Finite Group Databasebeta

← C107×#10292 #41036256

Subgroups — C107×#10292 #41036256

Order 27392.

640 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×#3230C211yesmaximal, characteristic, complemented
2C107×#3208C211yesmaximal, characteristic
3C107×#2858C211yesmaximal, characteristic
4C107×#1994C211yesmaximal, characteristic, complemented
5C107×#1549C211yesmaximal, characteristic, complemented
6C107×#1545C211yesmaximal, characteristic
7C107×#1276C211yesmaximal, characteristic, complemented
8#533×C107C2211yescharacteristic
9C2×C4⋊Q8×C107C2211yescharacteristic
10C2×#127×C107C2211yescharacteristic
11C2×#124×C107—22no—
12#500×C107—21no—
13#492×C107—21no—
14#487×C107—21no—
15#486×C107—21no—
16#484×C107—22no—
17#477×C107—22no—
18#460×C107—22no—
19#450×C107—22no—
20#431×C107C2211yescharacteristic
21#431×C107C2211yescharacteristic
22#423×C107C2211yescharacteristic
23#390×C107—22no—
24#390×C107—22no—
25C43×C107C2211yescharacteristic
26#339×C107—22no—
27#332×C107—22no—
28#331×C107—22no—
29C22×Q8×C107—21no—
30C22×D4×C107—21no—
31C22×D4×C107—21no—
32C22×D4×C107D412yes—
33C2×SD16×C107—24no—
34C2×M16×C107—21no—
35C4⋊Q8×C107—21no—
36C4⋊Q8×C107—21no—
37C4⋊Q8×C107—21no—
38C4⋊Q8×C107—21no—
39C4⋊Q8×C107D411yescharacteristic
40C4⋊Q8×C107D411yescharacteristic
41#127×C107—21no—
42#127×C107—21no—
43#127×C107—21no—
44#127×C107—21no—
45#125×C107—21no—
46#124×C107—48no—
47C22⋊Q8×C107—21no—
48C22⋊Q8×C107—21no—
49C4×Q8×C107—21no—
50C4×Q8×C107—21no—
51#117×C107—21no—
52C2×C4⋊C4×C107—21no—
53C2×C4⋊C4×C107D412yes—
54C2×C22⋊C4×C107—28no—
55C2×C42×C107—21no—
56C2×C42×C107—21no—
57C2×C42×C107D412yes—
58C2×C42×C107C2311yescharacteristic
59#107×C107—24no—
60C4⋊C8×C107—21no—
61C4⋊C8×C107—21no—
62C4⋊C8×C107D412yes—
63C4⋊C8×C107D412yes—
64#103×C107—24no—
65#102×C107—24no—
66C22⋊C8×C107—21no—
67C22⋊C8×C107—21no—
68C4×C8×C107—21no—
69C4×C8×C107—21no—
70C24×C107—22no—
71C2×Q8×C107—21no—
72C2×Q8×C107—21no—
73C2×Q8×C107—44no—
74C2×Q8×C107—41no—
75C2×Q8×C107—41no—
76C2×D4×C107—22no—
77C2×D4×C107—22no—
78C2×D4×C107—44no—
79C2×D4×C107—44no—
80C2×D4×C107—41no—
81C2×D4×C107—41no—
82C2×D4×C107—41no—
83C2×D4×C107—41no—
84C2×D4×C107—42no—
85C2×D4×C107—42no—
86C22×C4×C107—22no—
87C22×C4×C107—22no—
88C22×C4×C107C2×D411yescharacteristic
89C22×C4×C107C2×D411yescharacteristic
90C22×C4×C107C2×D411yescharacteristic
91SD16×C107—84no—
92M16×C107—42no—
93C2×C8×C107—22no—
94C2×C8×C107—22no—
95C2×C8×C107—41no—
96C4⋊C4×C107—21no—
97C4⋊C4×C107—22no—
98C4⋊C4×C107—21no—
99C4⋊C4×C107—22no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107—21no—
102C4⋊C4×C107—41no—
103C4⋊C4×C107—41no—
104C4⋊C4×C107—41no—
105C4⋊C4×C107—41no—
106C22⋊C4×C107—416no—
107C22⋊C4×C107—41no—
108C42×C107—24no—
109C42×C107—22no—
110C42×C107—22no—
111C42×C107—42no—
112C42×C107—41no—
113C42×C107C2×D411yescharacteristic
114C42×C107C2×D411yescharacteristic
115C42×C107C2×D411yescharacteristic
116C42×C107#4111yescharacteristic
117C23×C107—44no—
118C23×C107—44no—
119C23×C107—42no—
120C23×C107—44no—
121C23×C107#12011yescharacteristic
122Q8×C107—42no—
123Q8×C107—42no—
124Q8×C107—82no—
125Q8×C107—82no—
126D4×C107—44no—
127D4×C107—82no—
128D4×C107—82no—
129D4×C107—82no—
130D4×C107—82no—
131D4×C107—81no—
132D4×C107—81no—
133C2×C4×C107—22no—
134C2×C4×C107—22no—
135C2×C4×C107—24no—
136C2×C4×C107—42no—
137C2×C4×C107—42no—
138C2×C4×C107—44no—
139C2×C4×C107—41no—
140C2×C4×C107—41no—
141C2×C4×C107—42no—
142C2×C4×C107#12011yescharacteristic
143C2×C4×C107#12011yescharacteristic
144C2×C4×C107#12111yescharacteristic
145C2×C4×C107#12111yescharacteristic
146C2×C4×C107#12111yescharacteristic
147C2×C4×C107#12711yescharacteristic
148C2×C4×C107#13512yes—
149C2×C4×C107#13712yes—
150C8×C107—42no—
151C8×C107—42no—
152C8×C107—81no—
153C22×C107—21no—
154C22×C107—21no—
155C22×C107—88no—
156C22×C107—82no—
157C22×C107—82no—
158C22×C107—82no—
159C22×C107#39211yescharacteristic
160C22×C107#45212yes—
161C4×C107—21no—
162C4×C107—21no—
163C4×C107—44no—
164C4×C107—82no—
165C4×C107—81no—
166C4×C107—81no—
167C4×C107#45312yes—
168C4×C107#45412yes—
169C4×C107#46412yes—
170C4×C107#49511yescharacteristic
171C4×C107#49711yescharacteristic
172#10292C10711yesmaximal, characteristic, direct product factor, Sylow
173C2×C107—22no—
174C2×C107—162no—
175C2×C107#200211yescharacteristic
176C2×C107#200311yescharacteristic
177C2×C107#201511yescharacteristic
178#3230C2×C10711yescharacteristic, complemented
179#3208C2×C10711yescharacteristic
180#2858C2×C10711yescharacteristic
181#1994C2×C10711yescharacteristic, complemented
182#1549C2×C10711yescharacteristic, complemented
183#1545C2×C10711yescharacteristic
184#1276C2×C10711yescharacteristic, complemented
185C107#1029211yescharacteristic, direct product factor, Sylow
186#533C22×C10711yescharacteristic
187C2×C4⋊Q8C22×C10711yescharacteristic
188C2×#127C22×C10711yescharacteristic
189C2×#124—22no—
190#500—21no—
191#492—21no—
192#487—21no—
193#486—21no—
194#484—22no—
195#477—22no—
196#460—22no—
197#450—22no—
198#431C22×C10711yescharacteristic
199#431C22×C10711yescharacteristic
200#423C22×C10711yescharacteristic
201#390—22no—
202#390—22no—
203C43C22×C10711yescharacteristic
204#339—22no—
205#332—22no—
206#331—22no—
207C22×Q8—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4D4×C10712yes—
211C2×SD16—24no—
212C2×M16—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8D4×C10711yescharacteristic
218C4⋊Q8D4×C10711yescharacteristic
219#127—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#125—21no—
224#124—48no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229#117—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4D4×C10712yes—
232C2×C22⋊C4—28no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42D4×C10712yes—
236C2×C42C23×C10711yescharacteristic
237#107—24no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C10712yes—
241C4⋊C8D4×C10712yes—
242#103—24no—
243#102—24no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C4×C8—21no—
247C4×C8—21no—
248C24—22no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—44no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—44no—
257C2×D4—44no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4C2×D4×C10711yescharacteristic
267C22×C4C2×D4×C10711yescharacteristic
268C22×C4C2×D4×C10711yescharacteristic
269SD16—84no—
270M16—42no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C22⋊C4—416no—
285C22⋊C4—41no—
286C42—24no—
287C42—22no—
288C42—22no—
289C42—42no—
290C42—41no—
291C42C2×D4×C10711yescharacteristic
292C42C2×D4×C10711yescharacteristic
293C42C2×D4×C10711yescharacteristic
294C42#41×C10711yescharacteristic
295C23—44no—
296C23—44no—
297C23—42no—
298C23—44no—
299C23#120×C10711yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—82no—
303Q8—82no—
304D4—44no—
305D4—82no—
306D4—82no—
307D4—82no—
308D4—82no—
309D4—81no—
310D4—81no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4#120×C10711yescharacteristic
321C2×C4#120×C10711yescharacteristic
322C2×C4#121×C10711yescharacteristic
323C2×C4#121×C10711yescharacteristic
324C2×C4#121×C10711yescharacteristic
325C2×C4#127×C10711yescharacteristic
326C2×C4#135×C10712yes—
327C2×C4#137×C10712yes—
328C8—42no—
329C8—42no—
330C8—81no—
331C22—21no—
332C22—21no—
333C22—88no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22#392×C10711yescharacteristic
338C22#452×C10712yes—
339C4—21no—
340C4—21no—
341C4—44no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4#453×C10712yes—
346C4#454×C10712yes—
347C4#464×C10712yes—
348C4#495×C10711yescharacteristic
349C4#497×C10711yescharacteristic
350C2—22no—
351C2—162no—
352C2C107×#200211yescharacteristic
353C2C107×#200311yescharacteristic
354C2C107×#201511yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC2×#127×C107C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3230C2semidirect
4. C107×#1994C2semidirect
5. C107×#1549C2semidirect
7. C107×#1276C2semidirect
172. #10292C107direct (N × H)
178. #3230C2×C107semidirect
181. #1994C2×C107semidirect
182. #1549C2×C107semidirect
184. #1276C2×C107semidirect
185. C107#10292direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32302
C107×#32082
C107×#28582
C107×#19942
C107×#15492
C107×#15452
C107×#12762
#10292107