Finite Group Databasebeta

← #35218212

Subgroups — #35218212

Order 20864.

528 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
1C2×#19104714C211yesmaximal, characteristic
2C2×#19104694C211yesmaximal, characteristic
3#23781607C211yesmaximal, characteristic, complemented
4#23781599C211yesmaximal, characteristic, complemented
5#23781597C211yesmaximal, characteristic, complemented
6#23781586C211yesmaximal, characteristic, complemented
7#23781569C211yesmaximal, characteristic, complemented
8#23781562C211yesmaximal, characteristic, complemented
9#23781552C211yesmaximal, characteristic, complemented
10#23781548C211yesmaximal, characteristic, complemented
11#23781538C211yesmaximal, characteristic
12#23781538C211yesmaximal, characteristic
13#23781528C211yesmaximal, characteristic
14#23781525C211yesmaximal, characteristic
15C2×#95×C163C211yesmaximal, characteristic
16C22×Dic326C2211yescharacteristic
17#19104714—24no—
18#19104694—24no—
19C2×C4⋊Dic163C2211yescharacteristic
20C2×C4⋊Dic163C2211yescharacteristic
21C2×C4⋊Dic163C2211yescharacteristic
22C2×C4⋊Dic163C2211yescharacteristic
23C2×C4⋊Dic163C2211yescharacteristic
24C2×Dic163⋊C4C2211yescharacteristic
25C2×Dic163⋊C4C2211yescharacteristic
26C2×Dic163⋊C4C2211yescharacteristic
27C2×Dic163⋊C4C2211yescharacteristic
28C2×Dic163⋊C4C2211yescharacteristic
29C2×Dic163⋊C4C2211yescharacteristic
30C2×C22⋊Dic163C2211yescharacteristic
31C2×C22⋊Dic163C2211yescharacteristic
32C2×C22⋊Dic163C2211yescharacteristic
33C2×C22⋊Dic163C2211yescharacteristic
34C2×C4×Dic163C2211yescharacteristic
35C2×C4×Dic163C2211yescharacteristic
36C163⋊#95C2211yescharacteristic
37C163⋊#95C2211yescharacteristic
38C163⋊#95C2211yescharacteristic
39C163⋊#95C2211yescharacteristic
40C163⋊#95C2211yescharacteristic
41C163⋊#95C2211yescharacteristic
42C163⋊#95C2211yescharacteristic
43C163⋊#95C2211yescharacteristic
44C163⋊#95C2211yescharacteristic
45C163⋊#95C2211yescharacteristic
46C23×C4×C163C2211yescharacteristic
47C23×C4×C163C2211yescharacteristic
48C23×C4×C163C2211yescharacteristic
49#95×C163C2211yescharacteristic
50#95×C163C2211yescharacteristic
51#95×C163C2211yescharacteristic
52#95×C163C2211yescharacteristic
53C2×Dic326—22no—
54C2×Dic326—22no—
55C2×Dic326—41no—
56C22×Dic163C2311yescharacteristic
57C22×Dic163C2311yescharacteristic
58C22×Dic163C2311yescharacteristic
59C22×Dic163C2311yescharacteristic
60C22×Dic163C2311yescharacteristic
61C22×Dic163C2311yescharacteristic
62C22×Dic163C2311yescharacteristic
63C22×Dic163C2311yescharacteristic
64C4⋊Dic163—22no—
65C4⋊Dic163—22no—
66C4⋊Dic163—22no—
67C4⋊Dic163—22no—
68C4⋊Dic163—41no—
69Dic163⋊C4—22no—
70Dic163⋊C4—22no—
71Dic163⋊C4—22no—
72Dic163⋊C4—22no—
73Dic163⋊C4—41no—
74Dic163⋊C4—41no—
75C22⋊Dic163—22no—
76C22⋊Dic163—22no—
77C22⋊Dic163—22no—
78C22⋊Dic163D414yes—
79C4×Dic163—22no—
80C4×Dic163—22no—
81C24×C163C2311yescharacteristic
82C22×C4×C163—22no—
83C22×C4×C163—22no—
84C22×C4×C163—22no—
85C22×C4×C163—22no—
86C22×C4×C163—22no—
87C22×C4×C163—22no—
88C22×C4×C163—41no—
89C22×C4×C163—41no—
90C22×C4×C163Q814yescomplemented
91C22×C4×C163C2311yescharacteristic
92C22×C4×C163C2311yescharacteristic
93C22×C4×C163C2311yescharacteristic
94C22×C4×C163C2311yescharacteristic
95C22×C4×C163C2311yescharacteristic
96C22×C4×C163C2311yescharacteristic
97Dic326—44no—
98C2×Dic163—21no—
99C2×Dic163—21no—
100C2×Dic163—21no—
101C2×Dic163—21no—
102C2×Dic163—21no—
103C2×Dic163—21no—
104C2×Dic163—21no—
105C2×Dic163—21no—
106C2×Dic163—21no—
107C2×Dic163—21no—
108C2×Dic163—21no—
109C2×Dic163—21no—
110C2×Dic163—21no—
111C2×Dic163—21no—
112C2×Dic163—21no—
113C2×Dic163—21no—
114C2×Dic163—21no—
115C2×Dic163—21no—
116C2×Dic163—21no—
117C2×Dic163—21no—
118C2×Dic163—21no—
119C2×Dic163—21no—
120C2×Dic163C2×D412yes—
121C2×Dic163C2×D412yes—
122C23×C163—21no—
123C23×C163—21no—
124C23×C163—21no—
125C23×C163—21no—
126C23×C163C2×D412yes—
127C23×C163C2×Q812yes—
128C23×C163#4112yes—
129C23×C163C2411yescharacteristic
130C2×C4×C163—28no—
131C2×C4×C163—21no—
132C2×C4×C163—21no—
133C2×C4×C163—21no—
134C2×C4×C163—21no—
135C2×C4×C163—21no—
136C2×C4×C163—21no—
137C2×C4×C163—21no—
138C2×C4×C163—21no—
139C2×C4×C163—21no—
140C2×C4×C163—21no—
141C2×C4×C163—21no—
142C2×C4×C163—21no—
143C2×C4×C163—21no—
144C2×C4×C163—21no—
145C2×C4×C163—44no—
146C2×C4×C163—44no—
147C2×C4×C163C2×Q812yes—
148C2×C4×C163C2×Q812yes—
149C2×C4×C163#4112yes—
150C2×C4×C163#4112yes—
151C22×C163—22no—
152C22×C163—22no—
153C22×C163—22no—
154C22×C163—22no—
155C22×C163—22no—
156C22×C163—22no—
157C22×C163C22⋊Q814yes—
158C22×C163C22×D411yescharacteristic
159C22×C163C22×Q811yescharacteristic
160C22×C163C2×#4111yescharacteristic
161C22×C163C2×#4111yescharacteristic
162C22×C163C2×#4111yescharacteristic
163C22×C163H(5,𝔽2)11yescharacteristic
164C22×C1632−1+411yescharacteristic
165C4×C163—22no—
166C4×C163—22no—
167C4×C163—22no—
168C4×C163—22no—
169C4×C163—41no—
170C4×C163—41no—
171Dic163—22no—
172Dic163—22no—
173Dic163—41no—
174Dic163—41no—
175Dic163—41no—
176Dic163—41no—
177Dic163—41no—
178Dic163—41no—
179C2×C163—24no—
180C2×C163C2×C22⋊Q811yescharacteristic
181C2×C163#53311yescharacteristic
182C2×C163#54411yescharacteristic
183C2×C163#54611yescharacteristic
184C2×C163#54711yescharacteristic
185C2×C163#55111yescharacteristic
186C2×C163#55211yescharacteristic
187C163#243811yescharacteristic, complemented, Sylow
188#2438—1631nomaximal, Sylow
189C2×C22⋊Q8—1631no—
190C2×#117—1631no—
191#400—1631no—
192#398—1631no—
193#398—1631no—
194#395—1631no—
195#391—1631no—
196#389—1631no—
197#387—1631no—
198#387—1631no—
199#385—1631no—
200#385—1631no—
201#381—1631no—
202#380—1631no—
203C2×#95D16311yescharacteristic
204C22×Q8—1631no—
205C23×C4C2×D16311yescharacteristic
206C23×C4C2×D16311yescharacteristic
207C23×C4C2×D16311yescharacteristic
208C22⋊Q8—3264no—
209#117—3264no—
210C2×C4⋊C4—1631no—
211C2×C4⋊C4—1631no—
212C2×C4⋊C4—1631no—
213C2×C4⋊C4—1631no—
214C2×C4⋊C4—1631no—
215C2×C4⋊C4—1631no—
216C2×C4⋊C4—1631no—
217C2×C4⋊C4—1631no—
218C2×C4⋊C4—1631no—
219C2×C4⋊C4—1631no—
220C2×C4⋊C4—1631no—
221C2×C22⋊C4—1631no—
222C2×C22⋊C4—1631no—
223C2×C22⋊C4—1631no—
224C2×C22⋊C4—1631no—
225C2×C42—1631no—
226C2×C42—1631no—
227#95—1631no—
228#95—1631no—
229#95—1631no—
230#95—1631no—
231#95—1631no—
232#95—1631no—
233#95—1631no—
234#95—1631no—
235#95—1631no—
236#95—1631no—
237#95C2×D16311yescharacteristic
238#95C2×D16311yescharacteristic
239#95C2×D16311yescharacteristic
240#95C2×D16311yescharacteristic
241C24C22×D16311yescharacteristic
242C2×Q8—3262no—
243C2×Q8—3262no—
244C2×Q8—6521no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—1631no—
254C22×C4—1631no—
255C22×C4—1631no—
256C22×C4—1631no—
257C22×C4—1631no—
258C22×C4—1631no—
259C22×C4—1631no—
260C22×C4—1631no—
261C22×C4Dic32614yescomplemented
262C22×C4C22×D16311yescharacteristic
263C22×C4C22×D16311yescharacteristic
264C22×C4C22×D16311yescharacteristic
265C22×C4C22×D16311yescharacteristic
266C22×C4C22×D16311yescharacteristic
267C22×C4C22×D16311yescharacteristic
268C4⋊C4—3262no—
269C4⋊C4—3262no—
270C4⋊C4—3262no—
271C4⋊C4—3262no—
272C4⋊C4—3262no—
273C4⋊C4—3262no—
274C4⋊C4—3262no—
275C4⋊C4—3262no—
276C4⋊C4—6521no—
277C4⋊C4—6521no—
278C4⋊C4—6521no—
279C22⋊C4—3262no—
280C22⋊C4—3262no—
281C22⋊C4—3262no—
282C22⋊C4—1634no—
283C42—3262no—
284C42—3262no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23D4×D16312yes—
290C23C2×Dic32612yes—
291C23#1457969812yes—
292C23C23×D16311yescharacteristic
293Q8—6524no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—28no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—3261no—
312C2×C4—3261no—
313C2×C4—3261no—
314C2×C4—3261no—
315C2×C4—3261no—
316C2×C4—3261no—
317C2×C4—3261no—
318C2×C4—3261no—
319C2×C4—3261no—
320C2×C4—3261no—
321C2×C4—3261no—
322C2×C4—3261no—
323C2×C4—3261no—
324C2×C4—3261no—
325C2×C4—3261no—
326C2×C4—3261no—
327C2×C4—3261no—
328C2×C4—3261no—
329C2×C4—3261no—
330C2×C4—3261no—
331C2×C4—3261no—
332C2×C4—3261no—
333C2×C4—1632no—
334C2×C4—1632no—
335C2×C4C2×Dic32612yes—
336C2×C4C2×Dic32612yes—
337C2×C4#1457969912yes—
338C2×C4#1457969912yes—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22#1910471214yes—
346C22C2×D4×D16311yescharacteristic
347C22C22×Dic32611yescharacteristic
348C22C2×#1457969811yescharacteristic
349C22C2×#1457969911yescharacteristic
350C22C2×#1457969911yescharacteristic
351C22#1910478011yescharacteristic
352C22#1910478311yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—3262no—
360C4—3262no—
361C4—6521no—
362C4—6521no—
363C4—6521no—
364C4—6521no—
365C4—6521no—
366C4—6521no—
367C2—24no—
368C2C2×#1910471211yescharacteristic
369C2#2378222211yescharacteristic
370C2#2378229611yescharacteristic
371C2#2378230511yescharacteristic
372C2#2378231611yescharacteristic
373C2#2378234111yescharacteristic
374C2#2378235011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D163
commutator, socle, cosocleC23×C163C24
FittingC2×#95×C163C2
prime radicalC24×C163C23
hypercenterC2×#95D163
hypocenterC163#2438
LCSG ▷ C23×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #23781607C2semidirect
4. #23781599C2semidirect
5. #23781597C2semidirect
6. #23781586C2semidirect
7. #23781569C2semidirect
8. #23781562C2semidirect
9. #23781552C2semidirect
10. #23781548C2semidirect
90. C22×C4×C163Q8semidirect
187. C163#2438semidirect
261. C22×C4Dic326semidirect

Maximal subgroups

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

subgroupindex
C2×#191047142
C2×#191046942
#237816072
#237815992
#237815972
#237815862
#237815692
#237815622
#237815522
#237815482
#237815382
#237815282
#237815252
C2×#95×C1632
#2438163