
324C2×C4C22×C8×C10711yescharacteristic
325C2×C4C2×M16×C10711yescharacteristic
326C2×C4#131×C10711yescharacteristic
327C8—22no—
328C8—22no—
329C8—41no—
330C8#120×C10711yescharacteristic
331C8#121×C10711yescharacteristic
332C8#121×C10711yescharacteristic
333C8#123×C10711yescharacteristic
334C22—22no—
335C22—41no—
336C22—42no—
337C22—41no—
338C22—81no—
339C22#408×C10711yescharacteristic
340C22C8×D4×C10711yescharacteristic
341C22#435×C10711yescharacteristic
342C4—22no—
343C4—41no—
344C4—81no—
345C4#386×C10711yescharacteristic
346C4C2×C22⋊C8×C10711yescharacteristic
347C4C8×D4×C10711yescharacteristic
348C4#435×C10711yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—81no—
354C2C107×#186911yescharacteristic
subgroupG/H
centerC8×C107#120
commutatorC2×C4C22×C8×C107
Frattini, cosocleC22×C8C23×C107
socleC2×C107#1869
prime radical#575×C107C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C107 ◁ C22×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3407C2semidirect
3. C107×#2117C2semidirect
4. C2×#350×C107C2semidirect
5. C107×#2113C2semidirect
6. C107×#1379C2semidirect
7. C107×#1378C2semidirect
171. #12979C107direct (N × H)
178. #3407C2×C107semidirect
180. #2117C2×C107semidirect
181. C2×#350C2×C107semidirect
182. #2113C2×C107semidirect
183. #1379C2×C107semidirect
184. #1378C2×C107semidirect
185. C107#12979direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#34072
C107×#29552
C107×#21172
C2×#350×C1072
C107×#21132
C107×#13792
C107×#13782
#12979107