Finite Group Databasebeta

← #35217778

Subgroups — #35217778

Order 20864.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D163C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D163C211yesmaximal, characteristic, complemented
3C2×#19104694C211yesmaximal, characteristic, complemented
4#23781598C211yesmaximal, characteristic, complemented
5#23781593C211yesmaximal, characteristic, complemented
6#23781588C211yesmaximal, characteristic, complemented
7#23781587C211yesmaximal, characteristic, complemented
8#23781581C211yesmaximal, characteristic, complemented
9#23781580C211yesmaximal, characteristic, complemented
10#23781579C211yesmaximal, characteristic, complemented
11#23781573C211yesmaximal, characteristic
12C4×Dic163⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D163)⋊C4C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic163C211yesmaximal, characteristic, complemented
15C2×C4×D4×C163C211yesmaximal, characteristic, complemented
16C22×C22⋊D163C2211yescharacteristic
17C22×C22⋊D163C2211yescharacteristic
18C22×C4×D163C2211yescharacteristic
19C4×C22⋊D163—24no—
20C4×C22⋊D163—24no—
21#19104694—24no—
22C2×C4⋊Dic163C2211yescharacteristic
23C2×C4⋊Dic163C2211yescharacteristic
24C2×Dic163⋊C4C2211yescharacteristic
25C2×Dic163⋊C4C2211yescharacteristic
26C2×Dic163⋊C4C2211yescharacteristic
27C2×Dic163⋊C4C2211yescharacteristic
28C2×C22⋊Dic163C2211yescharacteristic
29C2×C22⋊Dic163C2211yescharacteristic
30C2×C22⋊Dic163C2211yescharacteristic
31C2×C22⋊Dic163C2211yescharacteristic
32C2×C22⋊Dic163C2211yescharacteristic
33C2×C22⋊Dic163C2211yescharacteristic
34C2×(C2×D163)⋊C4C2211yescharacteristic
35C2×(C2×D163)⋊C4C2211yescharacteristic
36C2×(C2×D163)⋊C4C2211yescharacteristic
37C2×(C2×D163)⋊C4C2211yescharacteristic
38C2×C4×Dic163C2211yescharacteristic
39C2×C4×Dic163C2211yescharacteristic
40C2×C4×Dic163C2211yescharacteristic
41C163⋊#95C2211yescharacteristic
42C163⋊#95C2211yescharacteristic
43C163⋊#95C2211yescharacteristic
44C163⋊#95C2211yescharacteristic
45C163⋊#95C2211yescharacteristic
46C163⋊#95C2211yescharacteristic
47C22×D4×C163C2211yescharacteristic
48C23×C4×C163C2211yescharacteristic
49C23×C4×C163C2211yescharacteristic
50C4×D4×C163—24no—
51C2×C4⋊C4×C163C2211yescharacteristic
52C2×C22⋊C4×C163C2211yescharacteristic
53C2×C22⋊C4×C163C2211yescharacteristic
54C2×C42×C163C2211yescharacteristic
55C23×D163C2311yescharacteristic
56C2×C22⋊D163—22no—
57C2×C22⋊D163—22no—
58C2×C22⋊D163—22no—
59C2×C22⋊D163—22no—
60C2×C22⋊D163—22no—
61C2×C22⋊D163—22no—
62C22×Dic163C2311yescharacteristic
63C22×Dic163C2311yescharacteristic
64C22×Dic163C2311yescharacteristic
65C22×Dic163C2311yescharacteristic
66C22×Dic163C2311yescharacteristic
67C22×Dic163C2311yescharacteristic
68C22×Dic163C2311yescharacteristic
69C2×C4×D163—22no—
70C2×C4×D163—22no—
71C2×C4×D163—22no—
72C4⋊Dic163—22no—
73C4⋊Dic163—22no—
74Dic163⋊C4—22no—
75Dic163⋊C4—22no—
76Dic163⋊C4—22no—
77Dic163⋊C4—22no—
78C22⋊Dic163—22no—
79C22⋊Dic163—22no—
80C22⋊Dic163—22no—
81C22⋊Dic163—22no—
82C22⋊Dic163—22no—
83C22⋊Dic163—22no—
84(C2×D163)⋊C4—22no—
85(C2×D163)⋊C4—22no—
86(C2×D163)⋊C4—22no—
87(C2×D163)⋊C4—22no—
88C4×Dic163—22no—
89C4×Dic163—22no—
90C4×Dic163D414yescomplemented
91C24×C163C2311yescharacteristic
92C24×C163C2311yescharacteristic
93C2×D4×C163—22no—
94C2×D4×C163—22no—
95C2×D4×C163—22no—
96C22×C4×C163—22no—
97C22×C4×C163—22no—
98C22×C4×C163—22no—
99C22×C4×C163—22no—
100C22×C4×C163—22no—
101C22×C4×C163D414yescomplemented
102C22×C4×C163C2311yescharacteristic
103C22×C4×C163C2311yescharacteristic
104C22×C4×C163C2311yescharacteristic
105C22×C4×C163C2311yescharacteristic
106C22×C4×C163C2311yescharacteristic
107C4⋊C4×C163—22no—
108C22⋊C4×C163—22no—
109C22⋊C4×C163—22no—
110C42×C163—22no—
111C22×D163—21no—
112C22×D163—21no—
113C22×D163—21no—
114C22×D163—21no—
115C22×D163—21no—
116C22×D163—21no—
117C22×D163#4112yes—
118C22⋊D163—28no—
119C22⋊D163—28no—
120C2×Dic163—21no—
121C2×Dic163—21no—
122C2×Dic163—21no—
123C2×Dic163—21no—
124C2×Dic163—21no—
125C2×Dic163—21no—
126C2×Dic163—21no—
127C2×Dic163—21no—
128C2×Dic163—21no—
129C2×Dic163—21no—
130C2×Dic163—21no—
131C2×Dic163—21no—
132C2×Dic163—21no—
133C2×Dic163—21no—
134C2×Dic163—21no—
135C2×Dic163—21no—
136C2×Dic163—21no—
137C2×Dic163—21no—
138C2×Dic163C2×D412yes—
139C2×Dic163C2×D412yes—
140C2×Dic163#4112yes—
141C4×D163—44no—
142C23×C163—21no—
143C23×C163—21no—
144C23×C163—21no—
145C23×C163—21no—
146C23×C163—21no—
147C23×C163—21no—
148C23×C163—21no—
149C23×C163—21no—
150C23×C163—21no—
151C23×C163—21no—
152C23×C163—21no—
153C23×C163—21no—
154C23×C163C2×D412yes—
155C23×C163#4112yes—
156C23×C163C2411yescharacteristic
157D4×C163—28no—
158C2×C4×C163—21no—
159C2×C4×C163—21no—
160C2×C4×C163—21no—
161C2×C4×C163—21no—
162C2×C4×C163—28no—
163C2×C4×C163—21no—
164C2×C4×C163—21no—
165C2×C4×C163—21no—
166C2×C4×C163—21no—
167C2×C4×C163—21no—
168C2×C4×C163—21no—
169C2×C4×C163—44no—
170C2×C4×C163C2×D412yes—
171C2×C4×C163C2×D412yes—
172C2×C4×C163C2×D412yes—
173C2×C4×C163#4112yes—
174C2×C4×C163#4112yes—
175C22×C163—22no—
176C22×C163—22no—
177C22×C163—22no—
178C22×C163—22no—
179C22×C163—22no—
180C22×C163—22no—
181C22×C163—41no—
182C22×C163—41no—
183C22×C163—41no—
184C22×C163—41no—
185C22×C163—41no—
186C22×C163—41no—
187C22×C163—41no—
188C22×C163—41no—
189C22×C163C22×D411yescharacteristic
190C22×C163C22×D411yescharacteristic
191C22×C163C2×#4111yescharacteristic
192C22×C163C2×#4111yescharacteristic
193C22×C163C2×#4111yescharacteristic
194C22×C163C2×#4111yescharacteristic
195C22×C163C2×#4111yescharacteristic
196C2×D163—22no—
197C2×D163—22no—
198C2×D163—22no—
199C2×D163—41no—
200C2×D163—41no—
201C2×D163—41no—
202C2×D163—41no—
203C4×C163—22no—
204C4×C163—22no—
205C4×C163—41no—
206C4×C163—41no—
207C4×C163#12114yes—
208Dic163—22no—
209Dic163—22no—
210Dic163—22no—
211Dic163—41no—
212Dic163—41no—
213Dic163—41no—
214Dic163—41no—
215C2×C163—42no—
216C2×C163—42no—
217C2×C163C2×#12111yescharacteristic
218C2×C163#52511yescharacteristic
219C2×C163#52511yescharacteristic
220C2×C163#52511yescharacteristic
221C2×C163#52911yescharacteristic
222C2×C163#52911yescharacteristic
223C2×C163#53211yescharacteristic
224D163—42no—
225C163#239211yescharacteristic, complemented, Sylow
226#2392—1631nomaximal, Sylow
227C2×C4×D4—1631no—
228C2×C4×D4—1631no—
229C2×C4×D4D16311yescharacteristic, complemented
230C2×#117—1631no—
231#398—1631no—
232#397—1631no—
233#396—1631no—
234#396—1631no—
235#394—1631no—
236#394—1631no—
237#394—1631no—
238#392—1631no—
239C4×C4⋊C4—1631no—
240C4×C22⋊C4—1631no—
241C4×C22⋊C4—1631no—
242C22×D4—1631no—
243C22×D4—1631no—
244C22×D4C2×D16311yescharacteristic
245C23×C4—1631no—
246C23×C4C2×D16311yescharacteristic
247C23×C4C2×D16311yescharacteristic
248C4×D4—24no—
249C4×D4—3264no—
250C4×D4—3264no—
251#117—3264no—
252C2×C4⋊C4—1631no—
253C2×C4⋊C4—1631no—
254C2×C4⋊C4—1631no—
255C2×C4⋊C4—1631no—
256C2×C4⋊C4—1631no—
257C2×C4⋊C4—1631no—
258C2×C4⋊C4C2×D16311yescharacteristic
259C2×C22⋊C4—1631no—
260C2×C22⋊C4—1631no—
261C2×C22⋊C4—1631no—
262C2×C22⋊C4—1631no—
263C2×C22⋊C4—1631no—
264C2×C22⋊C4—1631no—
265C2×C22⋊C4—1631no—
266C2×C22⋊C4—1631no—
267C2×C22⋊C4—1631no—
268C2×C22⋊C4—1631no—
269C2×C22⋊C4C2×D16311yescharacteristic
270C2×C22⋊C4C2×D16311yescharacteristic
271C2×C42—1631no—
272C2×C42—1631no—
273C2×C42—1631no—
274C2×C42C2×D16311yescharacteristic
275#95—1631no—
276#95—1631no—
277#95—1631no—
278#95—1631no—
279#95—1631no—
280#95—1631no—
281C24—1631no—
282C24C22×D16311yescharacteristic
283C24C22×D16311yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—3262no—
288C2×D4—3262no—
289C2×D4—3262no—
290C2×D4—3262no—
291C2×D4—3262no—
292C2×D4—3262no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—3262no—
299C22×C4—3262no—
300C22×C4—3262no—
301C22×C4—1631no—
302C22×C4—1631no—
303C22×C4—1631no—
304C22×C4—1631no—
305C22×C4—1631no—
306C22×C4—1631no—
307C22×C4—1631no—
308C22×C4C22⋊D16314yescomplemented
309C22×C4C22×D16311yescharacteristic
310C22×C4C22×D16311yescharacteristic
311C22×C4C22×D16311yescharacteristic
312C22×C4C22×D16311yescharacteristic
313C22×C4C22×D16311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—3262no—
316C4⋊C4—3262no—
317C4⋊C4—3262no—
318C4⋊C4—3262no—
319C4⋊C4—3262no—
320C4⋊C4—3262no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—3262no—
324C22⋊C4—3262no—
325C22⋊C4—3262no—
326C22⋊C4—3262no—
327C22⋊C4—3262no—
328C22⋊C4—3262no—
329C22⋊C4—3262no—
330C22⋊C4—3262no—
331C22⋊C4—3262no—
332C22⋊C4—3262no—
333C42—22no—
334C42—3262no—
335C42—3262no—
336C42—1634no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—3261no—
350C23—3261no—
351C23—3261no—
352C23—3261no—
353C23—3261no—
354C23—3261no—
355C23—1632no—
356C23C2×C22⋊D16312yes—
357C23#1457969912yes—
358C23C23×D16311yescharacteristic
359D4—28no—
360D4—3268no—
361D4—3268no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—28no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—3261no—
375C2×C4—3261no—
376C2×C4—3261no—
377C2×C4—3261no—
378C2×C4—3261no—
379C2×C4—3261no—
380C2×C4—3261no—
381C2×C4—3261no—
382C2×C4—3261no—
383C2×C4—3261no—
384C2×C4—3261no—
385C2×C4—3261no—
386C2×C4—3261no—
387C2×C4—3261no—
388C2×C4—3261no—
389C2×C4—3261no—
390C2×C4—3261no—
391C2×C4—3261no—
392C2×C4—6524no—
393C2×C4—1632no—
394C2×C4—1632no—
395C2×C4—1632no—
396C2×C4D4×D16312yes—
397C2×C4C2×C22⋊D16312yes—
398C2×C4C2×C22⋊D16312yes—
399C2×C4#1457969812yes—
400C2×C4#1457969912yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—3262no—
416C22—3262no—
417C22—3262no—
418C22—6521no—
419C22—6521no—
420C22—6521no—
421C22—6521no—
422C22C2×D4×D16311yescharacteristic
423C22C22×C22⋊D16311yescharacteristic
424C22#41×D16311yescharacteristic
425C22#41×D16311yescharacteristic
426C22C2×#1457969811yescharacteristic
427C22C2×#1457969911yescharacteristic
428C22C2×#1457969911yescharacteristic
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—3262no—
434C4—3262no—
435C4—3262no—
436C4—6521no—
437C4—6521no—
438C4—6521no—
439C4—6521no—
440C4#1910470714yes—
441C2—42no—
442C2—42no—
443C2—6522no—
444C2C2×#1910470711yescharacteristic
445C2#2378217211yescharacteristic
446C2#2378217411yescharacteristic
447C2#2378217611yescharacteristic
448C2#2378219511yescharacteristic
449C2#2378219711yescharacteristic
450C2#2378221211yescharacteristic
subgroupG/H
centerC22×C4C22×D163
commutator, socle, cosocleC23×C163C24
FrattiniC23C23×D163
FittingC2×C4×D4×C163C2
prime radical#23781573C2
hypercenterC2×C4×D4D163
hypocenterC163#2392
LCSG ▷ C23×C163 ▷ C163
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D163C2semidirect
2. C2×C4×C22⋊D163C2semidirect
3. C2×#19104694C2semidirect
4. #23781598C2semidirect
5. #23781593C2semidirect
6. #23781588C2semidirect
7. #23781587C2semidirect
8. #23781581C2semidirect
9. #23781580C2semidirect
10. #23781579C2semidirect
12. C4×Dic163⋊C4C2semidirect
13. C4×(C2×D163)⋊C4C2semidirect
14. C4×C22⋊Dic163C2semidirect
15. C2×C4×D4×C163C2semidirect
90. C4×Dic163D4semidirect
101. C22×C4×C163D4semidirect
225. C163#2392semidirect
229. C2×C4×D4D163semidirect
308. C22×C4C22⋊D163semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1632
C2×#191046942
#237815982
#237815932
#237815882
#237815872
#237815812
#237815802
#237815792
#237815732
C4×Dic163⋊C42
C4×(C2×D163)⋊C42
C4×C22⋊Dic1632
C2×C4×D4×C1632
#2392163