Finite Group Databasebeta

← C103×#33270 #39938545

Subgroups — C103×#33270 #39938545

Order 26368.

654 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2863C212yesmaximal
2C103×#1971C211yesmaximal, characteristic
3C103×#1971C211yesmaximal, characteristic
4C103×#1969C211yesmaximal, characteristic
5C103×#1944C211yesmaximal, characteristic
6C103×#1943C211yesmaximal, characteristic
7C103×#1941C211yesmaximal, characteristic
8C103×#1935C212yesmaximal
9C103×#1935C212yesmaximal
10C103×#1933C212yesmaximal
11C4×#97×C103C211yesmaximal, characteristic
12C22×Q16×C103C2211yescharacteristic
13C2×#107×C103C2211yescharacteristic
14C2×#106×C103C2211yescharacteristic
15C2×#106×C103C2211yescharacteristic
16C2×#103×C103C2212yes—
17C2×#103×C103C2212yes—
18C2×#103×C103C2212yes—
19C2×#97×C103C2211yescharacteristic
20C2×#97×C103C2211yescharacteristic
21C2×#97×C103C2211yescharacteristic
22C2×#97×C103C2211yescharacteristic
23C2×C4×C8×C103C2211yescharacteristic
24C2×C4×C8×C103C2211yescharacteristic
25#391×C103C2212yes—
26#391×C103C2212yes—
27#391×C103C2212yes—
28#389×C103C2212yes—
29#389×C103C2212yes—
30#389×C103C2212yes—
31#387×C103—22no—
32#387×C103—22no—
33#387×C103—22no—
34#383×C103—22no—
35C43×C103C2211yescharacteristic
36#340×C103C2212yes—
37#340×C103C2212yes—
38#340×C103C2212yes—
39C22×Q8×C103C2312yes—
40C2×Q16×C103—22no—
41C2×Q16×C103—22no—
42C2×Q16×C103—22no—
43C22×C8×C103C2311yescharacteristic
44C22×C8×C103C2311yescharacteristic
45C22×C8×C103C2311yescharacteristic
46C22×C8×C103C2311yescharacteristic
47C2×C4⋊C4×C103—22no—
48C2×C4⋊C4×C103—22no—
49C2×C4⋊C4×C103—22no—
50C2×C4⋊C4×C103C2312yes—
51C2×C4⋊C4×C103C2312yes—
52C2×C4⋊C4×C103C2312yes—
53C2×C42×C103D412yes—
54C2×C42×C103D412yes—
55C2×C42×C103C2311yescharacteristic
56C2×C42×C103C2311yescharacteristic
57C2×C42×C103C2311yescharacteristic
58#107×C103—22no—
59#106×C103—22no—
60#106×C103—22no—
61#103×C103—24no—
62#103×C103—24no—
63#103×C103—24no—
64#97×C103—22no—
65#97×C103—22no—
66#97×C103—22no—
67#97×C103—22no—
68C4×C8×C103—22no—
69C4×C8×C103—22no—
70#95×C103—22no—
71#95×C103—22no—
72#95×C103—22no—
73#95×C103—22no—
74#95×C103—22no—
75#95×C103—22no—
76#95×C103—22no—
77#95×C103—22no—
78#95×C103—22no—
79C2×Q8×C103—22no—
80C2×Q8×C103—22no—
81C2×Q8×C103—22no—
82C2×Q8×C103—22no—
83C2×Q8×C103—22no—
84C2×Q8×C103—22no—
85C22×C4×C103—22no—
86C22×C4×C103—22no—
87C22×C4×C103—22no—
88C22×C4×C103—22no—
89C22×C4×C103C2×D411yescharacteristic
90C22×C4×C103C2×D412yes—
91C22×C4×C103C2×D411yescharacteristic
92C22×C4×C103C2×D412yes—
93C22×C4×C103C2411yescharacteristic
94Q16×C103—44no—
95C2×C8×C103—21no—
96C2×C8×C103—21no—
97C2×C8×C103—21no—
98C2×C8×C103—21no—
99C2×C8×C103—21no—
100C2×C8×C103—21no—
101C2×C8×C103#4112yes—
102C2×C8×C103#4112yes—
103C2×C8×C103#4112yes—
104C2×C8×C103#4112yes—
105C2×C8×C103#4112yes—
106C2×C8×C103#4112yes—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—22no—
110C4⋊C4×C103—22no—
111C4⋊C4×C103—22no—
112C4⋊C4×C103—22no—
113C4⋊C4×C103—44no—
114C4⋊C4×C103—44no—
115C4⋊C4×C103—44no—
116C42×C103—24no—
117C42×C103—21no—
118C42×C103—21no—
119C42×C103—21no—
120C42×C103—21no—
121C42×C103—21no—
122C42×C103—21no—
123C42×C103—42no—
124C23×C103C22×D411yescharacteristic
125Q8×C103—42no—
126Q8×C103—42no—
127Q8×C103—42no—
128Q8×C103—42no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—22no—
135C2×C4×C103—22no—
136C2×C4×C103—22no—
137C2×C4×C103—22no—
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—42no—
148C2×C4×C103—42no—
149C2×C4×C103—42no—
150C2×C4×C103#13714yes—
151C2×C4×C103C2×#4111yescharacteristic
152C2×C4×C103C2×#4111yescharacteristic
153C2×C4×C103C2×#4111yescharacteristic
154C2×C4×C103C2×#4111yescharacteristic
155C2×C4×C103C2×#4111yescharacteristic
156C2×C4×C103C2×#4111yescharacteristic
157C8×C103—22no—
158C8×C103—22no—
159C8×C103—22no—
160C8×C103#12614yes—
161C22×C103#53211yescharacteristic
162C22×C103#53211yescharacteristic
163C22×C103#53211yescharacteristic
164C22×C103C2×#13712yes—
165C22×C103#57512yes—
166C4×C103—24no—
167C4×C103—42no—
168C4×C103—41no—
169C4×C103—41no—
170C4×C103—82no—
171C4×C103—82no—
172C4×C103—82no—
173C4×C103—82no—
174C4×C103C2×#12611yescharacteristic
175C4×C103#52911yescharacteristic
176C4×C103#52911yescharacteristic
177C4×C103#52911yescharacteristic
178#33270C10311yesmaximal, characteristic, direct product factor, Sylow
179C2×C103#286011yescharacteristic
180C2×C103#317212yes—
181C2×C103#318112yes—
182C2×C103#318311yescharacteristic
183C2×C103#318511yescharacteristic
184#2863C2×C10312yes—
185#1971C2×C10311yescharacteristic
186#1971C2×C10311yescharacteristic
187#1969C2×C10311yescharacteristic
188#1944C2×C10311yescharacteristic
189#1943C2×C10311yescharacteristic
190#1941C2×C10311yescharacteristic
191#1935C2×C10312yes—
192#1935C2×C10312yes—
193#1933C2×C10312yes—
194C4×#97C2×C10311yescharacteristic
195C103#3327011yescharacteristic, direct product factor, Sylow
196C22×Q16C22×C10311yescharacteristic
197C2×#107C22×C10311yescharacteristic
198C2×#106C22×C10311yescharacteristic
199C2×#106C22×C10311yescharacteristic
200C2×#103C22×C10312yes—
201C2×#103C22×C10312yes—
202C2×#103C22×C10312yes—
203C2×#97C22×C10311yescharacteristic
204C2×#97C22×C10311yescharacteristic
205C2×#97C22×C10311yescharacteristic
206C2×#97C22×C10311yescharacteristic
207C2×C4×C8C22×C10311yescharacteristic
208C2×C4×C8C22×C10311yescharacteristic
209#391C22×C10312yes—
210#391C22×C10312yes—
211#391C22×C10312yes—
212#389C22×C10312yes—
213#389C22×C10312yes—
214#389C22×C10312yes—
215#387—22no—
216#387—22no—
217#387—22no—
218#383—22no—
219C43C22×C10311yescharacteristic
220#340C22×C10312yes—
221#340C22×C10312yes—
222#340C22×C10312yes—
223C22×Q8C23×C10312yes—
224C2×Q16—22no—
225C2×Q16—22no—
226C2×Q16—22no—
227C22×C8C23×C10311yescharacteristic
228C22×C8C23×C10311yescharacteristic
229C22×C8C23×C10311yescharacteristic
230C22×C8C23×C10311yescharacteristic
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×C42D4×C10312yes—
238C2×C42D4×C10312yes—
239C2×C42C23×C10311yescharacteristic
240C2×C42C23×C10311yescharacteristic
241C2×C42C23×C10311yescharacteristic
242#107—22no—
243#106—22no—
244#106—22no—
245#103—24no—
246#103—24no—
247#103—24no—
248#97—22no—
249#97—22no—
250#97—22no—
251#97—22no—
252C4×C8—22no—
253C4×C8—22no—
254#95—22no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95—22no—
262#95—22no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4C2×D4×C10311yescharacteristic
274C22×C4C2×D4×C10312yes—
275C22×C4C2×D4×C10311yescharacteristic
276C22×C4C2×D4×C10312yes—
277C22×C4C24×C10311yescharacteristic
278Q16—44no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8#41×C10312yes—
286C2×C8#41×C10312yes—
287C2×C8#41×C10312yes—
288C2×C8#41×C10312yes—
289C2×C8#41×C10312yes—
290C2×C8#41×C10312yes—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—44no—
298C4⋊C4—44no—
299C4⋊C4—44no—
300C42—24no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—21no—
305C42—21no—
306C42—21no—
307C42—42no—
308C23C22×D4×C10311yescharacteristic
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—42no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4#137×C10314yes—
335C2×C4C2×#41×C10311yescharacteristic
336C2×C4C2×#41×C10311yescharacteristic
337C2×C4C2×#41×C10311yescharacteristic
338C2×C4C2×#41×C10311yescharacteristic
339C2×C4C2×#41×C10311yescharacteristic
340C2×C4C2×#41×C10311yescharacteristic
341C8—22no—
342C8—22no—
343C8—22no—
344C8#126×C10314yes—
345C22#532×C10311yescharacteristic
346C22#532×C10311yescharacteristic
347C22#532×C10311yescharacteristic
348C22C2×#137×C10312yes—
349C22#575×C10312yes—
350C4—24no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4—82no—
355C4—82no—
356C4—82no—
357C4—82no—
358C4C2×#126×C10311yescharacteristic
359C4#529×C10311yescharacteristic
360C4#529×C10311yescharacteristic
361C4#529×C10311yescharacteristic
362C2C103×#286011yescharacteristic
363C2C103×#317212yes—
364C2C103×#318112yes—
365C2C103×#318311yescharacteristic
366C2C103×#318511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C43×C103 ◁ G

Complements

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

NH ≅ G/Ntype
178. #33270C103direct (N × H)
195. C103#33270direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#28632
C103×#19712
C103×#19692
C103×#19442
C103×#19432
C103×#19412
C103×#19352
C103×#19332
C4×#97×C1032
#33270103