Finite Group Databasebeta

← C101×#13403 #38795554

Subgroups — C101×#13403 #38795554

Order 25856.

384 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#473×C101C211yesmaximal, characteristic
2C101×#2155C211yesmaximal, characteristic, complemented
3C2×#362×C101C211yesmaximal, characteristic, complemented
4C101×#2141C211yesmaximal, characteristic, complemented
5C101×#2115C211yesmaximal, characteristic
6C101×#1814C211yesmaximal, characteristic
7C101×#1388C211yesmaximal, characteristic, complemented
8C2×#137×C101—21no—
9C22×Q16×C101C2211yescharacteristic
10C2×#131×C101C2211yescharacteristic
11C2×M32×C101C2211yescharacteristic
12C2×M32×C101C2211yescharacteristic
13#473×C101—22no—
14#473×C101—22no—
15C2×#108×C101C2211yescharacteristic
16C2×#108×C101C2211yescharacteristic
17#427×C101C2211yescharacteristic
18#421×C101—21no—
19C2×#101×C101—21no—
20#365×C101—22no—
21#362×C101—22no—
22#358×C101—22no—
23#349×C101—22no—
24#344×C101—21no—
25C2×#41×C101D411yescharacteristic
26C22×Q8×C101—21no—
27#137×C101—24no—
28#137×C101—42no—
29C2×Q16×C101—21no—
30C2×Q16×C101—21no—
31C2×Q16×C101—21no—
32C2×Q16×C101—21no—
33C2×Q16×C101—21no—
34C2×Q16×C101—41no—
35C2×Q16×C101D412yes—
36C2×SD16×C101—41no—
37#131×C101—21no—
38#131×C101—21no—
39#131×C101—21no—
40#131×C101—21no—
41C2×M16×C101—21no—
42C2×M16×C101—21no—
43C2×M16×C101—21no—
44C2×M16×C101D411yescharacteristic
45C22×C8×C101—21no—
46C22×C8×C101C2311yescharacteristic
47#117×C101—21no—
48M32×C101—21no—
49M32×C101—21no—
50M32×C101—21no—
51M32×C101D412yes—
52C2×C16×C101—21no—
53C2×C16×C101—21no—
54#108×C101—21no—
55#108×C101—21no—
56#108×C101—21no—
57#108×C101D412yes—
58#107×C101—21no—
59#106×C101—21no—
60#104×C101—42no—
61#101×C101—24no—
62#41×C101—21no—
63#41×C101—21no—
64#41×C101—21no—
65#41×C101—21no—
66C2×Q8×C101—22no—
67C2×Q8×C101—41no—
68C2×Q8×C101—41no—
69C2×Q8×C101—41no—
70C2×Q8×C101—41no—
71C2×Q8×C101—41no—
72C2×Q8×C101SD1611yescharacteristic
73C2×D4×C101—21no—
74C2×D4×C101SD1611yescharacteristic
75C22×C4×C101—21no—
76C22×C4×C101—41no—
77C22×C4×C101C2×D411yescharacteristic
78Q16×C101—22no—
79Q16×C101—22no—
80Q16×C101—44no—
81Q16×C101—41no—
82Q16×C101—41no—
83SD16×C101—44no—
84M16×C101—21no—
85M16×C101—22no—
86M16×C101—21no—
87M16×C101—41no—
88M16×C101—41no—
89M16×C101—41no—
90M16×C101—41no—
91M16×C101—41no—
92C2×C8×C101—21no—
93C2×C8×C101—41no—
94C2×C8×C101—41no—
95C2×C8×C101—41no—
96C2×C8×C101—41no—
97C2×C8×C101C2×D411yescharacteristic
98C2×C8×C101C2×D411yescharacteristic
99C2×C8×C101C2×D411yescharacteristic
100C2×C8×C101#4111yescharacteristic
101C2×C8×C101#4111yescharacteristic
102C2×C8×C101#4111yescharacteristic
103C4⋊C4×C101—41no—
104C22⋊C4×C101—41no—
105C42×C101—41no—
106C16×C101—22no—
107C16×C101—41no—
108C23×C101—21no—
109C23×C101#13511yescharacteristic
110Q8×C101—21no—
111Q8×C101—21no—
112Q8×C101—42no—
113Q8×C101—42no—
114Q8×C101—81no—
115Q8×C101—81no—
116D4×C101—21no—
117D4×C101—21no—
118D4×C101—41no—
119D4×C101—41no—
120C2×C4×C101—21no—
121C2×C4×C101—41no—
122C2×C4×C101—41no—
123C2×C4×C101—42no—
124C2×C4×C101—81no—
125C2×C4×C101—81no—
126C2×C4×C101—81no—
127C2×C4×C101#12011yescharacteristic
128C2×C4×C101#12111yescharacteristic
129C2×C4×C101#12311yescharacteristic
130C2×C4×C101C2×SD1611yescharacteristic
131C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
133C8×C101—41no—
134C8×C101—42no—
135C8×C101—81no—
136C8×C101#12111yescharacteristic
137C8×C101#12111yescharacteristic
138C8×C101#12311yescharacteristic
139C8×C101#12411yescharacteristic
140C22×C101—41no—
141C22×C101—41no—
142C22×C101—81no—
143C22×C101#44911yescharacteristic
144C22×C101#46511yescharacteristic
145C22×C101#48211yescharacteristic
146C4×C101—41no—
147C4×C101—82no—
148C4×C101—161no—
149C4×C101#39411yescharacteristic
150C4×C101#45011yescharacteristic
151C4×C101#46911yescharacteristic
152C4×C101#48111yescharacteristic
153#13403C10111yesmaximal, characteristic, direct product factor, Sylow
154C2×C101—21no—
155C2×C101—21no—
156C2×C101—21no—
157C2×C101—81no—
158C2×C101#203411yescharacteristic
159C2×#473C2×C10111yescharacteristic
160#2155C2×C10111yescharacteristic, complemented
161C2×#362C2×C10111yescharacteristic, complemented
162#2141C2×C10111yescharacteristic, complemented
163#2115C2×C10111yescharacteristic
164#1814C2×C10111yescharacteristic
165#1388C2×C10111yescharacteristic, complemented
166C101#1340311yescharacteristic, direct product factor, Sylow
167C2×#137—21no—
168C22×Q16C22×C10111yescharacteristic
169C2×#131C22×C10111yescharacteristic
170C2×M32C22×C10111yescharacteristic
171C2×M32C22×C10111yescharacteristic
172#473—22no—
173#473—22no—
174C2×#108C22×C10111yescharacteristic
175C2×#108C22×C10111yescharacteristic
176#427C22×C10111yescharacteristic
177#421—21no—
178C2×#101—21no—
179#365—22no—
180#362—22no—
181#358—22no—
182#349—22no—
183#344—21no—
184C2×#41D4×C10111yescharacteristic
185C22×Q8—21no—
186#137—24no—
187#137—42no—
188C2×Q16—21no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—41no—
194C2×Q16D4×C10112yes—
195C2×SD16—41no—
196#131—21no—
197#131—21no—
198#131—21no—
199#131—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16D4×C10111yescharacteristic
204C22×C8—21no—
205C22×C8C23×C10111yescharacteristic
206#117—21no—
207M32—21no—
208M32—21no—
209M32—21no—
210M32D4×C10112yes—
211C2×C16—21no—
212C2×C16—21no—
213#108—21no—
214#108—21no—
215#108—21no—
216#108D4×C10112yes—
217#107—21no—
218#106—21no—
219#104—42no—
220#101—24no—
221#41—21no—
222#41—21no—
223#41—21no—
224#41—21no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8SD16×C10111yescharacteristic
232C2×D4—21no—
233C2×D4SD16×C10111yescharacteristic
234C22×C4—21no—
235C22×C4—41no—
236C22×C4C2×D4×C10111yescharacteristic
237Q16—22no—
238Q16—22no—
239Q16—44no—
240Q16—41no—
241Q16—41no—
242SD16—44no—
243M16—21no—
244M16—22no—
245M16—21no—
246M16—41no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—41no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8C2×D4×C10111yescharacteristic
257C2×C8C2×D4×C10111yescharacteristic
258C2×C8C2×D4×C10111yescharacteristic
259C2×C8#41×C10111yescharacteristic
260C2×C8#41×C10111yescharacteristic
261C2×C8#41×C10111yescharacteristic
262C4⋊C4—41no—
263C22⋊C4—41no—
264C42—41no—
265C16—22no—
266C16—41no—
267C23—21no—
268C23#135×C10111yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—42no—
272Q8—42no—
273Q8—81no—
274Q8—81no—
275D4—21no—
276D4—21no—
277D4—41no—
278D4—41no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4#120×C10111yescharacteristic
287C2×C4#121×C10111yescharacteristic
288C2×C4#123×C10111yescharacteristic
289C2×C4C2×SD16×C10111yescharacteristic
290C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
291C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
292C8—42no—
293C8—41no—
294C8—81no—
295C8#121×C10111yescharacteristic
296C8#121×C10111yescharacteristic
297C8#123×C10111yescharacteristic
298C8#124×C10111yescharacteristic
299C22—41no—
300C22—41no—
301C22—81no—
302C22#449×C10111yescharacteristic
303C22#465×C10111yescharacteristic
304C22#482×C10111yescharacteristic
305C4—41no—
306C4—82no—
307C4—161no—
308C4#394×C10111yescharacteristic
309C4#450×C10111yescharacteristic
310C4#469×C10111yescharacteristic
311C4#481×C10111yescharacteristic
312C2—21no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2C101×#203411yescharacteristic
subgroupG/H
center, socleC2×C101#2034
commutator, Frattini, cosocleC22×C8C23×C101
prime radicalC2×#41×C101D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ C2×#131×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2155C2semidirect
3. C2×#362×C101C2semidirect
4. C101×#2141C2semidirect
7. C101×#1388C2semidirect
153. #13403C101direct (N × H)
160. #2155C2×C101semidirect
161. C2×#362C2×C101semidirect
162. #2141C2×C101semidirect
165. #1388C2×C101semidirect
166. C101#13403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#473×C1012
C101×#21552
C2×#362×C1012
C101×#21412
C101×#21152
C101×#18142
C101×#13882
#13403101