Finite Group Databasebeta

← C101×#9204 #38791355

Subgroups — C101×#9204 #38791355

Order 25856.

622 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2618C211yesmaximal, characteristic
2C101×#2316C211yesmaximal, characteristic, complemented
3C101×#1519C212yesmaximal
4C2×#324×C101C211yesmaximal, characteristic, complemented
5C101×#1289C212yesmaximal, complemented
6C2×#123×C101—21no—
7C2×#121×C101C2211yescharacteristic
8C2×#117×C101—21no—
9C22×C4⋊C4×C101C2211yescharacteristic
10C2×C22⋊C8×C101C2212yes—
11#398×C101C412yescomplemented
12#396×C101—22no—
13#394×C101C412yescomplemented
14#389×C101—24no—
15#386×C101—21no—
16#380×C101—21no—
17#380×C101C2211yescharacteristic
18#380×C101C2212yes—
19#327×C101—24no—
20#324×C101—22no—
21C22×D4×C101—21no—
22C22×D4×C101C2×C411yescharacteristic
23C23×C4×C101D411yescharacteristic
24C23×C4×C101D411yescharacteristic
25C23×C4×C101C2311yescharacteristic
26C22×C8×C101—22no—
27#123×C101—42no—
28#123×C101—42no—
29#121×C101—22no—
30#121×C101—22no—
31#117×C101—42no—
32#117×C101—42no—
33C2×C4⋊C4×C101—22no—
34C2×C4⋊C4×C101—22no—
35C2×C4⋊C4×C101—22no—
36C2×C4⋊C4×C101—22no—
37C2×C4⋊C4×C101—22no—
38C2×C4⋊C4×C101—21no—
39C2×C4⋊C4×C101—22no—
40C2×C4⋊C4×C101C2×C411yescharacteristic
41C2×C4⋊C4×C101C2×C412yes—
42C2×C4⋊C4×C101D412yes—
43C2×C22⋊C4×C101—22no—
44C2×C22⋊C4×C101—21no—
45C2×C22⋊C4×C101—22no—
46C2×C22⋊C4×C101—21no—
47C2×C22⋊C4×C101—22no—
48C2×C42×C101—22no—
49C22⋊C8×C101—22no—
50C22⋊C8×C101—22no—
51#95×C101—22no—
52#95×C101—22no—
53#95×C101C2×C412yes—
54#95×C101D414yes—
55C24×C101—21no—
56C24×C101C2×D411yescharacteristic
57C2×D4×C101—22no—
58C2×D4×C101—41no—
59C2×D4×C101—41no—
60C2×D4×C101—41no—
61C2×D4×C101—41no—
62C2×D4×C101—41no—
63C2×D4×C101—41no—
64C2×D4×C101—81no—
65C22×C4×C101—21no—
66C22×C4×C101—21no—
67C22×C4×C101—21no—
68C22×C4×C101—21no—
69C22×C4×C101—21no—
70C22×C4×C101—21no—
71C22×C4×C101—21no—
72C22×C4×C101—22no—
73C22×C4×C101—24no—
74C22×C4×C101—81no—
75C22×C4×C101—81no—
76C22×C4×C101C22⋊C412yes—
77C22×C4×C101C22⋊C412yes—
78C22×C4×C101D812yes—
79C22×C4×C101SD1612yes—
80C22×C4×C101C22×C411yescharacteristic
81C22×C4×C101C2×D412yes—
82C22×C4×C101C2×D411yescharacteristic
83C22×C4×C101#4112yes—
84C2×C8×C101—42no—
85C2×C8×C101—82no—
86C4⋊C4×C101—24no—
87C4⋊C4×C101—24no—
88C4⋊C4×C101—22no—
89C4⋊C4×C101—44no—
90C4⋊C4×C101—44no—
91C4⋊C4×C101—81no—
92C4⋊C4×C101—82no—
93C4⋊C4×C101—82no—
94C22⋊C4×C101—42no—
95C22⋊C4×C101—41no—
96C22⋊C4×C101—41no—
97C22⋊C4×C101—42no—
98C22⋊C4×C101—44no—
99C22⋊C4×C101—42no—
100C22⋊C4×C101—82no—
101C42×C101—44no—
102C23×C101—41no—
103C23×C101—41no—
104C23×C101—42no—
105C23×C101—42no—
106C23×C101—41no—
107C23×C101—41no—
108C23×C101—41no—
109C23×C101C2×C22⋊C411yescharacteristic
110C23×C101#12011yescharacteristic
111C23×C101#12311yescharacteristic
112C23×C101C2×D811yescharacteristic
113C23×C101C2×SD1611yescharacteristic
114C23×C101AGL(1,ℤ/8)11yescharacteristic
115C23×C101#13711yescharacteristic
116D4×C101—82no—
117D4×C101—81no—
118D4×C101—81no—
119D4×C101—81no—
120D4×C101—81no—
121C2×C4×C101—22no—
122C2×C4×C101—22no—
123C2×C4×C101—22no—
124C2×C4×C101—22no—
125C2×C4×C101—22no—
126C2×C4×C101—22no—
127C2×C4×C101—22no—
128C2×C4×C101—41no—
129C2×C4×C101—42no—
130C2×C4×C101—42no—
131C2×C4×C101—41no—
132C2×C4×C101—42no—
133C2×C4×C101—42no—
134C2×C4×C101—42no—
135C2×C4×C101—44no—
136C2×C4×C101—44no—
137C2×C4×C101—42no—
138C2×C4×C101—41no—
139C2×C4×C101—42no—
140C2×C4×C101—41no—
141C2×C4×C101—41no—
142C2×C4×C101—44no—
143C2×C4×C101—81no—
144C2×C4×C101#10214yes—
145C2×C4×C101C4×D412yes—
146C2×C4×C101#12112yes—
147C8×C101—82no—
148C22×C101—21no—
149C22×C101—21no—
150C22×C101—21no—
151C22×C101—21no—
152C22×C101—21no—
153C22×C101—21no—
154C22×C101—41no—
155C22×C101—41no—
156C22×C101—41no—
157C22×C101—41no—
158C22×C101—82no—
159C22×C101—82no—
160C22×C101—81no—
161C22×C101—81no—
162C22×C101—81no—
163C22×C101#38611yescharacteristic
164C22×C101C2×#10211yescharacteristic
165C22×C101#41711yescharacteristic
166C22×C101#44711yescharacteristic
167C22×C101#44811yescharacteristic
168C22×C101#48011yescharacteristic
169C22×C101#48111yescharacteristic
170C4×C101—24no—
171C4×C101—22no—
172C4×C101—22no—
173C4×C101—42no—
174C4×C101—84no—
175C4×C101—82no—
176C4×C101—81no—
177#9204C10111yesmaximal, characteristic, direct product factor, Sylow
178C2×C101—21no—
179C2×C101—21no—
180C2×C101—21no—
181C2×C101—21no—
182C2×C101—21no—
183C2×C101—21no—
184C2×C101—161no—
185C2×C101#187411yescharacteristic
186C2×C101#191211yescharacteristic
187C2×C101#191311yescharacteristic
188#2618C2×C10111yescharacteristic
189#2316C2×C10111yescharacteristic, complemented
190#1519C2×C10112yes—
191C2×#324C2×C10111yescharacteristic, complemented
192#1289C2×C10112yescomplemented
193C101#920411yescharacteristic, direct product factor, Sylow
194C2×#123—21no—
195C2×#121C22×C10111yescharacteristic
196C2×#117—21no—
197C22×C4⋊C4C22×C10111yescharacteristic
198C2×C22⋊C8C22×C10112yes—
199#398C4×C10112yescomplemented
200#396—22no—
201#394C4×C10112yescomplemented
202#389—24no—
203#386—21no—
204#380—21no—
205#380C22×C10111yescharacteristic
206#380C22×C10112yes—
207#327—24no—
208#324—22no—
209C22×D4—21no—
210C22×D4C2×C4×C10111yescharacteristic
211C23×C4D4×C10111yescharacteristic
212C23×C4D4×C10111yescharacteristic
213C23×C4C23×C10111yescharacteristic
214C22×C8—22no—
215#123—42no—
216#123—42no—
217#121—22no—
218#121—22no—
219#117—42no—
220#117—42no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C10111yescharacteristic
229C2×C4⋊C4C2×C4×C10112yes—
230C2×C4⋊C4D4×C10112yes—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—22no—
236C2×C42—22no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239#95—22no—
240#95—22no—
241#95C2×C4×C10112yes—
242#95D4×C10114yes—
243C24—21no—
244C24C2×D4×C10111yescharacteristic
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4C22⋊C4×C10112yes—
265C22×C4C22⋊C4×C10112yes—
266C22×C4D8×C10112yes—
267C22×C4SD16×C10112yes—
268C22×C4C22×C4×C10111yescharacteristic
269C22×C4C2×D4×C10112yes—
270C22×C4C2×D4×C10111yescharacteristic
271C22×C4#41×C10112yes—
272C2×C8—42no—
273C2×C8—82no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—44no—
278C4⋊C4—44no—
279C4⋊C4—81no—
280C4⋊C4—82no—
281C4⋊C4—82no—
282C22⋊C4—42no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—42no—
286C22⋊C4—44no—
287C22⋊C4—42no—
288C22⋊C4—82no—
289C42—44no—
290C23—41no—
291C23—41no—
292C23—42no—
293C23—42no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊C4×C10111yescharacteristic
298C23#120×C10111yescharacteristic
299C23#123×C10111yescharacteristic
300C23C2×D8×C10111yescharacteristic
301C23C2×SD16×C10111yescharacteristic
302C23AGL(1,ℤ/8)×C10111yescharacteristic
303C23#137×C10111yescharacteristic
304D4—82no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—81no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—44no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4#102×C10114yes—
333C2×C4C4×D4×C10112yes—
334C2×C4#121×C10112yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—82no—
347C22—82no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22#386×C10111yescharacteristic
352C22C2×#102×C10111yescharacteristic
353C22#417×C10111yescharacteristic
354C22#447×C10111yescharacteristic
355C22#448×C10111yescharacteristic
356C22#480×C10111yescharacteristic
357C22#481×C10111yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—84no—
363C4—82no—
364C4—81no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—161no—
372C2C101×#187411yescharacteristic
373C2C101×#191211yescharacteristic
374C2C101×#191311yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC22×C4C22×C4×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC2×#121×C101C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2316C2semidirect
4. C2×#324×C101C2semidirect
5. C101×#1289C2semidirect
11. #398×C101C4semidirect
13. #394×C101C4semidirect
177. #9204C101direct (N × H)
189. #2316C2×C101semidirect
191. C2×#324C2×C101semidirect
192. #1289C2×C101semidirect
193. C101#9204direct (N × H)
199. #398C4×C101semidirect
201. #394C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#26182
C101×#23162
C101×#15192
C2×#324×C1012
C101×#12892
#9204101