Finite Group Databasebeta

← C103×#9744 #39915019

Subgroups — C103×#9744 #39915019

Order 26368.

574 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#492×C103C211yesmaximal, characteristic
2C103×#1988C211yesmaximal, characteristic, complemented
3C103×#1982C211yesmaximal, characteristic
4C103×#1770C211yesmaximal, characteristic, complemented
5C2×#335×C103C211yesmaximal, characteristic, complemented
6C2×#332×C103C211yesmaximal, characteristic, complemented
7C2×#331×C103C211yesmaximal, characteristic
8C22×SD16×C103—21no—
9C22×SD16×C103—21no—
10C2×C4⋊Q8×C103C2211yescharacteristic
11C2×#127×C103C2211yescharacteristic
12#492×C103—22no—
13#492×C103C414yescomplemented
14C2×C4⋊C8×C103C2211yescharacteristic
15C2×C4⋊C8×C103C2211yescharacteristic
16C2×C4⋊C8×C103C2211yescharacteristic
17C2×#102×C103—22no—
18C2×#97×C103—21no—
19C2×C4×C8×C103C2211yescharacteristic
20C4×C4⋊C4×C103C2211yescharacteristic
21#340×C103—22no—
22#336×C103—21no—
23#335×C103—22no—
24#332×C103—22no—
25#331×C103—22no—
26C22×Q8×C103—21no—
27C22×D4×C103—21no—
28C22×D4×C103—21no—
29C22×D4×C103—21no—
30C2×SD16×C103—24no—
31C2×SD16×C103—24no—
32C2×SD16×C103—42no—
33C2×SD16×C103—42no—
34C2×SD16×C103—42no—
35C2×SD16×C103—42no—
36C22×C8×C103—21no—
37C22×C8×C103—21no—
38C22×C8×C103—21no—
39C22×C8×C103D411yescharacteristic
40C22×C8×C103D411yescharacteristic
41C4⋊Q8×C103—21no—
42C4⋊Q8×C103—21no—
43C4⋊Q8×C103—21no—
44C4⋊Q8×C103C2×C412yes—
45#127×C103—21no—
46#127×C103—21no—
47#127×C103—21no—
48#127×C103C2×C412yes—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103D412yes—
52C2×C42×C103—21no—
53C2×C42×C103C2311yescharacteristic
54C4⋊C8×C103—21no—
55C4⋊C8×C103—21no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103—21no—
59C4⋊C8×C103D412yes—
60#102×C103—44no—
61#97×C103—42no—
62C4×C8×C103C2×C412yes—
63C4×C8×C103D412yes—
64#95×C103—21no—
65C24×C103—41no—
66C2×Q8×C103—22no—
67C2×Q8×C103—41no—
68C2×Q8×C103—41no—
69C2×Q8×C103—41no—
70C2×Q8×C103—41no—
71C2×Q8×C103—41no—
72C2×D4×C103—22no—
73C2×D4×C103—22no—
74C2×D4×C103—22no—
75C2×D4×C103—41no—
76C2×D4×C103—41no—
77C2×D4×C103—41no—
78C2×D4×C103—41no—
79C2×D4×C103—41no—
80C2×D4×C103—42no—
81C2×D4×C103—41no—
82C2×D4×C103—41no—
83C2×D4×C103—42no—
84C2×D4×C103—82no—
85C22×C4×C103—22no—
86C22×C4×C103—41no—
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103#4111yescharacteristic
90SD16×C103—48no—
91SD16×C103—48no—
92C2×C8×C103—21no—
93C2×C8×C103—21no—
94C2×C8×C103—22no—
95C2×C8×C103—41no—
96C2×C8×C103—41no—
97C2×C8×C103—41no—
98C2×C8×C103—41no—
99C2×C8×C103—42no—
100C2×C8×C103—42no—
101C2×C8×C103C22⋊C412yes—
102C2×C8×C103C22⋊C412yes—
103C2×C8×C103D812yes—
104C2×C8×C103SD1612yes—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—41no—
111C42×C103—41no—
112C42×C103—41no—
113C42×C103C22×C411yescharacteristic
114C42×C103C2×D411yescharacteristic
115C42×C103C2×D411yescharacteristic
116C42×C103#4111yescharacteristic
117C23×C103—42no—
118C23×C103—81no—
119C23×C103—81no—
120C23×C103—82no—
121C23×C103—82no—
122C23×C103#12111yescharacteristic
123Q8×C103—42no—
124Q8×C103—42no—
125Q8×C103—81no—
126Q8×C103—81no—
127D4×C103—42no—
128D4×C103—42no—
129D4×C103—44no—
130D4×C103—82no—
131D4×C103—82no—
132D4×C103—81no—
133D4×C103—81no—
134D4×C103—81no—
135D4×C103—81no—
136C2×C4×C103—22no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103—81no—
142C2×C4×C103—81no—
143C2×C4×C103C2×C22⋊C411yescharacteristic
144C2×C4×C103C4×D411yescharacteristic
145C2×C4×C103C4×D411yescharacteristic
146C2×C4×C103#12111yescharacteristic
147C2×C4×C103#12411yescharacteristic
148C2×C4×C103#12711yescharacteristic
149C2×C4×C103C2×D811yescharacteristic
150C2×C4×C103C2×SD1611yescharacteristic
151C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C103AGL(1,ℤ/8)12yes—
154C2×C4×C103#13712yes—
155C8×C103—22no—
156C8×C103—42no—
157C8×C103—81no—
158C8×C103—81no—
159C8×C103#10214yescomplemented
160C22×C103—82no—
161C22×C103—82no—
162C22×C103—82no—
163C22×C103—162no—
164C22×C103—162no—
165C22×C103#39011yescharacteristic
166C22×C103#45911yescharacteristic
167C22×C103#46011yescharacteristic
168C22×C103#46812yes—
169C22×C103#47112yes—
170C4×C103—21no—
171C4×C103—21no—
172C4×C103—82no—
173C4×C103—82no—
174C4×C103C2×#10211yescharacteristic
175C4×C103#41811yescharacteristic
176C4×C103#44012yes—
177C4×C103#45911yescharacteristic
178C4×C103#46011yescharacteristic
179C4×C103#49611yescharacteristic
180C4×C103#49711yescharacteristic
181#9744C10311yesmaximal, characteristic, direct product factor, Sylow
182C2×C103—162no—
183C2×C103#168512yes—
184C2×C103#168612yes—
185C2×C103#197311yescharacteristic
186C2×C103#197711yescharacteristic
187C2×C103#198211yescharacteristic
188C2×#492C2×C10311yescharacteristic
189#1988C2×C10311yescharacteristic, complemented
190#1982C2×C10311yescharacteristic
191#1770C2×C10311yescharacteristic, complemented
192C2×#335C2×C10311yescharacteristic, complemented
193C2×#332C2×C10311yescharacteristic, complemented
194C2×#331C2×C10311yescharacteristic
195C103#974411yescharacteristic, direct product factor, Sylow
196C22×SD16—21no—
197C22×SD16—21no—
198C2×C4⋊Q8C22×C10311yescharacteristic
199C2×#127C22×C10311yescharacteristic
200#492—22no—
201#492C4×C10314yescomplemented
202C2×C4⋊C8C22×C10311yescharacteristic
203C2×C4⋊C8C22×C10311yescharacteristic
204C2×C4⋊C8C22×C10311yescharacteristic
205C2×#102—22no—
206C2×#97—21no—
207C2×C4×C8C22×C10311yescharacteristic
208C4×C4⋊C4C22×C10311yescharacteristic
209#340—22no—
210#336—21no—
211#335—22no—
212#332—22no—
213#331—22no—
214C22×Q8—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C2×SD16—24no—
219C2×SD16—24no—
220C2×SD16—42no—
221C2×SD16—42no—
222C2×SD16—42no—
223C2×SD16—42no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8D4×C10311yescharacteristic
228C22×C8D4×C10311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C2×C4×C10312yes—
233#127—21no—
234#127—21no—
235#127—21no—
236#127C2×C4×C10312yes—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C10312yes—
240C2×C42—21no—
241C2×C42C23×C10311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C10312yes—
248#102—44no—
249#97—42no—
250C4×C8C2×C4×C10312yes—
251C4×C8D4×C10312yes—
252#95—21no—
253C24—41no—
254C2×Q8—22no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—82no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4C2×D4×C10311yescharacteristic
276C22×C4C2×D4×C10311yescharacteristic
277C22×C4#41×C10311yescharacteristic
278SD16—48no—
279SD16—48no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8C22⋊C4×C10312yes—
290C2×C8C22⋊C4×C10312yes—
291C2×C8D8×C10312yes—
292C2×C8SD16×C10312yes—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C42—41no—
300C42—41no—
301C42C22×C4×C10311yescharacteristic
302C42C2×D4×C10311yescharacteristic
303C42C2×D4×C10311yescharacteristic
304C42#41×C10311yescharacteristic
305C23—42no—
306C23—81no—
307C23—81no—
308C23—82no—
309C23—82no—
310C23#121×C10311yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—81no—
314Q8—81no—
315D4—42no—
316D4—42no—
317D4—44no—
318D4—82no—
319D4—82no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4C2×C22⋊C4×C10311yescharacteristic
332C2×C4C4×D4×C10311yescharacteristic
333C2×C4C4×D4×C10311yescharacteristic
334C2×C4#121×C10311yescharacteristic
335C2×C4#124×C10311yescharacteristic
336C2×C4#127×C10311yescharacteristic
337C2×C4C2×D8×C10311yescharacteristic
338C2×C4C2×SD16×C10311yescharacteristic
339C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
340C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
341C2×C4AGL(1,ℤ/8)×C10312yes—
342C2×C4#137×C10312yes—
343C8—22no—
344C8—42no—
345C8—81no—
346C8—81no—
347C8#102×C10314yescomplemented
348C22—82no—
349C22—82no—
350C22—82no—
351C22—162no—
352C22—162no—
353C22#390×C10311yescharacteristic
354C22#459×C10311yescharacteristic
355C22#460×C10311yescharacteristic
356C22#468×C10312yes—
357C22#471×C10312yes—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—82no—
362C4C2×#102×C10311yescharacteristic
363C4#418×C10311yescharacteristic
364C4#440×C10312yes—
365C4#459×C10311yescharacteristic
366C4#460×C10311yescharacteristic
367C4#496×C10311yescharacteristic
368C4#497×C10311yescharacteristic
369C2—162no—
370C2C103×#168512yes—
371C2C103×#168612yes—
372C2C103×#197311yescharacteristic
373C2C103×#197711yescharacteristic
374C2C103×#198211yescharacteristic
subgroupG/H
center, socleC23×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC2×#127×C103C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1988C2semidirect
4. C103×#1770C2semidirect
5. C2×#335×C103C2semidirect
6. C2×#332×C103C2semidirect
13. #492×C103C4semidirect
159. C8×C103#102semidirect
181. #9744C103direct (N × H)
189. #1988C2×C103semidirect
191. #1770C2×C103semidirect
192. C2×#335C2×C103semidirect
193. C2×#332C2×C103semidirect
195. C103#9744direct (N × H)
201. #492C4×C103semidirect
347. C8#102×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C1032
C103×#19882
C103×#19822
C103×#17702
C2×#335×C1032
C2×#332×C1032
C2×#331×C1032
#9744103