Finite Group Databasebeta

← C107×#13016 #41038980

Subgroups — C107×#13016 #41038980

Order 27392.

462 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#508×C107C211yesmaximal, characteristic
2C107×#2957C211yesmaximal, characteristic, complemented
3C107×#2145C211yesmaximal, characteristic, complemented
4C107×#2143C211yesmaximal, characteristic, complemented
5C107×#1976C211yesmaximal, characteristic, complemented
6C107×#1382C211yesmaximal, characteristic, complemented
7C107×#1379C211yesmaximal, characteristic, complemented
8C2×#135×C107C2211yescharacteristic
9C2×#135×C107C2211yescharacteristic
10#568×C107—21no—
11#508×C107—22no—
12#508×C107—22no—
13C2×Q32×C107C411yescharacteristic, complemented
14C2×SD32×C107C411yescharacteristic, complemented
15C2×SD32×C107C411yescharacteristic, complemented
16C2×D16×C107C411yescharacteristic, complemented
17C2×M32×C107C2211yescharacteristic
18C22×C16×C107C2211yescharacteristic
19#444×C107—22no—
20#443×C107—22no—
21C2×#108×C107C2211yescharacteristic
22#427×C107C2211yescharacteristic
23#421×C107—21no—
24#421×C107—21no—
25#410×C107—21no—
26#405×C107C2211yescharacteristic
27#360×C107—22no—
28#359×C107—22no—
29C2×#41×C107—21no—
30C2×#41×C107—21no—
31#135×C107—21no—
32#135×C107—21no—
33#135×C107—21no—
34#135×C107—21no—
35#135×C107—21no—
36#135×C107—21no—
37#135×C107D412yes—
38#135×C107D412yes—
39C2×Q16×C107C2×C411yescharacteristic
40C2×Q16×C107C2×C411yescharacteristic
41C2×SD16×C107—21no—
42C2×SD16×C107—21no—
43C2×D8×C107C2×C411yescharacteristic
44C2×D8×C107C2×C411yescharacteristic
45#131×C107—24no—
46#131×C107—42no—
47C2×M16×C107—21no—
48C2×M16×C107—42no—
49C2×M16×C107D411yescharacteristic
50C22×C8×C107C2311yescharacteristic
51#117×C107—21no—
52#117×C107D411yescharacteristic
53Q32×C107—22no—
54SD32×C107—22no—
55SD32×C107—22no—
56D16×C107—22no—
57M32×C107—21no—
58M32×C107—21no—
59C2×C16×C107—21no—
60C2×C16×C107—21no—
61C2×C16×C107—21no—
62C2×C16×C107C2×C411yescharacteristic
63C2×C16×C107C2×C411yescharacteristic
64#108×C107—21no—
65#108×C107D412yes—
66#107×C107—21no—
67#106×C107—21no—
68#104×C107—24no—
69#104×C107—42no—
70#99×C107—42no—
71#97×C107—21no—
72C4×C8×C107—21no—
73#41×C107—22no—
74#41×C107—22no—
75#41×C107—41no—
76#41×C107—41no—
77#41×C107—41no—
78#41×C107—41no—
79#41×C107—41no—
80#41×C107—41no—
81C2×Q8×C107—21no—
82C2×Q8×C107—21no—
83C2×D4×C107—21no—
84C2×D4×C107—21no—
85C2×D4×C107—41no—
86C2×D4×C107—41no—
87C22×C4×C107—41no—
88C22×C4×C107—41no—
89C22×C4×C107C2×D411yescharacteristic
90Q16×C107—21no—
91Q16×C107—21no—
92Q16×C107—21no—
93Q16×C107C22⋊C412yes—
94SD16×C107—22no—
95SD16×C107—22no—
96SD16×C107—41no—
97SD16×C107—41no—
98D8×C107—21no—
99D8×C107—21no—
100D8×C107—21no—
101D8×C107C22⋊C412yes—
102M16×C107—21no—
103M16×C107—22no—
104M16×C107—44no—
105M16×C107—41no—
106M16×C107D812yes—
107C2×C8×C107—21no—
108C2×C8×C107—44no—
109C2×C8×C107—41no—
110C2×C8×C107C22×C411yescharacteristic
111C2×C8×C107C2×D411yescharacteristic
112C2×C8×C107C2×D411yescharacteristic
113C2×C8×C107C2×D411yescharacteristic
114C2×C8×C107#4111yescharacteristic
115C2×C8×C107#4111yescharacteristic
116C4⋊C4×C107—21no—
117C4⋊C4×C107—41no—
118C22⋊C4×C107—21no—
119C22⋊C4×C107—41no—
120C42×C107—21no—
121C42×C107—41no—
122C16×C107—21no—
123C16×C107—21no—
124C16×C107—41no—
125C23×C107—41no—
126C23×C107—41no—
127C23×C107AGL(1,ℤ/8)11yescharacteristic
128Q8×C107—22no—
129Q8×C107—41no—
130Q8×C107—41no—
131Q8×C107—41no—
132D4×C107—22no—
133D4×C107—42no—
134D4×C107—42no—
135D4×C107—41no—
136D4×C107—41no—
137D4×C107—41no—
138D4×C107—81no—
139D4×C107—81no—
140C2×C4×C107—41no—
141C2×C4×C107—42no—
142C2×C4×C107—42no—
143C2×C4×C107—41no—
144C2×C4×C107—41no—
145C2×C4×C107—81no—
146C2×C4×C107—81no—
147C2×C4×C107—81no—
148C2×C4×C107C4×D411yescharacteristic
149C2×C4×C107#12011yescharacteristic
150C2×C4×C107#12111yescharacteristic
151C2×C4×C107C2×D811yescharacteristic
152C2×C4×C107#13511yescharacteristic
153C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
154C8×C107—22no—
155C8×C107—42no—
156C8×C107C2×C22⋊C411yescharacteristic
157C8×C107C4×D411yescharacteristic
158C8×C107#12111yescharacteristic
159C8×C107#12311yescharacteristic
160C22×C107—41no—
161C22×C107—42no—
162C22×C107—81no—
163C22×C107—161no—
164C22×C107—161no—
165C22×C107#44211yescharacteristic
166C22×C107#44911yescharacteristic
167C22×C107#45911yescharacteristic
168C4×C107—42no—
169C4×C107—81no—
170C4×C107—81no—
171C4×C107—161no—
172C4×C107#38611yescharacteristic
173C4×C107C4×D811yescharacteristic
174C4×C107#44711yescharacteristic
175C4×C107#46311yescharacteristic
176#13016C10711yesmaximal, characteristic, direct product factor, Sylow
177C2×C107—21no—
178C2×C107—21no—
179C2×C107—21no—
180C2×C107—82no—
181C2×C107—161no—
182C2×C107#187911yescharacteristic
183C2×#508C2×C10711yescharacteristic
184#2957C2×C10711yescharacteristic, complemented
185#2145C2×C10711yescharacteristic, complemented
186#2143C2×C10711yescharacteristic, complemented
187#1976C2×C10711yescharacteristic, complemented
188#1382C2×C10711yescharacteristic, complemented
189#1379C2×C10711yescharacteristic, complemented
190C107#1301611yescharacteristic, direct product factor, Sylow
191C2×#135C22×C10711yescharacteristic
192C2×#135C22×C10711yescharacteristic
193#568—21no—
194#508—22no—
195#508—22no—
196C2×Q32C4×C10711yescharacteristic, complemented
197C2×SD32C4×C10711yescharacteristic, complemented
198C2×SD32C4×C10711yescharacteristic, complemented
199C2×D16C4×C10711yescharacteristic, complemented
200C2×M32C22×C10711yescharacteristic
201C22×C16C22×C10711yescharacteristic
202#444—22no—
203#443—22no—
204C2×#108C22×C10711yescharacteristic
205#427C22×C10711yescharacteristic
206#421—21no—
207#421—21no—
208#410—21no—
209#405C22×C10711yescharacteristic
210#360—22no—
211#359—22no—
212C2×#41—21no—
213C2×#41—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135D4×C10712yes—
221#135D4×C10712yes—
222C2×Q16C2×C4×C10711yescharacteristic
223C2×Q16C2×C4×C10711yescharacteristic
224C2×SD16—21no—
225C2×SD16—21no—
226C2×D8C2×C4×C10711yescharacteristic
227C2×D8C2×C4×C10711yescharacteristic
228#131—24no—
229#131—42no—
230C2×M16—21no—
231C2×M16—42no—
232C2×M16D4×C10711yescharacteristic
233C22×C8C23×C10711yescharacteristic
234#117—21no—
235#117D4×C10711yescharacteristic
236Q32—22no—
237SD32—22no—
238SD32—22no—
239D16—22no—
240M32—21no—
241M32—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16C2×C4×C10711yescharacteristic
246C2×C16C2×C4×C10711yescharacteristic
247#108—21no—
248#108D4×C10712yes—
249#107—21no—
250#106—21no—
251#104—24no—
252#104—42no—
253#99—42no—
254#97—21no—
255C4×C8—21no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×D4×C10711yescharacteristic
273Q16—21no—
274Q16—21no—
275Q16—21no—
276Q16C22⋊C4×C10712yes—
277SD16—22no—
278SD16—22no—
279SD16—41no—
280SD16—41no—
281D8—21no—
282D8—21no—
283D8—21no—
284D8C22⋊C4×C10712yes—
285M16—21no—
286M16—22no—
287M16—44no—
288M16—41no—
289M16D8×C10712yes—
290C2×C8—21no—
291C2×C8—44no—
292C2×C8—41no—
293C2×C8C22×C4×C10711yescharacteristic
294C2×C8C2×D4×C10711yescharacteristic
295C2×C8C2×D4×C10711yescharacteristic
296C2×C8C2×D4×C10711yescharacteristic
297C2×C8#41×C10711yescharacteristic
298C2×C8#41×C10711yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—41no—
301C22⋊C4—21no—
302C22⋊C4—41no—
303C42—21no—
304C42—41no—
305C16—21no—
306C16—21no—
307C16—41no—
308C23—41no—
309C23—41no—
310C23AGL(1,ℤ/8)×C10711yescharacteristic
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4C4×D4×C10711yescharacteristic
332C2×C4#120×C10711yescharacteristic
333C2×C4#121×C10711yescharacteristic
334C2×C4C2×D8×C10711yescharacteristic
335C2×C4#135×C10711yescharacteristic
336C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
337C8—22no—
338C8—42no—
339C8C2×C22⋊C4×C10711yescharacteristic
340C8C4×D4×C10711yescharacteristic
341C8#121×C10711yescharacteristic
342C8#123×C10711yescharacteristic
343C22—41no—
344C22—42no—
345C22—81no—
346C22—161no—
347C22—161no—
348C22#442×C10711yescharacteristic
349C22#449×C10711yescharacteristic
350C22#459×C10711yescharacteristic
351C4—42no—
352C4—81no—
353C4—81no—
354C4—161no—
355C4#386×C10711yescharacteristic
356C4C4×D8×C10711yescharacteristic
357C4#447×C10711yescharacteristic
358C4#463×C10711yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—161no—
364C2C107×#187911yescharacteristic
subgroupG/H
centerC4×C107#447
commutatorC2×C8C22×C4×C107
Frattini, cosocleC22×C8C23×C107
socleC2×C107#1879
prime radicalC2×#508×C107C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C22×C4×C107 ◁ #405×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2957C2semidirect
3. C107×#2145C2semidirect
4. C107×#2143C2semidirect
5. C107×#1976C2semidirect
6. C107×#1382C2semidirect
7. C107×#1379C2semidirect
13. C2×Q32×C107C4semidirect
14. C2×SD32×C107C4semidirect
15. C2×SD32×C107C4semidirect
16. C2×D16×C107C4semidirect
176. #13016C107direct (N × H)
184. #2957C2×C107semidirect
185. #2145C2×C107semidirect
186. #2143C2×C107semidirect
187. #1976C2×C107semidirect
188. #1382C2×C107semidirect
189. #1379C2×C107semidirect
190. C107#13016direct (N × H)
196. C2×Q32C4×C107semidirect
197. C2×SD32C4×C107semidirect
198. C2×SD32C4×C107semidirect
199. C2×D16C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#508×C1072
C107×#29572
C107×#21452
C107×#21432
C107×#19762
C107×#13822
C107×#13792
#13016107