Finite Group Databasebeta

← #36564509

Subgroups — #36564509

Order 22784.

866 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#13083553C211yesmaximal, characteristic
2#26020809C214yesmaximal, complemented
3#26020807C214yesmaximal, complemented
4#26020318C212yesmaximal
5#26020230C212yesmaximal
6C4×C22⋊#10623494C211yesmaximal, characteristic
7C4×C22⋊C8×C89C211yesmaximal, characteristic
8C22×#13083553C411yescharacteristic
9C22×#13083553C411yescharacteristic
10C22×C4×Dic89C2211yescharacteristic
11C22×C4×Dic89C2211yescharacteristic
12C2×#15667941C2214yes—
13C2×C22⋊#10623494C2212yes—
14C2×C4×#10623494C2212yes—
15C4×#13083553C412yes—
16C4×#13083553C412yes—
17C4×#13083553C2212yes—
18C4×#13083553C2212yes—
19C2×#15667919C411yescharacteristic
20C2×#15667919C411yescharacteristic
21#19151353C2212yes—
22#19151352C2214yes—
23#19151352C2218yes—
24C22×C42×C89C2211yescharacteristic
25C2×C22⋊C8×C89C2212yes—
26C2×C4×C8×C89C2212yes—
27#336×C89C2212yes—
28C23×Dic89C2×C411yescharacteristic
29C23×Dic89C2×C411yescharacteristic
30C23×Dic89C2×C411yescharacteristic
31C23×Dic89C2×C411yescharacteristic
32C22×#10623494C2314yes—
33C2×#13083553—24no—
34C2×#13083553C818yescomplemented
35C2×#13083553C2×C412yes—
36C2×#13083553C2×C412yes—
37C2×#13083553C2×C412yes—
38C2×#13083553C2×C412yes—
39C2×C4×Dic89—24no—
40C2×C4×Dic89—42no—
41C2×C4×Dic89C2×C412yes—
42C2×C4×Dic89C2×C412yes—
43C2×C4×Dic89C2312yes—
44C2×C4×Dic89C2312yes—
45#15667941—44no—
46C22⋊#10623494—24no—
47C4×#10623494—42no—
48#15667919C2×C412yes—
49#15667919C2×C412yes—
50#15667919C2×C412yes—
51#15667919C2×C412yes—
52C23×C4×C89C2×C411yescharacteristic
53C23×C4×C89C2×C411yescharacteristic
54C23×C4×C89C2311yescharacteristic
55C22×C8×C89C2314yes—
56C2×C42×C89—42no—
57C2×C42×C89C2×C411yescharacteristic
58C2×C42×C89C2×C411yescharacteristic
59C2×C42×C89C2311yescharacteristic
60C2×C42×C89C2311yescharacteristic
61C22⋊C8×C89—24no—
62C4×C8×C89—42no—
63C22×Dic89—22no—
64C22×Dic89—22no—
65C22×Dic89—22no—
66C22×Dic89—22no—
67C22×Dic89—41no—
68C22×Dic89—41no—
69C22×Dic89—41no—
70C22×Dic89—41no—
71C22×Dic89—41no—
72C22×Dic89—41no—
73C22×Dic89C2×C814yes—
74C22×Dic89C2×C814yes—
75C22×Dic89C22×C412yes—
76C22×Dic89C22×C412yes—
77C22×Dic89C22×C412yes—
78C22×Dic89C22×C412yes—
79C2×#10623494—24no—
80C2×#10623494—24no—
81C2×#10623494—24no—
82#13083553—24no—
83#13083553—24no—
84#13083553C2×C818yes—
85#13083553C2×C818yes—
86C4×Dic89—24no—
87C4×Dic89—24no—
88C4×Dic89—24no—
89C4×Dic89—42no—
90C24×C89C22×C411yescharacteristic
91C22×C4×C89—22no—
92C22×C4×C89—22no—
93C22×C4×C89—41no—
94C22×C4×C89—41no—
95C22×C4×C89—41no—
96C22×C4×C89—41no—
97C22×C4×C89C2×C814yes—
98C22×C4×C89M1614yes—
99C22×C4×C89C22×C411yescharacteristic
100C22×C4×C89C22×C411yescharacteristic
101C22×C4×C89C22×C411yescharacteristic
102C22×C4×C89C22×C411yescharacteristic
103C22×C4×C89C22×C411yescharacteristic
104C22×C4×C89#4114yes—
105C22×C4×C89C2411yescharacteristic
106C2×C8×C89—24no—
107C2×C8×C89—24no—
108C2×C8×C89—24no—
109C42×C89—22no—
110C42×C89—22no—
111C42×C89—41no—
112C42×C89—41no—
113C23×C89—21no—
114C23×C89—21no—
115C23×C89—21no—
116C23×C89—21no—
117C23×C89#11712yes—
118C23×C89C22×C812yes—
119C23×C89C2×M1612yes—
120C23×C89C23×C411yescharacteristic
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—28no—
132C2×C4×C89—44no—
133C2×C4×C89—44no—
134C2×C4×C89#11712yes—
135C2×C4×C89C22×C812yes—
136C2×C4×C89C22×C812yes—
137C2×C4×C89C2×M1612yes—
138C2×C4×C89C2×M1612yes—
139C2×C4×C89C2×#4112yes—
140C2×C4×C89H(5,𝔽2)12yes—
141C2×C4×C892−1+412yes—
142C2×Dic89—22no—
143C2×Dic89—22no—
144C2×Dic89—22no—
145C2×Dic89—22no—
146C2×Dic89—28no—
147C2×Dic89—22no—
148C2×Dic89—22no—
149C2×Dic89—22no—
150C2×Dic89—22no—
151C2×Dic89—22no—
152C2×Dic89—22no—
153C2×Dic89—44no—
154C2×Dic89—44no—
155C2×Dic89—44no—
156C2×Dic89C22×C814yes—
157C2×Dic89C22×C814yes—
158C8×C89—44no—
159#10623494—44no—
160C22×C89—22no—
161C22×C89—22no—
162C22×C89—22no—
163C22×C89—22no—
164C22×C89—22no—
165C22×C89—22no—
166C22×C89#43114yes—
167C22×C89C2×#11711yescharacteristic
168C22×C89#51811yescharacteristic
169C22×C89#51911yescharacteristic
170C22×C89C23×C811yescharacteristic
171C22×C89C22×M1611yescharacteristic
172C22×C89#56811yescharacteristic
173C22×C89#56811yescharacteristic
174C4×C89—22no—
175C4×C89—22no—
176C4×C89—22no—
177C4×C89—22no—
178C4×C89—22no—
179C4×C89#53914yes—
180Dic89—24no—
181Dic89—24no—
182Dic89—42no—
183Dic89—42no—
184#21912—891nomaximal, Sylow
185C2×C89—24no—
186C2×C89#231311yescharacteristic
187C2×C89C2×#43111yescharacteristic
188C2×C89#292111yescharacteristic
189C2×C89#297211yescharacteristic
190C2×C89#297311yescharacteristic
191C2×C89#298211yescharacteristic
192C2×C89#298311yescharacteristic
193C2×C4×C4⋊C4—891no—
194#1916—894no—
195#1916—894no—
196#1817—892no—
197#1797—892no—
198C4×C22⋊C8—891no—
199C4×C22⋊C8D8911yescharacteristic
200C89#2191211yescharacteristic, complemented, Sylow
201C22×C4⋊C4—891no—
202C22×C4⋊C4—891no—
203C22×C42—891no—
204C22×C42—891no—
205C22×C42C2×D8911yescharacteristic
206C2×C4⋊C8—894no—
207C2×C22⋊C8—892no—
208C2×C22⋊C8C2×D8912yes—
209C2×C4×C8—892no—
210C2×C4×C8C2×D8912yes—
211C4×C4⋊C4—892no—
212C4×C4⋊C4—892no—
213C4×C4⋊C4—892no—
214C4×C4⋊C4—892no—
215C2×#95—891no—
216C2×#95—891no—
217#336—894no—
218#336—898no—
219#336—892no—
220#336C2×D8912yes—
221C23×C4—891no—
222C23×C4—891no—
223C23×C4—891no—
224C23×C4—891no—
225C23×C4C4×D8911yescharacteristic
226C23×C4C4×D8911yescharacteristic
227C23×C4C22×D8911yescharacteristic
228C22×C8—894no—
229C22×C8C22×D8914yes—
230C2×C4⋊C4—898no—
231C2×C4⋊C4—892no—
232C2×C4⋊C4—892no—
233C2×C4⋊C4—892no—
234C2×C4⋊C4—892no—
235C2×C4⋊C4—1784no—
236C2×C42—42no—
237C2×C42—892no—
238C2×C42—892no—
239C2×C42—892no—
240C2×C42—892no—
241C2×C42—3562no—
242C2×C42—1784no—
243C2×C42C4×D8911yescharacteristic
244C2×C42C4×D8911yescharacteristic
245C2×C42C22×D8911yescharacteristic
246C2×C42C22×D8911yescharacteristic
247C4⋊C8—3564no—
248C22⋊C8—24no—
249C22⋊C8—1784no—
250C4×C8—42no—
251C4×C8—3562no—
252#95—892no—
253#95—892no—
254#95—892no—
255#95—892no—
256C24C2×C4×D8911yescharacteristic
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—894no—
264C22×C4—894no—
265C22×C4—892no—
266C22×C4—892no—
267C22×C4—892no—
268C22×C4—892no—
269C22×C4—3561no—
270C22×C4—3561no—
271C22×C4—3561no—
272C22×C4—3561no—
273C22×C4—3561no—
274C22×C4—3561no—
275C22×C4—1782no—
276C22×C4—1782no—
277C22×C4—1782no—
278C22×C4—1782no—
279C22×C4C8×D8914yes—
280C22×C4#1308355714yes—
281C22×C4C2×C4×D8911yescharacteristic
282C22×C4C2×C4×D8911yescharacteristic
283C22×C4C2×C4×D8911yescharacteristic
284C22×C4C2×C4×D8911yescharacteristic
285C22×C4C2×C4×D8911yescharacteristic
286C22×C4#1308357414yes—
287C22×C4C23×D8911yescharacteristic
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—1784no—
292C2×C8—1784no—
293C2×C8—1784no—
294C4⋊C4—898no—
295C4⋊C4—898no—
296C4⋊C4—1784no—
297C4⋊C4—1784no—
298C42—22no—
299C42—22no—
300C42—41no—
301C42—41no—
302C42—3562no—
303C42—1784no—
304C42—1784no—
305C42—1784no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23#1566796912yes—
311C23C2×C8×D8912yes—
312C23C2×#1308355712yes—
313C23C22×C4×D8911yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—28no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—894no—
328C2×C4—894no—
329C2×C4—3564no—
330C2×C4—3564no—
331C2×C4—3564no—
332C2×C4—1782no—
333C2×C4—1782no—
334C2×C4—1782no—
335C2×C4—1782no—
336C2×C4—1782no—
337C2×C4—1782no—
338C2×C4—1788no—
339C2×C4—1782no—
340C2×C4—1782no—
341C2×C4—1782no—
342C2×C4—1782no—
343C2×C4#1566796912yes—
344C2×C4C2×C8×D8912yes—
345C2×C4C2×C8×D8912yes—
346C2×C4C2×#1308355712yes—
347C2×C4C2×#1308355712yes—
348C2×C4C2×#1308357412yes—
349C2×C4#1566805712yes—
350C2×C4#1566805912yes—
351C8—44no—
352C8—3564no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22#1915164914yes—
360C22C2×#1566796911yescharacteristic
361C22#1915207111yescharacteristic
362C22#1915207511yescharacteristic
363C22C22×C8×D8911yescharacteristic
364C22C22×#1308355711yescharacteristic
365C22#1915236411yescharacteristic
366C22#1915236411yescharacteristic
367C4—22no—
368C4—22no—
369C4—22no—
370C4—22no—
371C4—22no—
372C4—3562no—
373C4—3562no—
374C4—1784no—
375C4—1784no—
376C4#1915219014yes—
377C2—24no—
378C2#2602285211yescharacteristic
379C2C2×#1915164911yescharacteristic
380C2#2602888811yescharacteristic
381C2#2602927411yescharacteristic
382C2#2602927811yescharacteristic
383C2#2602933211yescharacteristic
384C2#2602933511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D89
commutatorC22×C89C23×C8
FittingC4×C22⋊C8×C89C2
socleC23×C89C23×C4
prime radicalC24×C89C22×C4
cosocleC22×C4×C89C24
hypercenterC4×C22⋊C8D89
hypocenterC89#21912
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #26020809C2semidirect
3. #26020807C2semidirect
34. C2×#13083553C8semidirect
200. C89#21912semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#130835532
#260208092
#260208072
#260203182
#260202302
C4×C22⋊#106234942
C4×C22⋊C8×C892
#2191289