Finite Group Databasebeta

← C107×#9376 #41035340

Subgroups — C107×#9376 #41035340

Order 27392.

430 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3218C211yesmaximal, characteristic
2C107×#2992C211yesmaximal, characteristic
3C107×#1987C211yesmaximal, characteristic, complemented
4C107×#1556C211yesmaximal, characteristic, complemented
5C107×#1509C211yesmaximal, characteristic
6C107×#1290C211yesmaximal, characteristic, complemented
7C107×#1285C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C107C2211yescharacteristic
9#529×C107C2211yescharacteristic
10#497×C107C412yescomplemented
11#491×C107C412yescomplemented
12#462×C107—21no—
13#461×C107—21no—
14#451×C107—21no—
15#448×C107—21no—
16#446×C107—21no—
17#435×C107—21no—
18#435×C107—21no—
19C8×D4×C107—21no—
20#433×C107—21no—
21#432×C107C2211yescharacteristic
22#432×C107C2211yescharacteristic
23#432×C107C2211yescharacteristic
24#424×C107—21no—
25C2×C4⋊C8×C107C2211yescharacteristic
26C4×C4⋊C4×C107C2211yescharacteristic
27#340×C107—21no—
28#340×C107—21no—
29#332×C107—21no—
30#332×C107—21no—
31#328×C107—21no—
32#327×C107—21no—
33C22×Q8×C107—21no—
34C2×Q16×C107—22no—
35C2×SD16×C107—22no—
36C2×M16×C107—21no—
37C22×C8×C107—21no—
38C22×C8×C107D411yescharacteristic
39C22×C8×C107D411yescharacteristic
40C4⋊Q8×C107—21no—
41C4⋊Q8×C107—21no—
42C4⋊Q8×C107—21no—
43C4⋊Q8×C107C2×C412yes—
44#126×C107—21no—
45#125×C107C2×C411yescharacteristic
46#124×C107C2×C411yescharacteristic
47#123×C107—21no—
48C22⋊Q8×C107D411yescharacteristic
49#121×C107D411yescharacteristic
50C4×Q8×C107D411yescharacteristic
51C4×D4×C107—21no—
52C4×D4×C107D411yescharacteristic
53#117×C107—21no—
54C2×C4⋊C4×C107—21no—
55C2×C4⋊C4×C107—21no—
56C2×C4⋊C4×C107—21no—
57C2×C42×C107—21no—
58C2×C42×C107C2311yescharacteristic
59C4⋊C8×C107—21no—
60C4⋊C8×C107—21no—
61C4⋊C8×C107—21no—
62C4⋊C8×C107—21no—
63C4⋊C8×C107—21no—
64C4⋊C8×C107—21no—
65C4⋊C8×C107D411yescharacteristic
66C4⋊C8×C107D411yescharacteristic
67#103×C107—22no—
68#103×C107—22no—
69C22⋊C8×C107—21no—
70C22⋊C8×C107—21no—
71C22⋊C8×C107—21no—
72C22⋊C8×C107—21no—
73C22⋊C8×C107—21no—
74#97×C107—21no—
75#97×C107—21no—
76#97×C107—21no—
77#97×C107C2×C412yes—
78C4×C8×C107—21no—
79#95×C107—21no—
80C2×Q8×C107—22no—
81C2×Q8×C107—41no—
82C2×Q8×C107—82no—
83C2×Q8×C107C22⋊C411yescharacteristic
84C2×D4×C107—21no—
85C2×D4×C107C22⋊C411yescharacteristic
86C22×C4×C107—21no—
87C22×C4×C107—41no—
88C22×C4×C107—41no—
89C22×C4×C107C2×D411yescharacteristic
90C22×C4×C107C2×D411yescharacteristic
91C22×C4×C107#4111yescharacteristic
92Q16×C107—82no—
93SD16×C107—82no—
94M16×C107—81no—
95C2×C8×C107—22no—
96C2×C8×C107—21no—
97C2×C8×C107—21no—
98C2×C8×C107—21no—
99C2×C8×C107—21no—
100C2×C8×C107—41no—
101C2×C8×C107—41no—
102C2×C8×C107—41no—
103C2×C8×C107—81no—
104C4⋊C4×C107—21no—
105C4⋊C4×C107—21no—
106C4⋊C4×C107—21no—
107C4⋊C4×C107—21no—
108C4⋊C4×C107—22no—
109C4⋊C4×C107—22no—
110C4⋊C4×C107—22no—
111C4⋊C4×C107—41no—
112C4⋊C4×C107—41no—
113C4⋊C4×C107—41no—
114C4⋊C4×C107C22⋊C411yescharacteristic
115C4⋊C4×C107C22⋊C411yescharacteristic
116C22⋊C4×C107—21no—
117C22⋊C4×C107—21no—
118C22⋊C4×C107—21no—
119C22⋊C4×C107—21no—
120C22⋊C4×C107—21no—
121C42×C107—21no—
122C42×C107—81no—
123C42×C107C22×C411yescharacteristic
124C42×C107C2×D411yescharacteristic
125C42×C107C2×D411yescharacteristic
126C42×C107#4111yescharacteristic
127C23×C107—21no—
128C23×C107#12111yescharacteristic
129Q8×C107—41no—
130Q8×C107—42no—
131Q8×C107—42no—
132Q8×C107—82no—
133D4×C107—41no—
134D4×C107—41no—
135D4×C107—41no—
136C2×C4×C107—21no—
137C2×C4×C107—21no—
138C2×C4×C107—21no—
139C2×C4×C107—21no—
140C2×C4×C107—21no—
141C2×C4×C107—21no—
142C2×C4×C107—21no—
143C2×C4×C107—41no—
144C2×C4×C107—41no—
145C2×C4×C107—41no—
146C2×C4×C107—42no—
147C2×C4×C107—42no—
148C2×C4×C107—81no—
149C2×C4×C107—82no—
150C2×C4×C107—81no—
151C2×C4×C107C2×C22⋊C411yescharacteristic
152C2×C4×C107C4×D411yescharacteristic
153C2×C4×C107C4×D411yescharacteristic
154C2×C4×C107#12011yescharacteristic
155C2×C4×C107#12111yescharacteristic
156C2×C4×C107#12311yescharacteristic
157C8×C107—42no—
158C8×C107—41no—
159C8×C107—41no—
160C8×C107—41no—
161C8×C107—41no—
162C8×C107—81no—
163C22×C107—21no—
164C22×C107—21no—
165C22×C107—41no—
166C22×C107—41no—
167C22×C107—41no—
168C22×C107#38611yescharacteristic
169C22×C107#47111yescharacteristic
170C22×C107#47311yescharacteristic
171C4×C107—21no—
172C4×C107—21no—
173C4×C107—21no—
174C4×C107—21no—
175C4×C107—21no—
176C4×C107—41no—
177C4×C107—41no—
178C4×C107—41no—
179C4×C107—82no—
180C4×C107—82no—
181C4×C107#45511yescharacteristic
182C4×C107#45611yescharacteristic
183#9376C10711yesmaximal, characteristic, direct product factor, Sylow
184C2×C107—21no—
185C2×C107—21no—
186C2×C107—81no—
187C2×C107#188211yescharacteristic
188C2×C107#190811yescharacteristic
189C2×C107#191011yescharacteristic
190#3218C2×C10711yescharacteristic
191#2992C2×C10711yescharacteristic
192#1987C2×C10711yescharacteristic, complemented
193#1556C2×C10711yescharacteristic, complemented
194#1509C2×C10711yescharacteristic
195#1290C2×C10711yescharacteristic, complemented
196#1285C2×C10711yescharacteristic, complemented
197C107#937611yescharacteristic, direct product factor, Sylow
198C2×C4⋊Q8C22×C10711yescharacteristic
199#529C22×C10711yescharacteristic
200#497C4×C10712yescomplemented
201#491C4×C10712yescomplemented
202#462—21no—
203#461—21no—
204#451—21no—
205#448—21no—
206#446—21no—
207#435—21no—
208#435—21no—
209C8×D4—21no—
210#433—21no—
211#432C22×C10711yescharacteristic
212#432C22×C10711yescharacteristic
213#432C22×C10711yescharacteristic
214#424—21no—
215C2×C4⋊C8C22×C10711yescharacteristic
216C4×C4⋊C4C22×C10711yescharacteristic
217#340—21no—
218#340—21no—
219#332—21no—
220#332—21no—
221#328—21no—
222#327—21no—
223C22×Q8—21no—
224C2×Q16—22no—
225C2×SD16—22no—
226C2×M16—21no—
227C22×C8—21no—
228C22×C8D4×C10711yescharacteristic
229C22×C8D4×C10711yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C2×C4×C10712yes—
234#126—21no—
235#125C2×C4×C10711yescharacteristic
236#124C2×C4×C10711yescharacteristic
237#123—21no—
238C22⋊Q8D4×C10711yescharacteristic
239#121D4×C10711yescharacteristic
240C4×Q8D4×C10711yescharacteristic
241C4×D4—21no—
242C4×D4D4×C10711yescharacteristic
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42C23×C10711yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8D4×C10711yescharacteristic
256C4⋊C8D4×C10711yescharacteristic
257#103—22no—
258#103—22no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264#97—21no—
265#97—21no—
266#97—21no—
267#97C2×C4×C10712yes—
268C4×C8—21no—
269#95—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—82no—
273C2×Q8C22⋊C4×C10711yescharacteristic
274C2×D4—21no—
275C2×D4C22⋊C4×C10711yescharacteristic
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C2×D4×C10711yescharacteristic
280C22×C4C2×D4×C10711yescharacteristic
281C22×C4#41×C10711yescharacteristic
282Q16—82no—
283SD16—82no—
284M16—81no—
285C2×C8—22no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—81no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4C22⋊C4×C10711yescharacteristic
305C4⋊C4C22⋊C4×C10711yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42—81no—
313C42C22×C4×C10711yescharacteristic
314C42C2×D4×C10711yescharacteristic
315C42C2×D4×C10711yescharacteristic
316C42#41×C10711yescharacteristic
317C23—21no—
318C23#121×C10711yescharacteristic
319Q8—41no—
320Q8—42no—
321Q8—42no—
322Q8—82no—
323D4—41no—
324D4—41no—
325D4—41no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4C2×C22⋊C4×C10711yescharacteristic
342C2×C4C4×D4×C10711yescharacteristic
343C2×C4C4×D4×C10711yescharacteristic
344C2×C4#120×C10711yescharacteristic
345C2×C4#121×C10711yescharacteristic
346C2×C4#123×C10711yescharacteristic
347C8—42no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—41no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22#386×C10711yescharacteristic
359C22#471×C10711yescharacteristic
360C22#473×C10711yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—82no—
370C4—82no—
371C4#455×C10711yescharacteristic
372C4#456×C10711yescharacteristic
373C2—21no—
374C2—21no—
375C2—81no—
376C2C107×#188211yescharacteristic
377C2C107×#190811yescharacteristic
378C2C107×#191011yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radical#121×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1987C2semidirect
4. C107×#1556C2semidirect
6. C107×#1290C2semidirect
7. C107×#1285C2semidirect
10. #497×C107C4semidirect
11. #491×C107C4semidirect
183. #9376C107direct (N × H)
192. #1987C2×C107semidirect
193. #1556C2×C107semidirect
195. #1290C2×C107semidirect
196. #1285C2×C107semidirect
197. C107#9376direct (N × H)
200. #497C4×C107semidirect
201. #491C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#32182
C107×#29922
C107×#19872
C107×#15562
C107×#15092
C107×#12902
C107×#12852
#9376107