Finite Group Databasebeta

← C107×#34551 #41060515

Subgroups — C107×#34551 #41060515

Order 27392.

2082 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2402C213yesmaximal, complemented
2C107×#2401C216yesmaximal, complemented
3C107×#2398C213yesmaximal, complemented
4C107×#2396C213yesmaximal, complemented
5C107×#2395C216yesmaximal, complemented
6C107×#2392C213yesmaximal
7C42×Q8×C107C211yesmaximal, characteristic, complemented
8C42×D4×C107C213yesmaximal, complemented
9C4×#117×C107C213yesmaximal, complemented
10C2×C4×Q8×C107C2213yes—
11C2×C4×D4×C107C2216yes—
12C2×C4×D4×C107C2213yes—
13C2×#117×C107C2213yes—
14C2×#117×C107C2213yes—
15C22×C42×C107C2213yes—
16#401×C107C2212yes—
17#400×C107C2216yes—
18#400×C107C2213yes—
19#400×C107C2216yes—
20#399×C107C2213yes—
21#398×C107C2213yes—
22#398×C107C2216yes—
23#397×C107C2213yes—
24#397×C107C2216yes—
25#397×C107C2216yes—
26#396×C107C2216yes—
27#395×C107C2211yescharacteristic
28#394×C107C2213yes—
29#394×C107C2216yes—
30#393×C107C2213yes—
31#392×C107C2211yescharacteristic
32C4×C4⋊C4×C107C2213yes—
33C4×C4⋊C4×C107C2216yes—
34C4×C4⋊C4×C107C2216yes—
35C4×C4⋊C4×C107C2216yes—
36C4×C4⋊C4×C107C2213yes—
37C4×C4⋊C4×C107C2216yes—
38C4×C22⋊C4×C107C2216yes—
39C4×C22⋊C4×C107C2216yes—
40C4×C22⋊C4×C107C2216yes—
41C4×C22⋊C4×C107C2216yes—
42C4×C22⋊C4×C107C2216yes—
43#376×C107C2213yes—
44#376×C107C2213yes—
45C43×C107C2211yescharacteristic
46C43×C107C2213yes—
47C22×Q8×C107C2311yescharacteristic
48C22×D4×C107C2313yes—
49C23×C4×C107C2316yes—
50C23×C4×C107C2313yes—
51C4×Q8×C107—212no—
52C4×D4×C107—224no—
53C4×D4×C107—212no—
54#117×C107—212no—
55#117×C107—212no—
56C2×C4⋊C4×C107C2316yes—
57C2×C4⋊C4×C107C2313yes—
58C2×C4⋊C4×C107C2313yes—
59C2×C4⋊C4×C107C2316yes—
60C2×C4⋊C4×C107C2313yes—
61C2×C4⋊C4×C107C2316yes—
62C2×C4⋊C4×C107C2313yes—
63C2×C22⋊C4×C107C2313yes—
64C2×C22⋊C4×C107C2313yes—
65C2×C22⋊C4×C107C2316yes—
66C2×C22⋊C4×C107C2316yes—
67C2×C22⋊C4×C107C2316yes—
68C2×C22⋊C4×C107C2316yes—
69C2×C42×C107—212no—
70C2×C42×C107C2313yes—
71C2×C42×C107C2313yes—
72C2×C42×C107C2313yes—
73C2×C42×C107C2316yes—
74C2×C42×C107C2316yes—
75C2×C42×C107C2313yes—
76C2×C42×C107C2316yes—
77C2×C42×C107C2313yes—
78C2×C42×C107C2311yescharacteristic
79#95×C107C2316yes—
80#95×C107C2316yes—
81#95×C107C2316yes—
82#95×C107C2316yes—
83#95×C107C2313yes—
84#95×C107C2313yes—
85#95×C107C2316yes—
86#95×C107C2316yes—
87#95×C107C2311yescharacteristic
88#95×C107C2313yes—
89#95×C107C2312yes—
90C24×C107C2413yes—
91C2×Q8×C107—26no—
92C2×D4×C107—212no—
93C2×D4×C107—26no—
94C22×C4×C107—26no—
95C22×C4×C107—26no—
96C22×C4×C107—212no—
97C22×C4×C107—212no—
98C22×C4×C107—212no—
99C22×C4×C107#41112yes—
100C22×C4×C107C2416yes—
101C22×C4×C107C2416yes—
102C22×C4×C107C2413yes—
103C22×C4×C107C2411yescharacteristic
104C22×C4×C107C2413yes—
105C22×C4×C107C2413yes—
106C22×C4×C107C2413yes—
107C22×C4×C107C2413yes—
108C4⋊C4×C107—26no—
109C4⋊C4×C107—26no—
110C4⋊C4×C107—212no—
111C4⋊C4×C107—212no—
112C4⋊C4×C107—26no—
113C4⋊C4×C107—212no—
114C4⋊C4×C107—26no—
115C22⋊C4×C107—212no—
116C22⋊C4×C107—212no—
117C22⋊C4×C107—26no—
118C22⋊C4×C107—26no—
119C22⋊C4×C107—212no—
120C22⋊C4×C107—212no—
121C42×C107—212no—
122C42×C107—26no—
123C42×C107—26no—
124C42×C107—26no—
125C42×C107—26no—
126C42×C107—212no—
127C42×C107—212no—
128C42×C107#4114yes—
129C42×C107#41112yes—
130C23×C107—23no—
131C23×C107—26no—
132C23×C107—26no—
133C23×C107—23no—
134C23×C107C2×#4116yes—
135C23×C107C2511yescharacteristic
136Q8×C107—28no—
137D4×C107—224no—
138C2×C4×C107—23no—
139C2×C4×C107—26no—
140C2×C4×C107—26no—
141C2×C4×C107—23no—
142C2×C4×C107—224no—
143C2×C4×C107—26no—
144C2×C4×C107—26no—
145C2×C4×C107—26no—
146C2×C4×C107—26no—
147C2×C4×C107—23no—
148C2×C4×C107—23no—
149C2×C4×C107—26no—
150C2×C4×C107—26no—
151C2×C4×C107—26no—
152C2×C4×C107—424no—
153C2×C4×C107C2×#4116yes—
154C2×C4×C107C2×#4116yes—
155C2×C4×C107C2×#4116yes—
156C2×C4×C107C2×#4116yes—
157C2×C4×C107C2×#4116yes—
158C2×C4×C107C2×#4116yes—
159C22×C107—26no—
160C22×C107—212no—
161C22×C107—46no—
162C22×C107—43no—
163C22×C107—43no—
164C22×C107C22×#4111yescharacteristic
165C22×C107C22×#4113yes—
166C22×C107C22×#4113yes—
167C4×C107—26no—
168C4×C107—26no—
169C4×C107—26no—
170C4×C107—46no—
171C4×C107—41no—
172C4×C107—46no—
173C4×C107—43no—
174C4×C107#529112yes—
175#34551C10711yesmaximal, characteristic, direct product factor, Sylow
176C2×C107—46no—
177C2×C107C2×#52913yes—
178C2×C107#344411yescharacteristic
179C2×C107#344413yes—
180#2402C2×C10713yescomplemented
181#2401C2×C10716yescomplemented
182#2398C2×C10713yescomplemented
183#2396C2×C10713yescomplemented
184#2395C2×C10716yescomplemented
185#2392C2×C10713yes—
186C42×Q8C2×C10711yescharacteristic, complemented
187C42×D4C2×C10713yescomplemented
188C4×#117C2×C10713yescomplemented
189C107#3455111yescharacteristic, direct product factor, Sylow
190C2×C4×Q8C22×C10713yes—
191C2×C4×D4C22×C10716yes—
192C2×C4×D4C22×C10713yes—
193C2×#117C22×C10713yes—
194C2×#117C22×C10713yes—
195C22×C42C22×C10713yes—
196#401C22×C10712yes—
197#400C22×C10716yes—
198#400C22×C10713yes—
199#400C22×C10716yes—
200#399C22×C10713yes—
201#398C22×C10713yes—
202#398C22×C10716yes—
203#397C22×C10713yes—
204#397C22×C10716yes—
205#397C22×C10716yes—
206#396C22×C10716yes—
207#395C22×C10711yescharacteristic
208#394C22×C10713yes—
209#394C22×C10716yes—
210#393C22×C10713yes—
211#392C22×C10711yescharacteristic
212C4×C4⋊C4C22×C10713yes—
213C4×C4⋊C4C22×C10716yes—
214C4×C4⋊C4C22×C10716yes—
215C4×C4⋊C4C22×C10716yes—
216C4×C4⋊C4C22×C10713yes—
217C4×C4⋊C4C22×C10716yes—
218C4×C22⋊C4C22×C10716yes—
219C4×C22⋊C4C22×C10716yes—
220C4×C22⋊C4C22×C10716yes—
221C4×C22⋊C4C22×C10716yes—
222C4×C22⋊C4C22×C10716yes—
223#376C22×C10713yes—
224#376C22×C10713yes—
225C43C22×C10711yescharacteristic
226C43C22×C10713yes—
227C22×Q8C23×C10711yescharacteristic
228C22×D4C23×C10713yes—
229C23×C4C23×C10716yes—
230C23×C4C23×C10713yes—
231C4×Q8—212no—
232C4×D4—224no—
233C4×D4—212no—
234#117—212no—
235#117—212no—
236C2×C4⋊C4C23×C10713yes—
237C2×C4⋊C4C23×C10713yes—
238C2×C4⋊C4C23×C10716yes—
239C2×C4⋊C4C23×C10716yes—
240C2×C4⋊C4C23×C10713yes—
241C2×C4⋊C4C23×C10716yes—
242C2×C4⋊C4C23×C10713yes—
243C2×C22⋊C4C23×C10713yes—
244C2×C22⋊C4C23×C10713yes—
245C2×C22⋊C4C23×C10716yes—
246C2×C22⋊C4C23×C10716yes—
247C2×C22⋊C4C23×C10716yes—
248C2×C22⋊C4C23×C10716yes—
249C2×C42—212no—
250C2×C42C23×C10713yes—
251C2×C42C23×C10713yes—
252C2×C42C23×C10713yes—
253C2×C42C23×C10716yes—
254C2×C42C23×C10716yes—
255C2×C42C23×C10713yes—
256C2×C42C23×C10716yes—
257C2×C42C23×C10713yes—
258C2×C42C23×C10711yescharacteristic
259#95C23×C10716yes—
260#95C23×C10716yes—
261#95C23×C10716yes—
262#95C23×C10716yes—
263#95C23×C10713yes—
264#95C23×C10713yes—
265#95C23×C10716yes—
266#95C23×C10716yes—
267#95C23×C10711yescharacteristic
268#95C23×C10713yes—
269#95C23×C10712yes—
270C24C24×C10713yes—
271C2×Q8—26no—
272C2×D4—212no—
273C2×D4—26no—
274C22×C4—26no—
275C22×C4—26no—
276C22×C4—212no—
277C22×C4—212no—
278C22×C4—212no—
279C22×C4#41×C107112yes—
280C22×C4C24×C10716yes—
281C22×C4C24×C10716yes—
282C22×C4C24×C10713yes—
283C22×C4C24×C10711yescharacteristic
284C22×C4C24×C10713yes—
285C22×C4C24×C10713yes—
286C22×C4C24×C10713yes—
287C22×C4C24×C10713yes—
288C4⋊C4—26no—
289C4⋊C4—26no—
290C4⋊C4—212no—
291C4⋊C4—212no—
292C4⋊C4—26no—
293C4⋊C4—212no—
294C4⋊C4—26no—
295C22⋊C4—212no—
296C22⋊C4—212no—
297C22⋊C4—26no—
298C22⋊C4—26no—
299C22⋊C4—212no—
300C22⋊C4—212no—
301C42—212no—
302C42—26no—
303C42—26no—
304C42—26no—
305C42—26no—
306C42—212no—
307C42—212no—
308C42#41×C10714yes—
309C42#41×C107112yes—
310C23—23no—
311C23—26no—
312C23—26no—
313C23—23no—
314C23C2×#41×C10716yes—
315C23C25×C10711yescharacteristic
316Q8—28no—
317D4—224no—
318C2×C4—23no—
319C2×C4—26no—
320C2×C4—26no—
321C2×C4—23no—
322C2×C4—224no—
323C2×C4—26no—
324C2×C4—26no—
325C2×C4—26no—
326C2×C4—26no—
327C2×C4—23no—
328C2×C4—23no—
329C2×C4—26no—
330C2×C4—26no—
331C2×C4—26no—
332C2×C4—424no—
333C2×C4C2×#41×C10716yes—
334C2×C4C2×#41×C10716yes—
335C2×C4C2×#41×C10716yes—
336C2×C4C2×#41×C10716yes—
337C2×C4C2×#41×C10716yes—
338C2×C4C2×#41×C10716yes—
339C22—26no—
340C22—212no—
341C22—46no—
342C22—43no—
343C22—43no—
344C22C22×#41×C10711yescharacteristic
345C22C22×#41×C10713yes—
346C22C22×#41×C10713yes—
347C4—26no—
348C4—26no—
349C4—26no—
350C4—46no—
351C4—41no—
352C4—46no—
353C4—43no—
354C4#529×C107112yes—
355C2—46no—
356C2C2×#529×C10713yes—
357C2C107×#344411yescharacteristic
358C2C107×#344413yes—
subgroupG/H
centerC2×C42×C107C23
commutator, Frattini, cosocleC23C25×C107
socleC23×C107C25
prime radical#392×C107C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2402C2semidirect
2. C107×#2401C2semidirect
3. C107×#2398C2semidirect
4. C107×#2396C2semidirect
5. C107×#2395C2semidirect
7. C42×Q8×C107C2semidirect
8. C42×D4×C107C2semidirect
9. C4×#117×C107C2semidirect
175. #34551C107direct (N × H)
180. #2402C2×C107semidirect
181. #2401C2×C107semidirect
182. #2398C2×C107semidirect
183. #2396C2×C107semidirect
184. #2395C2×C107semidirect
186. C42×Q8C2×C107semidirect
187. C42×D4C2×C107semidirect
188. C4×#117C2×C107semidirect
189. C107#34551direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#24022
C107×#24012
C107×#23982
C107×#23962
C107×#23952
C107×#23922
C42×Q8×C1072
C42×D4×C1072
C4×#117×C1072
#34551107