Finite Group Databasebeta

← #26024513

Subgroups — #26024513

Order 11392.

546 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15668006C211yesmaximal, characteristic, complemented
2C22×#13083553C211yesmaximal, characteristic, complemented
3#19151539C211yesmaximal, characteristic, complemented
4#19151539C211yesmaximal, characteristic, complemented
5#19151527C211yesmaximal, characteristic, complemented
6#19151522C211yesmaximal, characteristic, complemented
7#19151489C211yesmaximal, characteristic, complemented
8#19151482C211yesmaximal, characteristic, complemented
9#19151482C211yesmaximal, characteristic, complemented
10#19151477C211yesmaximal, characteristic
11#19151475C211yesmaximal, characteristic
12#19151475C211yesmaximal, characteristic
13#19151470C211yesmaximal, characteristic, complemented
14#19151456C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C89C211yesmaximal, characteristic, complemented
16C22×C22⋊D89C2211yescharacteristic
17C23×Dic89C2211yescharacteristic
18C23×Dic89C2211yescharacteristic
19#15668006—24no—
20C2×#13083553—24no—
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2211yescharacteristic
24C2×#13083553C2211yescharacteristic
25C2×#13083553C2211yescharacteristic
26C2×#13083553C2211yescharacteristic
27C2×#13083553C2211yescharacteristic
28C2×#13083553C2211yescharacteristic
29C2×C22⋊Dic89C2211yescharacteristic
30C2×#13083551C2211yescharacteristic
31C2×#13083551C2211yescharacteristic
32C2×#13083551C2211yescharacteristic
33C2×#13083551C2211yescharacteristic
34C2×#13083551C2211yescharacteristic
35C2×#13083551C2211yescharacteristic
36#15667919C2211yescharacteristic
37#15667919C2211yescharacteristic
38#15667919C2211yescharacteristic
39#15667919C2211yescharacteristic
40#15667919C2211yescharacteristic
41#15667919C2211yescharacteristic
42#15667919C2211yescharacteristic
43#15667919C2211yescharacteristic
44#15667919C2211yescharacteristic
45#15667919C2211yescharacteristic
46C23×C4×C89C2211yescharacteristic
47C2×C22⋊C4×C89C2211yescharacteristic
48C2×C22⋊C4×C89C2211yescharacteristic
49C2×C42×C89C2211yescharacteristic
50C2×C42×C89C2211yescharacteristic
51#95×C89C2211yescharacteristic
52#95×C89C2211yescharacteristic
53C23×D89C2311yescharacteristic
54C2×C22⋊D89—22no—
55C2×C22⋊D89—22no—
56C2×C22⋊D89—22no—
57C22×Dic89—22no—
58C22×Dic89—22no—
59C22×Dic89—22no—
60C22×Dic89—22no—
61C22×Dic89—22no—
62C22×Dic89—41no—
63C22×Dic89C2311yescharacteristic
64C22×Dic89C2311yescharacteristic
65C22×Dic89C2311yescharacteristic
66C22×Dic89C2311yescharacteristic
67C22×Dic89C2311yescharacteristic
68C22×Dic89C2311yescharacteristic
69C22×Dic89C2311yescharacteristic
70#13083553—22no—
71#13083553—22no—
72#13083553—22no—
73#13083553—22no—
74#13083553—22no—
75#13083553—22no—
76#13083553—41no—
77#13083553D414yescomplemented
78C22⋊Dic89—22no—
79#13083551—22no—
80#13083551—22no—
81#13083551—22no—
82#13083551—22no—
83#13083551—41no—
84#13083551—41no—
85C24×C89C2311yescharacteristic
86C22×C4×C89—22no—
87C22×C4×C89—22no—
88C22×C4×C89—41no—
89C22×C4×C89C2311yescharacteristic
90C22×C4×C89C2311yescharacteristic
91C22×C4×C89C2311yescharacteristic
92C22×C4×C89C2311yescharacteristic
93C22×C4×C89C2311yescharacteristic
94C22×C4×C89C2311yescharacteristic
95C22⋊C4×C89—22no—
96C22⋊C4×C89—22no—
97C42×C89—22no—
98C42×C89—41no—
99C23×C89—21no—
100C23×C89—21no—
101C23×C89—21no—
102C23×C89—21no—
103C23×C89#4112yes—
104C23×C89#4112yes—
105C23×C89#4112yes—
106C23×C89C2411yescharacteristic
107C22×D89—21no—
108C22×D89—21no—
109C22×D89—21no—
110C22×D89—21no—
111C22×D89—21no—
112C22×D89—21no—
113C22×D89—21no—
114C2×C4×C89—21no—
115C2×C4×C89—21no—
116C2×C4×C89—21no—
117C2×C4×C89—21no—
118C2×C4×C89—21no—
119C2×C4×C89—21no—
120C2×C4×C89—21no—
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—44no—
132C2×C4×C89C2×D412yes—
133C22⋊D89—44no—
134C2×Dic89—28no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138C2×Dic89—21no—
139C2×Dic89—21no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142C2×Dic89—21no—
143C2×Dic89—21no—
144C2×Dic89—21no—
145C2×Dic89—21no—
146C2×Dic89—21no—
147C2×Dic89—21no—
148C2×Dic89—21no—
149C2×Dic89—21no—
150C2×Dic89—21no—
151C2×Dic89—21no—
152C2×Dic89—21no—
153C2×Dic89—44no—
154C2×Dic89C2×D412yes—
155C2×Dic89C2×D412yes—
156C2×Dic89#4112yes—
157C22×C89—22no—
158C22×C89—22no—
159C22×C89—22no—
160C22×C89—22no—
161C22×C89—22no—
162C22×C89—22no—
163C22×C89#12614yescomplemented
164C22×C89C22×D411yescharacteristic
165C22×C89C2×#4111yescharacteristic
166C22×C89C2×#4111yescharacteristic
167C22×C89C2×#4111yescharacteristic
168C22×C89C2×#4111yescharacteristic
169C22×C89H(5,𝔽2)11yescharacteristic
170C22×C892−1+411yescharacteristic
171C2×D89—41no—
172C2×D89—41no—
173C2×D89—41no—
174C2×D89—41no—
175C2×D89—41no—
176C2×D89—41no—
177C2×D89—41no—
178C4×C89—22no—
179C4×C89—41no—
180C4×C89—41no—
181C4×C89—41no—
182C4×C89—41no—
183C4×C89—41no—
184Dic89—22no—
185Dic89—22no—
186Dic89—22no—
187Dic89—41no—
188Dic89—41no—
189Dic89—41no—
190Dic89—41no—
191C2×C89—24no—
192C2×C89#52511yescharacteristic
193C2×C89C2×#12611yescharacteristic
194C2×C89#53911yescharacteristic
195C2×C89#54611yescharacteristic
196C2×C89#54811yescharacteristic
197C2×C89#55211yescharacteristic
198C2×C89#55311yescharacteristic
199D89—81no—
200#2481—891nomaximal, Sylow
201C89#248111yescharacteristic, complemented, Sylow
202C2×#126—891no—
203C22×C4⋊C4—891no—
204#400—891no—
205#400—891no—
206#397—891no—
207#396—891no—
208#388—891no—
209#387—891no—
210#387—891no—
211#386—891no—
212#386—891no—
213#386—891no—
214#385—891no—
215#380—891no—
216C4×C22⋊C4D8911yescharacteristic, complemented
217C22×D4—891no—
218C23×C4—891no—
219C23×C4—891no—
220C23×C4C2×D8911yescharacteristic
221#126—1784no—
222C2×C4⋊C4—891no—
223C2×C4⋊C4—891no—
224C2×C4⋊C4—891no—
225C2×C4⋊C4—891no—
226C2×C4⋊C4—891no—
227C2×C4⋊C4—891no—
228C2×C4⋊C4—891no—
229C2×C4⋊C4—891no—
230C2×C4⋊C4—1784no—
231C2×C22⋊C4—891no—
232C2×C22⋊C4—891no—
233C2×C22⋊C4—891no—
234C2×C22⋊C4—891no—
235C2×C22⋊C4—891no—
236C2×C22⋊C4—891no—
237C2×C22⋊C4—891no—
238C2×C22⋊C4C2×D8911yescharacteristic
239C2×C22⋊C4C2×D8911yescharacteristic
240C2×C42C2×D8911yescharacteristic
241C2×C42C2×D8911yescharacteristic
242#95—891no—
243#95—891no—
244#95—891no—
245#95—891no—
246#95—891no—
247#95—891no—
248#95—891no—
249#95—891no—
250#95—891no—
251#95—891no—
252#95C2×D8911yescharacteristic
253#95C2×D8911yescharacteristic
254C24—891no—
255C24C22×D8911yescharacteristic
256C2×D4—1782no—
257C2×D4—1782no—
258C2×D4—1782no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—891no—
263C22×C4—891no—
264C22×C4—891no—
265C22×C4—891no—
266C22×C4—891no—
267C22×C4—891no—
268C22×C4—891no—
269C22×C4—3561no—
270C22×C4—1782no—
271C22×C4—1782no—
272C22×C4—1782no—
273C22×C4—1782no—
274C22×C4—1782no—
275C22×C4C22×D8911yescharacteristic
276C22×C4C22×D8911yescharacteristic
277C22×C4C22×D8911yescharacteristic
278C22×C4C22×D8911yescharacteristic
279C22×C4C22×D8911yescharacteristic
280C22×C4C22×D8911yescharacteristic
281C4⋊C4—894no—
282C4⋊C4—3561no—
283C4⋊C4—1782no—
284C4⋊C4—1782no—
285C4⋊C4—1782no—
286C4⋊C4—1782no—
287C4⋊C4—1782no—
288C4⋊C4—1782no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—3561no—
292C22⋊C4—3561no—
293C22⋊C4—1782no—
294C22⋊C4—1782no—
295C22⋊C4—1782no—
296C22⋊C4—1782no—
297C22⋊C4—1782no—
298C42—22no—
299C42—41no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—1781no—
305C23—1781no—
306C23—1781no—
307C23—1781no—
308C23—1781no—
309C23—1781no—
310C23—1781no—
311C23#1308357412yes—
312C23#1308357412yes—
313C23#1308357412yes—
314C23C23×D8911yescharacteristic
315D4—3564no—
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—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—44no—
334C2×C4—892no—
335C2×C4—892no—
336C2×C4—892no—
337C2×C4—3564no—
338C2×C4—1781no—
339C2×C4—1781no—
340C2×C4—1781no—
341C2×C4—1781no—
342C2×C4—1781no—
343C2×C4—1781no—
344C2×C4—1781no—
345C2×C4—1781no—
346C2×C4—1781no—
347C2×C4—1781no—
348C2×C4—1781no—
349C2×C4—1781no—
350C2×C4—1788no—
351C2×C4—1781no—
352C2×C4—1781no—
353C2×C4—1781no—
354C2×C4—1781no—
355C2×C4—1781no—
356C2×C4—1781no—
357C2×C4D4×D8912yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—3561no—
365C22—3561no—
366C22—3561no—
367C22—3561no—
368C22—3561no—
369C22—3561no—
370C22—3561no—
371C22#1566800614yescomplemented
372C22C2×D4×D8911yescharacteristic
373C22#41×D8911yescharacteristic
374C22C2×#1308357411yescharacteristic
375C22C2×#1308357411yescharacteristic
376C22C2×#1308357411yescharacteristic
377C22#1566805711yescharacteristic
378C22#1566805911yescharacteristic
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—3561no—
386C4—3561no—
387C4—3561no—
388C4—3561no—
389C4—1782no—
390C4—1782no—
391C4—1782no—
392C2—24no—
393C2—7121no—
394C2#1915210711yescharacteristic
395C2C2×#1566800611yescharacteristic
396C2#1915219011yescharacteristic
397C2#1915223811yescharacteristic
398C2#1915225711yescharacteristic
399C2#1915228111yescharacteristic
400C2#1915229711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
FittingC4×C22⋊C4×C89C2
prime radicalC22×C22⋊D89C22
hypercenterC4×C22⋊C4D89
hypocenterC89#2481
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#15668006C2semidirect
2. C22×#13083553C2semidirect
3. #19151539C2semidirect
4. #19151539C2semidirect
5. #19151527C2semidirect
6. #19151522C2semidirect
7. #19151489C2semidirect
8. #19151482C2semidirect
9. #19151482C2semidirect
13. #19151470C2semidirect
14. #19151456C2semidirect
15. C4×C22⋊C4×C89C2semidirect
77. #13083553D4semidirect
163. C22×C89#126semidirect
201. C89#2481semidirect
216. C4×C22⋊C4D89semidirect
371. C22#15668006semidirect

Maximal subgroups

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

subgroupindex
C2×#156680062
C22×#130835532
#191515392
#191515272
#191515222
#191514892
#191514822
#191514772
#191514752
#191514702
#191514562
C4×C22⋊C4×C892
#248189