Finite Group Databasebeta

← C103×#23834 #39929109

Subgroups — C103×#23834 #39929109

Order 26368.

608 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2961C211yesmaximal, characteristic, complemented
2C103×#2955C211yesmaximal, characteristic
3C103×#2103C211yesmaximal, characteristic, complemented
4C103×#2102C211yesmaximal, characteristic, complemented
5C103×#2080C212yesmaximal, complemented
6C103×#2053C211yesmaximal, characteristic
7C103×#2050C211yesmaximal, characteristic
8C103×#2031C212yesmaximal, complemented
9C103×#1765C212yesmaximal, complemented
10C103×#1757C212yesmaximal, complemented
11C103×#1747C211yesmaximal, characteristic, complemented
12#575×C103C2211yescharacteristic
13C2×#131×C103C2212yes—
14#533×C103C2211yescharacteristic
15#446×C103—22no—
16#446×C103—22no—
17#444×C103—22no—
18#443×C103—22no—
19#430×C103C2211yescharacteristic
20#424×C103C2211yescharacteristic
21#424×C103C2211yescharacteristic
22#423×C103C2211yescharacteristic
23#421×C103C2212yes—
24C2×#104×C103C2212yes—
25#416×C103C2212yes—
26#413×C103C2212yes—
27#410×C103C2212yes—
28#405×C103C2211yescharacteristic
29#405×C103C2212yes—
30#405×C103C2211yescharacteristic
31C2×#97×C103C2211yescharacteristic
32#344×C103C2212yes—
33#344×C103C2212yes—
34#341×C103C2212yes—
35#339×C103C2212yes—
36#338×C103C2211yescharacteristic
37H(3,ℤ/4)×C103C2212yes—
38H(3,ℤ/4)×C103C2211yescharacteristic
39C2×#41×C103C2312yes—
40#137×C103—22no—
41AGL(1,ℤ/8)×C103—22no—
42#135×C103—22no—
43#131×C103—22no—
44#131×C103—22no—
45#131×C103—22no—
46#131×C103—22no—
47C2×M16×C103—22no—
48C2×M16×C103C2312yes—
49C2×M16×C103C2312yes—
50C2×M16×C103C2311yescharacteristic
51C2×M16×C103C2311yescharacteristic
52C22×C8×C103—22no—
53C22×C8×C103C2311yescharacteristic
54C22×C8×C103C2311yescharacteristic
55C4⋊Q8×C103—21no—
56#125×C103—21no—
57C22⋊Q8×C103—22no—
58C4×Q8×C103—22no—
59#117×C103C2312yes—
60#117×C103C2311yescharacteristic
61#117×C103C2311yescharacteristic
62C2×C42×C103C2311yescharacteristic
63#108×C103—22no—
64C4⋊C8×C103—22no—
65C4⋊C8×C103—22no—
66C4⋊C8×C103—22no—
67#104×C103—24no—
68#104×C103—22no—
69#104×C103—22no—
70#103×C103—22no—
71#102×C103—22no—
72#101×C103—22no—
73#100×C103—22no—
74#99×C103—24no—
75#97×C103—21no—
76#97×C103—21no—
77#97×C103—21no—
78#97×C103—22no—
79#97×C103D412yes—
80C4×C8×C103—21no—
81C4×C8×C103—22no—
82C4×C8×C103D412yes—
83#41×C103—22no—
84#41×C103—22no—
85#41×C103—22no—
86#41×C103—22no—
87C2×Q8×C103—22no—
88C2×Q8×C103#4112yes—
89C2×D4×C103—22no—
90C2×D4×C103#4112yes—
91C22×C4×C103—21no—
92C22×C4×C103—22no—
93C22×C4×C103C2411yescharacteristic
94Q16×C103—22no—
95SD16×C103—24no—
96D8×C103—22no—
97M16×C103—22no—
98M16×C103—22no—
99M16×C103—22no—
100M16×C103—22no—
101M16×C103—22no—
102M16×C103—22no—
103M16×C103—42no—
104M16×C103—42no—
105C2×C8×C103—21no—
106C2×C8×C103—21no—
107C2×C8×C103—22no—
108C2×C8×C103—22no—
109C2×C8×C103—22no—
110C2×C8×C103—42no—
111C2×C8×C103—42no—
112C2×C8×C103C2×D412yes—
113C2×C8×C103C2×D411yescharacteristic
114C2×C8×C103C2×D411yescharacteristic
115C2×C8×C103#4112yes—
116C2×C8×C103#4112yes—
117C4⋊C4×C103—24no—
118C4⋊C4×C103—22no—
119C4⋊C4×C103—21no—
120C4⋊C4×C103—21no—
121C4⋊C4×C103—22no—
122C22⋊C4×C103—21no—
123C22⋊C4×C103—22no—
124C22⋊C4×C103#4112yes—
125C42×C103—21no—
126C42×C103—21no—
127C42×C103—22no—
128C42×C103C2×D412yes—
129C42×C103#4111yescharacteristic
130C42×C103#4111yescharacteristic
131C23×C103—22no—
132C23×C103C2×#4111yescharacteristic
133Q8×C103—22no—
134Q8×C103—22no—
135Q8×C103—82no—
136D4×C103—22no—
137D4×C103—22no—
138D4×C103—42no—
139D4×C103—42no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—22no—
143C2×C4×C103—22no—
144C2×C4×C103—22no—
145C2×C4×C103—42no—
146C2×C4×C103—42no—
147C2×C4×C103—42no—
148C2×C4×C103—81no—
149C2×C4×C103C22×D411yescharacteristic
150C2×C4×C103C2×#4112yes—
151C2×C4×C103C2×#4112yes—
152C2×C4×C103C2×#4111yescharacteristic
153C8×C103—22no—
154C8×C103—41no—
155C8×C103—41no—
156C8×C103—42no—
157C8×C103—42no—
158C8×C103#12411yescharacteristic
159C8×C103#12412yes—
160C8×C103#12411yescharacteristic
161C22×C103—41no—
162C22×C103—42no—
163C22×C103—82no—
164C22×C103#52511yescharacteristic
165C22×C103#52912yes—
166C4×C103—41no—
167C4×C103—41no—
168C4×C103—42no—
169C4×C103—42no—
170C4×C103—42no—
171C4×C103—82no—
172C4×C103#52511yescharacteristic
173C4×C103C2×#12411yescharacteristic
174C4×C103#52912yes—
175#23834C10311yesmaximal, characteristic, direct product factor, Sylow
176C2×C103—21no—
177C2×C103—22no—
178C2×C103—82no—
179C2×C103#239811yescharacteristic
180#2961C2×C10311yescharacteristic, complemented
181#2955C2×C10311yescharacteristic
182#2103C2×C10311yescharacteristic, complemented
183#2102C2×C10311yescharacteristic, complemented
184#2080C2×C10312yescomplemented
185#2053C2×C10311yescharacteristic
186#2050C2×C10311yescharacteristic
187#2031C2×C10312yescomplemented
188#1765C2×C10312yescomplemented
189#1757C2×C10312yescomplemented
190#1747C2×C10311yescharacteristic, complemented
191C103#2383411yescharacteristic, direct product factor, Sylow
192#575C22×C10311yescharacteristic
193C2×#131C22×C10312yes—
194#533C22×C10311yescharacteristic
195#446—22no—
196#446—22no—
197#444—22no—
198#443—22no—
199#430C22×C10311yescharacteristic
200#424C22×C10311yescharacteristic
201#424C22×C10311yescharacteristic
202#423C22×C10311yescharacteristic
203#421C22×C10312yes—
204C2×#104C22×C10312yes—
205#416C22×C10312yes—
206#413C22×C10312yes—
207#410C22×C10312yes—
208#405C22×C10311yescharacteristic
209#405C22×C10312yes—
210#405C22×C10311yescharacteristic
211C2×#97C22×C10311yescharacteristic
212#344C22×C10312yes—
213#344C22×C10312yes—
214#341C22×C10312yes—
215#339C22×C10312yes—
216#338C22×C10311yescharacteristic
217H(3,ℤ/4)C22×C10311yescharacteristic
218H(3,ℤ/4)C22×C10312yes—
219C2×#41C23×C10312yes—
220#137—22no—
221AGL(1,ℤ/8)—22no—
222#135—22no—
223#131—22no—
224#131—22no—
225#131—22no—
226#131—22no—
227C2×M16—22no—
228C2×M16C23×C10312yes—
229C2×M16C23×C10312yes—
230C2×M16C23×C10311yescharacteristic
231C2×M16C23×C10311yescharacteristic
232C22×C8—22no—
233C22×C8C23×C10311yescharacteristic
234C22×C8C23×C10311yescharacteristic
235C4⋊Q8—21no—
236#125—21no—
237C22⋊Q8—22no—
238C4×Q8—22no—
239#117C23×C10312yes—
240#117C23×C10311yescharacteristic
241#117C23×C10311yescharacteristic
242C2×C42C23×C10311yescharacteristic
243#108—22no—
244C4⋊C8—22no—
245C4⋊C8—22no—
246C4⋊C8—22no—
247#104—24no—
248#104—22no—
249#104—22no—
250#103—22no—
251#102—22no—
252#101—22no—
253#100—22no—
254#99—24no—
255#97—21no—
256#97—21no—
257#97—21no—
258#97—22no—
259#97D4×C10312yes—
260C4×C8—21no—
261C4×C8—22no—
262C4×C8D4×C10312yes—
263#41—22no—
264#41—22no—
265#41—22no—
266#41—22no—
267C2×Q8—22no—
268C2×Q8#41×C10312yes—
269C2×D4—22no—
270C2×D4#41×C10312yes—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4C24×C10311yescharacteristic
274Q16—22no—
275SD16—24no—
276D8—22no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—22no—
282M16—22no—
283M16—42no—
284M16—42no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8C2×D4×C10312yes—
293C2×C8C2×D4×C10311yescharacteristic
294C2×C8C2×D4×C10311yescharacteristic
295C2×C8#41×C10312yes—
296C2×C8#41×C10312yes—
297C4⋊C4—24no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C22⋊C4—21no—
303C22⋊C4—22no—
304C22⋊C4#41×C10312yes—
305C42—21no—
306C42—21no—
307C42—22no—
308C42C2×D4×C10312yes—
309C42#41×C10311yescharacteristic
310C42#41×C10311yescharacteristic
311C23—22no—
312C23C2×#41×C10311yescharacteristic
313Q8—22no—
314Q8—22no—
315Q8—82no—
316D4—22no—
317D4—22no—
318D4—42no—
319D4—42no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4C22×D4×C10311yescharacteristic
330C2×C4C2×#41×C10312yes—
331C2×C4C2×#41×C10312yes—
332C2×C4C2×#41×C10311yescharacteristic
333C8—22no—
334C8—41no—
335C8—41no—
336C8—42no—
337C8—42no—
338C8#124×C10311yescharacteristic
339C8#124×C10312yes—
340C8#124×C10311yescharacteristic
341C22—41no—
342C22—42no—
343C22—82no—
344C22#525×C10311yescharacteristic
345C22#529×C10312yes—
346C4—41no—
347C4—41no—
348C4—42no—
349C4—42no—
350C4—42no—
351C4—82no—
352C4#525×C10311yescharacteristic
353C4C2×#124×C10311yescharacteristic
354C4#529×C10312yes—
355C2—21no—
356C2—22no—
357C2—82no—
358C2C103×#239811yescharacteristic
subgroupG/H
centerC4×C103C2×#124
commutator, Frattini, cosocleC22×C4C24×C103
socleC2×C103#2398
prime radical#575×C103C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#2961C2semidirect
3. C103×#2103C2semidirect
4. C103×#2102C2semidirect
5. C103×#2080C2semidirect
8. C103×#2031C2semidirect
9. C103×#1765C2semidirect
10. C103×#1757C2semidirect
11. C103×#1747C2semidirect
175. #23834C103direct (N × H)
180. #2961C2×C103semidirect
182. #2103C2×C103semidirect
183. #2102C2×C103semidirect
184. #2080C2×C103semidirect
187. #2031C2×C103semidirect
188. #1765C2×C103semidirect
189. #1757C2×C103semidirect
190. #1747C2×C103semidirect
191. C103#23834direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#29612
C103×#29552
C103×#21032
C103×#21022
C103×#20802
C103×#20532
C103×#20502
C103×#20312
C103×#17652
C103×#17572
C103×#17472
#23834103