Finite Group Databasebeta

← C101×#9047 #38791198

Subgroups — C101×#9047 #38791198

Order 25856.

492 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3103C211yesmaximal, characteristic
2C101×#2932C211yesmaximal, characteristic
3C101×#1985C211yesmaximal, characteristic, complemented
4C101×#1540C211yesmaximal, characteristic
5C101×#1487C211yesmaximal, characteristic, complemented
6C101×#1301C211yesmaximal, characteristic, complemented
7C101×#1281C211yesmaximal, characteristic, complemented
8C2×#131×C101—21no—
9#532×C101C2211yescharacteristic
10C2×C4×Q8×C101C2211yescharacteristic
11#481×C101C412yes—
12#475×C101—21no—
13#460×C101—21no—
14#448×C101C412yes—
15C4×SD16×C101—22no—
16#435×C101—22no—
17#435×C101—22no—
18#431×C101C2211yescharacteristic
19#431×C101C2211yescharacteristic
20#423×C101C2211yescharacteristic
21C2×C4⋊C8×C101C2211yescharacteristic
22#408×C101—21no—
23C2×#97×C101C2211yescharacteristic
24#336×C101—21no—
25#336×C101—21no—
26#332×C101—21no—
27#331×C101—21no—
28Q8⋊C8×C101—22no—
29C2×#41×C101—21no—
30C22×Q8×C101C2×C411yescharacteristic
31C2×SD16×C101—22no—
32#131×C101—42no—
33#131×C101—42no—
34C2×M16×C101—22no—
35C2×M16×C101—21no—
36C22×C8×C101—22no—
37C22×C8×C101—21no—
38C22×C8×C101D411yescharacteristic
39C22×C8×C101D411yescharacteristic
40C4⋊Q8×C101D411yescharacteristic
41#127×C101D411yescharacteristic
42#124×C101—21no—
43#121×C101—21no—
44#121×C101C2×C412yes—
45C4×Q8×C101—21no—
46C4×Q8×C101—21no—
47C4×Q8×C101—21no—
48C4×Q8×C101—21no—
49C4×D4×C101—21no—
50C4×D4×C101D412yes—
51C2×C4⋊C4×C101—21no—
52C2×C4⋊C4×C101C2×C411yescharacteristic
53C2×C42×C101—21no—
54C2×C42×C101C2311yescharacteristic
55#106×C101—22no—
56C4⋊C8×C101—21no—
57C4⋊C8×C101—21no—
58C4⋊C8×C101—21no—
59C4⋊C8×C101—21no—
60C4⋊C8×C101—21no—
61C4⋊C8×C101D412yes—
62#103×C101—22no—
63#102×C101—22no—
64C22⋊C8×C101—24no—
65C22⋊C8×C101—21no—
66C22⋊C8×C101C2×C412yes—
67#97×C101—21no—
68#97×C101—21no—
69C4×C8×C101—21no—
70C4×C8×C101—21no—
71#41×C101—41no—
72#41×C101—41no—
73#41×C101—41no—
74#41×C101—41no—
75C2×Q8×C101—21no—
76C2×Q8×C101—21no—
77C2×Q8×C101—21no—
78C2×Q8×C101—42no—
79C2×D4×C101—22no—
80C2×D4×C101—21no—
81C2×D4×C101—21no—
82C2×D4×C101C22⋊C412yes—
83C22×C4×C101—21no—
84C22×C4×C101—22no—
85C22×C4×C101—21no—
86C22×C4×C101C22×C411yescharacteristic
87C22×C4×C101C2×D411yescharacteristic
88C22×C4×C101#4111yescharacteristic
89SD16×C101—44no—
90M16×C101—44no—
91M16×C101—41no—
92M16×C101—41no—
93C2×C8×C101—21no—
94C2×C8×C101—21no—
95C2×C8×C101—22no—
96C2×C8×C101—21no—
97C2×C8×C101—22no—
98C2×C8×C101—21no—
99C2×C8×C101—21no—
100C2×C8×C101—44no—
101C2×C8×C101—41no—
102C2×C8×C101—41no—
103C2×C8×C101—41no—
104C2×C8×C101—41no—
105C2×C8×C101SD1612yescomplemented
106C4⋊C4×C101—21no—
107C4⋊C4×C101—21no—
108C4⋊C4×C101—21no—
109C4⋊C4×C101—41no—
110C4⋊C4×C101—41no—
111C4⋊C4×C101C22⋊C412yes—
112C22⋊C4×C101—22no—
113C22⋊C4×C101—22no—
114C42×C101—41no—
115C42×C101—41no—
116C42×C101C2×D411yescharacteristic
117C42×C101C2×D411yescharacteristic
118C42×C101C2×D411yescharacteristic
119C42×C101#4111yescharacteristic
120C23×C101—22no—
121C23×C101C4×D411yescharacteristic
122Q8×C101—22no—
123Q8×C101—22no—
124Q8×C101—41no—
125Q8×C101—41no—
126Q8×C101—41no—
127Q8×C101—41no—
128D4×C101—42no—
129D4×C101—42no—
130D4×C101—42no—
131D4×C101—41no—
132D4×C101—41no—
133D4×C101—81no—
134C2×C4×C101—22no—
135C2×C4×C101—22no—
136C2×C4×C101—41no—
137C2×C4×C101—41no—
138C2×C4×C101—41no—
139C2×C4×C101—41no—
140C2×C4×C101—42no—
141C2×C4×C101—42no—
142C2×C4×C101—42no—
143C2×C4×C101—41no—
144C2×C4×C101C2×C22⋊C411yescharacteristic
145C2×C4×C101C4×D411yescharacteristic
146C2×C4×C101#12011yescharacteristic
147C2×C4×C101#12111yescharacteristic
148C2×C4×C101#12111yescharacteristic
149C2×C4×C101#12311yescharacteristic
150C2×C4×C101C2×SD1611yescharacteristic
151C2×C4×C101#13511yescharacteristic
152C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C101#13711yescharacteristic
154C8×C101—22no—
155C8×C101—42no—
156C8×C101—42no—
157C8×C101—41no—
158C8×C101—81no—
159C8×C101—81no—
160C22×C101—21no—
161C22×C101—21no—
162C22×C101—42no—
163C22×C101—42no—
164C22×C101—42no—
165C22×C101#38611yescharacteristic
166C22×C101C4×SD1611yescharacteristic
167C22×C101#44011yescharacteristic
168C4×C101—21no—
169C4×C101—21no—
170C4×C101—21no—
171C4×C101—21no—
172C4×C101—42no—
173C4×C101—42no—
174C4×C101—81no—
175C4×C101#45011yescharacteristic
176C4×C101#45211yescharacteristic
177C4×C101#46111yescharacteristic
178C4×C101#46311yescharacteristic
179#9047C10111yesmaximal, characteristic, direct product factor, Sylow
180C2×C101—21no—
181C2×C101—21no—
182C2×C101—82no—
183C2×C101#187711yescharacteristic
184C2×C101#188111yescharacteristic
185C2×C101#189111yescharacteristic
186#3103C2×C10111yescharacteristic
187#2932C2×C10111yescharacteristic
188#1985C2×C10111yescharacteristic, complemented
189#1540C2×C10111yescharacteristic
190#1487C2×C10111yescharacteristic, complemented
191#1301C2×C10111yescharacteristic, complemented
192#1281C2×C10111yescharacteristic, complemented
193C101#904711yescharacteristic, direct product factor, Sylow
194C2×#131—21no—
195#532C22×C10111yescharacteristic
196C2×C4×Q8C22×C10111yescharacteristic
197#481C4×C10112yes—
198#475—21no—
199#460—21no—
200#448C4×C10112yes—
201C4×SD16—22no—
202#435—22no—
203#435—22no—
204#431C22×C10111yescharacteristic
205#431C22×C10111yescharacteristic
206#423C22×C10111yescharacteristic
207C2×C4⋊C8C22×C10111yescharacteristic
208#408—21no—
209C2×#97C22×C10111yescharacteristic
210#336—21no—
211#336—21no—
212#332—21no—
213#331—21no—
214Q8⋊C8—22no—
215C2×#41—21no—
216C22×Q8C2×C4×C10111yescharacteristic
217C2×SD16—22no—
218#131—42no—
219#131—42no—
220C2×M16—22no—
221C2×M16—21no—
222C22×C8—22no—
223C22×C8—21no—
224C22×C8D4×C10111yescharacteristic
225C22×C8D4×C10111yescharacteristic
226C4⋊Q8D4×C10111yescharacteristic
227#127D4×C10111yescharacteristic
228#124—21no—
229#121—21no—
230#121C2×C4×C10112yes—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4D4×C10112yes—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C10111yescharacteristic
239C2×C42—21no—
240C2×C42C23×C10111yescharacteristic
241#106—22no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C10112yes—
248#103—22no—
249#102—22no—
250C22⋊C8—24no—
251C22⋊C8—21no—
252C22⋊C8C2×C4×C10112yes—
253#97—21no—
254#97—21no—
255C4×C8—21no—
256C4×C8—21no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—42no—
265C2×D4—22no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4C22⋊C4×C10112yes—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4C22×C4×C10111yescharacteristic
273C22×C4C2×D4×C10111yescharacteristic
274C22×C4#41×C10111yescharacteristic
275SD16—44no—
276M16—44no—
277M16—41no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—44no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8SD16×C10112yescomplemented
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4C22⋊C4×C10112yes—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C42—41no—
301C42—41no—
302C42C2×D4×C10111yescharacteristic
303C42C2×D4×C10111yescharacteristic
304C42C2×D4×C10111yescharacteristic
305C42#41×C10111yescharacteristic
306C23—22no—
307C23C4×D4×C10111yescharacteristic
308Q8—22no—
309Q8—22no—
310Q8—41no—
311Q8—41no—
312Q8—41no—
313Q8—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—41no—
318D4—41no—
319D4—81no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4C2×C22⋊C4×C10111yescharacteristic
331C2×C4C4×D4×C10111yescharacteristic
332C2×C4#120×C10111yescharacteristic
333C2×C4#121×C10111yescharacteristic
334C2×C4#121×C10111yescharacteristic
335C2×C4#123×C10111yescharacteristic
336C2×C4C2×SD16×C10111yescharacteristic
337C2×C4#135×C10111yescharacteristic
338C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
339C2×C4#137×C10111yescharacteristic
340C8—22no—
341C8—42no—
342C8—42no—
343C8—41no—
344C8—81no—
345C8—81no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#386×C10111yescharacteristic
352C22C4×SD16×C10111yescharacteristic
353C22#440×C10111yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—81no—
361C4#450×C10111yescharacteristic
362C4#452×C10111yescharacteristic
363C4#461×C10111yescharacteristic
364C4#463×C10111yescharacteristic
365C2—21no—
366C2—21no—
367C2—82no—
368C2C101×#187711yescharacteristic
369C2C101×#188111yescharacteristic
370C2C101×#189111yescharacteristic
subgroupG/H
centerC2×C4×C101#120
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
socleC22×C101#386
prime radical#532×C101C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1985C2semidirect
5. C101×#1487C2semidirect
6. C101×#1301C2semidirect
7. C101×#1281C2semidirect
105. C2×C8×C101SD16semidirect
179. #9047C101direct (N × H)
188. #1985C2×C101semidirect
190. #1487C2×C101semidirect
191. #1301C2×C101semidirect
192. #1281C2×C101semidirect
193. C101#9047direct (N × H)
291. C2×C8SD16×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31032
C101×#29322
C101×#19852
C101×#15402
C101×#14872
C101×#13012
C101×#12812
#9047101