Finite Group Databasebeta

← C103×#10980 #39916255

Subgroups — C103×#10980 #39916255

Order 26368.

1946 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
1C22×#121×C103C211yesmaximal, characteristic
2C22×#99×C103C214yesmaximal, complemented
3C103×C22⋊#95C212yesmaximal, complemented
4C23×D4×C103C411yescharacteristic, complemented
5C23×D4×C103C2212yes—
6C24×C4×C103C2211yescharacteristic
7C2×#121×C103—28no—
8C2×#121×C103—24no—
9C22×C4⋊C4×C103C411yescharacteristic, complemented
10C22×C22⋊C4×C103C412yescomplemented
11C22×C22⋊C4×C103C2214yes—
12C2×#99×C103—28no—
13C2×#99×C103—216no—
14C2×#95×C103—24no—
15C25×C103C2×C412yes—
16C25×C103C2311yescharacteristic
17C22×D4×C103—24no—
18C22×D4×C103—28no—
19C22×D4×C103—24no—
20C22×D4×C103—24no—
21C22×D4×C103—28no—
22C22×D4×C103—22no—
23C22×D4×C103—44no—
24C22×D4×C103D418yes—
25C23×C4×C103—24no—
26C23×C4×C103—24no—
27C23×C4×C103—44no—
28C23×C4×C103C2×C412yes—
29C23×C4×C103C2×C411yescharacteristic
30C23×C4×C103C2×C411yescharacteristic
31C23×C4×C103D414yes—
32#121×C103—232no—
33C2×C4⋊C4×C103—24no—
34C2×C4⋊C4×C103—22no—
35C2×C22⋊C4×C103—24no—
36C2×C22⋊C4×C103—24no—
37C2×C22⋊C4×C103—24no—
38C2×C22⋊C4×C103—28no—
39C2×C22⋊C4×C103—28no—
40C2×C22⋊C4×C103—24no—
41C2×C22⋊C4×C103D418yescomplemented
42#99×C103—232no—
43#95×C103—48no—
44C24×C103—22no—
45C24×C103—22no—
46C24×C103—28no—
47C24×C103—42no—
48C24×C103—42no—
49C24×C103—44no—
50C24×C103—44no—
51C24×C103C22⋊C414yes—
52C24×C103C22×C411yescharacteristic
53C24×C103C2×D412yes—
54C24×C103C2×D414yes—
55C24×C103C2×D414yes—
56C24×C103#4114yes—
57C2×D4×C103—28no—
58C2×D4×C103—28no—
59C2×D4×C103—216no—
60C2×D4×C103—216no—
61C2×D4×C103—28no—
62C2×D4×C103—416no—
63C2×D4×C103—44no—
64C2×D4×C103—44no—
65C2×D4×C103—48no—
66C2×D4×C103—48no—
67C2×D4×C103—44no—
68C2×D4×C103—44no—
69C2×D4×C103—44no—
70C2×D4×C103—44no—
71C22×C4×C103—22no—
72C22×C4×C103—24no—
73C22×C4×C103—22no—
74C22×C4×C103—22no—
75C22×C4×C103—22no—
76C22×C4×C103—28no—
77C22×C4×C103—28no—
78C22×C4×C103—28no—
79C22×C4×C103—28no—
80C22×C4×C103—42no—
81C22×C4×C103—44no—
82C22×C4×C103—416no—
83C22×C4×C103—48no—
84C22×C4×C103—48no—
85C22×C4×C103—44no—
86C22×C4×C103—44no—
87C22×C4×C103C22⋊C414yes—
88C22×C4×C103C22⋊C412yes—
89C22×C4×C103C22⋊C412yes—
90C4⋊C4×C103—28no—
91C22⋊C4×C103—216no—
92C22⋊C4×C103—216no—
93C22⋊C4×C103—48no—
94C23×C103—24no—
95C23×C103—22no—
96C23×C103—24no—
97C23×C103—22no—
98C23×C103—24no—
99C23×C103—28no—
100C23×C103—44no—
101C23×C103—48no—
102C23×C103—44no—
103C23×C103—48no—
104C23×C103—44no—
105C23×C103—44no—
106C23×C103—44no—
107C23×C103—44no—
108C23×C103—44no—
109C23×C103—44no—
110C23×C103—44no—
111C23×C103—44no—
112C23×C103—816no—
113C23×C103C2×C22⋊C412yes—
114C23×C103C2×C22⋊C411yescharacteristic
115C23×C103C4×D414yes—
116C23×C103#12014yes—
117C23×C103#12014yes—
118C23×C103#12114yes—
119C23×C103#12118yes—
120C23×C103#12314yes—
121C23×C103#12412yes—
122C23×C103#12712yes—
123D4×C103—416no—
124D4×C103—416no—
125D4×C103—416no—
126C2×C4×C103—28no—
127C2×C4×C103—22no—
128C2×C4×C103—22no—
129C2×C4×C103—22no—
130C2×C4×C103—24no—
131C2×C4×C103—28no—
132C2×C4×C103—24no—
133C2×C4×C103—416no—
134C2×C4×C103—44no—
135C2×C4×C103—44no—
136C2×C4×C103—44no—
137C2×C4×C103—416no—
138C2×C4×C103—48no—
139C2×C4×C103—88no—
140C2×C4×C103—84no—
141C2×C4×C103—84no—
142C2×C4×C103#9914yescomplemented
143C22×C103—28no—
144C22×C103—24no—
145C22×C103—28no—
146C22×C103—24no—
147C22×C103—22no—
148C22×C103—24no—
149C22×C103—24no—
150C22×C103—22no—
151C22×C103—44no—
152C22×C103—48no—
153C22×C103—44no—
154C22×C103—44no—
155C22×C103—44no—
156C22×C103—44no—
157C22×C103—88no—
158C22×C103—88no—
159C22×C103—88no—
160C22×C103#37911yescharacteristic
161C22×C103#38614yes—
162C22×C103#39012yes—
163C22×C103#39214yes—
164C22×C103#39414yes—
165C22×C103C2×#9912yes—
166C22×C103#41012yes—
167C4×C103—24no—
168C4×C103—44no—
169C4×C103—42no—
170C4×C103—88no—
171#10980C10311yesmaximal, characteristic, direct product factor, Sylow
172C2×C103—24no—
173C2×C103—24no—
174C2×C103—24no—
175C2×C103—84no—
176C2×C103#143811yescharacteristic
177C2×C103#178111yescharacteristic
178C2×C103#178211yescharacteristic
179C2×C103#196414yes—
180C22×#121C2×C10311yescharacteristic
181C22×#99C2×C10314yescomplemented
182C22⋊#95C2×C10312yescomplemented
183C103#1098011yescharacteristic, direct product factor, Sylow
184C23×D4C4×C10311yescharacteristic, complemented
185C23×D4C22×C10312yes—
186C24×C4C22×C10311yescharacteristic
187C2×#121—28no—
188C2×#121—24no—
189C22×C4⋊C4C4×C10311yescharacteristic, complemented
190C22×C22⋊C4C4×C10312yescomplemented
191C22×C22⋊C4C22×C10314yes—
192C2×#99—28no—
193C2×#99—216no—
194C2×#95—24no—
195C25C2×C4×C10312yes—
196C25C23×C10311yescharacteristic
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—24no—
200C22×D4—28no—
201C22×D4—28no—
202C22×D4—22no—
203C22×D4—44no—
204C22×D4D4×C10318yes—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—44no—
208C23×C4C2×C4×C10312yes—
209C23×C4C2×C4×C10311yescharacteristic
210C23×C4C2×C4×C10311yescharacteristic
211C23×C4D4×C10314yes—
212#121—232no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—22no—
215C2×C22⋊C4—24no—
216C2×C22⋊C4—24no—
217C2×C22⋊C4—24no—
218C2×C22⋊C4—28no—
219C2×C22⋊C4—28no—
220C2×C22⋊C4—24no—
221C2×C22⋊C4D4×C10318yescomplemented
222#99—232no—
223#95—48no—
224C24—22no—
225C24—22no—
226C24—28no—
227C24—42no—
228C24—42no—
229C24—44no—
230C24—44no—
231C24C22⋊C4×C10314yes—
232C24C22×C4×C10311yescharacteristic
233C24C2×D4×C10312yes—
234C24C2×D4×C10314yes—
235C24C2×D4×C10314yes—
236C24#41×C10314yes—
237C2×D4—28no—
238C2×D4—28no—
239C2×D4—216no—
240C2×D4—216no—
241C2×D4—28no—
242C2×D4—416no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—48no—
246C2×D4—48no—
247C2×D4—44no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—44no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—42no—
261C22×C4—44no—
262C22×C4—416no—
263C22×C4—48no—
264C22×C4—48no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4C22⋊C4×C10312yes—
268C22×C4C22⋊C4×C10314yes—
269C22×C4C22⋊C4×C10312yes—
270C4⋊C4—28no—
271C22⋊C4—216no—
272C22⋊C4—216no—
273C22⋊C4—48no—
274C23—24no—
275C23—22no—
276C23—24no—
277C23—22no—
278C23—24no—
279C23—28no—
280C23—44no—
281C23—48no—
282C23—44no—
283C23—48no—
284C23—44no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23—44no—
289C23—44no—
290C23—44no—
291C23—44no—
292C23—816no—
293C23C2×C22⋊C4×C10312yes—
294C23C2×C22⋊C4×C10311yescharacteristic
295C23C4×D4×C10314yes—
296C23#120×C10314yes—
297C23#120×C10314yes—
298C23#121×C10314yes—
299C23#121×C10318yes—
300C23#123×C10314yes—
301C23#124×C10312yes—
302C23#127×C10312yes—
303D4—416no—
304D4—416no—
305D4—416no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—416no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—416no—
318C2×C4—48no—
319C2×C4—88no—
320C2×C4—84no—
321C2×C4—84no—
322C2×C4#99×C10314yescomplemented
323C22—28no—
324C22—24no—
325C22—28no—
326C22—24no—
327C22—22no—
328C22—24no—
329C22—24no—
330C22—22no—
331C22—44no—
332C22—48no—
333C22—44no—
334C22—44no—
335C22—44no—
336C22—44no—
337C22—88no—
338C22—88no—
339C22—88no—
340C22#379×C10311yescharacteristic
341C22#386×C10314yes—
342C22#390×C10312yes—
343C22#392×C10314yes—
344C22#394×C10314yes—
345C22C2×#99×C10312yes—
346C22#410×C10312yes—
347C4—24no—
348C4—44no—
349C4—42no—
350C4—88no—
351C2—24no—
352C2—24no—
353C2—24no—
354C2—84no—
355C2C103×#143811yescharacteristic
356C2C103×#178111yescharacteristic
357C2C103×#178211yescharacteristic
358C2C103×#196414yes—
subgroupG/H
center, socleC23×C103C2×C22⋊C4
commutatorC24C22×C4×C103
Frattini, cosocleC25C23×C103
prime radicalC22×#121×C103C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C24×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C103C2semidirect
3. C103×C22⋊#95C2semidirect
4. C23×D4×C103C4semidirect
9. C22×C4⋊C4×C103C4semidirect
10. C22×C22⋊C4×C103C4semidirect
41. C2×C22⋊C4×C103D4semidirect
142. C2×C4×C103#99semidirect
171. #10980C103direct (N × H)
181. C22×#99C2×C103semidirect
182. C22⋊#95C2×C103semidirect
183. C103#10980direct (N × H)
184. C23×D4C4×C103semidirect
189. C22×C4⋊C4C4×C103semidirect
190. C22×C22⋊C4C4×C103semidirect
221. C2×C22⋊C4D4×C103semidirect
322. C2×C4#99×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1032
C22×#99×C1032
C103×C22⋊#952
#10980103