Finite Group Databasebeta

← C107×#10168 #41036132

Subgroups — C107×#10168 #41036132

Order 27392.

642 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×#3205C211yesmaximal, characteristic
2C107×#3152C211yesmaximal, characteristic, complemented
3C2×#486×C107C211yesmaximal, characteristic, complemented
4C107×#1965C211yesmaximal, characteristic, complemented
5C107×#1546C211yesmaximal, characteristic, complemented
6C107×#1492C211yesmaximal, characteristic, complemented
7C107×#1278C211yesmaximal, characteristic, complemented
8C2×#137×C107—22no—
9#532×C107C2211yescharacteristic
10C2×C4⋊Q8×C107C2211yescharacteristic
11C2×#127×C107C2211yescharacteristic
12#497×C107—22no—
13#494×C107—21no—
14#493×C107—21no—
15#492×C107—21no—
16#486×C107—21no—
17#486×C107—22no—
18#486×C107—22no—
19#459×C107—22no—
20#447×C107—22no—
21#431×C107C2211yescharacteristic
22#423×C107C2211yescharacteristic
23C2×#102×C107—22no—
24C2×#100×C107—22no—
25C4×M16×C107C2211yescharacteristic
26C2×C4×C8×C107C2211yescharacteristic
27#332×C107—22no—
28D4⋊C8×C107—22no—
29C2×#41×C107—21no—
30C22×Q8×C107—21no—
31C22×D4×C107—21no—
32C22×D4×C107—21no—
33C22×D4×C107D412yes—
34#137×C107—44no—
35#137×C107—44no—
36C2×Q16×C107—24no—
37C2×SD16×C107—24no—
38C2×D8×C107—24no—
39C2×M16×C107—21no—
40C2×M16×C107D412yes—
41C22×C8×C107—21no—
42C4⋊Q8×C107—21no—
43C4⋊Q8×C107—21no—
44C4⋊Q8×C107—21no—
45C4⋊Q8×C107D411yescharacteristic
46C4⋊Q8×C107D412yes—
47#127×C107—21no—
48#127×C107—21no—
49#127×C107—21no—
50#127×C107—21no—
51#127×C107D411yescharacteristic
52#124×C107—21no—
53#121×C107—21no—
54#121×C107—21no—
55C4×D4×C107—21no—
56C4×D4×C107—21no—
57C2×C4⋊C4×C107—21no—
58C2×C4⋊C4×C107—21no—
59C2×C42×C107C2311yescharacteristic
60C4⋊C8×C107—21no—
61C4⋊C8×C107—21no—
62C4⋊C8×C107D412yes—
63#102×C107—28no—
64#102×C107—24no—
65#100×C107—44no—
66C22⋊C8×C107—21no—
67#97×C107—21no—
68C4×C8×C107—21no—
69C4×C8×C107—21no—
70C4×C8×C107—21no—
71C4×C8×C107D412yes—
72C24×C107—22no—
73#41×C107—42no—
74#41×C107—42no—
75C2×Q8×C107—21no—
76C2×Q8×C107—22no—
77C2×Q8×C107—41no—
78C2×Q8×C107—42no—
79C2×Q8×C107—42no—
80C2×D4×C107—22no—
81C2×D4×C107—22no—
82C2×D4×C107—21no—
83C2×D4×C107—21no—
84C2×D4×C107—21no—
85C2×D4×C107—44no—
86C2×D4×C107—41no—
87C2×D4×C107—41no—
88C2×D4×C107—41no—
89C2×D4×C107—41no—
90C2×D4×C107—41no—
91C2×D4×C107—42no—
92C2×D4×C107—42no—
93C2×D4×C107—82no—
94C22×C4×C107—41no—
95C22×C4×C107—41no—
96C22×C4×C107C2×D411yescharacteristic
97C22×C4×C107C2×D411yescharacteristic
98C22×C4×C107#4111yescharacteristic
99Q16×C107—48no—
100SD16×C107—48no—
101D8×C107—84no—
102M16×C107—22no—
103M16×C107—42no—
104M16×C107D814yescomplemented
105C2×C8×C107—22no—
106C2×C8×C107—22no—
107C2×C8×C107—22no—
108C2×C8×C107—42no—
109C2×C8×C107—41no—
110C4⋊C4×C107—22no—
111C4⋊C4×C107—21no—
112C4⋊C4×C107—22no—
113C4⋊C4×C107—21no—
114C4⋊C4×C107—41no—
115C4⋊C4×C107—41no—
116C22⋊C4×C107—41no—
117C22⋊C4×C107—41no—
118C42×C107C2×D411yescharacteristic
119C42×C107C2×D411yescharacteristic
120C42×C107C2×D411yescharacteristic
121C42×C107C2×D411yescharacteristic
122C23×C107—41no—
123C23×C107—42no—
124C23×C107—44no—
125C23×C107—82no—
126C23×C107—82no—
127C23×C107#12111yescharacteristic
128Q8×C107—44no—
129Q8×C107—42no—
130Q8×C107—81no—
131Q8×C107—81no—
132D4×C107—44no—
133D4×C107—42no—
134D4×C107—42no—
135D4×C107—44no—
136D4×C107—42no—
137D4×C107—82no—
138D4×C107—82no—
139D4×C107—82no—
140D4×C107—82no—
141D4×C107—81no—
142D4×C107—81no—
143C2×C4×C107—22no—
144C2×C4×C107—22no—
145C2×C4×C107—41no—
146C2×C4×C107—42no—
147C2×C4×C107—82no—
148C2×C4×C107—81no—
149C2×C4×C107—81no—
150C2×C4×C107#12011yescharacteristic
151C2×C4×C107#12011yescharacteristic
152C2×C4×C107#12011yescharacteristic
153C2×C4×C107#12111yescharacteristic
154C2×C4×C107#12111yescharacteristic
155C2×C4×C107#12711yescharacteristic
156C2×C4×C107C2×D812yes—
157C2×C4×C107AGL(1,ℤ/8)12yes—
158C8×C107—24no—
159C8×C107—42no—
160C8×C107—42no—
161C8×C107—81no—
162C22×C107—21no—
163C22×C107—21no—
164C22×C107—82no—
165C22×C107—81no—
166C22×C107—81no—
167C22×C107—82no—
168C22×C107—81no—
169C22×C107—82no—
170C22×C107—164no—
171C22×C107#39211yescharacteristic
172C22×C107#45912yes—
173C4×C107—21no—
174C4×C107—21no—
175C4×C107—81no—
176C4×C107—82no—
177C4×C107#44712yes—
178C4×C107#45512yes—
179C4×C107#47112yes—
180C4×C107#49311yescharacteristic
181C4×C107#49611yescharacteristic
182#10168C10711yesmaximal, characteristic, direct product factor, Sylow
183C2×C107—22no—
184C2×C107—161no—
185C2×C107—162no—
186C2×C107#200411yescharacteristic
187C2×C107#201111yescharacteristic
188C2×C107#201911yescharacteristic
189#3205C2×C10711yescharacteristic
190#3152C2×C10711yescharacteristic, complemented
191C2×#486C2×C10711yescharacteristic, complemented
192#1965C2×C10711yescharacteristic, complemented
193#1546C2×C10711yescharacteristic, complemented
194#1492C2×C10711yescharacteristic, complemented
195#1278C2×C10711yescharacteristic, complemented
196C107#1016811yescharacteristic, direct product factor, Sylow
197C2×#137—22no—
198#532C22×C10711yescharacteristic
199C2×C4⋊Q8C22×C10711yescharacteristic
200C2×#127C22×C10711yescharacteristic
201#497—22no—
202#494—21no—
203#493—21no—
204#492—21no—
205#486—22no—
206#486—21no—
207#486—22no—
208#459—22no—
209#447—22no—
210#431C22×C10711yescharacteristic
211#423C22×C10711yescharacteristic
212C2×#102—22no—
213C2×#100—22no—
214C4×M16C22×C10711yescharacteristic
215C2×C4×C8C22×C10711yescharacteristic
216#332—22no—
217D4⋊C8—22no—
218C2×#41—21no—
219C22×Q8—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4D4×C10712yes—
223#137—44no—
224#137—44no—
225C2×Q16—24no—
226C2×SD16—24no—
227C2×D8—24no—
228C2×M16—21no—
229C2×M16D4×C10712yes—
230C22×C8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8D4×C10712yes—
235C4⋊Q8D4×C10711yescharacteristic
236#127—21no—
237#127—21no—
238#127—21no—
239#127—21no—
240#127D4×C10711yescharacteristic
241#124—21no—
242#121—21no—
243#121—21no—
244C4×D4—21no—
245C4×D4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C42C23×C10711yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C10712yes—
252#102—28no—
253#102—24no—
254#100—44no—
255C22⋊C8—21no—
256#97—21no—
257C4×C8—21no—
258C4×C8—21no—
259C4×C8—21no—
260C4×C8D4×C10712yes—
261C24—22no—
262#41—42no—
263#41—42no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—44no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—82no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4C2×D4×C10711yescharacteristic
286C22×C4C2×D4×C10711yescharacteristic
287C22×C4#41×C10711yescharacteristic
288Q16—48no—
289SD16—48no—
290D8—84no—
291M16—22no—
292M16—42no—
293M16D8×C10714yescomplemented
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—42no—
298C2×C8—41no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42C2×D4×C10711yescharacteristic
308C42C2×D4×C10711yescharacteristic
309C42C2×D4×C10711yescharacteristic
310C42C2×D4×C10711yescharacteristic
311C23—41no—
312C23—42no—
313C23—44no—
314C23—82no—
315C23—82no—
316C23#121×C10711yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—81no—
320Q8—81no—
321D4—44no—
322D4—42no—
323D4—42no—
324D4—44no—
325D4—42no—
326D4—82no—
327D4—82no—
328D4—82no—
329D4—82no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4#120×C10711yescharacteristic
340C2×C4#120×C10711yescharacteristic
341C2×C4#120×C10711yescharacteristic
342C2×C4#121×C10711yescharacteristic
343C2×C4#121×C10711yescharacteristic
344C2×C4#127×C10711yescharacteristic
345C2×C4C2×D8×C10712yes—
346C2×C4AGL(1,ℤ/8)×C10712yes—
347C8—24no—
348C8—42no—
349C8—42no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—82no—
354C22—81no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22—164no—
360C22#392×C10711yescharacteristic
361C22#459×C10712yes—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—82no—
366C4#447×C10712yes—
367C4#455×C10712yes—
368C4#471×C10712yes—
369C4#493×C10711yescharacteristic
370C4#496×C10711yescharacteristic
371C2—22no—
372C2—162no—
373C2—161no—
374C2C107×#200411yescharacteristic
375C2C107×#201111yescharacteristic
376C2C107×#201911yescharacteristic
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
2. C107×#3152C2semidirect
3. C2×#486×C107C2semidirect
4. C107×#1965C2semidirect
5. C107×#1546C2semidirect
6. C107×#1492C2semidirect
7. C107×#1278C2semidirect
104. M16×C107D8semidirect
182. #10168C107direct (N × H)
190. #3152C2×C107semidirect
191. C2×#486C2×C107semidirect
192. #1965C2×C107semidirect
193. #1546C2×C107semidirect
194. #1492C2×C107semidirect
195. #1278C2×C107semidirect
196. C107#10168direct (N × H)
293. M16D8×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#32052
C107×#31522
C2×#486×C1072
C107×#19652
C107×#15462
C107×#14922
C107×#12782
#10168107