Finite Group Databasebeta

← C103×#16297 #39921572

Subgroups — C103×#16297 #39921572

Order 26368.

2894 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×#393×C103C213yesmaximal, complemented
2C2×#379×C103C213yesmaximal
3C103×#1439C213yesmaximal, complemented
4C103×#1439C216yesmaximal, complemented
5C26×C103C2211yescharacteristic
6C23×Q8×C103C2211yescharacteristic, complemented
7C22×C4⋊C4×C103C2213yescomplemented
8C22×C22⋊C4×C103C2216yes—
9C22×C22⋊C4×C103C2216yes—
10C22×C22⋊C4×C103C2213yes—
11C22×C22⋊C4×C103C2213yes—
12#393×C103—212no—
13#379×C103—212no—
14C2×#95×C103C2213yescomplemented
15C2×#95×C103C2216yescomplemented
16C2×#95×C103C2212yescomplemented
17C2×#95×C103C2211yescharacteristic, complemented
18C25×C103—26no—
19C25×C103—26no—
20C25×C103—43no—
21C25×C103—43no—
22C25×C103—41no—
23C25×C103—41no—
24C25×C103Q814yescomplemented
25C25×C103C2313yes—
26C22×Q8×C103—26no—
27C22×Q8×C103—43no—
28C22×Q8×C103—41no—
29C23×C4×C103C2316yes—
30C23×C4×C103C2313yes—
31C23×C4×C103C2313yes—
32C2×C4⋊C4×C103—43no—
33C2×C4⋊C4×C103—46no—
34C2×C22⋊C4×C103—26no—
35C2×C22⋊C4×C103—212no—
36C2×C22⋊C4×C103—212no—
37C2×C22⋊C4×C103—212no—
38C2×C22⋊C4×C103—212no—
39C2×C22⋊C4×C103—43no—
40C2×C22⋊C4×C103—43no—
41C2×C22⋊C4×C103—46no—
42C2×C22⋊C4×C103—46no—
43C2×C22⋊C4×C103—43no—
44C2×C22⋊C4×C103—43no—
45C2×C22⋊C4×C103D4112yes—
46#95×C103—212no—
47#95×C103—26no—
48#95×C103—41no—
49#95×C103—42no—
50C24×C103—26no—
51C24×C103—26no—
52C24×C103—23no—
53C24×C103—23no—
54C24×C103—23no—
55C24×C103—23no—
56C24×C103—26no—
57C24×C103—26no—
58C24×C103—224no—
59C24×C103—412no—
60C24×C103—44no—
61C24×C103—412no—
62C24×C103—424no—
63C24×C103—412no—
64C24×C103—412no—
65C24×C103—412no—
66C24×C103—412no—
67C24×C103—412no—
68C24×C103—412no—
69C24×C103—44no—
70C24×C103C2×D416yes—
71C24×C103C2×Q816yes—
72C24×C103#4116yes—
73C24×C103C2411yescharacteristic
74C2×Q8×C103—412no—
75C2×Q8×C103—412no—
76C2×Q8×C103—44no—
77C22×C4×C103—26no—
78C22×C4×C103—26no—
79C22×C4×C103—23no—
80C22×C4×C103—23no—
81C22×C4×C103—26no—
82C22×C4×C103—23no—
83C22×C4×C103—23no—
84C22×C4×C103—26no—
85C22×C4×C103—26no—
86C22×C4×C103—26no—
87C22×C4×C103—26no—
88C22×C4×C103—26no—
89C22×C4×C103—26no—
90C22×C4×C103—26no—
91C22×C4×C103—26no—
92C22×C4×C103C2×D416yes—
93C22×C4×C103C2×D416yes—
94C4⋊C4×C103—412no—
95C22⋊C4×C103—412no—
96C22⋊C4×C103—424no—
97C22⋊C4×C103—424no—
98C22⋊C4×C103—412no—
99C23×C103—212no—
100C23×C103—26no—
101C23×C103—26no—
102C23×C103—26no—
103C23×C103—26no—
104C23×C103—26no—
105C23×C103—26no—
106C23×C103—212no—
107C23×C103—212no—
108C23×C103—212no—
109C23×C103—212no—
110C23×C103—212no—
111C23×C103—448no—
112C23×C103—448no—
113C23×C103—416no—
114C23×C103—448no—
115C23×C103—416no—
116C23×C103—448no—
117C23×C103—416no—
118C23×C103—46no—
119C23×C103—46no—
120C23×C103—46no—
121C23×C103—46no—
122C23×C103—43no—
123C23×C103—46no—
124C23×C103—43no—
125C23×C103—46no—
126C23×C103—43no—
127C23×C103—43no—
128C23×C103C22⋊Q8112yes—
129C23×C103C22×D413yes—
130C23×C103C22×Q811yescharacteristic
131C23×C103C2×#4113yes—
132C23×C103H(5,𝔽2)11yescharacteristic
133C23×C103H(5,𝔽2)13yes—
134C23×C103H(5,𝔽2)11yescharacteristic
135C23×C103H(5,𝔽2)13yes—
136Q8×C103—416no—
137C2×C4×C103—26no—
138C2×C4×C103—26no—
139C2×C4×C103—212no—
140C2×C4×C103—212no—
141C2×C4×C103—46no—
142C2×C4×C103—46no—
143C2×C4×C103—43no—
144C2×C4×C103—43no—
145C2×C4×C103—43no—
146C2×C4×C103—43no—
147C2×C4×C103—46no—
148C2×C4×C103—46no—
149C2×C4×C103—46no—
150C2×C4×C103—46no—
151C2×C4×C103—46no—
152C2×C4×C103—46no—
153C2×C4×C103—46no—
154C22×C103—212no—
155C22×C103—224no—
156C22×C103—464no—
157C22×C103—46no—
158C22×C103—412no—
159C22×C103—412no—
160C22×C103—46no—
161C22×C103—46no—
162C22×C103—46no—
163C22×C103—412no—
164C22×C103—46no—
165C22×C103—46no—
166C22×C103C2×C22⋊Q813yes—
167C22×C103#53413yes—
168C22×C103#53513yes—
169C22×C103#53813yes—
170C22×C103#53813yes—
171C22×C103#54313yes—
172C22×C103#54311yescharacteristic
173C22×C103D4213yes—
174C22×C103#54616yes—
175C22×C103#55113yes—
176C22×C103H(3,𝔽4)13yes—
177C22×C103H(3,𝔽4)11yescharacteristic
178C4×C103—46no—
179C4×C103—46no—
180C4×C103—86no—
181#16297C10311yesmaximal, characteristic, direct product factor, Sylow
182C2×C103—412no—
183C2×C103#243713yes—
184C2×C103#262613yes—
185C2×C103#267013yes—
186C2×C103#267911yescharacteristic
187C2×C103#268413yes—
188C2×C103#273611yescharacteristic
189C2×C103#284011yescharacteristic
190C2×#393C2×C10313yescomplemented
191C2×#379C2×C10313yes—
192#1439C2×C10316yescomplemented
193#1439C2×C10313yescomplemented
194C103#1629711yescharacteristic, direct product factor, Sylow
195C26C22×C10311yescharacteristic
196C23×Q8C22×C10311yescharacteristic, complemented
197C22×C4⋊C4C22×C10313yescomplemented
198C22×C22⋊C4C22×C10316yes—
199C22×C22⋊C4C22×C10316yes—
200C22×C22⋊C4C22×C10313yes—
201C22×C22⋊C4C22×C10313yes—
202#393—212no—
203#379—212no—
204C2×#95C22×C10313yescomplemented
205C2×#95C22×C10316yescomplemented
206C2×#95C22×C10312yescomplemented
207C2×#95C22×C10311yescharacteristic, complemented
208C25—26no—
209C25—26no—
210C25—43no—
211C25—43no—
212C25—41no—
213C25—41no—
214C25Q8×C10314yescomplemented
215C25C23×C10313yes—
216C22×Q8—26no—
217C22×Q8—43no—
218C22×Q8—41no—
219C23×C4C23×C10316yes—
220C23×C4C23×C10313yes—
221C23×C4C23×C10313yes—
222C2×C4⋊C4—43no—
223C2×C4⋊C4—46no—
224C2×C22⋊C4—26no—
225C2×C22⋊C4—212no—
226C2×C22⋊C4—212no—
227C2×C22⋊C4—212no—
228C2×C22⋊C4—212no—
229C2×C22⋊C4—43no—
230C2×C22⋊C4—43no—
231C2×C22⋊C4—46no—
232C2×C22⋊C4—46no—
233C2×C22⋊C4—43no—
234C2×C22⋊C4—43no—
235C2×C22⋊C4D4×C103112yes—
236#95—212no—
237#95—26no—
238#95—41no—
239#95—42no—
240C24—26no—
241C24—26no—
242C24—23no—
243C24—23no—
244C24—23no—
245C24—23no—
246C24—26no—
247C24—26no—
248C24—224no—
249C24—412no—
250C24—44no—
251C24—412no—
252C24—424no—
253C24—412no—
254C24—412no—
255C24—412no—
256C24—412no—
257C24—412no—
258C24—44no—
259C24—412no—
260C24C2×D4×C10316yes—
261C24C2×Q8×C10316yes—
262C24#41×C10316yes—
263C24C24×C10311yescharacteristic
264C2×Q8—412no—
265C2×Q8—412no—
266C2×Q8—44no—
267C22×C4—26no—
268C22×C4—26no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—26no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—26no—
275C22×C4—26no—
276C22×C4—26no—
277C22×C4—26no—
278C22×C4—26no—
279C22×C4—26no—
280C22×C4—26no—
281C22×C4—26no—
282C22×C4C2×D4×C10316yes—
283C22×C4C2×D4×C10316yes—
284C4⋊C4—412no—
285C22⋊C4—412no—
286C22⋊C4—424no—
287C22⋊C4—424no—
288C22⋊C4—412no—
289C23—212no—
290C23—26no—
291C23—26no—
292C23—26no—
293C23—26no—
294C23—26no—
295C23—26no—
296C23—212no—
297C23—212no—
298C23—212no—
299C23—212no—
300C23—212no—
301C23—448no—
302C23—448no—
303C23—416no—
304C23—416no—
305C23—448no—
306C23—416no—
307C23—448no—
308C23—46no—
309C23—46no—
310C23—46no—
311C23—46no—
312C23—43no—
313C23—46no—
314C23—43no—
315C23—43no—
316C23—46no—
317C23—43no—
318C23C22⋊Q8×C103112yes—
319C23C22×D4×C10313yes—
320C23C22×Q8×C10311yescharacteristic
321C23C2×#41×C10313yes—
322C23H(5,𝔽2)×C10311yescharacteristic
323C23H(5,𝔽2)×C10313yes—
324C23H(5,𝔽2)×C10311yescharacteristic
325C23H(5,𝔽2)×C10313yes—
326Q8—416no—
327C2×C4—26no—
328C2×C4—26no—
329C2×C4—212no—
330C2×C4—212no—
331C2×C4—46no—
332C2×C4—46no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—46no—
338C2×C4—46no—
339C2×C4—46no—
340C2×C4—46no—
341C2×C4—46no—
342C2×C4—46no—
343C2×C4—46no—
344C22—212no—
345C22—224no—
346C22—464no—
347C22—46no—
348C22—46no—
349C22—412no—
350C22—412no—
351C22—46no—
352C22—46no—
353C22—46no—
354C22—412no—
355C22—46no—
356C22C2×C22⋊Q8×C10313yes—
357C22#534×C10313yes—
358C22#535×C10313yes—
359C22#538×C10313yes—
360C22#538×C10313yes—
361C22#543×C10313yes—
362C22#543×C10311yescharacteristic
363C22D42×C10313yes—
364C22#546×C10316yes—
365C22#551×C10313yes—
366C22H(3,𝔽4)×C10311yescharacteristic
367C22H(3,𝔽4)×C10313yes—
368C4—46no—
369C4—46no—
370C4—86no—
371C2—412no—
372C2C103×#243713yes—
373C2C103×#262613yes—
374C2C103×#267013yes—
375C2C103×#267911yescharacteristic
376C2C103×#268413yes—
377C2C103×#273611yescharacteristic
378C2C103×#284011yescharacteristic
subgroupG/H
center, socleC24×C103C24
commutator, Frattini, cosocleC24C24×C103
prime radicalC26×C103C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#393×C103C2semidirect
3. C103×#1439C2semidirect
4. C103×#1439C2semidirect
6. C23×Q8×C103C22semidirect
7. C22×C4⋊C4×C103C22semidirect
14. C2×#95×C103C22semidirect
15. C2×#95×C103C22semidirect
16. C2×#95×C103C22semidirect
17. C2×#95×C103C22semidirect
24. C25×C103Q8semidirect
181. #16297C103direct (N × H)
190. C2×#393C2×C103semidirect
192. #1439C2×C103semidirect
193. #1439C2×C103semidirect
194. C103#16297direct (N × H)
196. C23×Q8C22×C103semidirect
197. C22×C4⋊C4C22×C103semidirect
204. C2×#95C22×C103semidirect
205. C2×#95C22×C103semidirect
206. C2×#95C22×C103semidirect
207. C2×#95C22×C103semidirect
214. C25Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1032
C2×#379×C1032
C103×#14392
#16297103