Finite Group Databasebeta

← C107×#8932 #41034896

Subgroups — C107×#8932 #41034896

Order 27392.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2935C211yesmaximal, characteristic
2C107×#1950C211yesmaximal, characteristic, complemented
3C107×#1570C211yesmaximal, characteristic, complemented
4C107×#1540C211yesmaximal, characteristic
5C107×#1492C211yesmaximal, characteristic
6C107×#1278C211yesmaximal, characteristic, complemented
7C107×#1277C211yesmaximal, characteristic, complemented
8C2×#131×C107—21no—
9#532×C107C2211yescharacteristic
10#436×C107—21no—
11#435×C107—22no—
12C8×D4×C107—21no—
13#431×C107C2211yescharacteristic
14C2×#108×C107—21no—
15#423×C107C2211yescharacteristic
16C2×C4⋊C8×C107C2211yescharacteristic
17C2×C4⋊C8×C107C2211yescharacteristic
18#408×C107—21no—
19C4×M16×C107C2211yescharacteristic
20C2×C4×C8×C107C2211yescharacteristic
21#341×C107—21no—
22#334×C107—21no—
23#334×C107—21no—
24#332×C107C411yescharacteristic
25#332×C107C411yescharacteristic
26#331×C107C411yescharacteristic
27#331×C107C411yescharacteristic
28D4⋊C8×C107—22no—
29C2×#41×C107—21no—
30#131×C107—42no—
31#131×C107—42no—
32C2×M16×C107—22no—
33C2×M16×C107—21no—
34C2×M16×C107D411yescharacteristic
35C2×M16×C107D411yescharacteristic
36C22×C8×C107—22no—
37C22×C8×C107—21no—
38C22×C8×C107—21no—
39C22×C8×C107—21no—
40C4⋊Q8×C107C2×C411yescharacteristic
41#127×C107C2×C411yescharacteristic
42#124×C107—21no—
43#121×C107—21no—
44#121×C107Q812yes—
45C4×D4×C107—21no—
46C4×D4×C107D412yes—
47C2×C42×C107C2311yescharacteristic
48#108×C107—42no—
49C4⋊C8×C107—21no—
50C4⋊C8×C107—21no—
51C4⋊C8×C107—21no—
52C4⋊C8×C107—21no—
53C4⋊C8×C107C2×C411yescharacteristic
54C4⋊C8×C107C2×C411yescharacteristic
55C4⋊C8×C107C2×C411yescharacteristic
56C4⋊C8×C107C2×C411yescharacteristic
57C4⋊C8×C107D411yescharacteristic
58C4⋊C8×C107D411yescharacteristic
59C22⋊C8×C107—22no—
60C22⋊C8×C107—22no—
61C22⋊C8×C107—21no—
62#97×C107—21no—
63C4×C8×C107—21no—
64C4×C8×C107—21no—
65C4×C8×C107—21no—
66C4×C8×C107—21no—
67#41×C107—41no—
68#41×C107—41no—
69#41×C107—41no—
70#41×C107—41no—
71C2×Q8×C107—21no—
72C2×D4×C107—22no—
73C2×D4×C107—21no—
74C2×D4×C107—21no—
75C2×D4×C107C4⋊C412yes—
76C22×C4×C107—22no—
77C22×C4×C107C2×D411yescharacteristic
78C22×C4×C107C2×Q811yescharacteristic
79C22×C4×C107#4111yescharacteristic
80M16×C107—21no—
81M16×C107—21no—
82M16×C107—21no—
83M16×C107—44no—
84M16×C107—41no—
85M16×C107—41no—
86M16×C107SD1612yes—
87C2×C8×C107—21no—
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—44no—
97C2×C8×C107—41no—
98C2×C8×C107—41no—
99C2×C8×C107—41no—
100C2×C8×C107—41no—
101C2×C8×C107—41no—
102C2×C8×C107—41no—
103C2×C8×C107—41no—
104C4⋊C4×C107—21no—
105C4⋊C4×C107C4⋊C412yes—
106C22⋊C4×C107—22no—
107C22⋊C4×C107—22no—
108C42×C107C22×C411yescharacteristic
109C42×C107C2×D411yescharacteristic
110C42×C107C2×D411yescharacteristic
111C42×C107#4111yescharacteristic
112C23×C107—22no—
113C23×C107C22⋊Q811yescharacteristic
114Q8×C107—41no—
115Q8×C107—41no—
116D4×C107—42no—
117D4×C107—42no—
118D4×C107—42no—
119D4×C107—41no—
120D4×C107—41no—
121D4×C107—41no—
122D4×C107—41no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—22no—
126C2×C4×C107—41no—
127C2×C4×C107—42no—
128C2×C4×C107—42no—
129C2×C4×C107C2×C4⋊C411yescharacteristic
130C2×C4×C107C4×D411yescharacteristic
131C2×C4×C107C4×D411yescharacteristic
132C2×C4×C107#12011yescharacteristic
133C2×C4×C107C22⋊Q811yescharacteristic
134C2×C4×C107#12311yescharacteristic
135C2×C4×C107C2×SD1611yescharacteristic
136C2×C4×C107#13511yescharacteristic
137C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
139C8×C107—22no—
140C8×C107—42no—
141C8×C107—41no—
142C8×C107—41no—
143C8×C107—41no—
144C8×C107—41no—
145C8×C107—41no—
146C8×C107—41no—
147C8×C107—41no—
148C8×C107—81no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107—42no—
152C22×C107—42no—
153C22×C107—42no—
154C22×C107#38511yescharacteristic
155C22×C107#47611yescharacteristic
156C22×C107#47811yescharacteristic
157C4×C107—21no—
158C4×C107—21no—
159C4×C107—21no—
160C4×C107—42no—
161C4×C107C4×SD1611yescharacteristic
162C4×C107#44211yescharacteristic
163C4×C107#44311yescharacteristic
164C4×C107#44411yescharacteristic
165C4×C107#44911yescharacteristic
166C4×C107#45011yescharacteristic
167#8932C10711yesmaximal, characteristic, direct product factor, Sylow
168C2×C107—21no—
169C2×C107—21no—
170C2×C107—82no—
171C2×C107#185811yescharacteristic
172C2×C107#186411yescharacteristic
173C2×C107#186611yescharacteristic
174#2935C2×C10711yescharacteristic
175#1950C2×C10711yescharacteristic, complemented
176#1570C2×C10711yescharacteristic, complemented
177#1540C2×C10711yescharacteristic
178#1492C2×C10711yescharacteristic
179#1278C2×C10711yescharacteristic, complemented
180#1277C2×C10711yescharacteristic, complemented
181C107#893211yescharacteristic, direct product factor, Sylow
182C2×#131—21no—
183#532C22×C10711yescharacteristic
184#436—21no—
185#435—22no—
186C8×D4—21no—
187#431C22×C10711yescharacteristic
188C2×#108—21no—
189#423C22×C10711yescharacteristic
190C2×C4⋊C8C22×C10711yescharacteristic
191C2×C4⋊C8C22×C10711yescharacteristic
192#408—21no—
193C4×M16C22×C10711yescharacteristic
194C2×C4×C8C22×C10711yescharacteristic
195#341—21no—
196#334—21no—
197#334—21no—
198#332C4×C10711yescharacteristic
199#332C4×C10711yescharacteristic
200#331C4×C10711yescharacteristic
201#331C4×C10711yescharacteristic
202D4⋊C8—22no—
203C2×#41—21no—
204#131—42no—
205#131—42no—
206C2×M16—22no—
207C2×M16—21no—
208C2×M16D4×C10711yescharacteristic
209C2×M16D4×C10711yescharacteristic
210C22×C8—22no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C4⋊Q8C2×C4×C10711yescharacteristic
215#127C2×C4×C10711yescharacteristic
216#124—21no—
217#121—21no—
218#121Q8×C10712yes—
219C4×D4—21no—
220C4×D4D4×C10712yes—
221C2×C42C23×C10711yescharacteristic
222#108—42no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8C2×C4×C10711yescharacteristic
228C4⋊C8C2×C4×C10711yescharacteristic
229C4⋊C8C2×C4×C10711yescharacteristic
230C4⋊C8C2×C4×C10711yescharacteristic
231C4⋊C8D4×C10711yescharacteristic
232C4⋊C8D4×C10711yescharacteristic
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—21no—
236#97—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8—21no—
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C4⋊C4×C10712yes—
250C22×C4—22no—
251C22×C4C2×D4×C10711yescharacteristic
252C22×C4C2×Q8×C10711yescharacteristic
253C22×C4#41×C10711yescharacteristic
254M16—21no—
255M16—21no—
256M16—21no—
257M16—44no—
258M16—41no—
259M16—41no—
260M16SD16×C10712yes—
261C2×C8—21no—
262C2×C8—22no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—44no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C4⋊C4—21no—
279C4⋊C4C4⋊C4×C10712yes—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C42C22×C4×C10711yescharacteristic
283C42C2×D4×C10711yescharacteristic
284C42C2×D4×C10711yescharacteristic
285C42#41×C10711yescharacteristic
286C23—22no—
287C23C22⋊Q8×C10711yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×C4⋊C4×C10711yescharacteristic
304C2×C4C4×D4×C10711yescharacteristic
305C2×C4C4×D4×C10711yescharacteristic
306C2×C4#120×C10711yescharacteristic
307C2×C4C22⋊Q8×C10711yescharacteristic
308C2×C4#123×C10711yescharacteristic
309C2×C4C2×SD16×C10711yescharacteristic
310C2×C4#135×C10711yescharacteristic
311C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
312C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
313C8—22no—
314C8—42no—
315C8—41no—
316C8—41no—
317C8—41no—
318C8—41no—
319C8—41no—
320C8—41no—
321C8—41no—
322C8—81no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#385×C10711yescharacteristic
329C22#476×C10711yescharacteristic
330C22#478×C10711yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4C4×SD16×C10711yescharacteristic
336C4#442×C10711yescharacteristic
337C4#443×C10711yescharacteristic
338C4#444×C10711yescharacteristic
339C4#449×C10711yescharacteristic
340C4#450×C10711yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2C107×#185811yescharacteristic
345C2C107×#186411yescharacteristic
346C2C107×#186611yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#385
prime radical#532×C107C22
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×#1950C2semidirect
3. C107×#1570C2semidirect
6. C107×#1278C2semidirect
7. C107×#1277C2semidirect
167. #8932C107direct (N × H)
175. #1950C2×C107semidirect
176. #1570C2×C107semidirect
179. #1278C2×C107semidirect
180. #1277C2×C107semidirect
181. C107#8932direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#29352
C107×#19502
C107×#15702
C107×#15402
C107×#14922
C107×#12782
C107×#12772
#8932107