Finite Group Databasebeta

← C103×#7724 #39912999

Subgroups — C103×#7724 #39912999

Order 26368.

634 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×#2856C211yesmaximal, characteristic
2C103×#1817C211yesmaximal, characteristic, complemented
3C103×#1797C211yesmaximal, characteristic, complemented
4C103×#1270C214yesmaximal, complemented
5C2×#127×C103C411yescharacteristic
6C2×#121×C103—21no—
7C2×#121×C103—21no—
8C2×#121×C103C412yes—
9C22×C42×C103C2211yescharacteristic
10C2×C4⋊C8×C103—21no—
11C2×C22⋊C8×C103—21no—
12C2×C22⋊C8×C103—21no—
13#390×C103—21no—
14#390×C103—21no—
15#390×C103C2212yes—
16#384×C103C411yescharacteristic
17#336×C103—21no—
18#336×C103C2212yes—
19#336×C103C2212yes—
20C22×D4×C103—22no—
21C22×D4×C103—21no—
22C22×D4×C103—21no—
23C22×D4×C103C2×C412yes—
24C23×C4×C103C2×C411yescharacteristic
25C23×C4×C103D411yescharacteristic
26C23×C4×C103D411yescharacteristic
27C22×C8×C103—22no—
28C22×C8×C103—22no—
29#127×C103—42no—
30#121×C103—44no—
31#121×C103—42no—
32#121×C103—42no—
33#121×C103—44no—
34C2×C4⋊C4×C103—21no—
35C2×C4⋊C4×C103—21no—
36C2×C4⋊C4×C103C2×C412yes—
37C2×C22⋊C4×C103—22no—
38C2×C22⋊C4×C103—22no—
39C2×C22⋊C4×C103—22no—
40C2×C42×C103—42no—
41C2×C42×C103C2×C411yescharacteristic
42C2×C42×C103D411yescharacteristic
43C2×C42×C103D411yescharacteristic
44C2×C42×C103C2311yescharacteristic
45C4⋊C8×C103—42no—
46C22⋊C8×C103—42no—
47C22⋊C8×C103—42no—
48C24×C103—22no—
49C24×C103C22⋊C411yescharacteristic
50C2×D4×C103—24no—
51C2×D4×C103—42no—
52C2×D4×C103—42no—
53C2×D4×C103—42no—
54C2×D4×C103—42no—
55C2×D4×C103—42no—
56C2×D4×C103—42no—
57C2×D4×C103—44no—
58C2×D4×C103—44no—
59C2×D4×C103—44no—
60C2×D4×C103—42no—
61C2×D4×C103—42no—
62C22×C4×C103—22no—
63C22×C4×C103—22no—
64C22×C4×C103—22no—
65C22×C4×C103—22no—
66C22×C4×C103—22no—
67C22×C4×C103—41no—
68C22×C4×C103—41no—
69C22×C4×C103—41no—
70C22×C4×C103—41no—
71C22×C4×C103C22⋊C411yescharacteristic
72C22×C4×C103C22⋊C411yescharacteristic
73C22×C4×C103C22⋊C411yescharacteristic
74C22×C4×C103D812yes—
75C22×C4×C103SD1612yes—
76C22×C4×C103C22×C411yescharacteristic
77C22×C4×C103C2×D411yescharacteristic
78C22×C4×C103C2×D411yescharacteristic
79C2×C8×C103—42no—
80C2×C8×C103—42no—
81C2×C8×C103—42no—
82C2×C8×C103—42no—
83C2×C8×C103—42no—
84C2×C8×C103—42no—
85C4⋊C4×C103—42no—
86C4⋊C4×C103—42no—
87C4⋊C4×C103—42no—
88C22⋊C4×C103—44no—
89C22⋊C4×C103—42no—
90C22⋊C4×C103—42no—
91C22⋊C4×C103—44no—
92C42×C103—22no—
93C42×C103—22no—
94C42×C103—41no—
95C42×C103—41no—
96C23×C103—21no—
97C23×C103—21no—
98C23×C103—21no—
99C23×C103—21no—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—42no—
103C23×C103—42no—
104C23×C103—42no—
105C23×C103—42no—
106C23×C103—42no—
107C23×C103—42no—
108C23×C103—42no—
109C23×C103#10212yes—
110C23×C103C2×C22⋊C411yescharacteristic
111D4×C103—84no—
112D4×C103—84no—
113D4×C103—84no—
114D4×C103—88no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—42no—
128C2×C4×C103—42no—
129C2×C4×C103—44no—
130C2×C4×C103—44no—
131C2×C4×C103—42no—
132C2×C4×C103—42no—
133C2×C4×C103—42no—
134C2×C4×C103#9912yes—
135C2×C4×C103#10012yes—
136C2×C4×C103#10212yes—
137C2×C4×C103#13112yes—
138C2×C4×C103C2×D811yescharacteristic
139C2×C4×C103C2×SD1611yescharacteristic
140C2×C4×C103AGL(1,ℤ/8)12yes—
141C8×C103—82no—
142C8×C103—82no—
143C22×C103—22no—
144C22×C103—22no—
145C22×C103—22no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103—41no—
149C22×C103—41no—
150C22×C103—82no—
151C22×C103—82no—
152C22×C103—82no—
153C22×C103—82no—
154C22×C103—82no—
155C22×C103—82no—
156C22×C103—82no—
157C22×C103#40811yescharacteristic
158C22×C103C2×#9911yescharacteristic
159C22×C103C2×#10011yescharacteristic
160C22×C103C2×#10211yescharacteristic
161C22×C103#41811yescharacteristic
162C22×C103#42111yescharacteristic
163C22×C103#42111yescharacteristic
164C4×C103—22no—
165C4×C103—22no—
166C4×C103—22no—
167C4×C103—22no—
168C4×C103—21no—
169C4×C103—22no—
170C4×C103—21no—
171C4×C103—82no—
172#7724C10311yesmaximal, characteristic, direct product factor, Sylow
173C2×C103—42no—
174C2×C103—162no—
175C2×C103#147111yescharacteristic
176C2×C103#148011yescharacteristic
177C2×C103#149611yescharacteristic
178C2×C103#151011yescharacteristic
179C2×C103#151911yescharacteristic
180C2×C103#153611yescharacteristic
181C2×C103#154511yescharacteristic
182#2856C2×C10311yescharacteristic
183#1817C2×C10311yescharacteristic, complemented
184#1797C2×C10311yescharacteristic, complemented
185#1270C2×C10314yescomplemented
186C103#772411yescharacteristic, direct product factor, Sylow
187C2×#127C4×C10311yescharacteristic
188C2×#121—21no—
189C2×#121—21no—
190C2×#121C4×C10312yes—
191C22×C42C22×C10311yescharacteristic
192C2×C4⋊C8—21no—
193C2×C22⋊C8—21no—
194C2×C22⋊C8—21no—
195#390—21no—
196#390—21no—
197#390C22×C10312yes—
198#384C4×C10311yescharacteristic
199#336—21no—
200#336C22×C10312yes—
201#336C22×C10312yes—
202C22×D4—22no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4C2×C4×C10312yes—
206C23×C4C2×C4×C10311yescharacteristic
207C23×C4D4×C10311yescharacteristic
208C23×C4D4×C10311yescharacteristic
209C22×C8—22no—
210C22×C8—22no—
211#127—42no—
212#121—44no—
213#121—42no—
214#121—42no—
215#121—44no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C10312yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C42—42no—
223C2×C42C2×C4×C10311yescharacteristic
224C2×C42D4×C10311yescharacteristic
225C2×C42D4×C10311yescharacteristic
226C2×C42C23×C10311yescharacteristic
227C4⋊C8—42no—
228C22⋊C8—42no—
229C22⋊C8—42no—
230C24—22no—
231C24C22⋊C4×C10311yescharacteristic
232C2×D4—24no—
233C2×D4—42no—
234C2×D4—42no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—44no—
240C2×D4—44no—
241C2×D4—44no—
242C2×D4—42no—
243C2×D4—42no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4C22⋊C4×C10311yescharacteristic
254C22×C4C22⋊C4×C10311yescharacteristic
255C22×C4C22⋊C4×C10311yescharacteristic
256C22×C4D8×C10312yes—
257C22×C4SD16×C10312yes—
258C22×C4C22×C4×C10311yescharacteristic
259C22×C4C2×D4×C10311yescharacteristic
260C22×C4C2×D4×C10311yescharacteristic
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C22⋊C4—44no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—44no—
274C42—22no—
275C42—22no—
276C42—41no—
277C42—41no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—42no—
285C23—42no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23#102×C10312yes—
292C23C2×C22⋊C4×C10311yescharacteristic
293D4—84no—
294D4—84no—
295D4—84no—
296D4—88no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4#99×C10312yes—
317C2×C4#100×C10312yes—
318C2×C4#102×C10312yes—
319C2×C4#131×C10312yes—
320C2×C4C2×D8×C10311yescharacteristic
321C2×C4C2×SD16×C10311yescharacteristic
322C2×C4AGL(1,ℤ/8)×C10312yes—
323C8—82no—
324C8—82no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22#408×C10311yescharacteristic
340C22C2×#99×C10311yescharacteristic
341C22C2×#100×C10311yescharacteristic
342C22C2×#102×C10311yescharacteristic
343C22#418×C10311yescharacteristic
344C22#421×C10311yescharacteristic
345C22#421×C10311yescharacteristic
346C4—22no—
347C4—22no—
348C4—22no—
349C4—22no—
350C4—21no—
351C4—22no—
352C4—21no—
353C4—82no—
354C2—42no—
355C2—162no—
356C2C103×#147111yescharacteristic
357C2C103×#148011yescharacteristic
358C2C103×#149611yescharacteristic
359C2C103×#151011yescharacteristic
360C2C103×#151911yescharacteristic
361C2C103×#153611yescharacteristic
362C2C103×#154511yescharacteristic
subgroupG/H
center, socleC23×C103C2×C22⋊C4
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC103×#2856C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1817C2semidirect
3. C103×#1797C2semidirect
4. C103×#1270C2semidirect
172. #7724C103direct (N × H)
183. #1817C2×C103semidirect
184. #1797C2×C103semidirect
185. #1270C2×C103semidirect
186. C103#7724direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#28562
C103×#18172
C103×#17972
C103×#12702
#7724103