Finite Group Databasebeta

← C101×#13011 #38795162

Subgroups — C101×#13011 #38795162

Order 25856.

476 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#508×C101C211yesmaximal, characteristic
2C2×#443×C101C211yesmaximal, characteristic, complemented
3C2×#359×C101C211yesmaximal, characteristic, complemented
4C2×#359×C101C211yesmaximal, characteristic, complemented
5C101×#1974C211yesmaximal, characteristic, complemented
6C101×#1381C211yesmaximal, characteristic, complemented
7C101×#1374C211yesmaximal, characteristic, complemented
8C2×#135×C101C2211yescharacteristic
9C2×#135×C101C2211yescharacteristic
10C2×#131×C101—21no—
11#508×C101—22no—
12#508×C101—22no—
13C2×Q32×C101C411yescharacteristic, complemented
14C2×SD32×C101C411yescharacteristic, complemented
15C2×SD32×C101C411yescharacteristic, complemented
16C2×D16×C101C411yescharacteristic, complemented
17C22×C16×C101C2211yescharacteristic
18C22×C16×C101C2211yescharacteristic
19#443×C101—22no—
20#443×C101—22no—
21C2×#108×C101C2211yescharacteristic
22C2×#108×C101C2211yescharacteristic
23C2×#104×C101—21no—
24C2×#104×C101—21no—
25#408×C101—21no—
26C2×C4×C8×C101C2211yescharacteristic
27#359×C101—22no—
28#359×C101—22no—
29C2×#41×C101—21no—
30C2×#41×C101—21no—
31#135×C101—21no—
32#135×C101—21no—
33#135×C101—21no—
34#135×C101—21no—
35#135×C101—21no—
36#135×C101—21no—
37#135×C101D412yes—
38#135×C101D412yes—
39C2×Q16×C101C2×C411yescharacteristic
40C2×Q16×C101C2×C411yescharacteristic
41C2×SD16×C101—21no—
42C2×SD16×C101—21no—
43C2×D8×C101C2×C411yescharacteristic
44C2×D8×C101C2×C411yescharacteristic
45#131×C101—24no—
46#131×C101—42no—
47C2×M16×C101—21no—
48C2×M16×C101—21no—
49C2×M16×C101—41no—
50C22×C8×C101—41no—
51C22×C8×C101D411yescharacteristic
52C22×C8×C101C2311yescharacteristic
53C2×C42×C101D411yescharacteristic
54Q32×C101—22no—
55SD32×C101—22no—
56SD32×C101—22no—
57D16×C101—22no—
58C2×C16×C101—21no—
59C2×C16×C101—21no—
60C2×C16×C101—21no—
61C2×C16×C101—21no—
62C2×C16×C101—21no—
63C2×C16×C101C2×C411yescharacteristic
64C2×C16×C101C2×C411yescharacteristic
65#108×C101—21no—
66#108×C101—21no—
67#108×C101—21no—
68#108×C101D412yes—
69#104×C101—24no—
70#104×C101—42no—
71C22⋊C8×C101—41no—
72C22⋊C8×C101—41no—
73C4×C8×C101—21no—
74C4×C8×C101—21no—
75#41×C101—22no—
76#41×C101—22no—
77#41×C101—41no—
78#41×C101—41no—
79#41×C101—41no—
80#41×C101—41no—
81#41×C101—41no—
82#41×C101—41no—
83C2×Q8×C101—21no—
84C2×Q8×C101—21no—
85C2×D4×C101—21no—
86C2×D4×C101—21no—
87C2×D4×C101—41no—
88C2×D4×C101—41no—
89C22×C4×C101—21no—
90C22×C4×C101—41no—
91C22×C4×C101—41no—
92C22×C4×C101C2×D411yescharacteristic
93Q16×C101—21no—
94Q16×C101—21no—
95Q16×C101—21no—
96Q16×C101C22⋊C412yes—
97SD16×C101—22no—
98SD16×C101—22no—
99SD16×C101—41no—
100SD16×C101—41no—
101D8×C101—21no—
102D8×C101—21no—
103D8×C101—21no—
104D8×C101C22⋊C412yes—
105M16×C101—22no—
106M16×C101—44no—
107M16×C101—41no—
108M16×C101—41no—
109M16×C101—41no—
110C2×C8×C101—21no—
111C2×C8×C101—21no—
112C2×C8×C101—44no—
113C2×C8×C101—41no—
114C2×C8×C101—41no—
115C2×C8×C101D811yescharacteristic
116C2×C8×C101D811yescharacteristic
117C2×C8×C101C22×C411yescharacteristic
118C2×C8×C101C2×D411yescharacteristic
119C2×C8×C101C2×D411yescharacteristic
120C2×C8×C101C2×D411yescharacteristic
121C2×C8×C101#4111yescharacteristic
122C2×C8×C101#4111yescharacteristic
123C42×C101—21no—
124C42×C101—21no—
125C16×C101—21no—
126C16×C101—21no—
127C16×C101—41no—
128C23×C101—41no—
129C23×C101—41no—
130C23×C101#13511yescharacteristic
131Q8×C101—22no—
132Q8×C101—41no—
133Q8×C101—41no—
134Q8×C101—41no—
135D4×C101—22no—
136D4×C101—42no—
137D4×C101—42no—
138D4×C101—41no—
139D4×C101—41no—
140D4×C101—41no—
141D4×C101—81no—
142D4×C101—81no—
143C2×C4×C101—22no—
144C2×C4×C101—41no—
145C2×C4×C101—41no—
146C2×C4×C101—41no—
147C2×C4×C101—42no—
148C2×C4×C101—42no—
149C2×C4×C101—41no—
150C2×C4×C101—81no—
151C2×C4×C101—81no—
152C2×C4×C101C4×D411yescharacteristic
153C2×C4×C101#12011yescharacteristic
154C2×C4×C101#12111yescharacteristic
155C2×C4×C101C2×D811yescharacteristic
156C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
158C8×C101—21no—
159C8×C101—21no—
160C8×C101—42no—
161C8×C101—81no—
162C8×C101C2×C22⋊C411yescharacteristic
163C8×C101C4×D411yescharacteristic
164C8×C101#12111yescharacteristic
165C8×C101#12311yescharacteristic
166C22×C101—21no—
167C22×C101—21no—
168C22×C101—42no—
169C22×C101—81no—
170C22×C101—81no—
171C22×C101—81no—
172C22×C101—81no—
173C22×C101—81no—
174C22×C101C4×D811yescharacteristic
175C22×C101#44911yescharacteristic
176C22×C101#46311yescharacteristic
177C4×C101—42no—
178C4×C101—42no—
179C4×C101—81no—
180C4×C101#38611yescharacteristic
181C4×C101#44211yescharacteristic
182C4×C101#44711yescharacteristic
183C4×C101#45911yescharacteristic
184#13011C10111yesmaximal, characteristic, direct product factor, Sylow
185C2×C101—21no—
186C2×C101—21no—
187C2×C101—82no—
188C2×C101—161no—
189C2×C101#187911yescharacteristic
190C2×C101#217811yescharacteristic
191C2×C101#217911yescharacteristic
192C2×#508C2×C10111yescharacteristic
193C2×#443C2×C10111yescharacteristic, complemented
194C2×#359C2×C10111yescharacteristic, complemented
195C2×#359C2×C10111yescharacteristic, complemented
196#1974C2×C10111yescharacteristic, complemented
197#1381C2×C10111yescharacteristic, complemented
198#1374C2×C10111yescharacteristic, complemented
199C101#1301111yescharacteristic, direct product factor, Sylow
200C2×#135C22×C10111yescharacteristic
201C2×#135C22×C10111yescharacteristic
202C2×#131—21no—
203#508—22no—
204#508—22no—
205C2×Q32C4×C10111yescharacteristic, complemented
206C2×SD32C4×C10111yescharacteristic, complemented
207C2×SD32C4×C10111yescharacteristic, complemented
208C2×D16C4×C10111yescharacteristic, complemented
209C22×C16C22×C10111yescharacteristic
210C22×C16C22×C10111yescharacteristic
211#443—22no—
212#443—22no—
213C2×#108C22×C10111yescharacteristic
214C2×#108C22×C10111yescharacteristic
215C2×#104—21no—
216C2×#104—21no—
217#408—21no—
218C2×C4×C8C22×C10111yescharacteristic
219#359—22no—
220#359—22no—
221C2×#41—21no—
222C2×#41—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—21no—
228#135—21no—
229#135D4×C10112yes—
230#135D4×C10112yes—
231C2×Q16C2×C4×C10111yescharacteristic
232C2×Q16C2×C4×C10111yescharacteristic
233C2×SD16—21no—
234C2×SD16—21no—
235C2×D8C2×C4×C10111yescharacteristic
236C2×D8C2×C4×C10111yescharacteristic
237#131—24no—
238#131—42no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—41no—
242C22×C8—41no—
243C22×C8D4×C10111yescharacteristic
244C22×C8C23×C10111yescharacteristic
245C2×C42D4×C10111yescharacteristic
246Q32—22no—
247SD32—22no—
248SD32—22no—
249D16—22no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—21no—
255C2×C16C2×C4×C10111yescharacteristic
256C2×C16C2×C4×C10111yescharacteristic
257#108—21no—
258#108—21no—
259#108—21no—
260#108D4×C10112yes—
261#104—24no—
262#104—42no—
263C22⋊C8—41no—
264C22⋊C8—41no—
265C4×C8—21no—
266C4×C8—21no—
267#41—22no—
268#41—22no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C10111yescharacteristic
285Q16—21no—
286Q16—21no—
287Q16—21no—
288Q16C22⋊C4×C10112yes—
289SD16—22no—
290SD16—22no—
291SD16—41no—
292SD16—41no—
293D8—21no—
294D8—21no—
295D8—21no—
296D8C22⋊C4×C10112yes—
297M16—22no—
298M16—44no—
299M16—41no—
300M16—41no—
301M16—41no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—44no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8D8×C10111yescharacteristic
308C2×C8D8×C10111yescharacteristic
309C2×C8C22×C4×C10111yescharacteristic
310C2×C8C2×D4×C10111yescharacteristic
311C2×C8C2×D4×C10111yescharacteristic
312C2×C8C2×D4×C10111yescharacteristic
313C2×C8#41×C10111yescharacteristic
314C2×C8#41×C10111yescharacteristic
315C42—21no—
316C42—21no—
317C16—21no—
318C16—21no—
319C16—41no—
320C23—41no—
321C23—41no—
322C23#135×C10111yescharacteristic
323Q8—22no—
324Q8—41no—
325Q8—41no—
326Q8—41no—
327D4—22no—
328D4—42no—
329D4—42no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—81no—
334D4—81no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4C4×D4×C10111yescharacteristic
345C2×C4#120×C10111yescharacteristic
346C2×C4#121×C10111yescharacteristic
347C2×C4C2×D8×C10111yescharacteristic
348C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
349C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
350C8—21no—
351C8—21no—
352C8—42no—
353C8—81no—
354C8C2×C22⋊C4×C10111yescharacteristic
355C8C4×D4×C10111yescharacteristic
356C8#121×C10111yescharacteristic
357C8#123×C10111yescharacteristic
358C22—21no—
359C22—21no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22C4×D8×C10111yescharacteristic
367C22#449×C10111yescharacteristic
368C22#463×C10111yescharacteristic
369C4—42no—
370C4—42no—
371C4—81no—
372C4#386×C10111yescharacteristic
373C4#442×C10111yescharacteristic
374C4#447×C10111yescharacteristic
375C4#459×C10111yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—161no—
380C2C101×#187911yescharacteristic
381C2C101×#217811yescharacteristic
382C2C101×#217911yescharacteristic
subgroupG/H
centerC2×C4×C101C2×D8
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC22×C101C4×D8
prime radicalC2×#508×C101C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C22×C8×C101 ◁ C2×C4×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C101C2semidirect
3. C2×#359×C101C2semidirect
4. C2×#359×C101C2semidirect
5. C101×#1974C2semidirect
6. C101×#1381C2semidirect
7. C101×#1374C2semidirect
13. C2×Q32×C101C4semidirect
14. C2×SD32×C101C4semidirect
15. C2×SD32×C101C4semidirect
16. C2×D16×C101C4semidirect
184. #13011C101direct (N × H)
193. C2×#443C2×C101semidirect
194. C2×#359C2×C101semidirect
195. C2×#359C2×C101semidirect
196. #1974C2×C101semidirect
197. #1381C2×C101semidirect
198. #1374C2×C101semidirect
199. C101#13011direct (N × H)
205. C2×Q32C4×C101semidirect
206. C2×SD32C4×C101semidirect
207. C2×SD32C4×C101semidirect
208. C2×D16C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#508×C1012
C2×#443×C1012
C2×#359×C1012
C101×#19742
C101×#13812
C101×#13742
#13011101