Finite Group Databasebeta

← C101×#10202 #38792353

Subgroups — C101×#10202 #38792353

Order 25856.

512 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3246C211yesmaximal, characteristic
2C101×#3230C211yesmaximal, characteristic, complemented
3C101×#3141C211yesmaximal, characteristic
4C101×#1986C211yesmaximal, characteristic, complemented
5C101×#1981C211yesmaximal, characteristic, complemented
6C101×#1502C211yesmaximal, characteristic
7C101×#1283C211yesmaximal, characteristic, complemented
8#533×C101C2211yescharacteristic
9#532×C101C2211yescharacteristic
10C2×C4⋊Q8×C101C2211yescharacteristic
11#500×C101—21no—
12#489×C101—22no—
13#487×C101—21no—
14#487×C101—21no—
15#486×C101—21no—
16#484×C101—22no—
17#477×C101—22no—
18#476×C101—21no—
19#475×C101—21no—
20#465×C101—22no—
21#461×C101—21no—
22#460×C101—21no—
23#431×C101C2211yescharacteristic
24C2×C4⋊C8×C101C2211yescharacteristic
25#417×C101—22no—
26C2×#103×C101—22no—
27C4×M16×C101C2211yescharacteristic
28C4×C4⋊C4×C101C2211yescharacteristic
29#339×C101—22no—
30#327×C101—22no—
31C2×#41×C101—21no—
32C22×Q8×C101—21no—
33C2×SD16×C101—22no—
34C2×M16×C101D412yes—
35C22×C8×C101D412yes—
36C4⋊Q8×C101—21no—
37C4⋊Q8×C101—21no—
38C4⋊Q8×C101—21no—
39C4⋊Q8×C101D411yescharacteristic
40C4⋊Q8×C101D411yescharacteristic
41C4⋊Q8×C101D411yescharacteristic
42C4⋊Q8×C101D412yes—
43#127×C101D411yescharacteristic
44#125×C101—21no—
45#124×C101—21no—
46C22⋊Q8×C101—21no—
47C22⋊Q8×C101—21no—
48#121×C101—21no—
49#121×C101—21no—
50C4×Q8×C101—21no—
51C4×Q8×C101—21no—
52C4×D4×C101—21no—
53C4×D4×C101—21no—
54#117×C101—21no—
55C2×C4⋊C4×C101—21no—
56C2×C4⋊C4×C101—21no—
57C2×C4⋊C4×C101—21no—
58C2×C42×C101—21no—
59C2×C42×C101C2311yescharacteristic
60#107×C101—24no—
61#106×C101—22no—
62C4⋊C8×C101—21no—
63C4⋊C8×C101—21no—
64C4⋊C8×C101—21no—
65#103×C101—24no—
66#103×C101—22no—
67#103×C101—24no—
68#103×C101—44no—
69#102×C101—24no—
70#102×C101—22no—
71C22⋊C8×C101D412yes—
72#97×C101—21no—
73C4×C8×C101—21no—
74C4×C8×C101—21no—
75#95×C101—21no—
76#41×C101—42no—
77#41×C101—42no—
78C2×Q8×C101—21no—
79C2×Q8×C101—21no—
80C2×Q8×C101—21no—
81C2×Q8×C101—22no—
82C2×Q8×C101—42no—
83C2×Q8×C101—42no—
84C2×Q8×C101—41no—
85C2×D4×C101—21no—
86C2×D4×C101—21no—
87C2×D4×C101—21no—
88C2×D4×C101—41no—
89C22×C4×C101—41no—
90C22×C4×C101—41no—
91C22×C4×C101—41no—
92C22×C4×C101C2×D411yescharacteristic
93C22×C4×C101C2×D411yescharacteristic
94C22×C4×C101C2×D411yescharacteristic
95SD16×C101—82no—
96M16×C101—22no—
97M16×C101—22no—
98C2×C8×C101—22no—
99C2×C8×C101—22no—
100C2×C8×C101—22no—
101C2×C8×C101—42no—
102C4⋊C4×C101—22no—
103C4⋊C4×C101—22no—
104C4⋊C4×C101—21no—
105C4⋊C4×C101—21no—
106C4⋊C4×C101—22no—
107C4⋊C4×C101—21no—
108C4⋊C4×C101—21no—
109C4⋊C4×C101—21no—
110C4⋊C4×C101—21no—
111C4⋊C4×C101—41no—
112C4⋊C4×C101—41no—
113C4⋊C4×C101—41no—
114C4⋊C4×C101—41no—
115C4⋊C4×C101—41no—
116C22⋊C4×C101—41no—
117C22⋊C4×C101—41no—
118C22⋊C4×C101—41no—
119C42×C101—41no—
120C42×C101—42no—
121C42×C101C2×D411yescharacteristic
122C42×C101C2×D411yescharacteristic
123C42×C101C2×D411yescharacteristic
124C42×C101#4111yescharacteristic
125C23×C101—41no—
126C23×C101#12711yescharacteristic
127Q8×C101—42no—
128Q8×C101—44no—
129Q8×C101—42no—
130Q8×C101—41no—
131Q8×C101—41no—
132Q8×C101—81no—
133Q8×C101—81no—
134D4×C101—42no—
135D4×C101—41no—
136D4×C101—41no—
137D4×C101—81no—
138D4×C101—81no—
139D4×C101—81no—
140C2×C4×C101—21no—
141C2×C4×C101—21no—
142C2×C4×C101—41no—
143C2×C4×C101—42no—
144C2×C4×C101—41no—
145C2×C4×C101—41no—
146C2×C4×C101—41no—
147C2×C4×C101—42no—
148C2×C4×C101—81no—
149C2×C4×C101—82no—
150C2×C4×C101—81no—
151C2×C4×C101—82no—
152C2×C4×C101#12011yescharacteristic
153C2×C4×C101#12011yescharacteristic
154C2×C4×C101#12011yescharacteristic
155C2×C4×C101#12111yescharacteristic
156C2×C4×C101#12111yescharacteristic
157C2×C4×C101#12111yescharacteristic
158C2×C4×C101#13512yes—
159C2×C4×C101#13712yes—
160C8×C101—42no—
161C8×C101—42no—
162C8×C101—42no—
163C22×C101—21no—
164C22×C101—21no—
165C22×C101—81no—
166C22×C101—81no—
167C22×C101—81no—
168C22×C101#39211yescharacteristic
169C22×C101#49511yescharacteristic
170C22×C101#49711yescharacteristic
171C4×C101—21no—
172C4×C101—21no—
173C4×C101—21no—
174C4×C101—82no—
175C4×C101—82no—
176C4×C101—81no—
177C4×C101—81no—
178C4×C101—81no—
179C4×C101#45212yes—
180C4×C101#45311yescharacteristic
181C4×C101#45411yescharacteristic
182C4×C101#46412yes—
183#10202C10111yesmaximal, characteristic, direct product factor, Sylow
184C2×C101—21no—
185C2×C101—21no—
186C2×C101—161no—
187C2×C101#200611yescharacteristic
188C2×C101#200911yescharacteristic
189C2×C101#201511yescharacteristic
190#3246C2×C10111yescharacteristic
191#3230C2×C10111yescharacteristic, complemented
192#3141C2×C10111yescharacteristic
193#1986C2×C10111yescharacteristic, complemented
194#1981C2×C10111yescharacteristic, complemented
195#1502C2×C10111yescharacteristic
196#1283C2×C10111yescharacteristic, complemented
197C101#1020211yescharacteristic, direct product factor, Sylow
198#533C22×C10111yescharacteristic
199#532C22×C10111yescharacteristic
200C2×C4⋊Q8C22×C10111yescharacteristic
201#500—21no—
202#489—22no—
203#487—21no—
204#487—21no—
205#486—21no—
206#484—22no—
207#477—22no—
208#476—21no—
209#475—21no—
210#465—22no—
211#461—21no—
212#460—21no—
213#431C22×C10111yescharacteristic
214C2×C4⋊C8C22×C10111yescharacteristic
215#417—22no—
216C2×#103—22no—
217C4×M16C22×C10111yescharacteristic
218C4×C4⋊C4C22×C10111yescharacteristic
219#339—22no—
220#327—22no—
221C2×#41—21no—
222C22×Q8—21no—
223C2×SD16—22no—
224C2×M16D4×C10112yes—
225C22×C8D4×C10112yes—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C10112yes—
230C4⋊Q8D4×C10111yescharacteristic
231C4⋊Q8D4×C10111yescharacteristic
232C4⋊Q8D4×C10111yescharacteristic
233#127D4×C10111yescharacteristic
234#125—21no—
235#124—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238#121—21no—
239#121—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—21no—
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C42—21no—
249C2×C42C23×C10111yescharacteristic
250#107—24no—
251#106—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255#103—24no—
256#103—22no—
257#103—24no—
258#103—44no—
259#102—24no—
260#102—22no—
261C22⋊C8D4×C10112yes—
262#97—21no—
263C4×C8—21no—
264C4×C8—21no—
265#95—21no—
266#41—42no—
267#41—42no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—41no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C2×D4×C10111yescharacteristic
283C22×C4C2×D4×C10111yescharacteristic
284C22×C4C2×D4×C10111yescharacteristic
285SD16—82no—
286M16—22no—
287M16—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—42no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—41no—
310C42—42no—
311C42C2×D4×C10111yescharacteristic
312C42C2×D4×C10111yescharacteristic
313C42C2×D4×C10111yescharacteristic
314C42#41×C10111yescharacteristic
315C23—41no—
316C23#127×C10111yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—42no—
320Q8—41no—
321Q8—41no—
322Q8—81no—
323Q8—81no—
324D4—42no—
325D4—41no—
326D4—41no—
327D4—81no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4#120×C10111yescharacteristic
343C2×C4#120×C10111yescharacteristic
344C2×C4#120×C10111yescharacteristic
345C2×C4#121×C10111yescharacteristic
346C2×C4#121×C10111yescharacteristic
347C2×C4#121×C10111yescharacteristic
348C2×C4#135×C10112yes—
349C2×C4#137×C10112yes—
350C8—42no—
351C8—42no—
352C8—42no—
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22#392×C10111yescharacteristic
359C22#495×C10111yescharacteristic
360C22#497×C10111yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—82no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4#452×C10112yes—
370C4#453×C10111yescharacteristic
371C4#454×C10111yescharacteristic
372C4#464×C10112yes—
373C2—21no—
374C2—21no—
375C2—161no—
376C2C101×#200611yescharacteristic
377C2C101×#200911yescharacteristic
378C2C101×#201511yescharacteristic
subgroupG/H
center, socleC22×C101#392
commutator, Frattini, cosocleC2×C42C23×C101
prime radical#532×C101C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3230C2semidirect
4. C101×#1986C2semidirect
5. C101×#1981C2semidirect
7. C101×#1283C2semidirect
183. #10202C101direct (N × H)
191. #3230C2×C101semidirect
193. #1986C2×C101semidirect
194. #1981C2×C101semidirect
196. #1283C2×C101semidirect
197. C101#10202direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32462
C101×#32302
C101×#31412
C101×#19862
C101×#19812
C101×#15022
C101×#12832
#10202101