Finite Group Databasebeta

← C103×#13402 #39918677

Subgroups — C103×#13402 #39918677

Order 26368.

404 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C103C211yesmaximal, characteristic
2C103×#2155C211yesmaximal, characteristic, complemented
3C2×#361×C103C211yesmaximal, characteristic, complemented
4C103×#2140C211yesmaximal, characteristic, complemented
5C103×#2115C211yesmaximal, characteristic, complemented
6C103×#1814C211yesmaximal, characteristic, complemented
7C103×#1388C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C103—21no—
9C22×D8×C103C2211yescharacteristic
10C2×#131×C103C2211yescharacteristic
11C2×M32×C103C2211yescharacteristic
12C2×M32×C103C2211yescharacteristic
13#472×C103—22no—
14#472×C103—22no—
15C2×#108×C103C2211yescharacteristic
16C2×#108×C103C2211yescharacteristic
17#427×C103C2211yescharacteristic
18#421×C103—21no—
19C2×#100×C103—21no—
20#365×C103—22no—
21#361×C103—22no—
22#357×C103—22no—
23#349×C103—22no—
24#344×C103—21no—
25C2×#41×C103D411yescharacteristic
26C22×D4×C103—21no—
27AGL(1,ℤ/8)×C103—24no—
28AGL(1,ℤ/8)×C103—42no—
29C2×SD16×C103—41no—
30C2×D8×C103—21no—
31C2×D8×C103—21no—
32C2×D8×C103—21no—
33C2×D8×C103—21no—
34C2×D8×C103—21no—
35C2×D8×C103—41no—
36C2×D8×C103D412yes—
37#131×C103—21no—
38#131×C103—21no—
39#131×C103—21no—
40#131×C103—21no—
41C2×M16×C103—21no—
42C2×M16×C103—21no—
43C2×M16×C103—21no—
44C2×M16×C103D411yescharacteristic
45C22×C8×C103—21no—
46C22×C8×C103C2311yescharacteristic
47#117×C103—21no—
48M32×C103—21no—
49M32×C103—21no—
50M32×C103—21no—
51M32×C103D412yes—
52C2×C16×C103—21no—
53C2×C16×C103—21no—
54#108×C103—21no—
55#108×C103—21no—
56#108×C103—21no—
57#108×C103D412yes—
58#107×C103—21no—
59#106×C103—21no—
60#104×C103—42no—
61#100×C103—24no—
62C24×C103—41no—
63#41×C103—21no—
64#41×C103—21no—
65#41×C103—21no—
66#41×C103—21no—
67C2×Q8×C103SD1611yescharacteristic
68C2×D4×C103—21no—
69C2×D4×C103—22no—
70C2×D4×C103—41no—
71C2×D4×C103—41no—
72C2×D4×C103—41no—
73C2×D4×C103—41no—
74C2×D4×C103—41no—
75C2×D4×C103SD1611yescharacteristic
76C22×C4×C103—21no—
77C22×C4×C103C2×D411yescharacteristic
78SD16×C103—44no—
79D8×C103—22no—
80D8×C103—22no—
81D8×C103—44no—
82D8×C103—41no—
83D8×C103—41no—
84M16×C103—21no—
85M16×C103—22no—
86M16×C103—21no—
87M16×C103—41no—
88M16×C103—41no—
89M16×C103—41no—
90M16×C103—41no—
91M16×C103—41no—
92C2×C8×C103—21no—
93C2×C8×C103—41no—
94C2×C8×C103—41no—
95C2×C8×C103—41no—
96C2×C8×C103—41no—
97C2×C8×C103C2×D411yescharacteristic
98C2×C8×C103C2×D411yescharacteristic
99C2×C8×C103C2×D411yescharacteristic
100C2×C8×C103#4111yescharacteristic
101C2×C8×C103#4111yescharacteristic
102C2×C8×C103#4111yescharacteristic
103C4⋊C4×C103—41no—
104C22⋊C4×C103—41no—
105C42×C103—41no—
106C16×C103—22no—
107C16×C103—41no—
108C23×C103—21no—
109C23×C103—42no—
110C23×C103—81no—
111C23×C103—81no—
112C23×C103—162no—
113C23×C103#13511yescharacteristic
114Q8×C103—21no—
115Q8×C103—21no—
116D4×C103—21no—
117D4×C103—21no—
118D4×C103—41no—
119D4×C103—41no—
120D4×C103—42no—
121D4×C103—42no—
122D4×C103—81no—
123D4×C103—81no—
124C2×C4×C103—21no—
125C2×C4×C103—41no—
126C2×C4×C103—41no—
127C2×C4×C103—81no—
128C2×C4×C103#12011yescharacteristic
129C2×C4×C103#12111yescharacteristic
130C2×C4×C103#12311yescharacteristic
131C2×C4×C103C2×SD1611yescharacteristic
132C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
134C8×C103—41no—
135C8×C103—42no—
136C8×C103—81no—
137C8×C103#12111yescharacteristic
138C8×C103#12111yescharacteristic
139C8×C103#12311yescharacteristic
140C8×C103#12411yescharacteristic
141C22×C103—41no—
142C22×C103—41no—
143C22×C103—81no—
144C22×C103—82no—
145C22×C103—162no—
146C22×C103—162no—
147C22×C103—162no—
148C22×C103#44911yescharacteristic
149C22×C103#46511yescharacteristic
150C22×C103#48211yescharacteristic
151C4×C103—41no—
152C4×C103—161no—
153C4×C103#39411yescharacteristic
154C4×C103#45011yescharacteristic
155C4×C103#46911yescharacteristic
156C4×C103#48111yescharacteristic
157#13402C10311yesmaximal, characteristic, direct product factor, Sylow
158C2×C103—21no—
159C2×C103—21no—
160C2×C103—21no—
161C2×C103—81no—
162C2×C103—162no—
163C2×C103#203411yescharacteristic
164C2×#472C2×C10311yescharacteristic
165#2155C2×C10311yescharacteristic, complemented
166C2×#361C2×C10311yescharacteristic, complemented
167#2140C2×C10311yescharacteristic, complemented
168#2115C2×C10311yescharacteristic, complemented
169#1814C2×C10311yescharacteristic, complemented
170#1388C2×C10311yescharacteristic, complemented
171C103#1340211yescharacteristic, direct product factor, Sylow
172C2×AGL(1,ℤ/8)—21no—
173C22×D8C22×C10311yescharacteristic
174C2×#131C22×C10311yescharacteristic
175C2×M32C22×C10311yescharacteristic
176C2×M32C22×C10311yescharacteristic
177#472—22no—
178#472—22no—
179C2×#108C22×C10311yescharacteristic
180C2×#108C22×C10311yescharacteristic
181#427C22×C10311yescharacteristic
182#421—21no—
183C2×#100—21no—
184#365—22no—
185#361—22no—
186#357—22no—
187#349—22no—
188#344—21no—
189C2×#41D4×C10311yescharacteristic
190C22×D4—21no—
191AGL(1,ℤ/8)—24no—
192AGL(1,ℤ/8)—42no—
193C2×SD16—41no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—41no—
200C2×D8D4×C10312yes—
201#131—21no—
202#131—21no—
203#131—21no—
204#131—21no—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16D4×C10311yescharacteristic
209C22×C8—21no—
210C22×C8C23×C10311yescharacteristic
211#117—21no—
212M32—21no—
213M32—21no—
214M32—21no—
215M32D4×C10312yes—
216C2×C16—21no—
217C2×C16—21no—
218#108—21no—
219#108—21no—
220#108—21no—
221#108D4×C10312yes—
222#107—21no—
223#106—21no—
224#104—42no—
225#100—24no—
226C24—41no—
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231C2×Q8SD16×C10311yescharacteristic
232C2×D4—21no—
233C2×D4—22no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4SD16×C10311yescharacteristic
240C22×C4—21no—
241C22×C4C2×D4×C10311yescharacteristic
242SD16—44no—
243D8—22no—
244D8—22no—
245D8—44no—
246D8—41no—
247D8—41no—
248M16—21no—
249M16—22no—
250M16—21no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—41no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8C2×D4×C10311yescharacteristic
262C2×C8C2×D4×C10311yescharacteristic
263C2×C8C2×D4×C10311yescharacteristic
264C2×C8#41×C10311yescharacteristic
265C2×C8#41×C10311yescharacteristic
266C2×C8#41×C10311yescharacteristic
267C4⋊C4—41no—
268C22⋊C4—41no—
269C42—41no—
270C16—22no—
271C16—41no—
272C23—21no—
273C23—42no—
274C23—81no—
275C23—81no—
276C23—162no—
277C23#135×C10311yescharacteristic
278Q8—21no—
279Q8—21no—
280D4—21no—
281D4—21no—
282D4—41no—
283D4—41no—
284D4—42no—
285D4—42no—
286D4—81no—
287D4—81no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4#120×C10311yescharacteristic
293C2×C4#121×C10311yescharacteristic
294C2×C4#123×C10311yescharacteristic
295C2×C4C2×SD16×C10311yescharacteristic
296C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
297C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
298C8—41no—
299C8—42no—
300C8—81no—
301C8#121×C10311yescharacteristic
302C8#121×C10311yescharacteristic
303C8#123×C10311yescharacteristic
304C8#124×C10311yescharacteristic
305C22—41no—
306C22—41no—
307C22—81no—
308C22—82no—
309C22—162no—
310C22—162no—
311C22—162no—
312C22#449×C10311yescharacteristic
313C22#465×C10311yescharacteristic
314C22#482×C10311yescharacteristic
315C4—41no—
316C4—161no—
317C4#394×C10311yescharacteristic
318C4#450×C10311yescharacteristic
319C4#469×C10311yescharacteristic
320C4#481×C10311yescharacteristic
321C2—21no—
322C2—21no—
323C2—21no—
324C2—81no—
325C2—162no—
326C2C103×#203411yescharacteristic
subgroupG/H
center, socleC2×C103#2034
commutator, Frattini, cosocleC22×C8C23×C103
prime radicalC2×#472×C103C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C22×C4×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2155C2semidirect
3. C2×#361×C103C2semidirect
4. C103×#2140C2semidirect
5. C103×#2115C2semidirect
6. C103×#1814C2semidirect
7. C103×#1388C2semidirect
157. #13402C103direct (N × H)
165. #2155C2×C103semidirect
166. C2×#361C2×C103semidirect
167. #2140C2×C103semidirect
168. #2115C2×C103semidirect
169. #1814C2×C103semidirect
170. #1388C2×C103semidirect
171. C103#13402direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#472×C1032
C103×#21552
C2×#361×C1032
C103×#21402
C103×#21152
C103×#18142
C103×#13882
#13402103