Finite Group Databasebeta

← C103×#34209 #39939484

Subgroups — C103×#34209 #39939484

Order 26368.

2854 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Q8×C103C211yesmaximal, characteristic
2C2×#519×C103C212yesmaximal
3C103×#2365C218yesmaximal, complemented
4C103×#2344C218yesmaximal
5C103×#2327C214yesmaximal, complemented
6C103×#2310C212yesmaximal
7C4×C4⋊Q8×C103C214yesmaximal, complemented
8C103×#2285C211yesmaximal, characteristic
9C4×#117×C103C211yesmaximal, characteristic
10C23×Q8×C103C2212yes—
11C2×C4⋊Q8×C103C4116yescomplemented
12C2×C4⋊Q8×C103C2212yes—
13C2×C4⋊Q8×C103C2212yes—
14C2×C4⋊Q8×C103C2214yes—
15#519×C103—216no—
16C2×C4×Q8×C103C2218yes—
17C2×C4×Q8×C103C2218yes—
18C2×#117×C103C2211yescharacteristic
19C2×#117×C103C2212yes—
20C2×#117×C103C2218yes—
21C2×#117×C103C2211yescharacteristic
22C22×C4⋊C4×C103C2214yes—
23C22×C42×C103C2211yescharacteristic
24#391×C103C2218yes—
25#391×C103C2218yes—
26#389×C103C22116yes—
27#387×C103C22132yes—
28#384×C103C2212yes—
29#382×C103C2212yes—
30#381×C103C2218yes—
31#380×C103C2214yes—
32C4×C4⋊C4×C103C2214yes—
33C4×C4⋊C4×C103C2214yes—
34C4×C4⋊C4×C103C22116yes—
35C4×C22⋊C4×C103C2214yes—
36#376×C103C2212yes—
37C43×C103C2212yes—
38C22×Q8×C103—28no—
39C22×Q8×C103—28no—
40C22×Q8×C103C2×C4116yes—
41C22×Q8×C103C2314yes—
42C22×Q8×C103C2314yes—
43C23×C4×C103C2312yes—
44C23×C4×C103C2314yes—
45C23×C4×C103C2311yescharacteristic
46C4⋊Q8×C103C2×C4116yes—
47C4⋊Q8×C103C2×C4116yes—
48C4⋊Q8×C103C2×C4132yes—
49C4×Q8×C103—232no—
50C4×Q8×C103—232no—
51#117×C103—28no—
52#117×C103—24no—
53#117×C103—232no—
54#117×C103D418yes—
55C2×C4⋊C4×C103C2×C4132yes—
56C2×C4⋊C4×C103C2318yes—
57C2×C4⋊C4×C103C2312yes—
58C2×C4⋊C4×C103C2314yes—
59C2×C4⋊C4×C103C23116yes—
60C2×C4⋊C4×C103C2318yes—
61C2×C4⋊C4×C103C2318yes—
62C2×C4⋊C4×C103C2312yes—
63C2×C22⋊C4×C103C2312yes—
64C2×C22⋊C4×C103C2314yes—
65C2×C22⋊C4×C103C2312yes—
66C2×C42×C103C2×C418yes—
67C2×C42×C103C2312yes—
68C2×C42×C103C2318yes—
69C2×C42×C103C23116yes—
70C2×C42×C103C2314yes—
71C2×C42×C103C2311yescharacteristic
72C2×C42×C103C2311yescharacteristic
73C2×C42×C103C2312yes—
74C2×C42×C103C2312yes—
75#95×C103C2318yes—
76#95×C103C2318yes—
77#95×C103C23132yes—
78C24×C103C2411yescharacteristic
79C2×Q8×C103—264no—
80C2×Q8×C103—28no—
81C2×Q8×C103—28no—
82C2×Q8×C103—28no—
83C2×Q8×C103—28no—
84C2×Q8×C103C22×C4116yes—
85C2×Q8×C103C22×C4116yes—
86C22×C4×C103—28no—
87C22×C4×C103—28no—
88C22×C4×C103—28no—
89C22×C4×C103C22×C418yes—
90C22×C4×C103C22×C4116yes—
91C22×C4×C103C22×C414yes—
92C22×C4×C103C2×D414yes—
93C22×C4×C103#4114yes—
94C22×C4×C103C2414yes—
95C22×C4×C103C2418yes—
96C22×C4×C103C2412yes—
97C22×C4×C103C2418yes—
98C22×C4×C103C2414yes—
99C22×C4×C103C2411yescharacteristic
100C22×C4×C103C2411yescharacteristic
101C22×C4×C103C2412yes—
102C4⋊C4×C103—232no—
103C4⋊C4×C103—28no—
104C4⋊C4×C103—24no—
105C4⋊C4×C103—216no—
106C4⋊C4×C103C22×C4132yes—
107C4⋊C4×C103C22×C4132yes—
108C4⋊C4×C103C2×D418yes—
109C22⋊C4×C103—28no—
110C22⋊C4×C103—24no—
111C22⋊C4×C103C2×D418yes—
112C42×C103—232no—
113C42×C103—28no—
114C42×C103—24no—
115C42×C103—216no—
116C42×C103C22×C414yes—
117C42×C103C22×C418yes—
118C42×C103C22×C414yes—
119C42×C103C2×D418yes—
120C23×C103—24no—
121C23×C103C23×C412yes—
122C23×C103C22×D412yes—
123C23×C103C2×#4112yes—
124C23×C103C2511yescharacteristic
125Q8×C103—232no—
126Q8×C103—232no—
127C2×C4×C103—232no—
128C2×C4×C103—28no—
129C2×C4×C103—28no—
130C2×C4×C103—28no—
131C2×C4×C103—24no—
132C2×C4×C103—216no—
133C2×C4×C103—28no—
134C2×C4×C103—24no—
135C2×C4×C103—28no—
136C2×C4×C103—216no—
137C2×C4×C103C4×D4116yes—
138C2×C4×C103C23×C414yes—
139C2×C4×C103C23×C4116yes—
140C2×C4×C103C23×C412yes—
141C2×C4×C103C23×C412yes—
142C2×C4×C103C23×C414yes—
143C2×C4×C103C22×D418yes—
144C2×C4×C103C22×D412yes—
145C2×C4×C103C22×D412yes—
146C2×C4×C103C2×#4112yes—
147C2×C4×C103C2×#4112yes—
148C2×C4×C1032−1+418yes—
149C22×C103—24no—
150C22×C103—24no—
151C22×C103—24no—
152C22×C103C2×C4×D414yes—
153C22×C103C24×C411yescharacteristic
154C22×C103C23×D411yescharacteristic
155C22×C103C22×#4111yescharacteristic
156C22×C103C2×2−1+414yes—
157C4×C103—216no—
158C4×C103—24no—
159C4×C103—28no—
160C4×C103—48no—
161C4×C103—44no—
162C4×C103C2×C4×D414yes—
163C4×C103C2×C4×D414yes—
164C4×C103#51918yescomplemented
165#34209C10311yesmaximal, characteristic, direct product factor, Sylow
166C2×C103—24no—
167C2×C103C22×C4×D411yescharacteristic
168C2×C103C2×#51912yes—
169C2×C103#349912yes—
170C2×C103#350912yes—
171C22×C4⋊Q8C2×C10311yescharacteristic
172C2×#519C2×C10312yes—
173#2365C2×C10318yescomplemented
174#2344C2×C10318yes—
175#2327C2×C10314yescomplemented
176#2310C2×C10312yes—
177C4×C4⋊Q8C2×C10314yescomplemented
178#2285C2×C10311yescharacteristic
179C4×#117C2×C10311yescharacteristic
180C103#3420911yescharacteristic, direct product factor, Sylow
181C23×Q8C22×C10312yes—
182C2×C4⋊Q8C4×C103116yescomplemented
183C2×C4⋊Q8C22×C10312yes—
184C2×C4⋊Q8C22×C10312yes—
185C2×C4⋊Q8C22×C10314yes—
186#519—216no—
187C2×C4×Q8C22×C10318yes—
188C2×C4×Q8C22×C10318yes—
189C2×#117C22×C10311yescharacteristic
190C2×#117C22×C10312yes—
191C2×#117C22×C10318yes—
192C2×#117C22×C10311yescharacteristic
193C22×C4⋊C4C22×C10314yes—
194C22×C42C22×C10311yescharacteristic
195#391C22×C10318yes—
196#391C22×C10318yes—
197#389C22×C103116yes—
198#387C22×C103132yes—
199#384C22×C10312yes—
200#382C22×C10312yes—
201#381C22×C10318yes—
202#380C22×C10314yes—
203C4×C4⋊C4C22×C103116yes—
204C4×C4⋊C4C22×C10314yes—
205C4×C4⋊C4C22×C10314yes—
206C4×C22⋊C4C22×C10314yes—
207#376C22×C10312yes—
208C43C22×C10312yes—
209C22×Q8—28no—
210C22×Q8—28no—
211C22×Q8C2×C4×C103116yes—
212C22×Q8C23×C10314yes—
213C22×Q8C23×C10314yes—
214C23×C4C23×C10314yes—
215C23×C4C23×C10312yes—
216C23×C4C23×C10311yescharacteristic
217C4⋊Q8C2×C4×C103116yes—
218C4⋊Q8C2×C4×C103116yes—
219C4⋊Q8C2×C4×C103132yes—
220C4×Q8—232no—
221C4×Q8—232no—
222#117—28no—
223#117—24no—
224#117—232no—
225#117D4×C10318yes—
226C2×C4⋊C4C2×C4×C103132yes—
227C2×C4⋊C4C23×C10314yes—
228C2×C4⋊C4C23×C103116yes—
229C2×C4⋊C4C23×C10312yes—
230C2×C4⋊C4C23×C10318yes—
231C2×C4⋊C4C23×C10318yes—
232C2×C4⋊C4C23×C10318yes—
233C2×C4⋊C4C23×C10312yes—
234C2×C22⋊C4C23×C10314yes—
235C2×C22⋊C4C23×C10312yes—
236C2×C22⋊C4C23×C10312yes—
237C2×C42C2×C4×C10318yes—
238C2×C42C23×C103116yes—
239C2×C42C23×C10314yes—
240C2×C42C23×C10312yes—
241C2×C42C23×C10318yes—
242C2×C42C23×C10311yescharacteristic
243C2×C42C23×C10311yescharacteristic
244C2×C42C23×C10312yes—
245C2×C42C23×C10312yes—
246#95C23×C10318yes—
247#95C23×C10318yes—
248#95C23×C103132yes—
249C24C24×C10311yescharacteristic
250C2×Q8—264no—
251C2×Q8—28no—
252C2×Q8—28no—
253C2×Q8—28no—
254C2×Q8—28no—
255C2×Q8C22×C4×C103116yes—
256C2×Q8C22×C4×C103116yes—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4C22×C4×C10318yes—
261C22×C4C22×C4×C103116yes—
262C22×C4C22×C4×C10314yes—
263C22×C4C2×D4×C10314yes—
264C22×C4#41×C10314yes—
265C22×C4C24×C10314yes—
266C22×C4C24×C10318yes—
267C22×C4C24×C10312yes—
268C22×C4C24×C10318yes—
269C22×C4C24×C10314yes—
270C22×C4C24×C10311yescharacteristic
271C22×C4C24×C10311yescharacteristic
272C22×C4C24×C10312yes—
273C4⋊C4—232no—
274C4⋊C4—28no—
275C4⋊C4—24no—
276C4⋊C4—216no—
277C4⋊C4C22×C4×C103132yes—
278C4⋊C4C22×C4×C103132yes—
279C4⋊C4C2×D4×C10318yes—
280C22⋊C4—28no—
281C22⋊C4—24no—
282C22⋊C4C2×D4×C10318yes—
283C42—232no—
284C42—28no—
285C42—24no—
286C42—216no—
287C42C22×C4×C10314yes—
288C42C22×C4×C10318yes—
289C42C22×C4×C10314yes—
290C42C2×D4×C10318yes—
291C23—24no—
292C23C23×C4×C10312yes—
293C23C22×D4×C10312yes—
294C23C2×#41×C10312yes—
295C23C25×C10311yescharacteristic
296Q8—232no—
297Q8—232no—
298C2×C4—232no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—24no—
303C2×C4—216no—
304C2×C4—28no—
305C2×C4—24no—
306C2×C4—28no—
307C2×C4—216no—
308C2×C4C4×D4×C103116yes—
309C2×C4C23×C4×C10314yes—
310C2×C4C23×C4×C103116yes—
311C2×C4C23×C4×C10312yes—
312C2×C4C23×C4×C10312yes—
313C2×C4C23×C4×C10314yes—
314C2×C4C22×D4×C10318yes—
315C2×C4C22×D4×C10312yes—
316C2×C4C22×D4×C10312yes—
317C2×C4C2×#41×C10312yes—
318C2×C4C2×#41×C10312yes—
319C2×C42−1+4×C10318yes—
320C22—24no—
321C22—24no—
322C22—24no—
323C22C2×C4×D4×C10314yes—
324C22C24×C4×C10311yescharacteristic
325C22C23×D4×C10311yescharacteristic
326C22C22×#41×C10311yescharacteristic
327C22C2×2−1+4×C10314yes—
328C4—28no—
329C4—216no—
330C4—24no—
331C4—48no—
332C4—44no—
333C4C2×C4×D4×C10314yes—
334C4C2×C4×D4×C10314yes—
335C4#519×C10318yescomplemented
336C2—24no—
337C2C22×C4×D4×C10311yescharacteristic
338C2C2×#519×C10312yes—
339C2C103×#349912yes—
340C2C103×#350912yes—
subgroupG/H
center, socleC23×C103C25
commutatorC22C24×C4×C103
Frattini, cosocleC23C25×C103
prime radicalC24×C103C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2365C2semidirect
5. C103×#2327C2semidirect
7. C4×C4⋊Q8×C103C2semidirect
11. C2×C4⋊Q8×C103C4semidirect
164. C4×C103#519semidirect
165. #34209C103direct (N × H)
173. #2365C2×C103semidirect
175. #2327C2×C103semidirect
177. C4×C4⋊Q8C2×C103semidirect
180. C103#34209direct (N × H)
182. C2×C4⋊Q8C4×C103semidirect
335. C4#519×C103semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Q8×C1032
C2×#519×C1032
C103×#23652
C103×#23442
C103×#23272
C103×#23102
C4×C4⋊Q8×C1032
C103×#22852
C4×#117×C1032
#34209103