Finite Group Databasebeta

← C107×#3401 #28334084

Subgroups — C107×#3401 #28334084

Order 13696.

368 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
1#559×C107C211yesmaximal, characteristic, complemented
2#556×C107C211yesmaximal, characteristic, complemented
3#497×C107C211yesmaximal, characteristic, complemented
4#496×C107C211yesmaximal, characteristic
5#495×C107C211yesmaximal, characteristic, complemented
6#464×C107C211yesmaximal, characteristic, complemented
7#464×C107C211yesmaximal, characteristic, complemented
8#463×C107C211yesmaximal, characteristic, complemented
9#463×C107C211yesmaximal, characteristic, complemented
10#461×C107C211yesmaximal, characteristic, complemented
11#460×C107C211yesmaximal, characteristic, complemented
12#446×C107C211yesmaximal, characteristic, complemented
13#442×C107C211yesmaximal, characteristic, complemented
14#441×C107C211yesmaximal, characteristic, complemented
15C4×SD16×C107C211yesmaximal, characteristic, complemented
16C2×Q16×C107C2211yescharacteristic
17C2×Q16×C107C2211yescharacteristic
18C2×SD16×C107C2211yescharacteristic
19C2×SD16×C107C2211yescharacteristic
20C2×SD16×C107C2211yescharacteristic
21C2×SD16×C107C2211yescharacteristic
22C2×SD16×C107C2211yescharacteristic
23C2×D8×C107C2211yescharacteristic
24C2×D8×C107C2211yescharacteristic
25C4⋊Q8×C107C2211yescharacteristic
26#127×C107C2211yescharacteristic
27#126×C107—21no—
28#126×C107—21no—
29#124×C107—21no—
30#124×C107C2211yescharacteristic
31#124×C107C2211yescharacteristic
32#124×C107C2211yescharacteristic
33#124×C107C2211yescharacteristic
34#123×C107—21no—
35#123×C107—21no—
36C22⋊Q8×C107—21no—
37C4×Q8×C107C2211yescharacteristic
38C4×Q8×C107C2211yescharacteristic
39C4×Q8×C107C2211yescharacteristic
40C4×Q8×C107C2211yescharacteristic
41C4×D4×C107—21no—
42C4×D4×C107C2211yescharacteristic
43C4×D4×C107C2211yescharacteristic
44C4×D4×C107C2211yescharacteristic
45#117×C107—21no—
46#106×C107C2211yescharacteristic
47C4⋊C8×C107C2211yescharacteristic
48C4⋊C8×C107C2211yescharacteristic
49C4⋊C8×C107C2211yescharacteristic
50#103×C107C2211yescharacteristic
51#103×C107C2211yescharacteristic
52#103×C107C2211yescharacteristic
53#102×C107C2211yescharacteristic
54#102×C107C2211yescharacteristic
55#102×C107C2211yescharacteristic
56#97×C107C2211yescharacteristic
57#97×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59C2×Q8×C107D411yescharacteristic
60C2×Q8×C107C2311yescharacteristic
61C2×Q8×C107C2311yescharacteristic
62C2×Q8×C107C2311yescharacteristic
63C2×D4×C107—21no—
64C2×D4×C107—21no—
65C2×D4×C107C2311yescharacteristic
66C2×D4×C107C2311yescharacteristic
67C2×D4×C107C2311yescharacteristic
68C22×C4×C107—21no—
69C22×C4×C107—21no—
70C22×C4×C107—21no—
71Q16×C107—22no—
72Q16×C107—41no—
73SD16×C107—22no—
74SD16×C107—41no—
75SD16×C107—41no—
76SD16×C107—41no—
77SD16×C107—41no—
78D8×C107—22no—
79D8×C107—41no—
80C2×C8×C107C2311yescharacteristic
81C2×C8×C107C2311yescharacteristic
82C2×C8×C107C2311yescharacteristic
83C2×C8×C107C2311yescharacteristic
84C4⋊C4×C107—21no—
85C4⋊C4×C107—21no—
86C4⋊C4×C107—21no—
87C4⋊C4×C107—21no—
88C4⋊C4×C107—21no—
89C4⋊C4×C107D411yescharacteristic
90C4⋊C4×C107D411yescharacteristic
91C4⋊C4×C107D411yescharacteristic
92C4⋊C4×C107C2311yescharacteristic
93C4⋊C4×C107C2311yescharacteristic
94C22⋊C4×C107—21no—
95C22⋊C4×C107—21no—
96C22⋊C4×C107—21no—
97C22⋊C4×C107—21no—
98C22⋊C4×C107—21no—
99C22⋊C4×C107—21no—
100C22⋊C4×C107—21no—
101C22⋊C4×C107—21no—
102C22⋊C4×C107—21no—
103C22⋊C4×C107—21no—
104C22⋊C4×C107—21no—
105C42×C107—21no—
106C42×C107—21no—
107C42×C107—21no—
108C42×C107C2311yescharacteristic
109C42×C107C2311yescharacteristic
110C42×C107C2311yescharacteristic
111C23×C107—21no—
112C23×C107—21no—
113C23×C107—21no—
114Q8×C107—21no—
115Q8×C107—21no—
116Q8×C107—21no—
117Q8×C107—21no—
118Q8×C107—21no—
119Q8×C107—21no—
120Q8×C107—41no—
121D4×C107—21no—
122D4×C107—21no—
123D4×C107—21no—
124D4×C107—21no—
125D4×C107—21no—
126D4×C107—21no—
127D4×C107—42no—
128D4×C107—81no—
129C2×C4×C107—21no—
130C2×C4×C107—21no—
131C2×C4×C107—21no—
132C2×C4×C107—21no—
133C2×C4×C107—21no—
134C2×C4×C107—42no—
135C2×C4×C107—81no—
136C2×C4×C107—81no—
137C2×C4×C107C2×D411yescharacteristic
138C2×C4×C107C2×D411yescharacteristic
139C2×C4×C107C2×D411yescharacteristic
140C2×C4×C107C2×D411yescharacteristic
141C2×C4×C107C2×D411yescharacteristic
142C2×C4×C107C2×D411yescharacteristic
143C2×C4×C107C2411yescharacteristic
144C8×C107—21no—
145C8×C107—21no—
146C8×C107—21no—
147C8×C107#4112yes—
148C22×C107—41no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107—41no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107C22×D411yescharacteristic
158C4×C107—21no—
159C4×C107—21no—
160C4×C107—21no—
161C4×C107—21no—
162C4×C107—21no—
163C4×C107—21no—
164C4×C107—41no—
165C4×C107—41no—
166C4×C107—41no—
167C4×C107—41no—
168C4×C107—41no—
169C4×C107C2×#4111yescharacteristic
170C4×C107H(5,𝔽2)11yescharacteristic
171C2×C107—81no—
172C2×C107—81no—
173C2×C107—81no—
174C2×C107#55011yescharacteristic
175C2×C107#57511yescharacteristic
176C2×C107#57711yescharacteristic
177#3401C10711yesmaximal, characteristic, direct product factor, Sylow
178C107#340111yescharacteristic, direct product factor, Sylow
179#559C2×C10711yescharacteristic, complemented
180#556C2×C10711yescharacteristic, complemented
181#497C2×C10711yescharacteristic, complemented
182#496C2×C10711yescharacteristic
183#495C2×C10711yescharacteristic, complemented
184#464C2×C10711yescharacteristic, complemented
185#464C2×C10711yescharacteristic, complemented
186#463C2×C10711yescharacteristic, complemented
187#463C2×C10711yescharacteristic, complemented
188#461C2×C10711yescharacteristic, complemented
189#460C2×C10711yescharacteristic, complemented
190#446C2×C10711yescharacteristic, complemented
191#442C2×C10711yescharacteristic, complemented
192#441C2×C10711yescharacteristic, complemented
193C4×SD16C2×C10711yescharacteristic, complemented
194C2×Q16C22×C10711yescharacteristic
195C2×Q16C22×C10711yescharacteristic
196C2×SD16C22×C10711yescharacteristic
197C2×SD16C22×C10711yescharacteristic
198C2×SD16C22×C10711yescharacteristic
199C2×SD16C22×C10711yescharacteristic
200C2×SD16C22×C10711yescharacteristic
201C2×D8C22×C10711yescharacteristic
202C2×D8C22×C10711yescharacteristic
203C4⋊Q8C22×C10711yescharacteristic
204#127C22×C10711yescharacteristic
205#126—21no—
206#126—21no—
207#124—21no—
208#124C22×C10711yescharacteristic
209#124C22×C10711yescharacteristic
210#124C22×C10711yescharacteristic
211#124C22×C10711yescharacteristic
212#123—21no—
213#123—21no—
214C22⋊Q8—21no—
215C4×Q8C22×C10711yescharacteristic
216C4×Q8C22×C10711yescharacteristic
217C4×Q8C22×C10711yescharacteristic
218C4×Q8C22×C10711yescharacteristic
219C4×D4—21no—
220C4×D4C22×C10711yescharacteristic
221C4×D4C22×C10711yescharacteristic
222C4×D4C22×C10711yescharacteristic
223#117—21no—
224#106C22×C10711yescharacteristic
225C4⋊C8C22×C10711yescharacteristic
226C4⋊C8C22×C10711yescharacteristic
227C4⋊C8C22×C10711yescharacteristic
228#103C22×C10711yescharacteristic
229#103C22×C10711yescharacteristic
230#103C22×C10711yescharacteristic
231#102C22×C10711yescharacteristic
232#102C22×C10711yescharacteristic
233#102C22×C10711yescharacteristic
234#97C22×C10711yescharacteristic
235#97C22×C10711yescharacteristic
236C4×C8C22×C10711yescharacteristic
237C2×Q8D4×C10711yescharacteristic
238C2×Q8C23×C10711yescharacteristic
239C2×Q8C23×C10711yescharacteristic
240C2×Q8C23×C10711yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C23×C10711yescharacteristic
244C2×D4C23×C10711yescharacteristic
245C2×D4C23×C10711yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249Q16—22no—
250Q16—41no—
251SD16—22no—
252SD16—41no—
253SD16—41no—
254SD16—41no—
255SD16—41no—
256D8—22no—
257D8—41no—
258C2×C8C23×C10711yescharacteristic
259C2×C8C23×C10711yescharacteristic
260C2×C8C23×C10711yescharacteristic
261C2×C8C23×C10711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4D4×C10711yescharacteristic
268C4⋊C4D4×C10711yescharacteristic
269C4⋊C4D4×C10711yescharacteristic
270C4⋊C4C23×C10711yescharacteristic
271C4⋊C4C23×C10711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42C23×C10711yescharacteristic
287C42C23×C10711yescharacteristic
288C42C23×C10711yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—41no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4C2×D4×C10711yescharacteristic
316C2×C4C2×D4×C10711yescharacteristic
317C2×C4C2×D4×C10711yescharacteristic
318C2×C4C2×D4×C10711yescharacteristic
319C2×C4C2×D4×C10711yescharacteristic
320C2×C4C2×D4×C10711yescharacteristic
321C2×C4C24×C10711yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#41×C10712yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C22×D4×C10711yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4C2×#41×C10711yescharacteristic
348C4H(5,𝔽2)×C10711yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2#550×C10711yescharacteristic
353C2#575×C10711yescharacteristic
354C2#577×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C22×D4
commutator, Frattini, cosocleC2×C4C24×C107
prime radical#496×C107C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C4×Q8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. #559×C107C2semidirect
2. #556×C107C2semidirect
3. #497×C107C2semidirect
5. #495×C107C2semidirect
6. #464×C107C2semidirect
7. #464×C107C2semidirect
8. #463×C107C2semidirect
9. #463×C107C2semidirect
10. #461×C107C2semidirect
11. #460×C107C2semidirect
12. #446×C107C2semidirect
13. #442×C107C2semidirect
14. #441×C107C2semidirect
15. C4×SD16×C107C2semidirect
177. #3401C107direct (N × H)
178. C107#3401direct (N × H)
179. #559C2×C107semidirect
180. #556C2×C107semidirect
181. #497C2×C107semidirect
183. #495C2×C107semidirect
184. #464C2×C107semidirect
185. #464C2×C107semidirect
186. #463C2×C107semidirect
187. #463C2×C107semidirect
188. #461C2×C107semidirect
189. #460C2×C107semidirect
190. #446C2×C107semidirect
191. #442C2×C107semidirect
192. #441C2×C107semidirect
193. C4×SD16C2×C107semidirect

Maximal subgroups

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

subgroupindex
#559×C1072
#556×C1072
#497×C1072
#496×C1072
#495×C1072
#464×C1072
#463×C1072
#461×C1072
#460×C1072
#446×C1072
#442×C1072
#441×C1072
C4×SD16×C1072
#3401107