Finite Group Databasebeta

← C101×#13404 #38795555

Subgroups — C101×#13404 #38795555

Order 25856.

406 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C101C211yesmaximal, characteristic
2C101×#2155C211yesmaximal, characteristic, complemented
3C101×#2140C211yesmaximal, characteristic, complemented
4C101×#2140C211yesmaximal, characteristic, complemented
5C101×#2117C211yesmaximal, characteristic, complemented
6C101×#1812C211yesmaximal, characteristic, complemented
7C101×#1389C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C101—21no—
9C22×D8×C101C2211yescharacteristic
10C2×#131×C101C2211yescharacteristic
11C2×M32×C101C2211yescharacteristic
12C2×M32×C101C2211yescharacteristic
13#472×C101—22no—
14#472×C101—22no—
15C2×#108×C101C2211yescharacteristic
16#427×C101C2211yescharacteristic
17#427×C101C2211yescharacteristic
18C2×#100×C101—21no—
19#410×C101—21no—
20#365×C101—22no—
21#357×C101—22no—
22#357×C101—22no—
23#350×C101—22no—
24H(3,ℤ/4)×C101—21no—
25C2×#41×C101D411yescharacteristic
26C22×D4×C101—21no—
27AGL(1,ℤ/8)×C101—24no—
28AGL(1,ℤ/8)×C101—42no—
29C2×SD16×C101—41no—
30C2×D8×C101—21no—
31C2×D8×C101—21no—
32C2×D8×C101—21no—
33C2×D8×C101—21no—
34C2×D8×C101—21no—
35C2×D8×C101—41no—
36C2×D8×C101D412yes—
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×C101D411yescharacteristic
44C22×C8×C101—21no—
45C22×C8×C101C2311yescharacteristic
46#117×C101—21no—
47#117×C101—21no—
48M32×C101—21no—
49M32×C101—21no—
50M32×C101—21no—
51M32×C101—21no—
52C2×C16×C101—21no—
53C2×C16×C101D412yes—
54#108×C101—21no—
55#108×C101D412yes—
56#107×C101—21no—
57#107×C101—21no—
58#106×C101—21no—
59#106×C101—21no—
60#100×C101—24no—
61#99×C101—42no—
62C24×C101—41no—
63#41×C101—21no—
64#41×C101—21no—
65#41×C101—21no—
66#41×C101—21no—
67C2×Q8×C101SD1611yescharacteristic
68C2×D4×C101—21no—
69C2×D4×C101—22no—
70C2×D4×C101—41no—
71C2×D4×C101—41no—
72C2×D4×C101—41no—
73C2×D4×C101—41no—
74C2×D4×C101—41no—
75C2×D4×C101SD1611yescharacteristic
76C22×C4×C101—21no—
77C22×C4×C101C2×D411yescharacteristic
78SD16×C101—44no—
79D8×C101—22no—
80D8×C101—22no—
81D8×C101—44no—
82D8×C101—41no—
83D8×C101—41no—
84M16×C101—21no—
85M16×C101—22no—
86M16×C101—21no—
87M16×C101—41no—
88M16×C101—41no—
89M16×C101—41no—
90C2×C8×C101—21no—
91C2×C8×C101—41no—
92C2×C8×C101—41no—
93C2×C8×C101—41no—
94C2×C8×C101C2×D411yescharacteristic
95C2×C8×C101C2×D411yescharacteristic
96C2×C8×C101C2×D411yescharacteristic
97C2×C8×C101#4111yescharacteristic
98C2×C8×C101#4111yescharacteristic
99C2×C8×C101#4111yescharacteristic
100C4⋊C4×C101—41no—
101C4⋊C4×C101—41no—
102C22⋊C4×C101—41no—
103C22⋊C4×C101—41no—
104C42×C101—41no—
105C42×C101—41no—
106C16×C101—22no—
107C16×C101—41no—
108C23×C101—21no—
109C23×C101—42no—
110C23×C101—81no—
111C23×C101—81no—
112C23×C101—162no—
113C23×C101AGL(1,ℤ/8)11yescharacteristic
114Q8×C101—21no—
115Q8×C101—21no—
116D4×C101—21no—
117D4×C101—21no—
118D4×C101—41no—
119D4×C101—41no—
120D4×C101—42no—
121D4×C101—42no—
122D4×C101—81no—
123D4×C101—81no—
124C2×C4×C101—21no—
125C2×C4×C101—41no—
126C2×C4×C101—41no—
127C2×C4×C101—81no—
128C2×C4×C101—81no—
129C2×C4×C101#12011yescharacteristic
130C2×C4×C101#12111yescharacteristic
131C2×C4×C101#12311yescharacteristic
132C2×C4×C101C2×SD1611yescharacteristic
133C2×C4×C101#13511yescharacteristic
134C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
135C8×C101—41no—
136C8×C101—42no—
137C8×C101#12111yescharacteristic
138C8×C101#12111yescharacteristic
139C8×C101#12311yescharacteristic
140C8×C101#12411yescharacteristic
141C22×C101—41no—
142C22×C101—41no—
143C22×C101—81no—
144C22×C101—82no—
145C22×C101—162no—
146C22×C101—162no—
147C22×C101—162no—
148C22×C101#44911yescharacteristic
149C22×C101#46911yescharacteristic
150C22×C101#48111yescharacteristic
151C4×C101—41no—
152C4×C101—161no—
153C4×C101—161no—
154C4×C101#39411yescharacteristic
155C4×C101#45011yescharacteristic
156C4×C101#46511yescharacteristic
157C4×C101#48211yescharacteristic
158#13404C10111yesmaximal, characteristic, direct product factor, Sylow
159C2×C101—21no—
160C2×C101—21no—
161C2×C101—21no—
162C2×C101—81no—
163C2×C101—162no—
164C2×C101#203411yescharacteristic
165C2×#472C2×C10111yescharacteristic
166#2155C2×C10111yescharacteristic, complemented
167#2140C2×C10111yescharacteristic, complemented
168#2140C2×C10111yescharacteristic, complemented
169#2117C2×C10111yescharacteristic, complemented
170#1812C2×C10111yescharacteristic, complemented
171#1389C2×C10111yescharacteristic, complemented
172C101#1340411yescharacteristic, direct product factor, Sylow
173C2×AGL(1,ℤ/8)—21no—
174C22×D8C22×C10111yescharacteristic
175C2×#131C22×C10111yescharacteristic
176C2×M32C22×C10111yescharacteristic
177C2×M32C22×C10111yescharacteristic
178#472—22no—
179#472—22no—
180C2×#108C22×C10111yescharacteristic
181#427C22×C10111yescharacteristic
182#427C22×C10111yescharacteristic
183C2×#100—21no—
184#410—21no—
185#365—22no—
186#357—22no—
187#357—22no—
188#350—22no—
189H(3,ℤ/4)—21no—
190C2×#41D4×C10111yescharacteristic
191C22×D4—21no—
192AGL(1,ℤ/8)—24no—
193AGL(1,ℤ/8)—42no—
194C2×SD16—41no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—21no—
200C2×D8—41no—
201C2×D8D4×C10112yes—
202#131—21no—
203#131—21no—
204#131—21no—
205#131—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16D4×C10111yescharacteristic
209C22×C8—21no—
210C22×C8C23×C10111yescharacteristic
211#117—21no—
212#117—21no—
213M32—21no—
214M32—21no—
215M32—21no—
216M32—21no—
217C2×C16—21no—
218C2×C16D4×C10112yes—
219#108—21no—
220#108D4×C10112yes—
221#107—21no—
222#107—21no—
223#106—21no—
224#106—21no—
225#100—24no—
226#99—42no—
227C24—41no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—21no—
232C2×Q8SD16×C10111yescharacteristic
233C2×D4—21no—
234C2×D4—22no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4SD16×C10111yescharacteristic
241C22×C4—21no—
242C22×C4C2×D4×C10111yescharacteristic
243SD16—44no—
244D8—22no—
245D8—22no—
246D8—44no—
247D8—41no—
248D8—41no—
249M16—21no—
250M16—22no—
251M16—21no—
252M16—41no—
253M16—41no—
254M16—41no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8C2×D4×C10111yescharacteristic
260C2×C8C2×D4×C10111yescharacteristic
261C2×C8C2×D4×C10111yescharacteristic
262C2×C8#41×C10111yescharacteristic
263C2×C8#41×C10111yescharacteristic
264C2×C8#41×C10111yescharacteristic
265C4⋊C4—41no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—41no—
270C42—41no—
271C16—22no—
272C16—41no—
273C23—21no—
274C23—42no—
275C23—81no—
276C23—81no—
277C23—162no—
278C23AGL(1,ℤ/8)×C10111yescharacteristic
279Q8—21no—
280Q8—21no—
281D4—21no—
282D4—21no—
283D4—41no—
284D4—41no—
285D4—42no—
286D4—42no—
287D4—81no—
288D4—81no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4#120×C10111yescharacteristic
295C2×C4#121×C10111yescharacteristic
296C2×C4#123×C10111yescharacteristic
297C2×C4C2×SD16×C10111yescharacteristic
298C2×C4#135×C10111yescharacteristic
299C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
300C8—42no—
301C8—41no—
302C8#121×C10111yescharacteristic
303C8#121×C10111yescharacteristic
304C8#123×C10111yescharacteristic
305C8#124×C10111yescharacteristic
306C22—41no—
307C22—41no—
308C22—81no—
309C22—82no—
310C22—162no—
311C22—162no—
312C22—162no—
313C22#449×C10111yescharacteristic
314C22#469×C10111yescharacteristic
315C22#481×C10111yescharacteristic
316C4—41no—
317C4—161no—
318C4—161no—
319C4#394×C10111yescharacteristic
320C4#450×C10111yescharacteristic
321C4#465×C10111yescharacteristic
322C4#482×C10111yescharacteristic
323C2—21no—
324C2—21no—
325C2—21no—
326C2—81no—
327C2—162no—
328C2C101×#203411yescharacteristic
subgroupG/H
center, socleC2×C101#2034
commutator, Frattini, cosocleC22×C8C23×C101
prime radicalC2×#472×C101C2
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. C101×#2140C2semidirect
4. C101×#2140C2semidirect
5. C101×#2117C2semidirect
6. C101×#1812C2semidirect
7. C101×#1389C2semidirect
158. #13404C101direct (N × H)
166. #2155C2×C101semidirect
167. #2140C2×C101semidirect
168. #2140C2×C101semidirect
169. #2117C2×C101semidirect
170. #1812C2×C101semidirect
171. #1389C2×C101semidirect
172. C101#13404direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#472×C1012
C101×#21552
C101×#21402
C101×#21172
C101×#18122
C101×#13892
#13404101