Finite Group Databasebeta

← C103×#13399 #39918674

Subgroups — C103×#13399 #39918674

Order 26368.

406 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C103C211yesmaximal, characteristic
2C2×#365×C103C211yesmaximal, characteristic, complemented
3C2×#362×C103C211yesmaximal, characteristic, complemented
4C2×#362×C103C211yesmaximal, characteristic, complemented
5C2×#349×C103C211yesmaximal, characteristic
6C103×#1811C211yesmaximal, characteristic
7C103×#1383C211yesmaximal, characteristic, complemented
8C22×Q16×C103C2211yescharacteristic
9C22×M16×C103C2211yescharacteristic
10C2×C22⋊Q8×C103—21no—
11C2×M32×C103C2211yescharacteristic
12C2×M32×C103C2211yescharacteristic
13#470×C103—22no—
14#470×C103—22no—
15C2×#108×C103C2211yescharacteristic
16C2×#108×C103C2211yescharacteristic
17C2×#106×C103C2211yescharacteristic
18C2×#103×C103—21no—
19#407×C103—21no—
20#365×C103—22no—
21#362×C103—22no—
22#362×C103—22no—
23#349×C103—22no—
24#341×C103—21no—
25C22×Q8×C103—21no—
26C23×C4×C103D411yescharacteristic
27C2×Q16×C103—21no—
28C2×Q16×C103—21no—
29C2×Q16×C103—21no—
30C2×Q16×C103—21no—
31C2×Q16×C103—21no—
32C2×Q16×C103D412yes—
33C2×M16×C103—21no—
34C2×M16×C103—21no—
35C2×M16×C103—21no—
36C2×M16×C103—21no—
37C2×M16×C103—21no—
38C2×M16×C103—21no—
39C2×M16×C103—21no—
40C2×M16×C103—21no—
41C22×C8×C103D411yescharacteristic
42C22×C8×C103C2311yescharacteristic
43C22⋊Q8×C103—24no—
44C22⋊Q8×C103—42no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103—41no—
47C2×C22⋊C4×C103—41no—
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×C103—21no—
58#106×C103—21no—
59#106×C103D412yes—
60#103×C103—24no—
61C22⋊C8×C103—42no—
62C24×C103SD1611yescharacteristic
63C2×Q8×C103—22no—
64C2×Q8×C103—41no—
65C2×Q8×C103—41no—
66C2×Q8×C103—41no—
67C2×Q8×C103—41no—
68C2×Q8×C103—41no—
69C22×C4×C103—21no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103—21no—
74C22×C4×C103—21no—
75C22×C4×C103—41no—
76C22×C4×C103—41no—
77C22×C4×C103SD1611yescharacteristic
78C22×C4×C103C2×D411yescharacteristic
79Q16×C103—22no—
80Q16×C103—22no—
81Q16×C103—41no—
82Q16×C103—41no—
83M16×C103—41no—
84M16×C103—41no—
85M16×C103—41no—
86M16×C103—41no—
87M16×C103—41no—
88M16×C103—41no—
89M16×C103—41no—
90M16×C103—41no—
91C2×C8×C103—21no—
92C2×C8×C103—21no—
93C2×C8×C103—21no—
94C2×C8×C103—41no—
95C2×C8×C103—41no—
96C2×C8×C103C2×D411yescharacteristic
97C2×C8×C103C2×D411yescharacteristic
98C2×C8×C103C2×D411yescharacteristic
99C2×C8×C103#4111yescharacteristic
100C2×C8×C103#4111yescharacteristic
101C2×C8×C103#4111yescharacteristic
102C4⋊C4×C103—22no—
103C4⋊C4×C103—44no—
104C4⋊C4×C103—41no—
105C22⋊C4×C103—44no—
106C16×C103—22no—
107C16×C103—41no—
108C23×C103—21no—
109C23×C103—21no—
110C23×C103—21no—
111C23×C103—42no—
112C23×C103C2×SD1611yescharacteristic
113Q8×C103—42no—
114Q8×C103—42no—
115Q8×C103—81no—
116Q8×C103—81no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—41no—
121C2×C4×C103—41no—
122C2×C4×C103—41no—
123C2×C4×C103—41no—
124C2×C4×C103—42no—
125C2×C4×C103—42no—
126C2×C4×C103—82no—
127C2×C4×C103—81no—
128C2×C4×C103—81no—
129C2×C4×C103#12011yescharacteristic
130C2×C4×C103#12111yescharacteristic
131C2×C4×C103#12311yescharacteristic
132C2×C4×C103#13511yescharacteristic
133C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
135C8×C103—41no—
136C8×C103—81no—
137C8×C103—81no—
138C8×C103#12111yescharacteristic
139C8×C103#12111yescharacteristic
140C8×C103#12311yescharacteristic
141C8×C103#12411yescharacteristic
142C22×C103—22no—
143C22×C103—42no—
144C22×C103—42no—
145C22×C103—41no—
146C22×C103—81no—
147C22×C103#45011yescharacteristic
148C22×C103#46511yescharacteristic
149C22×C103#48111yescharacteristic
150C4×C103—41no—
151C4×C103—82no—
152C4×C103—82no—
153C4×C103#39411yescharacteristic
154C4×C103#44911yescharacteristic
155C4×C103#46911yescharacteristic
156C4×C103#48211yescharacteristic
157#13399C10311yesmaximal, characteristic, direct product factor, Sylow
158C2×C103—21no—
159C2×C103—21no—
160C2×C103—81no—
161C2×C103#203411yescharacteristic
162C2×C103#223912yes—
163C2×#470C2×C10311yescharacteristic
164C2×#365C2×C10311yescharacteristic, complemented
165C2×#362C2×C10311yescharacteristic, complemented
166C2×#362C2×C10311yescharacteristic, complemented
167C2×#349C2×C10311yescharacteristic
168#1811C2×C10311yescharacteristic
169#1383C2×C10311yescharacteristic, complemented
170C103#1339911yescharacteristic, direct product factor, Sylow
171C22×Q16C22×C10311yescharacteristic
172C22×M16C22×C10311yescharacteristic
173C2×C22⋊Q8—21no—
174C2×M32C22×C10311yescharacteristic
175C2×M32C22×C10311yescharacteristic
176#470—22no—
177#470—22no—
178C2×#108C22×C10311yescharacteristic
179C2×#108C22×C10311yescharacteristic
180C2×#106C22×C10311yescharacteristic
181C2×#103—21no—
182#407—21no—
183#365—22no—
184#362—22no—
185#362—22no—
186#349—22no—
187#341—21no—
188C22×Q8—21no—
189C23×C4D4×C10311yescharacteristic
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16D4×C10312yes—
196C2×M16—21no—
197C2×M16—21no—
198C2×M16—21no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16—21no—
204C22×C8D4×C10311yescharacteristic
205C22×C8C23×C10311yescharacteristic
206C22⋊Q8—24no—
207C22⋊Q8—42no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—41no—
210C2×C22⋊C4—41no—
211M32—21no—
212M32—21no—
213M32—21no—
214M32D4×C10312yes—
215C2×C16—21no—
216C2×C16—21no—
217#108—21no—
218#108—21no—
219#108—21no—
220#108—21no—
221#106—21no—
222#106D4×C10312yes—
223#103—24no—
224C22⋊C8—42no—
225C24SD16×C10311yescharacteristic
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4SD16×C10311yescharacteristic
241C22×C4C2×D4×C10311yescharacteristic
242Q16—22no—
243Q16—22no—
244Q16—41no—
245Q16—41no—
246M16—41no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8C2×D4×C10311yescharacteristic
260C2×C8C2×D4×C10311yescharacteristic
261C2×C8C2×D4×C10311yescharacteristic
262C2×C8#41×C10311yescharacteristic
263C2×C8#41×C10311yescharacteristic
264C2×C8#41×C10311yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—44no—
267C4⋊C4—41no—
268C22⋊C4—44no—
269C16—22no—
270C16—41no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—42no—
275C23C2×SD16×C10311yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4#120×C10311yescharacteristic
293C2×C4#121×C10311yescharacteristic
294C2×C4#123×C10311yescharacteristic
295C2×C4#135×C10311yescharacteristic
296C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
297C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
298C8—41no—
299C8—81no—
300C8—81no—
301C8#121×C10311yescharacteristic
302C8#121×C10311yescharacteristic
303C8#123×C10311yescharacteristic
304C8#124×C10311yescharacteristic
305C22—22no—
306C22—42no—
307C22—42no—
308C22—41no—
309C22—81no—
310C22#450×C10311yescharacteristic
311C22#465×C10311yescharacteristic
312C22#481×C10311yescharacteristic
313C4—41no—
314C4—82no—
315C4—82no—
316C4#394×C10311yescharacteristic
317C4#449×C10311yescharacteristic
318C4#469×C10311yescharacteristic
319C4#482×C10311yescharacteristic
320C2—21no—
321C2—21no—
322C2—81no—
323C2C103×#203411yescharacteristic
324C2C103×#223912yes—
subgroupG/H
center, socleC22×C103#481
commutator, Frattini, cosocleC22×C8C23×C103
prime radicalC24×C103SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C22×M16×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#365×C103C2semidirect
3. C2×#362×C103C2semidirect
4. C2×#362×C103C2semidirect
7. C103×#1383C2semidirect
157. #13399C103direct (N × H)
164. C2×#365C2×C103semidirect
165. C2×#362C2×C103semidirect
166. C2×#362C2×C103semidirect
169. #1383C2×C103semidirect
170. C103#13399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#470×C1032
C2×#365×C1032
C2×#362×C1032
C2×#349×C1032
C103×#18112
C103×#13832
#13399103