Finite Group Databasebeta

← C103×#9232 #39914507

Subgroups — C103×#9232 #39914507

Order 26368.

566 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3104C211yesmaximal, characteristic
2C42×Q8×C103C211yesmaximal, characteristic
3C103×#1994C211yesmaximal, characteristic
4C103×#1503C211yesmaximal, characteristic
5C103×#1487C211yesmaximal, characteristic
6C103×#1303C211yesmaximal, characteristic
7C103×#1276C211yesmaximal, characteristic
8#533×C103C2211yescharacteristic
9C2×C4×Q8×C103—21no—
10C2×C4×Q8×C103C2211yescharacteristic
11#484×C103—21no—
12#477×C103C412yescomplemented
13#462×C103C412yescomplemented
14#451×C103—21no—
15C4×Q16×C103—22no—
16#431×C103C2211yescharacteristic
17#431×C103C2211yescharacteristic
18#423×C103C2211yescharacteristic
19C4×C4⋊C4×C103—21no—
20C4×C4⋊C4×C103—21no—
21C4×C4⋊C4×C103—22no—
22C4×C4⋊C4×C103C2211yescharacteristic
23C43×C103—21no—
24C43×C103C2211yescharacteristic
25#339×C103—21no—
26#339×C103—21no—
27#328×C103—22no—
28Q8⋊C8×C103—22no—
29C22×Q8×C103D411yescharacteristic
30C2×Q16×C103—22no—
31C2×M16×C103—21no—
32C4⋊Q8×C103C2×C411yescharacteristic
33C4⋊Q8×C103C2×C411yescharacteristic
34#125×C103—21no—
35C22⋊Q8×C103—21no—
36C22⋊Q8×C103—21no—
37C4×Q8×C103—28no—
38C4×Q8×C103—21no—
39C4×Q8×C103—21no—
40C4×Q8×C103—21no—
41C4×Q8×C103—21no—
42C4×Q8×C103C2×C412yes—
43C4×Q8×C103D412yes—
44#117×C103—21no—
45C2×C4⋊C4×C103—22no—
46C2×C4⋊C4×C103—21no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103D411yescharacteristic
49C2×C42×C103—22no—
50C2×C42×C103—21no—
51C2×C42×C103—21no—
52C2×C42×C103—22no—
53C2×C42×C103—21no—
54C2×C42×C103—21no—
55C2×C42×C103D411yescharacteristic
56C2×C42×C103D411yescharacteristic
57C2×C42×C103C2311yescharacteristic
58#107×C103—22no—
59C4⋊C8×C103—21no—
60C4⋊C8×C103—21no—
61C4⋊C8×C103—21no—
62C4⋊C8×C103C2×C412yes—
63#103×C103—22no—
64#103×C103—22no—
65C22⋊C8×C103—21no—
66C22⋊C8×C103—21no—
67C4×C8×C103—21no—
68C4×C8×C103—21no—
69#95×C103—22no—
70#95×C103D412yes—
71C2×Q8×C103—24no—
72C2×Q8×C103—21no—
73C2×Q8×C103—21no—
74C2×Q8×C103—21no—
75C2×Q8×C103C22⋊C412yes—
76C22×C4×C103—21no—
77C22×C4×C103—21no—
78C22×C4×C103—21no—
79C22×C4×C103—21no—
80C22×C4×C103—22no—
81C22×C4×C103C2×D411yescharacteristic
82C22×C4×C103C2×D411yescharacteristic
83C22×C4×C103C2×D411yescharacteristic
84Q16×C103—44no—
85M16×C103—41no—
86M16×C103—41no—
87C2×C8×C103—22no—
88C2×C8×C103—41no—
89C2×C8×C103—41no—
90C4⋊C4×C103—28no—
91C4⋊C4×C103—24no—
92C4⋊C4×C103—22no—
93C4⋊C4×C103—22no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103—21no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103—41no—
100C4⋊C4×C103—41no—
101C4⋊C4×C103C22⋊C412yes—
102C22⋊C4×C103—41no—
103C42×C103—28no—
104C42×C103—24no—
105C42×C103—22no—
106C42×C103—22no—
107C42×C103—21no—
108C42×C103—21no—
109C42×C103—21no—
110C42×C103—42no—
111C42×C103—44no—
112C42×C103—41no—
113C42×C103—41no—
114C42×C103—41no—
115C42×C103Q1612yescomplemented
116C42×C103C22×C411yescharacteristic
117C42×C103C2×D411yescharacteristic
118C42×C103#4111yescharacteristic
119C42×C103#4111yescharacteristic
120C23×C103#12011yescharacteristic
121Q8×C103—24no—
122Q8×C103—22no—
123Q8×C103—42no—
124Q8×C103—81no—
125Q8×C103#10414yes—
126C2×C4×C103—22no—
127C2×C4×C103—24no—
128C2×C4×C103—22no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—22no—
133C2×C4×C103—24no—
134C2×C4×C103—22no—
135C2×C4×C103—41no—
136C2×C4×C103—41no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—41no—
140C2×C4×C103—42no—
141C2×C4×C103—41no—
142C2×C4×C103—41no—
143C2×C4×C103C2×C22⋊C411yescharacteristic
144C2×C4×C103C4×D411yescharacteristic
145C2×C4×C103C4×D411yescharacteristic
146C2×C4×C103#12111yescharacteristic
147C2×C4×C103#12111yescharacteristic
148C2×C4×C103#12311yescharacteristic
149C2×C4×C103C2×Q1611yescharacteristic
150C2×C4×C103#13511yescharacteristic
151C2×C4×C103#13711yescharacteristic
152C2×C4×C103#13711yescharacteristic
153C8×C103—42no—
154C8×C103—81no—
155C8×C103—81no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103#38611yescharacteristic
159C22×C103#45111yescharacteristic
160C22×C103#45211yescharacteristic
161C4×C103—24no—
162C4×C103—24no—
163C4×C103—21no—
164C4×C103—21no—
165C4×C103—21no—
166C4×C103—42no—
167C4×C103—44no—
168C4×C103—42no—
169C4×C103—81no—
170C4×C103—81no—
171C4×C103C2×#10412yes—
172C4×C103C4×Q1611yescharacteristic
173C4×C103#44111yescharacteristic
174C4×C103#46211yescharacteristic
175C4×C103#46411yescharacteristic
176#9232C10311yesmaximal, characteristic, direct product factor, Sylow
177C2×C103—21no—
178C2×C103—21no—
179C2×C103#187811yescharacteristic
180C2×C103#189611yescharacteristic
181C2×C103#190611yescharacteristic
182#3104C2×C10311yescharacteristic
183C42×Q8C2×C10311yescharacteristic
184#1994C2×C10311yescharacteristic
185#1503C2×C10311yescharacteristic
186#1487C2×C10311yescharacteristic
187#1303C2×C10311yescharacteristic
188#1276C2×C10311yescharacteristic
189C103#923211yescharacteristic, direct product factor, Sylow
190#533C22×C10311yescharacteristic
191C2×C4×Q8—21no—
192C2×C4×Q8C22×C10311yescharacteristic
193#484—21no—
194#477C4×C10312yescomplemented
195#462C4×C10312yescomplemented
196#451—21no—
197C4×Q16—22no—
198#431C22×C10311yescharacteristic
199#431C22×C10311yescharacteristic
200#423C22×C10311yescharacteristic
201C4×C4⋊C4—21no—
202C4×C4⋊C4—21no—
203C4×C4⋊C4—22no—
204C4×C4⋊C4C22×C10311yescharacteristic
205C43—21no—
206C43C22×C10311yescharacteristic
207#339—21no—
208#339—21no—
209#328—22no—
210Q8⋊C8—22no—
211C22×Q8D4×C10311yescharacteristic
212C2×Q16—22no—
213C2×M16—21no—
214C4⋊Q8C2×C4×C10311yescharacteristic
215C4⋊Q8C2×C4×C10311yescharacteristic
216#125—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—28no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8C2×C4×C10312yes—
225C4×Q8D4×C10312yes—
226#117—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C10311yescharacteristic
231C2×C42—22no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—22no—
235C2×C42—21no—
236C2×C42—21no—
237C2×C42D4×C10311yescharacteristic
238C2×C42D4×C10311yescharacteristic
239C2×C42C23×C10311yescharacteristic
240#107—22no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8C2×C4×C10312yes—
245#103—22no—
246#103—22no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C4×C8—21no—
250C4×C8—21no—
251#95—22no—
252#95D4×C10312yes—
253C2×Q8—24no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8C22⋊C4×C10312yes—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4C2×D4×C10311yescharacteristic
264C22×C4C2×D4×C10311yescharacteristic
265C22×C4C2×D4×C10311yescharacteristic
266Q16—44no—
267M16—41no—
268M16—41no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C4⋊C4—28no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4C22⋊C4×C10312yes—
284C22⋊C4—41no—
285C42—28no—
286C42—24no—
287C42—22no—
288C42—22no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—42no—
293C42—44no—
294C42—41no—
295C42—41no—
296C42—41no—
297C42Q16×C10312yescomplemented
298C42C22×C4×C10311yescharacteristic
299C42C2×D4×C10311yescharacteristic
300C42#41×C10311yescharacteristic
301C42#41×C10311yescharacteristic
302C23#120×C10311yescharacteristic
303Q8—24no—
304Q8—22no—
305Q8—42no—
306Q8—81no—
307Q8#104×C10314yes—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4C2×C22⋊C4×C10311yescharacteristic
326C2×C4C4×D4×C10311yescharacteristic
327C2×C4C4×D4×C10311yescharacteristic
328C2×C4#121×C10311yescharacteristic
329C2×C4#121×C10311yescharacteristic
330C2×C4#123×C10311yescharacteristic
331C2×C4C2×Q16×C10311yescharacteristic
332C2×C4#135×C10311yescharacteristic
333C2×C4#137×C10311yescharacteristic
334C2×C4#137×C10311yescharacteristic
335C8—42no—
336C8—81no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22#386×C10311yescharacteristic
341C22#451×C10311yescharacteristic
342C22#452×C10311yescharacteristic
343C4—24no—
344C4—24no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—44no—
350C4—42no—
351C4—81no—
352C4—81no—
353C4C2×#104×C10312yes—
354C4C4×Q16×C10311yescharacteristic
355C4#441×C10311yescharacteristic
356C4#462×C10311yescharacteristic
357C4#464×C10311yescharacteristic
358C2—21no—
359C2—21no—
360C2C103×#187811yescharacteristic
361C2C103×#189611yescharacteristic
362C2C103×#190611yescharacteristic
subgroupG/H
centerC2×C4×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#386
prime radicalC23×C103#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
12. #477×C103C4semidirect
13. #462×C103C4semidirect
115. C42×C103Q16semidirect
176. #9232C103direct (N × H)
189. C103#9232direct (N × H)
194. #477C4×C103semidirect
195. #462C4×C103semidirect
297. C42Q16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31042
C42×Q8×C1032
C103×#19942
C103×#15032
C103×#14872
C103×#13032
C103×#12762
#9232103