Finite Group Databasebeta

← C103×#8589 #39913864

Subgroups — C103×#8589 #39913864

Order 26368.

496 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊Q8×C103C211yesmaximal, characteristic
2C103×#1842C211yesmaximal, characteristic
3C103×#1831C211yesmaximal, characteristic
4C2×#332×C103C212yesmaximal
5C103×#1296C212yesmaximal
6C2×C4⋊Q8×C103C2211yescharacteristic
7C2×C4×Q8×C103—21no—
8C2×C4⋊C8×C103—21no—
9C2×C4⋊C8×C103—21no—
10C2×C4⋊C8×C103C2212yes—
11C2×C4⋊C8×C103C2212yes—
12#391×C103—21no—
13#389×C103—21no—
14#389×C103C412yes—
15#384×C103C2211yescharacteristic
16C4×C4⋊C4×C103—21no—
17C4×C4⋊C4×C103C412yes—
18C43×C103C2211yescharacteristic
19#336×C103—21no—
20#336×C103—21no—
21#332×C103—24no—
22C22×Q8×C103—21no—
23C22×C8×C103—22no—
24C22×C8×C103—22no—
25C4⋊Q8×C103—21no—
26C4⋊Q8×C103—21no—
27C4⋊Q8×C103D412yes—
28C4⋊Q8×C103Q812yes—
29C4×Q8×C103—42no—
30C4×Q8×C103—42no—
31C2×C4⋊C4×C103—21no—
32C2×C4⋊C4×C103—22no—
33C2×C4⋊C4×C103—21no—
34C2×C4⋊C4×C103—21no—
35C2×C4⋊C4×C103C2×C412yes—
36C2×C4⋊C4×C103C2×C412yes—
37C2×C42×C103—22no—
38C2×C42×C103C2×C411yescharacteristic
39C2×C42×C103C2×C411yescharacteristic
40C2×C42×C103D411yescharacteristic
41C2×C42×C103D411yescharacteristic
42C2×C42×C103D411yescharacteristic
43C2×C42×C103D411yescharacteristic
44C2×C42×C103C2311yescharacteristic
45C4⋊C8×C103—22no—
46C4⋊C8×C103—22no—
47C4⋊C8×C103—22no—
48C4⋊C8×C103—22no—
49C4⋊C8×C103—42no—
50C4⋊C8×C103—42no—
51#95×C103—22no—
52#95×C103—22no—
53C2×Q8×C103—22no—
54C2×Q8×C103—22no—
55C2×Q8×C103—41no—
56C2×Q8×C103—41no—
57C2×Q8×C103—41no—
58C2×Q8×C103—41no—
59C22×C4×C103—22no—
60C22×C4×C103—22no—
61C22×C4×C103C22⋊C411yescharacteristic
62C22×C4×C103C22⋊C411yescharacteristic
63C22×C4×C103C22⋊C411yescharacteristic
64C22×C4×C103C22⋊C411yescharacteristic
65C22×C4×C103C22×C411yescharacteristic
66C22×C4×C103C2×D411yescharacteristic
67C22×C4×C103C2×D411yescharacteristic
68C2×C8×C103—42no—
69C2×C8×C103—42no—
70C2×C8×C103—42no—
71C2×C8×C103—42no—
72C2×C8×C103—42no—
73C2×C8×C103—42no—
74C4⋊C4×C103—22no—
75C4⋊C4×C103—22no—
76C4⋊C4×C103—22no—
77C4⋊C4×C103—42no—
78C4⋊C4×C103—44no—
79C4⋊C4×C103—41no—
80C4⋊C4×C103—41no—
81C4⋊C4×C103—42no—
82C4⋊C4×C103C4⋊C414yes—
83C42×C103—22no—
84C42×C103—22no—
85C42×C103—21no—
86C42×C103—21no—
87C42×C103—22no—
88C42×C103—41no—
89C42×C103—44no—
90C42×C103D812yes—
91C42×C103SD1612yes—
92C42×C103C2×D411yescharacteristic
93C42×C103C2×Q811yescharacteristic
94C42×C103#4111yescharacteristic
95C42×C103#4111yescharacteristic
96C23×C103C2×C22⋊C411yescharacteristic
97Q8×C103—42no—
98Q8×C103—42no—
99Q8×C103—42no—
100Q8×C103—42no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—24no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—42no—
114C2×C4×C103—42no—
115C2×C4×C103—42no—
116C2×C4×C103—42no—
117C2×C4×C103—42no—
118C2×C4×C103#10112yes—
119C2×C4×C103#10212yes—
120C2×C4×C103#10212yes—
121C2×C4×C103C2×C4⋊C411yescharacteristic
122C2×C4×C103#11711yescharacteristic
123C2×C4×C103#12111yescharacteristic
124C2×C4×C103#12111yescharacteristic
125C2×C4×C103C22⋊Q811yescharacteristic
126C2×C4×C103C22⋊Q811yescharacteristic
127C2×C4×C103C2×D811yescharacteristic
128C2×C4×C103C2×SD1611yescharacteristic
129C2×C4×C103#13512yes—
130C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C103#13711yescharacteristic
132C2×C4×C103#13712yes—
133C8×C103—82no—
134C8×C103—82no—
135C22×C103#38011yescharacteristic
136C22×C103C2×#10111yescharacteristic
137C22×C103#41311yescharacteristic
138C22×C103C2×#10211yescharacteristic
139C22×C103#41611yescharacteristic
140C22×C103#41711yescharacteristic
141C22×C103#41911yescharacteristic
142C4×C103—22no—
143C4×C103—21no—
144C4×C103—21no—
145C4×C103—22no—
146C4×C103—22no—
147C4×C103—44no—
148C4×C103—41no—
149C4×C103—82no—
150C4×C103#45911yescharacteristic
151C4×C103#46111yescharacteristic
152C4×C103#46412yes—
153C4×C103#47411yescharacteristic
154C4×C103#47611yescharacteristic
155C4×C103#47912yes—
156#8589C10311yesmaximal, characteristic, direct product factor, Sylow
157C2×C103#154011yescharacteristic
158C2×C103#154611yescharacteristic
159C2×C103#155211yescharacteristic
160C2×C103#155911yescharacteristic
161C2×C103#180111yescharacteristic
162C2×C103#180211yescharacteristic
163C2×C103#180511yescharacteristic
164C4×C4⋊Q8C2×C10311yescharacteristic
165#1842C2×C10311yescharacteristic
166#1831C2×C10311yescharacteristic
167C2×#332C2×C10312yes—
168#1296C2×C10312yes—
169C103#858911yescharacteristic, direct product factor, Sylow
170C2×C4⋊Q8C22×C10311yescharacteristic
171C2×C4×Q8—21no—
172C2×C4⋊C8—21no—
173C2×C4⋊C8—21no—
174C2×C4⋊C8C22×C10312yes—
175C2×C4⋊C8C22×C10312yes—
176#391—21no—
177#389—21no—
178#389C4×C10312yes—
179#384C22×C10311yescharacteristic
180C4×C4⋊C4—21no—
181C4×C4⋊C4C4×C10312yes—
182C43C22×C10311yescharacteristic
183#336—21no—
184#336—21no—
185#332—24no—
186C22×Q8—21no—
187C22×C8—22no—
188C22×C8—22no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8D4×C10312yes—
192C4⋊Q8Q8×C10312yes—
193C4×Q8—42no—
194C4×Q8—42no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C2×C4×C10312yes—
200C2×C4⋊C4C2×C4×C10312yes—
201C2×C42—22no—
202C2×C42C2×C4×C10311yescharacteristic
203C2×C42C2×C4×C10311yescharacteristic
204C2×C42D4×C10311yescharacteristic
205C2×C42D4×C10311yescharacteristic
206C2×C42D4×C10311yescharacteristic
207C2×C42D4×C10311yescharacteristic
208C2×C42C23×C10311yescharacteristic
209C4⋊C8—22no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—42no—
214C4⋊C8—42no—
215#95—22no—
216#95—22no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—41no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4C22⋊C4×C10311yescharacteristic
226C22×C4C22⋊C4×C10311yescharacteristic
227C22×C4C22⋊C4×C10311yescharacteristic
228C22×C4C22⋊C4×C10311yescharacteristic
229C22×C4C22×C4×C10311yescharacteristic
230C22×C4C2×D4×C10311yescharacteristic
231C22×C4C2×D4×C10311yescharacteristic
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—44no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4C4⋊C4×C10314yes—
247C42—22no—
248C42—22no—
249C42—21no—
250C42—21no—
251C42—22no—
252C42—41no—
253C42—44no—
254C42D8×C10312yes—
255C42SD16×C10312yes—
256C42C2×D4×C10311yescharacteristic
257C42C2×Q8×C10311yescharacteristic
258C42#41×C10311yescharacteristic
259C42#41×C10311yescharacteristic
260C23C2×C22⋊C4×C10311yescharacteristic
261Q8—42no—
262Q8—42no—
263Q8—42no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—24no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4#101×C10312yes—
283C2×C4#102×C10312yes—
284C2×C4#102×C10312yes—
285C2×C4C2×C4⋊C4×C10311yescharacteristic
286C2×C4#117×C10311yescharacteristic
287C2×C4#121×C10311yescharacteristic
288C2×C4#121×C10311yescharacteristic
289C2×C4C22⋊Q8×C10311yescharacteristic
290C2×C4C22⋊Q8×C10311yescharacteristic
291C2×C4C2×D8×C10311yescharacteristic
292C2×C4C2×SD16×C10311yescharacteristic
293C2×C4#135×C10312yes—
294C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
295C2×C4#137×C10311yescharacteristic
296C2×C4#137×C10312yes—
297C8—82no—
298C8—82no—
299C22#380×C10311yescharacteristic
300C22C2×#101×C10311yescharacteristic
301C22#413×C10311yescharacteristic
302C22C2×#102×C10311yescharacteristic
303C22#416×C10311yescharacteristic
304C22#417×C10311yescharacteristic
305C22#419×C10311yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—22no—
310C4—22no—
311C4—44no—
312C4—41no—
313C4—82no—
314C4#459×C10311yescharacteristic
315C4#461×C10311yescharacteristic
316C4#464×C10312yes—
317C4#474×C10311yescharacteristic
318C4#476×C10311yescharacteristic
319C4#479×C10312yes—
320C2C103×#154011yescharacteristic
321C2C103×#154611yescharacteristic
322C2C103×#155211yescharacteristic
323C2C103×#155911yescharacteristic
324C2C103×#180111yescharacteristic
325C2C103×#180211yescharacteristic
326C2C103×#180511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103C2×C22⋊C4
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C43×C103 ◁ G

Complements

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

NH ≅ G/Ntype
156. #8589C103direct (N × H)
169. C103#8589direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C4⋊Q8×C1032
C103×#18422
C103×#18312
C2×#332×C1032
C103×#12962
#8589103