Finite Group Databasebeta

← C103×#13778 #39919053

Subgroups — C103×#13778 #39919053

Order 26368.

2102 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#380×C103C212yesmaximal
2C2×C4×C22⋊C4×C103C212yesmaximal
3C22×#95×C103C211yesmaximal, characteristic
4C103×#1436C218yesmaximal, complemented
5C103×C22⋊#95C212yesmaximal
6C24×C4×C103C2211yescharacteristic
7C24×C4×C103C2211yescharacteristic
8C24×C4×C103C2211yescharacteristic
9C22×C4⋊C4×C103C2214yes—
10C22×C22⋊C4×C103C2214yes—
11C22×C42×C103C2214yes—
12#380×C103C4116yescomplemented
13C4×C22⋊C4×C103—28no—
14C2×#95×C103C418yescomplemented
15C2×#95×C103C2214yes—
16C2×#95×C103C2214yes—
17C2×#95×C103C2214yes—
18C2×#95×C103C2214yes—
19C2×#95×C103C2214yes—
20C25×C103C2311yescharacteristic
21C23×C4×C103—24no—
22C23×C4×C103—42no—
23C23×C4×C103—42no—
24C23×C4×C103—42no—
25C23×C4×C103—42no—
26C23×C4×C103—42no—
27C23×C4×C103—42no—
28C23×C4×C103C2×C414yes—
29C23×C4×C103C2×C414yes—
30C23×C4×C103C2×C418yes—
31C23×C4×C103C2×C414yes—
32C23×C4×C103D414yes—
33C23×C4×C103Q814yes—
34C23×C4×C103C2312yes—
35C23×C4×C103C2318yes—
36C23×C4×C103C2312yes—
37C23×C4×C103C2312yes—
38C2×C4⋊C4×C103—44no—
39C2×C4⋊C4×C103—44no—
40C2×C4⋊C4×C103C2×C4116yescomplemented
41C2×C22⋊C4×C103—28no—
42C2×C22⋊C4×C103—28no—
43C2×C22⋊C4×C103C2×C4116yes—
44C2×C42×C103—28no—
45C2×C42×C103—44no—
46C2×C42×C103—44no—
47#95×C103—28no—
48#95×C103—44no—
49#95×C103—44no—
50#95×C103C2×C4116yes—
51#95×C103C2×C4116yescomplemented
52C24×C103—22no—
53C24×C103—22no—
54C24×C103—22no—
55C24×C103—22no—
56C24×C103C22×C412yes—
57C24×C103C22×C414yes—
58C24×C103C2×D412yes—
59C24×C103C2×Q812yes—
60C24×C103#4114yes—
61C24×C103C2411yescharacteristic
62C22×C4×C103—24no—
63C22×C4×C103—24no—
64C22×C4×C103—24no—
65C22×C4×C103—24no—
66C22×C4×C103—28no—
67C22×C4×C103—28no—
68C22×C4×C103—28no—
69C22×C4×C103—24no—
70C22×C4×C103—28no—
71C22×C4×C103—28no—
72C22×C4×C103—24no—
73C22×C4×C103—24no—
74C22×C4×C103—28no—
75C22×C4×C103—28no—
76C22×C4×C103—416no—
77C22×C4×C103—44no—
78C22×C4×C103—44no—
79C22×C4×C103—44no—
80C22×C4×C103—44no—
81C22×C4×C103—44no—
82C22×C4×C103—44no—
83C22×C4×C103—48no—
84C22×C4×C103—48no—
85C22×C4×C103—416no—
86C22×C4×C103C42116yescomplemented
87C22×C4×C103C4⋊C4116yescomplemented
88C22×C4×C103C22×C414yes—
89C22×C4×C103C22×C4116yes—
90C22×C4×C103C22×C414yes—
91C22×C4×C103C22×C414yes—
92C22×C4×C103C22×C414yes—
93C22×C4×C103C22×C414yes—
94C22×C4×C103C2×D414yes—
95C22×C4×C103C2×Q814yes—
96C4⋊C4×C103—416no—
97C22⋊C4×C103—232no—
98C42×C103—416no—
99C23×C103—22no—
100C23×C103—22no—
101C23×C103—22no—
102C23×C103—28no—
103C23×C103—22no—
104C23×C103—28no—
105C23×C103—24no—
106C23×C103—24no—
107C23×C103—28no—
108C23×C103—28no—
109C23×C103—24no—
110C23×C103—24no—
111C23×C103C2×C4214yes—
112C23×C103C2×C4⋊C414yes—
113C23×C103#11714yes—
114C23×C103C4×D418yes—
115C23×C103C4×Q818yes—
116C23×C103C23×C411yescharacteristic
117C23×C103C23×C412yes—
118C23×C103C22×D411yescharacteristic
119C23×C103C22×Q811yescharacteristic
120C23×C103C2×#4112yes—
121C23×C103H(5,𝔽2)12yes—
122C23×C103H(5,𝔽2)12yes—
123C23×C103H(5,𝔽2)12yes—
124C23×C1032−1+412yes—
125C2×C4×C103—28no—
126C2×C4×C103—24no—
127C2×C4×C103—24no—
128C2×C4×C103—24no—
129C2×C4×C103—24no—
130C2×C4×C103—28no—
131C2×C4×C103—28no—
132C2×C4×C103—28no—
133C2×C4×C103—24no—
134C2×C4×C103—216no—
135C2×C4×C103—216no—
136C2×C4×C103—24no—
137C2×C4×C103—24no—
138C2×C4×C103—216no—
139C2×C4×C103—416no—
140C2×C4×C103—416no—
141C2×C4×C103—416no—
142C2×C4×C103—48no—
143C2×C4×C103—48no—
144C2×C4×C103—48no—
145C2×C4×C103—48no—
146C2×C4×C103—48no—
147C2×C4×C103C2×C4218yes—
148C2×C4×C103C2×C4⋊C418yes—
149C22×C103—24no—
150C22×C103—24no—
151C22×C103—24no—
152C22×C103—24no—
153C22×C103—216no—
154C22×C103—216no—
155C22×C103—24no—
156C22×C103—24no—
157C22×C103C4×C4⋊C418yes—
158C22×C103C22×C4211yescharacteristic
159C22×C103C22×C4⋊C411yescharacteristic
160C22×C103C2×#11711yescharacteristic
161C22×C103C2×C4×D412yes—
162C22×C103C2×C4×Q812yes—
163C22×C103#51811yescharacteristic
164C22×C103#51811yescharacteristic
165C22×C103#51811yescharacteristic
166C22×C103#51814yes—
167C22×C103#51911yescharacteristic
168C22×C103#52014yes—
169C22×C103#53412yes—
170C22×C103#53712yes—
171C22×C103#53814yes—
172C22×C103#53914yes—
173C22×C103#54312yes—
174C22×C103#54412yes—
175C4×C103—28no—
176C4×C103—28no—
177C4×C103—44no—
178C4×C103—416no—
179#13778C10311yesmaximal, characteristic, direct product factor, Sylow
180C2×C103—28no—
181C2×C103C2×C4×C4⋊C411yescharacteristic
182C2×C103#227311yescharacteristic
183C2×C103#227411yescharacteristic
184C2×C103#231211yescharacteristic
185C2×C103#231311yescharacteristic
186C2×C103#231511yescharacteristic
187C2×C103#231611yescharacteristic
188C2×C103#232514yes—
189C2×C103#232914yes—
190C2×#380C2×C10312yes—
191C2×C4×C22⋊C4C2×C10312yes—
192C22×#95C2×C10311yescharacteristic
193#1436C2×C10318yescomplemented
194C22⋊#95C2×C10312yes—
195C103#1377811yescharacteristic, direct product factor, Sylow
196C24×C4C22×C10311yescharacteristic
197C24×C4C22×C10311yescharacteristic
198C24×C4C22×C10311yescharacteristic
199C22×C4⋊C4C22×C10314yes—
200C22×C22⋊C4C22×C10314yes—
201C22×C42C22×C10314yes—
202#380C4×C103116yescomplemented
203C4×C22⋊C4—28no—
204C2×#95C4×C10318yescomplemented
205C2×#95C22×C10314yes—
206C2×#95C22×C10314yes—
207C2×#95C22×C10314yes—
208C2×#95C22×C10314yes—
209C2×#95C22×C10314yes—
210C25C23×C10311yescharacteristic
211C23×C4—24no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4C2×C4×C10314yes—
219C23×C4C2×C4×C10314yes—
220C23×C4C2×C4×C10318yes—
221C23×C4C2×C4×C10314yes—
222C23×C4D4×C10314yes—
223C23×C4Q8×C10314yes—
224C23×C4C23×C10318yes—
225C23×C4C23×C10312yes—
226C23×C4C23×C10312yes—
227C23×C4C23×C10312yes—
228C2×C4⋊C4—44no—
229C2×C4⋊C4—44no—
230C2×C4⋊C4C2×C4×C103116yescomplemented
231C2×C22⋊C4—28no—
232C2×C22⋊C4—28no—
233C2×C22⋊C4C2×C4×C103116yes—
234C2×C42—28no—
235C2×C42—44no—
236C2×C42—44no—
237#95—28no—
238#95—44no—
239#95—44no—
240#95C2×C4×C103116yes—
241#95C2×C4×C103116yescomplemented
242C24—22no—
243C24—22no—
244C24—22no—
245C24—22no—
246C24C22×C4×C10312yes—
247C24C22×C4×C10314yes—
248C24C2×D4×C10312yes—
249C24C2×Q8×C10312yes—
250C24#41×C10314yes—
251C24C24×C10311yescharacteristic
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—24no—
260C22×C4—28no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—28no—
265C22×C4—28no—
266C22×C4—416no—
267C22×C4—44no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4—48no—
274C22×C4—48no—
275C22×C4—416no—
276C22×C4C42×C103116yescomplemented
277C22×C4C4⋊C4×C103116yescomplemented
278C22×C4C22×C4×C10314yes—
279C22×C4C22×C4×C103116yes—
280C22×C4C22×C4×C10314yes—
281C22×C4C22×C4×C10314yes—
282C22×C4C22×C4×C10314yes—
283C22×C4C22×C4×C10314yes—
284C22×C4C2×D4×C10314yes—
285C22×C4C2×Q8×C10314yes—
286C4⋊C4—416no—
287C22⋊C4—232no—
288C42—416no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—28no—
293C23—22no—
294C23—28no—
295C23—24no—
296C23—24no—
297C23—28no—
298C23—28no—
299C23—24no—
300C23—24no—
301C23C2×C42×C10314yes—
302C23C2×C4⋊C4×C10314yes—
303C23#117×C10314yes—
304C23C4×D4×C10318yes—
305C23C4×Q8×C10318yes—
306C23C23×C4×C10311yescharacteristic
307C23C23×C4×C10312yes—
308C23C22×D4×C10311yescharacteristic
309C23C22×Q8×C10311yescharacteristic
310C23C2×#41×C10312yes—
311C23H(5,𝔽2)×C10312yes—
312C23H(5,𝔽2)×C10312yes—
313C23H(5,𝔽2)×C10312yes—
314C232−1+4×C10312yes—
315C2×C4—28no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—28no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—28no—
322C2×C4—28no—
323C2×C4—24no—
324C2×C4—216no—
325C2×C4—216no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—216no—
329C2×C4—416no—
330C2×C4—416no—
331C2×C4—416no—
332C2×C4—48no—
333C2×C4—48no—
334C2×C4—48no—
335C2×C4—48no—
336C2×C4—48no—
337C2×C4C2×C42×C10318yes—
338C2×C4C2×C4⋊C4×C10318yes—
339C22—24no—
340C22—24no—
341C22—24no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—216no—
346C22—216no—
347C22C4×C4⋊C4×C10318yes—
348C22C22×C42×C10311yescharacteristic
349C22C22×C4⋊C4×C10311yescharacteristic
350C22C2×#117×C10311yescharacteristic
351C22C2×C4×D4×C10312yes—
352C22C2×C4×Q8×C10312yes—
353C22#518×C10311yescharacteristic
354C22#518×C10311yescharacteristic
355C22#518×C10314yes—
356C22#518×C10311yescharacteristic
357C22#519×C10311yescharacteristic
358C22#520×C10314yes—
359C22#534×C10312yes—
360C22#537×C10312yes—
361C22#538×C10314yes—
362C22#539×C10314yes—
363C22#543×C10312yes—
364C22#544×C10312yes—
365C4—28no—
366C4—28no—
367C4—44no—
368C4—416no—
369C2—28no—
370C2C2×C4×C4⋊C4×C10311yescharacteristic
371C2C103×#227311yescharacteristic
372C2C103×#227411yescharacteristic
373C2C103×#231211yescharacteristic
374C2C103×#231311yescharacteristic
375C2C103×#231511yescharacteristic
376C2C103×#231611yescharacteristic
377C2C103×#232514yes—
378C2C103×#232914yes—
subgroupG/H
center, socleC24×C103C24
commutatorC22C22×C42×C103
Frattini, cosocleC24C24×C103
prime radicalC25×C103C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1436C2semidirect
12. #380×C103C4semidirect
14. C2×#95×C103C4semidirect
40. C2×C4⋊C4×C103C2×C4semidirect
51. #95×C103C2×C4semidirect
86. C22×C4×C103C42semidirect
87. C22×C4×C103C4⋊C4semidirect
179. #13778C103direct (N × H)
193. #1436C2×C103semidirect
195. C103#13778direct (N × H)
202. #380C4×C103semidirect
204. C2×#95C4×C103semidirect
230. C2×C4⋊C4C2×C4×C103semidirect
241. #95C2×C4×C103semidirect
276. C22×C4C42×C103semidirect
277. C22×C4C4⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#380×C1032
C2×C4×C22⋊C4×C1032
C22×#95×C1032
C103×#14362
C103×C22⋊#952
#13778103