Finite Group Databasebeta

← C103×#29153 #39934428

Subgroups — C103×#29153 #39934428

Order 26368.

686 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×#2660C211yesmaximal, characteristic
2C103×#2327C211yesmaximal, characteristic
3C103×#2026C212yesmaximal
4C103×#2024C212yesmaximal
5C103×#1960C211yesmaximal, characteristic
6C103×#1956C211yesmaximal, characteristic
7C103×#1836C211yesmaximal, characteristic
8C103×#1835C211yesmaximal, characteristic
9C103×#1805C212yesmaximal
10C103×#1803C212yesmaximal
11C103×#1768C211yesmaximal, characteristic
12C2×C4⋊Q8×C103C2211yescharacteristic
13C2×C4⋊Q8×C103C2211yescharacteristic
14C2×#125×C103C2211yescharacteristic
15C2×C4×Q8×C103C2212yes—
16C2×C4⋊C8×C103C2212yes—
17C2×#103×C103C2212yes—
18C2×#103×C103C2212yes—
19C2×#103×C103C2212yes—
20C2×#103×C103C2212yes—
21C2×#97×C103C2211yescharacteristic
22C2×C4×C8×C103C2211yescharacteristic
23#398×C103—22no—
24#395×C103—22no—
25#391×C103C2212yes—
26#387×C103—22no—
27#387×C103—22no—
28#384×C103C2211yescharacteristic
29#384×C103C2211yescharacteristic
30#382×C103C2211yescharacteristic
31#382×C103C2211yescharacteristic
32#382×C103C2211yescharacteristic
33#376×C103C2211yescharacteristic
34#340×C103C2212yes—
35#340×C103C2212yes—
36#340×C103C2212yes—
37#340×C103C2212yes—
38#336×C103C2212yes—
39C22×Q8×C103—21no—
40C22×Q8×C103C2312yes—
41C22×C8×C103C2312yes—
42C22×C8×C103C2312yes—
43C4⋊Q8×C103—22no—
44C4⋊Q8×C103—42no—
45C4⋊Q8×C103Q814yescomplemented
46#125×C103—42no—
47C4×Q8×C103—24no—
48C4×Q8×C103—24no—
49C2×C4⋊C4×C103—22no—
50C2×C4⋊C4×C103—22no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103—22no—
55C2×C4⋊C4×C103—22no—
56C2×C4⋊C4×C103C2311yescharacteristic
57C2×C4⋊C4×C103C2311yescharacteristic
58C2×C4⋊C4×C103C2311yescharacteristic
59C2×C4⋊C4×C103C2312yes—
60C2×C4⋊C4×C103C2311yescharacteristic
61C2×C42×C103—22no—
62C2×C42×C103C2311yescharacteristic
63C2×C42×C103C2311yescharacteristic
64C2×C42×C103C2311yescharacteristic
65C4⋊C8×C103—24no—
66#103×C103—42no—
67#103×C103—42no—
68#103×C103—42no—
69#103×C103—42no—
70#97×C103—22no—
71C4×C8×C103—22no—
72#95×C103—22no—
73#95×C103—22no—
74#95×C103—22no—
75#95×C103—22no—
76#95×C103—22no—
77#95×C103D412yes—
78#95×C103D412yes—
79C2×Q8×C103—22no—
80C2×Q8×C103—22no—
81C2×Q8×C103—22no—
82C2×Q8×C103—22no—
83C2×Q8×C103—22no—
84C2×Q8×C103—42no—
85C2×Q8×C103—82no—
86C2×Q8×C103C2×Q814yes—
87C22×C4×C103—22no—
88C22×C4×C103—22no—
89C22×C4×C103—21no—
90C22×C4×C103—21no—
91C22×C4×C103—21no—
92C22×C4×C103—21no—
93C22×C4×C103C2×D411yescharacteristic
94C22×C4×C103C2×D411yescharacteristic
95C22×C4×C103C2×D412yes—
96C22×C4×C103C2×D412yes—
97C22×C4×C103C2411yescharacteristic
98C2×C8×C103—22no—
99C2×C8×C103—22no—
100C2×C8×C103—22no—
101C2×C8×C103—22no—
102C2×C8×C103—22no—
103C2×C8×C103—22no—
104C4⋊C4×C103—28no—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—22no—
110C4⋊C4×C103—22no—
111C4⋊C4×C103—42no—
112C4⋊C4×C103—42no—
113C4⋊C4×C103—42no—
114C4⋊C4×C103—44no—
115C4⋊C4×C103—82no—
116C4⋊C4×C103—82no—
117C42×C103—22no—
118C42×C103—44no—
119C42×C103C2×Q812yes—
120C42×C103#4112yes—
121C42×C103#4114yes—
122C23×C103C22×D411yescharacteristic
123Q8×C103—24no—
124Q8×C103—24no—
125Q8×C103—42no—
126Q8×C103—42no—
127Q8×C103—84no—
128C2×C4×C103—22no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—24no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—22no—
136C2×C4×C103—22no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—42no—
140C2×C4×C103—41no—
141C2×C4×C103—41no—
142C2×C4×C103—41no—
143C2×C4×C103—41no—
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×C103C22⋊Q814yes—
151C2×C4×C103#12414yes—
152C2×C4×C103C22×Q811yescharacteristic
153C2×C4×C103C2×#4112yes—
154C2×C4×C103C2×#4111yescharacteristic
155C2×C4×C103H(5,𝔽2)12yes—
156C8×C103—42no—
157C8×C103—42no—
158C22×C103C2×C22⋊Q811yescharacteristic
159C22×C103C2×#12411yescharacteristic
160C22×C103#53511yescharacteristic
161C22×C103#57712yes—
162C22×C103#57812yes—
163C4×C103—24no—
164C4×C103—24no—
165C4×C103—44no—
166C4×C103—41no—
167C4×C103—41no—
168C4×C103—82no—
169C4×C103—81no—
170C4×C103—81no—
171C4×C103—81no—
172C4×C103—81no—
173C4×C103#55412yes—
174C4×C103#55512yes—
175#29153C10311yesmaximal, characteristic, direct product factor, Sylow
176C2×C103#256311yescharacteristic
177C2×C103#308212yes—
178C2×C103#313712yes—
179C2×C103#322211yescharacteristic
180C2×C103#322311yescharacteristic
181#2660C2×C10311yescharacteristic
182#2327C2×C10311yescharacteristic
183#2026C2×C10312yes—
184#2024C2×C10312yes—
185#1960C2×C10311yescharacteristic
186#1956C2×C10311yescharacteristic
187#1836C2×C10311yescharacteristic
188#1835C2×C10311yescharacteristic
189#1805C2×C10312yes—
190#1803C2×C10312yes—
191#1768C2×C10311yescharacteristic
192C103#2915311yescharacteristic, direct product factor, Sylow
193C2×C4⋊Q8C22×C10311yescharacteristic
194C2×C4⋊Q8C22×C10311yescharacteristic
195C2×#125C22×C10311yescharacteristic
196C2×C4×Q8C22×C10312yes—
197C2×C4⋊C8C22×C10312yes—
198C2×#103C22×C10312yes—
199C2×#103C22×C10312yes—
200C2×#103C22×C10312yes—
201C2×#103C22×C10312yes—
202C2×#97C22×C10311yescharacteristic
203C2×C4×C8C22×C10311yescharacteristic
204#398—22no—
205#395—22no—
206#391C22×C10312yes—
207#387—22no—
208#387—22no—
209#384C22×C10311yescharacteristic
210#384C22×C10311yescharacteristic
211#382C22×C10311yescharacteristic
212#382C22×C10311yescharacteristic
213#382C22×C10311yescharacteristic
214#376C22×C10311yescharacteristic
215#340C22×C10312yes—
216#340C22×C10312yes—
217#340C22×C10312yes—
218#340C22×C10312yes—
219#336C22×C10312yes—
220C22×Q8—21no—
221C22×Q8C23×C10312yes—
222C22×C8C23×C10312yes—
223C22×C8C23×C10312yes—
224C4⋊Q8—22no—
225C4⋊Q8—42no—
226C4⋊Q8Q8×C10314yescomplemented
227#125—42no—
228C4×Q8—24no—
229C4×Q8—24no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4C23×C10312yes—
238C2×C4⋊C4C23×C10311yescharacteristic
239C2×C4⋊C4C23×C10311yescharacteristic
240C2×C4⋊C4C23×C10311yescharacteristic
241C2×C4⋊C4C23×C10311yescharacteristic
242C2×C42—22no—
243C2×C42C23×C10311yescharacteristic
244C2×C42C23×C10311yescharacteristic
245C2×C42C23×C10311yescharacteristic
246C4⋊C8—24no—
247#103—42no—
248#103—42no—
249#103—42no—
250#103—42no—
251#97—22no—
252C4×C8—22no—
253#95—22no—
254#95—22no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95D4×C10312yes—
259#95D4×C10312yes—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—42no—
266C2×Q8—82no—
267C2×Q8C2×Q8×C10314yes—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4C2×D4×C10311yescharacteristic
275C22×C4C2×D4×C10311yescharacteristic
276C22×C4C2×D4×C10312yes—
277C22×C4C2×D4×C10312yes—
278C22×C4C24×C10311yescharacteristic
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C4⋊C4—28no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—44no—
296C4⋊C4—82no—
297C4⋊C4—82no—
298C42—22no—
299C42—44no—
300C42C2×Q8×C10312yes—
301C42#41×C10312yes—
302C42#41×C10314yes—
303C23C22×D4×C10311yescharacteristic
304Q8—24no—
305Q8—24no—
306Q8—42no—
307Q8—42no—
308Q8—84no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4C22⋊Q8×C10314yes—
332C2×C4#124×C10314yes—
333C2×C4C22×Q8×C10311yescharacteristic
334C2×C4C2×#41×C10312yes—
335C2×C4C2×#41×C10311yescharacteristic
336C2×C4H(5,𝔽2)×C10312yes—
337C8—42no—
338C8—42no—
339C22C2×C22⋊Q8×C10311yescharacteristic
340C22C2×#124×C10311yescharacteristic
341C22#535×C10311yescharacteristic
342C22#577×C10312yes—
343C22#578×C10312yes—
344C4—24no—
345C4—24no—
346C4—41no—
347C4—41no—
348C4—44no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—82no—
354C4#554×C10312yes—
355C4#555×C10312yes—
356C2C103×#256311yescharacteristic
357C2C103×#308212yes—
358C2C103×#313712yes—
359C2C103×#322211yescharacteristic
360C2C103×#322311yescharacteristic
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
45. C4⋊Q8×C103Q8semidirect
175. #29153C103direct (N × H)
192. C103#29153direct (N × H)
226. C4⋊Q8Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#26602
C103×#23272
C103×#20262
C103×#20242
C103×#19602
C103×#19562
C103×#18362
C103×#18352
C103×#18052
C103×#18032
C103×#17682
#29153103