Finite Group Databasebeta

← C103×#33285 #39938560

Subgroups — C103×#33285 #39938560

Order 26368.

634 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2647C211yesmaximal, characteristic
2C103×#2642C211yesmaximal, characteristic
3C103×#1992C211yesmaximal, characteristic
4C103×#1991C211yesmaximal, characteristic
5C103×#1960C211yesmaximal, characteristic
6C103×#1956C211yesmaximal, characteristic
7C103×#1935C212yesmaximal
8C103×#1935C212yesmaximal
9C103×#1933C212yesmaximal
10C103×#1933C212yesmaximal
11C103×#1726C211yesmaximal, characteristic
12C2×C4⋊Q8×C103C2211yescharacteristic
13C2×#125×C103C2211yescharacteristic
14C2×#103×C103C2212yes—
15C2×#103×C103C2212yes—
16C2×#103×C103C2212yes—
17C2×#103×C103C2212yes—
18C2×#97×C103C2211yescharacteristic
19C2×#97×C103C2211yescharacteristic
20C2×#97×C103C2211yescharacteristic
21C2×C4×C8×C103C2211yescharacteristic
22C2×C4×C8×C103C2211yescharacteristic
23C2×C4×C8×C103C2211yescharacteristic
24#400×C103—22no—
25#400×C103—22no—
26#400×C103—22no—
27#398×C103—22no—
28#391×C103C2212yes—
29#391×C103C2212yes—
30#389×C103C2212yes—
31#389×C103C2212yes—
32#384×C103C2211yescharacteristic
33#382×C103C2211yescharacteristic
34#376×C103C2211yescharacteristic
35#340×C103C2212yes—
36#340×C103C2212yes—
37#340×C103C2212yes—
38#340×C103C2212yes—
39C22×Q8×C103C2312yes—
40C22×C8×C103C2311yescharacteristic
41C22×C8×C103C2311yescharacteristic
42C22×C8×C103C2311yescharacteristic
43C22×C8×C103C2311yescharacteristic
44C4⋊Q8×C103—22no—
45C4⋊Q8×C103—22no—
46#125×C103—22no—
47#125×C103—22no—
48C2×C4⋊C4×C103—22no—
49C2×C4⋊C4×C103—22no—
50C2×C4⋊C4×C103—22no—
51C2×C4⋊C4×C103—22no—
52C2×C4⋊C4×C103—22no—
53C2×C4⋊C4×C103C2312yes—
54C2×C4⋊C4×C103C2312yes—
55C2×C4⋊C4×C103C2312yes—
56C2×C42×C103C2311yescharacteristic
57C2×C42×C103C2311yescharacteristic
58C2×C42×C103C2311yescharacteristic
59#103×C103—24no—
60#103×C103—24no—
61#103×C103—24no—
62#103×C103—24no—
63#97×C103—22no—
64#97×C103—22no—
65#97×C103—22no—
66C4×C8×C103—22no—
67C4×C8×C103—22no—
68C4×C8×C103—22no—
69#95×C103—22no—
70#95×C103—22no—
71#95×C103—22no—
72#95×C103—22no—
73#95×C103—24no—
74#95×C103—22no—
75#95×C103D412yes—
76#95×C103D412yes—
77C2×Q8×C103—22no—
78C2×Q8×C103—22no—
79C2×Q8×C103—22no—
80C2×Q8×C103—22no—
81C2×Q8×C103—22no—
82C2×Q8×C103—22no—
83C22×C4×C103—22no—
84C22×C4×C103—22no—
85C22×C4×C103—22no—
86C22×C4×C103—22no—
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103C2×D412yes—
89C22×C4×C103C2×D411yescharacteristic
90C22×C4×C103C2×D412yes—
91C22×C4×C103C2411yescharacteristic
92C2×C8×C103—21no—
93C2×C8×C103—21no—
94C2×C8×C103—21no—
95C2×C8×C103—21no—
96C2×C8×C103—21no—
97C2×C8×C103—21no—
98C2×C8×C103—21no—
99C2×C8×C103—21no—
100C2×C8×C103#4112yes—
101C2×C8×C103#4112yes—
102C2×C8×C103#4112yes—
103C2×C8×C103#4112yes—
104C4⋊C4×C103—22no—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—22no—
110C4⋊C4×C103—44no—
111C4⋊C4×C103—44no—
112C4⋊C4×C103—82no—
113C4⋊C4×C103—82no—
114C4⋊C4×C103—82no—
115C42×C103—21no—
116C42×C103—21no—
117C42×C103—21no—
118C42×C103—21no—
119C42×C103#4112yes—
120C42×C103#4112yes—
121C23×C103C22×D411yescharacteristic
122Q8×C103—42no—
123Q8×C103—42no—
124Q8×C103—42no—
125Q8×C103—42no—
126C2×C4×C103—22no—
127C2×C4×C103—22no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—22no—
133C2×C4×C103—22no—
134C2×C4×C103—22no—
135C2×C4×C103—42no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103—42no—
142C2×C4×C103—42no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103—42no—
146C2×C4×C103—42no—
147C2×C4×C103#12414yes—
148C2×C4×C103C2×#4111yescharacteristic
149C2×C4×C103C2×#4111yescharacteristic
150C2×C4×C103C2×#4111yescharacteristic
151C2×C4×C103C2×#4111yescharacteristic
152C2×C4×C103C2×#4111yescharacteristic
153C2×C4×C103C2×#4111yescharacteristic
154C8×C103—22no—
155C8×C103—22no—
156C8×C103—22no—
157C8×C103—22no—
158C22×C103C2×#12411yescharacteristic
159C22×C103#53211yescharacteristic
160C22×C103#53211yescharacteristic
161C22×C103#57712yes—
162C22×C103#57812yes—
163C4×C103—24no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103—42no—
167C4×C103—82no—
168C4×C103—82no—
169C4×C103—82no—
170C4×C103—82no—
171C4×C103#52911yescharacteristic
172C4×C103#52911yescharacteristic
173C4×C103#52911yescharacteristic
174C4×C103#52911yescharacteristic
175#33285C10311yesmaximal, characteristic, direct product factor, Sylow
176C2×C103#286111yescharacteristic
177C2×C103#313712yes—
178C2×C103#317411yescharacteristic
179C2×C103#317711yescharacteristic
180C2×C103#317812yes—
181#2647C2×C10311yescharacteristic
182#2642C2×C10311yescharacteristic
183#1992C2×C10311yescharacteristic
184#1991C2×C10311yescharacteristic
185#1960C2×C10311yescharacteristic
186#1956C2×C10311yescharacteristic
187#1935C2×C10312yes—
188#1935C2×C10312yes—
189#1933C2×C10312yes—
190#1933C2×C10312yes—
191#1726C2×C10311yescharacteristic
192C103#3328511yescharacteristic, direct product factor, Sylow
193C2×C4⋊Q8C22×C10311yescharacteristic
194C2×#125C22×C10311yescharacteristic
195C2×#103C22×C10312yes—
196C2×#103C22×C10312yes—
197C2×#103C22×C10312yes—
198C2×#103C22×C10312yes—
199C2×#97C22×C10311yescharacteristic
200C2×#97C22×C10311yescharacteristic
201C2×#97C22×C10311yescharacteristic
202C2×C4×C8C22×C10311yescharacteristic
203C2×C4×C8C22×C10311yescharacteristic
204C2×C4×C8C22×C10311yescharacteristic
205#400—22no—
206#400—22no—
207#400—22no—
208#398—22no—
209#391C22×C10312yes—
210#391C22×C10312yes—
211#389C22×C10312yes—
212#389C22×C10312yes—
213#384C22×C10311yescharacteristic
214#382C22×C10311yescharacteristic
215#376C22×C10311yescharacteristic
216#340C22×C10312yes—
217#340C22×C10312yes—
218#340C22×C10312yes—
219#340C22×C10312yes—
220C22×Q8C23×C10312yes—
221C22×C8C23×C10311yescharacteristic
222C22×C8C23×C10311yescharacteristic
223C22×C8C23×C10311yescharacteristic
224C22×C8C23×C10311yescharacteristic
225C4⋊Q8—22no—
226C4⋊Q8—22no—
227#125—22no—
228#125—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4C23×C10312yes—
235C2×C4⋊C4C23×C10312yes—
236C2×C4⋊C4C23×C10312yes—
237C2×C42C23×C10311yescharacteristic
238C2×C42C23×C10311yescharacteristic
239C2×C42C23×C10311yescharacteristic
240#103—24no—
241#103—24no—
242#103—24no—
243#103—24no—
244#97—22no—
245#97—22no—
246#97—22no—
247C4×C8—22no—
248C4×C8—22no—
249C4×C8—22no—
250#95—22no—
251#95—22no—
252#95—22no—
253#95—22no—
254#95—24no—
255#95—22no—
256#95D4×C10312yes—
257#95D4×C10312yes—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4C2×D4×C10311yescharacteristic
269C22×C4C2×D4×C10312yes—
270C22×C4C2×D4×C10311yescharacteristic
271C22×C4C2×D4×C10312yes—
272C22×C4C24×C10311yescharacteristic
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8#41×C10312yes—
282C2×C8#41×C10312yes—
283C2×C8#41×C10312yes—
284C2×C8#41×C10312yes—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—44no—
292C4⋊C4—44no—
293C4⋊C4—82no—
294C4⋊C4—82no—
295C4⋊C4—82no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42#41×C10312yes—
301C42#41×C10312yes—
302C23C22×D4×C10311yescharacteristic
303Q8—42no—
304Q8—42no—
305Q8—42no—
306Q8—42no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4#124×C10314yes—
329C2×C4C2×#41×C10311yescharacteristic
330C2×C4C2×#41×C10311yescharacteristic
331C2×C4C2×#41×C10311yescharacteristic
332C2×C4C2×#41×C10311yescharacteristic
333C2×C4C2×#41×C10311yescharacteristic
334C2×C4C2×#41×C10311yescharacteristic
335C8—22no—
336C8—22no—
337C8—22no—
338C8—22no—
339C22C2×#124×C10311yescharacteristic
340C22#532×C10311yescharacteristic
341C22#532×C10311yescharacteristic
342C22#577×C10312yes—
343C22#578×C10312yes—
344C4—24no—
345C4—41no—
346C4—41no—
347C4—42no—
348C4—82no—
349C4—82no—
350C4—82no—
351C4—82no—
352C4#529×C10311yescharacteristic
353C4#529×C10311yescharacteristic
354C4#529×C10311yescharacteristic
355C4#529×C10311yescharacteristic
356C2C103×#286111yescharacteristic
357C2C103×#313712yes—
358C2C103×#317411yescharacteristic
359C2C103×#317711yescharacteristic
360C2C103×#317812yes—
subgroupG/H
center, socle, prime radicalC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ #376×C103 ◁ G

Complements

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

NH ≅ G/Ntype
175. #33285C103direct (N × H)
192. C103#33285direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#26472
C103×#26422
C103×#19922
C103×#19912
C103×#19602
C103×#19562
C103×#19352
C103×#19332
C103×#17262
#33285103