Finite Group Databasebeta

← C103×#13039 #39918314

Subgroups — C103×#13039 #39918314

Order 26368.

472 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C103C211yesmaximal, characteristic
2C2×#444×C103C211yesmaximal, characteristic
3C2×#362×C103C211yesmaximal, characteristic, complemented
4C2×#360×C103C211yesmaximal, characteristic
5C103×#1971C211yesmaximal, characteristic, complemented
6C103×#1383C211yesmaximal, characteristic, complemented
7C103×#1375C211yesmaximal, characteristic, complemented
8C2×#135×C103C2211yescharacteristic
9C22×Q16×C103C2211yescharacteristic
10C2×#131×C103—21no—
11#510×C103—22no—
12#510×C103—22no—
13C2×Q32×C103C412yescomplemented
14C2×SD32×C103C412yescomplemented
15C2×M32×C103C2211yescharacteristic
16C2×M32×C103C2211yescharacteristic
17#444×C103—22no—
18#444×C103—22no—
19C2×#108×C103C2211yescharacteristic
20C2×#106×C103C2211yescharacteristic
21C2×#104×C103—21no—
22C2×#103×C103—21no—
23C2×#97×C103C2211yescharacteristic
24#391×C103—21no—
25#362×C103—22no—
26#360×C103—22no—
27C2×#41×C103—21no—
28C22×Q8×C103—21no—
29#135×C103—21no—
30#135×C103—21no—
31#135×C103D412yes—
32#135×C103D412yes—
33C2×Q16×C103—21no—
34C2×Q16×C103—21no—
35C2×Q16×C103—21no—
36C2×Q16×C103—21no—
37C2×Q16×C103—21no—
38C2×Q16×C103C2×C412yes—
39C2×Q16×C103C2×C411yescharacteristic
40C2×SD16×C103—21no—
41C2×D8×C103C2×C411yescharacteristic
42#131×C103—24no—
43#131×C103—42no—
44C2×M16×C103—21no—
45C2×M16×C103—41no—
46C22×C8×C103—41no—
47C22×C8×C103D411yescharacteristic
48C22×C8×C103C2311yescharacteristic
49C2×C4⋊C4×C103—21no—
50C2×C42×C103D411yescharacteristic
51Q32×C103—24no—
52SD32×C103—24no—
53M32×C103—21no—
54M32×C103—21no—
55M32×C103—21no—
56M32×C103—21no—
57C2×C16×C103—21no—
58C2×C16×C103C2×C412yes—
59#108×C103—21no—
60#108×C103D412yes—
61#106×C103—21no—
62#106×C103—21no—
63#104×C103—24no—
64#103×C103—42no—
65#97×C103—21no—
66#97×C103—21no—
67#95×C103—42no—
68#41×C103—22no—
69#41×C103—22no—
70#41×C103—41no—
71#41×C103—41no—
72C2×Q8×C103—21no—
73C2×Q8×C103—22no—
74C2×Q8×C103—41no—
75C2×Q8×C103—41no—
76C2×Q8×C103—41no—
77C2×Q8×C103—41no—
78C2×Q8×C103—41no—
79C2×D4×C103—21no—
80C2×D4×C103—41no—
81C22×C4×C103—21no—
82C22×C4×C103—41no—
83C22×C4×C103—41no—
84C22×C4×C103—41no—
85C22×C4×C103C2×D411yescharacteristic
86Q16×C103—22no—
87Q16×C103—21no—
88Q16×C103—22no—
89Q16×C103—41no—
90Q16×C103—41no—
91Q16×C103C22⋊C412yes—
92SD16×C103—22no—
93SD16×C103—22no—
94D8×C103—21no—
95D8×C103C22⋊C412yes—
96M16×C103—22no—
97M16×C103—44no—
98M16×C103—41no—
99C2×C8×C103—21no—
100C2×C8×C103—21no—
101C2×C8×C103—44no—
102C2×C8×C103—41no—
103C2×C8×C103D812yes—
104C2×C8×C103C22×C411yescharacteristic
105C2×C8×C103C2×D411yescharacteristic
106C2×C8×C103C2×D411yescharacteristic
107C2×C8×C103C2×D411yescharacteristic
108C2×C8×C103#4111yescharacteristic
109C2×C8×C103#4111yescharacteristic
110C4⋊C4×C103—41no—
111C4⋊C4×C103—41no—
112C42×C103—21no—
113C42×C103—21no—
114C16×C103—22no—
115C16×C103—41no—
116C23×C103—41no—
117C23×C103AGL(1,ℤ/8)11yescharacteristic
118Q8×C103—22no—
119Q8×C103—41no—
120Q8×C103—42no—
121Q8×C103—42no—
122Q8×C103—81no—
123Q8×C103—81no—
124D4×C103—22no—
125D4×C103—42no—
126D4×C103—42no—
127D4×C103—41no—
128C2×C4×C103—41no—
129C2×C4×C103—42no—
130C2×C4×C103—42no—
131C2×C4×C103—42no—
132C2×C4×C103—42no—
133C2×C4×C103—41no—
134C2×C4×C103—81no—
135C2×C4×C103—81no—
136C2×C4×C103—82no—
137C2×C4×C103—81no—
138C2×C4×C103C4×D411yescharacteristic
139C2×C4×C103#12011yescharacteristic
140C2×C4×C103#12111yescharacteristic
141C2×C4×C103C2×D811yescharacteristic
142C2×C4×C103#13511yescharacteristic
143C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
144C8×C103—22no—
145C8×C103—42no—
146C8×C103C2×C22⋊C411yescharacteristic
147C8×C103C4×D411yescharacteristic
148C8×C103#12111yescharacteristic
149C8×C103#12311yescharacteristic
150C22×C103—22no—
151C22×C103—42no—
152C22×C103—82no—
153C22×C103#44211yescharacteristic
154C22×C103#44911yescharacteristic
155C22×C103#45911yescharacteristic
156C4×C103—42no—
157C4×C103—81no—
158C4×C103—82no—
159C4×C103—161no—
160C4×C103#38611yescharacteristic
161C4×C103C4×D811yescharacteristic
162C4×C103#44711yescharacteristic
163C4×C103#46311yescharacteristic
164#13039C10311yesmaximal, characteristic, direct product factor, Sylow
165C2×C103—21no—
166C2×C103—21no—
167C2×C103—82no—
168C2×C103#187911yescharacteristic
169C2×C103#218012yes—
170C2×#510C2×C10311yescharacteristic
171C2×#444C2×C10311yescharacteristic
172C2×#362C2×C10311yescharacteristic, complemented
173C2×#360C2×C10311yescharacteristic
174#1971C2×C10311yescharacteristic, complemented
175#1383C2×C10311yescharacteristic, complemented
176#1375C2×C10311yescharacteristic, complemented
177C103#1303911yescharacteristic, direct product factor, Sylow
178C2×#135C22×C10311yescharacteristic
179C22×Q16C22×C10311yescharacteristic
180C2×#131—21no—
181#510—22no—
182#510—22no—
183C2×Q32C4×C10312yescomplemented
184C2×SD32C4×C10312yescomplemented
185C2×M32C22×C10311yescharacteristic
186C2×M32C22×C10311yescharacteristic
187#444—22no—
188#444—22no—
189C2×#108C22×C10311yescharacteristic
190C2×#106C22×C10311yescharacteristic
191C2×#104—21no—
192C2×#103—21no—
193C2×#97C22×C10311yescharacteristic
194#391—21no—
195#362—22no—
196#360—22no—
197C2×#41—21no—
198C22×Q8—21no—
199#135—21no—
200#135—21no—
201#135D4×C10312yes—
202#135D4×C10312yes—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16C2×C4×C10312yes—
209C2×Q16C2×C4×C10311yescharacteristic
210C2×SD16—21no—
211C2×D8C2×C4×C10311yescharacteristic
212#131—24no—
213#131—42no—
214C2×M16—21no—
215C2×M16—41no—
216C22×C8—41no—
217C22×C8D4×C10311yescharacteristic
218C22×C8C23×C10311yescharacteristic
219C2×C4⋊C4—21no—
220C2×C42D4×C10311yescharacteristic
221Q32—24no—
222SD32—24no—
223M32—21no—
224M32—21no—
225M32—21no—
226M32—21no—
227C2×C16—21no—
228C2×C16C2×C4×C10312yes—
229#108—21no—
230#108D4×C10312yes—
231#106—21no—
232#106—21no—
233#104—24no—
234#103—42no—
235#97—21no—
236#97—21no—
237#95—42no—
238#41—22no—
239#41—22no—
240#41—41no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×D4—21no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4C2×D4×C10311yescharacteristic
256Q16—22no—
257Q16—21no—
258Q16—22no—
259Q16—41no—
260Q16—41no—
261Q16C22⋊C4×C10312yes—
262SD16—22no—
263SD16—22no—
264D8—21no—
265D8C22⋊C4×C10312yes—
266M16—22no—
267M16—44no—
268M16—41no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—44no—
272C2×C8—41no—
273C2×C8D8×C10312yes—
274C2×C8C22×C4×C10311yescharacteristic
275C2×C8C2×D4×C10311yescharacteristic
276C2×C8C2×D4×C10311yescharacteristic
277C2×C8C2×D4×C10311yescharacteristic
278C2×C8#41×C10311yescharacteristic
279C2×C8#41×C10311yescharacteristic
280C4⋊C4—41no—
281C4⋊C4—41no—
282C42—21no—
283C42—21no—
284C16—22no—
285C16—41no—
286C23—41no—
287C23AGL(1,ℤ/8)×C10311yescharacteristic
288Q8—22no—
289Q8—41no—
290Q8—42no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294D4—22no—
295D4—42no—
296D4—42no—
297D4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—81no—
308C2×C4C4×D4×C10311yescharacteristic
309C2×C4#120×C10311yescharacteristic
310C2×C4#121×C10311yescharacteristic
311C2×C4C2×D8×C10311yescharacteristic
312C2×C4#135×C10311yescharacteristic
313C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
314C8—22no—
315C8—42no—
316C8C2×C22⋊C4×C10311yescharacteristic
317C8C4×D4×C10311yescharacteristic
318C8#121×C10311yescharacteristic
319C8#123×C10311yescharacteristic
320C22—22no—
321C22—42no—
322C22—82no—
323C22#442×C10311yescharacteristic
324C22#449×C10311yescharacteristic
325C22#459×C10311yescharacteristic
326C4—42no—
327C4—81no—
328C4—82no—
329C4—161no—
330C4#386×C10311yescharacteristic
331C4C4×D8×C10311yescharacteristic
332C4#447×C10311yescharacteristic
333C4#463×C10311yescharacteristic
334C2—21no—
335C2—21no—
336C2—82no—
337C2C103×#187911yescharacteristic
338C2C103×#218012yes—
subgroupG/H
center, socleC22×C103#442
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
prime radicalC2×#135×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×#97×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#362×C103C2semidirect
5. C103×#1971C2semidirect
6. C103×#1383C2semidirect
7. C103×#1375C2semidirect
13. C2×Q32×C103C4semidirect
14. C2×SD32×C103C4semidirect
164. #13039C103direct (N × H)
172. C2×#362C2×C103semidirect
174. #1971C2×C103semidirect
175. #1383C2×C103semidirect
176. #1375C2×C103semidirect
177. C103#13039direct (N × H)
183. C2×Q32C4×C103semidirect
184. C2×SD32C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C1032
C2×#444×C1032
C2×#362×C1032
C2×#360×C1032
C103×#19712
C103×#13832
C103×#13752
#13039103