Finite Group Databasebeta

← C107×#10282 #41036246

Subgroups — C107×#10282 #41036246

Order 27392.

678 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3227C211yesmaximal, characteristic, complemented
2C107×#3205C211yesmaximal, characteristic
3C107×#2858C211yesmaximal, characteristic, complemented
4C107×#1962C211yesmaximal, characteristic, complemented
5C107×#1549C211yesmaximal, characteristic, complemented
6C107×#1545C211yesmaximal, characteristic, complemented
7C107×#1276C211yesmaximal, characteristic, complemented
8#532×C107C2211yescharacteristic
9C2×C4⋊Q8×C107C2211yescharacteristic
10C2×#127×C107C2211yescharacteristic
11C2×#124×C107—22no—
12#498×C107—21no—
13#493×C107—21no—
14#486×C107—21no—
15#486×C107—21no—
16#481×C107—22no—
17#476×C107—22no—
18#459×C107—22no—
19#447×C107—22no—
20#431×C107C2211yescharacteristic
21#431×C107C2211yescharacteristic
22#423×C107C2211yescharacteristic
23C2×#104×C107—22no—
24#390×C107—22no—
25#390×C107—22no—
26C43×C107C2211yescharacteristic
27#332×C107—22no—
28#331×C107—22no—
29C2×#41×C107—21no—
30C22×Q8×C107—21no—
31C22×D4×C107—21no—
32C22×D4×C107—21no—
33C22×D4×C107D412yes—
34C2×D8×C107—24no—
35C2×M16×C107—21no—
36C4⋊Q8×C107—21no—
37C4⋊Q8×C107—21no—
38C4⋊Q8×C107—21no—
39C4⋊Q8×C107—21no—
40C4⋊Q8×C107D411yescharacteristic
41#127×C107—21no—
42#127×C107—21no—
43#127×C107—21no—
44#127×C107—21no—
45#127×C107D411yescharacteristic
46#124×C107—21no—
47#124×C107—48no—
48#121×C107—21no—
49#121×C107—21no—
50C4×D4×C107—21no—
51C4×D4×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#106×C107—24no—
60C4⋊C8×C107—21no—
61C4⋊C8×C107—21no—
62C4⋊C8×C107D412yes—
63C4⋊C8×C107D412yes—
64#104×C107—44no—
65#102×C107—24no—
66#102×C107—24no—
67C22⋊C8×C107—21no—
68C22⋊C8×C107—21no—
69C4×C8×C107—21no—
70C4×C8×C107—21no—
71C24×C107—22no—
72#41×C107—42no—
73#41×C107—42no—
74C2×Q8×C107—21no—
75C2×Q8×C107—44no—
76C2×Q8×C107—41no—
77C2×Q8×C107—41no—
78C2×D4×C107—21no—
79C2×D4×C107—22no—
80C2×D4×C107—21no—
81C2×D4×C107—21no—
82C2×D4×C107—22no—
83C2×D4×C107—44no—
84C2×D4×C107—44no—
85C2×D4×C107—41no—
86C2×D4×C107—41no—
87C2×D4×C107—41no—
88C2×D4×C107—41no—
89C2×D4×C107—41no—
90C2×D4×C107—42no—
91C2×D4×C107—42no—
92C22×C4×C107—22no—
93C22×C4×C107—22no—
94C22×C4×C107—41no—
95C22×C4×C107C2×D411yescharacteristic
96C22×C4×C107C2×D411yescharacteristic
97C22×C4×C107C2×D411yescharacteristic
98D8×C107—84no—
99M16×C107—42no—
100C2×C8×C107—22no—
101C2×C8×C107—22no—
102C2×C8×C107—41no—
103C4⋊C4×C107—21no—
104C4⋊C4×C107—22no—
105C4⋊C4×C107—21no—
106C4⋊C4×C107—22no—
107C4⋊C4×C107—41no—
108C4⋊C4×C107—41no—
109C22⋊C4×C107—416no—
110C22⋊C4×C107—41no—
111C22⋊C4×C107—41no—
112C42×C107—24no—
113C42×C107—22no—
114C42×C107—22no—
115C42×C107—42no—
116C42×C107C2×D411yescharacteristic
117C42×C107C2×D411yescharacteristic
118C42×C107C2×D411yescharacteristic
119C42×C107#4111yescharacteristic
120C23×C107—44no—
121C23×C107—44no—
122C23×C107—41no—
123C23×C107—42no—
124C23×C107—44no—
125C23×C107#12011yescharacteristic
126Q8×C107—42no—
127Q8×C107—82no—
128Q8×C107—82no—
129D4×C107—42no—
130D4×C107—44no—
131D4×C107—42no—
132D4×C107—42no—
133D4×C107—82no—
134D4×C107—82no—
135D4×C107—82no—
136D4×C107—82no—
137D4×C107—82no—
138D4×C107—81no—
139D4×C107—81no—
140C2×C4×C107—22no—
141C2×C4×C107—22no—
142C2×C4×C107—24no—
143C2×C4×C107—42no—
144C2×C4×C107—42no—
145C2×C4×C107—44no—
146C2×C4×C107—41no—
147C2×C4×C107—42no—
148C2×C4×C107—81no—
149C2×C4×C107—81no—
150C2×C4×C107#12011yescharacteristic
151C2×C4×C107#12011yescharacteristic
152C2×C4×C107#12111yescharacteristic
153C2×C4×C107#12111yescharacteristic
154C2×C4×C107#12111yescharacteristic
155C2×C4×C107#12711yescharacteristic
156C2×C4×C107#13512yes—
157C2×C4×C107AGL(1,ℤ/8)12yes—
158C8×C107—42no—
159C8×C107—42no—
160C8×C107—81no—
161C22×C107—21no—
162C22×C107—21no—
163C22×C107—88no—
164C22×C107—82no—
165C22×C107—81no—
166C22×C107—81no—
167C22×C107—82no—
168C22×C107—81no—
169C22×C107—82no—
170C22×C107#39211yescharacteristic
171C22×C107#44912yes—
172C4×C107—21no—
173C4×C107—21no—
174C4×C107—44no—
175C4×C107—82no—
176C4×C107—81no—
177C4×C107#45312yes—
178C4×C107#45412yes—
179C4×C107#46312yes—
180C4×C107#49511yescharacteristic
181C4×C107#49611yescharacteristic
182#10282C10711yesmaximal, characteristic, direct product factor, Sylow
183C2×C107—22no—
184C2×C107—161no—
185C2×C107—162no—
186C2×C107#200211yescharacteristic
187C2×C107#200311yescharacteristic
188C2×C107#201211yescharacteristic
189#3227C2×C10711yescharacteristic, complemented
190#3205C2×C10711yescharacteristic
191#2858C2×C10711yescharacteristic, complemented
192#1962C2×C10711yescharacteristic, complemented
193#1549C2×C10711yescharacteristic, complemented
194#1545C2×C10711yescharacteristic, complemented
195#1276C2×C10711yescharacteristic, complemented
196C107#1028211yescharacteristic, direct product factor, Sylow
197#532C22×C10711yescharacteristic
198C2×C4⋊Q8C22×C10711yescharacteristic
199C2×#127C22×C10711yescharacteristic
200C2×#124—22no—
201#498—21no—
202#493—21no—
203#486—21no—
204#486—21no—
205#481—22no—
206#476—22no—
207#459—22no—
208#447—22no—
209#431C22×C10711yescharacteristic
210#431C22×C10711yescharacteristic
211#423C22×C10711yescharacteristic
212C2×#104—22no—
213#390—22no—
214#390—22no—
215C43C22×C10711yescharacteristic
216#332—22no—
217#331—22no—
218C2×#41—21no—
219C22×Q8—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4D4×C10712yes—
223C2×D8—24no—
224C2×M16—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C10711yescharacteristic
230#127—21no—
231#127—21no—
232#127—21no—
233#127—21no—
234#127D4×C10711yescharacteristic
235#124—21no—
236#124—48no—
237#121—21no—
238#121—21no—
239C4×D4—21no—
240C4×D4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4D4×C10712yes—
243C2×C22⋊C4—28no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42D4×C10712yes—
247C2×C42C23×C10711yescharacteristic
248#106—24no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C10712yes—
252C4⋊C8D4×C10712yes—
253#104—44no—
254#102—24no—
255#102—24no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C4×C8—21no—
259C4×C8—21no—
260C24—22no—
261#41—42no—
262#41—42no—
263C2×Q8—21no—
264C2×Q8—44no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—21no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—42no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4C2×D4×C10711yescharacteristic
285C22×C4C2×D4×C10711yescharacteristic
286C22×C4C2×D4×C10711yescharacteristic
287D8—84no—
288M16—42no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—416no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C42—24no—
302C42—22no—
303C42—22no—
304C42—42no—
305C42C2×D4×C10711yescharacteristic
306C42C2×D4×C10711yescharacteristic
307C42C2×D4×C10711yescharacteristic
308C42#41×C10711yescharacteristic
309C23—44no—
310C23—44no—
311C23—41no—
312C23—42no—
313C23—44no—
314C23#120×C10711yescharacteristic
315Q8—42no—
316Q8—82no—
317Q8—82no—
318D4—42no—
319D4—44no—
320D4—42no—
321D4—42no—
322D4—82no—
323D4—82no—
324D4—82no—
325D4—82no—
326D4—82no—
327D4—81no—
328D4—81no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4#120×C10711yescharacteristic
340C2×C4#120×C10711yescharacteristic
341C2×C4#121×C10711yescharacteristic
342C2×C4#121×C10711yescharacteristic
343C2×C4#121×C10711yescharacteristic
344C2×C4#127×C10711yescharacteristic
345C2×C4#135×C10712yes—
346C2×C4AGL(1,ℤ/8)×C10712yes—
347C8—42no—
348C8—42no—
349C8—81no—
350C22—21no—
351C22—21no—
352C22—88no—
353C22—82no—
354C22—81no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22#392×C10711yescharacteristic
360C22#449×C10712yes—
361C4—21no—
362C4—21no—
363C4—44no—
364C4—82no—
365C4—81no—
366C4#453×C10712yes—
367C4#454×C10712yes—
368C4#463×C10712yes—
369C4#495×C10711yescharacteristic
370C4#496×C10711yescharacteristic
371C2—22no—
372C2—162no—
373C2—161no—
374C2C107×#200211yescharacteristic
375C2C107×#200311yescharacteristic
376C2C107×#201211yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC107×#3205C2
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×#3227C2semidirect
3. C107×#2858C2semidirect
4. C107×#1962C2semidirect
5. C107×#1549C2semidirect
6. C107×#1545C2semidirect
7. C107×#1276C2semidirect
182. #10282C107direct (N × H)
189. #3227C2×C107semidirect
191. #2858C2×C107semidirect
192. #1962C2×C107semidirect
193. #1549C2×C107semidirect
194. #1545C2×C107semidirect
195. #1276C2×C107semidirect
196. C107#10282direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32272
C107×#32052
C107×#28582
C107×#19622
C107×#15492
C107×#15452
C107×#12762
#10282107