Finite Group Databasebeta

← C2×C103×#2214 #39938868

Subgroups — C2×C103×#2214 #39938868

Order 26368.

686 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C103C212yesmaximal
2C2×#494×C103C211yesmaximal, characteristic, complemented
3C2×#443×C103C211yesmaximal, characteristic
4C103×#2214C218yesmaximal, direct product factor
5C2×#364×C103C211yesmaximal, characteristic, complemented
6C2×#362×C103C212yesmaximal, complemented
7C2×#135×C103C2211yescharacteristic
8C22×Q16×C103—21no—
9C22×Q16×C103C2212yes—
10C2×#131×C103—21no—
11C2×C4⋊Q8×C103—21no—
12#510×C103—24no—
13#510×C103C2218yes—
14C2×Q32×C103—22no—
15C2×SD32×C103—22no—
16C2×M32×C103C2212yes—
17#494×C103—22no—
18#494×C103C2214yescomplemented
19#443×C103—22no—
20#443×C103C2214yes—
21C2×#108×C103C2211yescharacteristic
22C2×#104×C103—21no—
23C2×C4×C8×C103C2211yescharacteristic
24#364×C103C2214yescomplemented
25#362×C103C2218yescomplemented
26C2×#41×C103—21no—
27C22×Q8×C103—22no—
28#135×C103—21no—
29#135×C103—21no—
30#135×C103D412yes—
31#135×C103C2312yes—
32C2×Q16×C103—22no—
33C2×Q16×C103—22no—
34C2×Q16×C103—22no—
35C2×Q16×C103—24no—
36C2×Q16×C103—22no—
37C2×Q16×C103—22no—
38C2×Q16×C103—41no—
39C2×Q16×C103—41no—
40C2×Q16×C103—42no—
41C2×Q16×C103D411yescharacteristic
42C2×Q16×C103C2314yes—
43C2×SD16×C103—21no—
44C2×D8×C103D411yescharacteristic
45#131×C103—24no—
46#131×C103—42no—
47C2×M16×C103—21no—
48C2×M16×C103—41no—
49C22×C8×C103—41no—
50C22×C8×C103D411yescharacteristic
51C22×C8×C103C2311yescharacteristic
52C4⋊Q8×C103—24no—
53C4⋊Q8×C103—42no—
54C2×C4⋊C4×C103—42no—
55C2×C42×C103D411yescharacteristic
56Q32×C103—28no—
57SD32×C103—28no—
58M32×C103—22no—
59M32×C103C2314yes—
60C2×C16×C103—22no—
61#108×C103—21no—
62#108×C103C2312yes—
63#104×C103—24no—
64C4×C8×C103D412yes—
65C4×C8×C103C2312yes—
66#41×C103—22no—
67#41×C103—22no—
68#41×C103—41no—
69#41×C103—41no—
70C2×Q8×C103—21no—
71C2×Q8×C103—24no—
72C2×Q8×C103—42no—
73C2×Q8×C103—42no—
74C2×Q8×C103—42no—
75C2×Q8×C103—42no—
76C2×Q8×C103—42no—
77C2×D4×C103—21no—
78C2×D4×C103—41no—
79C22×C4×C103—21no—
80C22×C4×C103—41no—
81C22×C4×C103—42no—
82C22×C4×C103C2×D411yescharacteristic
83Q16×C103—21no—
84Q16×C103—24no—
85Q16×C103—24no—
86Q16×C103—42no—
87Q16×C103—42no—
88Q16×C103—44no—
89Q16×C103—44no—
90Q16×C103C2×D412yes—
91SD16×C103—22no—
92SD16×C103—22no—
93D8×C103—21no—
94D8×C103C2×D412yes—
95M16×C103—22no—
96M16×C103—41no—
97M16×C103—44no—
98C2×C8×C103—41no—
99C2×C8×C103—44no—
100C2×C8×C103D811yescharacteristic
101C2×C8×C103D811yescharacteristic
102C2×C8×C103D812yes—
103C2×C8×C103C2×D411yescharacteristic
104C2×C8×C103C2×D411yescharacteristic
105C2×C8×C103C2×D411yescharacteristic
106C2×C8×C103C2×D412yes—
107C2×C8×C103#4111yescharacteristic
108C2×C8×C103#4111yescharacteristic
109C2×C8×C103C2411yescharacteristic
110C4⋊C4×C103—48no—
111C42×C103—21no—
112C42×C103C2×D412yes—
113C16×C103—24no—
114C23×C103—41no—
115C23×C103AGL(1,ℤ/8)11yescharacteristic
116Q8×C103—22no—
117Q8×C103—41no—
118Q8×C103—44no—
119Q8×C103—44no—
120Q8×C103—82no—
121Q8×C103—82no—
122D4×C103—22no—
123D4×C103—42no—
124D4×C103—42no—
125D4×C103—41no—
126C2×C4×C103—24no—
127C2×C4×C103—22no—
128C2×C4×C103—41no—
129C2×C4×C103—42no—
130C2×C4×C103—42no—
131C2×C4×C103—44no—
132C2×C4×C103—82no—
133C2×C4×C103—82no—
134C2×C4×C103#12111yescharacteristic
135C2×C4×C103#12111yescharacteristic
136C2×C4×C103C2×D811yescharacteristic
137C2×C4×C103C2×D811yescharacteristic
138C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C103C22×D411yescharacteristic
140C8×C103—42no—
141C8×C103#12111yescharacteristic
142C8×C103#12111yescharacteristic
143C8×C103C2×D812yes—
144C8×C103C2×D812yes—
145C8×C103C22×D411yescharacteristic
146C8×C103C2×#4111yescharacteristic
147C22×C103—22no—
148C22×C103—42no—
149C22×C103—82no—
150C22×C103#45911yescharacteristic
151C22×C103#45911yescharacteristic
152C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
153C4×C103—24no—
154C4×C103—42no—
155C4×C103—84no—
156C4×C103#45911yescharacteristic
157C4×C103#45911yescharacteristic
158C4×C103C2×#12111yescharacteristic
159C4×C103C22×D811yescharacteristic
160C2×#2214C10311yesmaximal, characteristic, direct product factor, Sylow
161C2×C103—21no—
162C2×C103—21no—
163C2×C103—82no—
164C2×C103#221412yesdirect product factor
165C2×C103C2×#45911yescharacteristic
166C2×#510C2×C10312yes—
167C2×#494C2×C10311yescharacteristic, complemented
168C2×#443C2×C10311yescharacteristic
169#2214C2×C10318yesdirect product factor
170C2×#364C2×C10311yescharacteristic, complemented
171C2×#362C2×C10312yescomplemented
172C103C2×#221411yescharacteristic, direct product factor, Sylow
173C2×#135C22×C10311yescharacteristic
174C22×Q16—21no—
175C22×Q16C22×C10312yes—
176C2×#131—21no—
177C2×C4⋊Q8—21no—
178#510—24no—
179#510C22×C10318yes—
180C2×Q32—22no—
181C2×SD32—22no—
182C2×M32C22×C10312yes—
183#494—22no—
184#494C22×C10314yescomplemented
185#443—22no—
186#443C22×C10314yes—
187C2×#108C22×C10311yescharacteristic
188C2×#104—21no—
189C2×C4×C8C22×C10311yescharacteristic
190#364C22×C10314yescomplemented
191#362C22×C10318yescomplemented
192C2×#41—21no—
193C22×Q8—22no—
194#135—21no—
195#135—21no—
196#135D4×C10312yes—
197#135C23×C10312yes—
198C2×Q16—22no—
199C2×Q16—22no—
200C2×Q16—24no—
201C2×Q16—22no—
202C2×Q16—22no—
203C2×Q16—22no—
204C2×Q16—41no—
205C2×Q16—41no—
206C2×Q16—42no—
207C2×Q16D4×C10311yescharacteristic
208C2×Q16C23×C10314yes—
209C2×SD16—21no—
210C2×D8D4×C10311yescharacteristic
211#131—24no—
212#131—42no—
213C2×M16—21no—
214C2×M16—41no—
215C22×C8—41no—
216C22×C8D4×C10311yescharacteristic
217C22×C8C23×C10311yescharacteristic
218C4⋊Q8—24no—
219C4⋊Q8—42no—
220C2×C4⋊C4—42no—
221C2×C42D4×C10311yescharacteristic
222Q32—28no—
223SD32—28no—
224M32—22no—
225M32C23×C10314yes—
226C2×C16—22no—
227#108—21no—
228#108C23×C10312yes—
229#104—24no—
230C4×C8D4×C10312yes—
231C4×C8C23×C10312yes—
232#41—22no—
233#41—22no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×Q8—24no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×D4—21no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4C2×D4×C10311yescharacteristic
249Q16—21no—
250Q16—24no—
251Q16—24no—
252Q16—42no—
253Q16—42no—
254Q16—44no—
255Q16—44no—
256Q16C2×D4×C10312yes—
257SD16—22no—
258SD16—22no—
259D8—21no—
260D8C2×D4×C10312yes—
261M16—22no—
262M16—41no—
263M16—44no—
264C2×C8—41no—
265C2×C8—44no—
266C2×C8D8×C10311yescharacteristic
267C2×C8D8×C10311yescharacteristic
268C2×C8D8×C10312yes—
269C2×C8C2×D4×C10311yescharacteristic
270C2×C8C2×D4×C10311yescharacteristic
271C2×C8C2×D4×C10311yescharacteristic
272C2×C8C2×D4×C10312yes—
273C2×C8#41×C10311yescharacteristic
274C2×C8#41×C10311yescharacteristic
275C2×C8C24×C10311yescharacteristic
276C4⋊C4—48no—
277C42—21no—
278C42C2×D4×C10312yes—
279C16—24no—
280C23—41no—
281C23AGL(1,ℤ/8)×C10311yescharacteristic
282Q8—22no—
283Q8—41no—
284Q8—44no—
285Q8—44no—
286Q8—82no—
287Q8—82no—
288D4—22no—
289D4—42no—
290D4—42no—
291D4—41no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—82no—
299C2×C4—82no—
300C2×C4#121×C10311yescharacteristic
301C2×C4#121×C10311yescharacteristic
302C2×C4C2×D8×C10311yescharacteristic
303C2×C4C2×D8×C10311yescharacteristic
304C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
305C2×C4C22×D4×C10311yescharacteristic
306C8—42no—
307C8#121×C10311yescharacteristic
308C8#121×C10311yescharacteristic
309C8C2×D8×C10312yes—
310C8C2×D8×C10312yes—
311C8C22×D4×C10311yescharacteristic
312C8C2×#41×C10311yescharacteristic
313C22—22no—
314C22—42no—
315C22—82no—
316C22#459×C10311yescharacteristic
317C22#459×C10311yescharacteristic
318C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
319C4—24no—
320C4—42no—
321C4—84no—
322C4#459×C10311yescharacteristic
323C4#459×C10311yescharacteristic
324C4C2×#121×C10311yescharacteristic
325C4C22×D8×C10311yescharacteristic
326C2—21no—
327C2—21no—
328C2—82no—
329C2C103×#221412yesdirect product factor
330C2C2×#459×C10311yescharacteristic
subgroupG/H
center, socleC22×C103#459
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC2×#135×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#494×C103C2semidirect
4. C103×#2214C2direct (N × H)
5. C2×#364×C103C2semidirect
6. C2×#362×C103C2semidirect
18. #494×C103C22semidirect
24. #364×C103C22semidirect
25. #362×C103C22semidirect
160. C2×#2214C103direct (N × H)
164. C2×C103#2214direct (N × H)
167. C2×#494C2×C103semidirect
169. #2214C2×C103direct (N × H)
170. C2×#364C2×C103semidirect
171. C2×#362C2×C103semidirect
172. C103C2×#2214direct (N × H)
184. #494C22×C103semidirect
190. #364C22×C103semidirect
191. #362C22×C103semidirect
329. C2C103×#2214direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#510×C1032
C2×#494×C1032
C2×#443×C1032
C103×#22142
C2×#364×C1032
C2×#362×C1032
C2×#2214103