Finite Group Databasebeta

← #24996701

Subgroups — #24996701

Order 11008.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142980C211yesmaximal, characteristic
2#19134449C211yesmaximal, characteristic
3#19134343C211yesmaximal, characteristic
4#19132477C211yesmaximal, characteristic
5#19132477C211yesmaximal, characteristic
6#19132476C211yesmaximal, characteristic
7C43×#1295C211yesmaximal, characteristic
8C2×Dic43⋊C8—21no—
9C2×#13063236C2211yescharacteristic
10C2×#13063236C2211yescharacteristic
11#14582798C411yescharacteristic
12#14582798C411yescharacteristic
13#14582795C411yescharacteristic
14#14582795C411yescharacteristic
15#14582786—21no—
16#14582786—21no—
17#14582782—21no—
18#14582782—21no—
19#14582765C2211yescharacteristic
20C42×Dic43C2211yescharacteristic
21#14582653—21no—
22#14582653—21no—
23#14582653—21no—
24C2×#97×C43C2211yescharacteristic
25C2×#97×C43C2211yescharacteristic
26C43×#382C2211yescharacteristic
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43D411yescharacteristic
38C2×C4×Dic43D411yescharacteristic
39C2×C4×Dic43D411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41Dic43⋊C8—24no—
42#13063236—21no—
43#13063236—21no—
44#13063236—21no—
45#13063236Q812yes—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C22×C8×C43—21no—
53C22×C8×C43—21no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57#97×C43—21no—
58#97×C43—21no—
59#97×C43—21no—
60#97×C43Q812yes—
61#95×C43—21no—
62#95×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C2×C8×C43—22no—
75C2×C8×C43—22no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C42×C43C2×Q811yescharacteristic
83C42×C43C2×Q811yescharacteristic
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C4⋊Dic43—42no—
87C4⋊Dic43—42no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92C4×Dic43—22no—
93C4×Dic43—41no—
94C4×Dic43—41no—
95C4×Dic43—41no—
96C4×Dic43—41no—
97C4×Dic43—41no—
98C2×C43⋊C8—22no—
99C2×C43⋊C8—22no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43C4×Q811yescharacteristic
118C2×C4×C43C4×Q811yescharacteristic
119C2×C4×C43C22⋊Q811yescharacteristic
120C2×C4×C43C22⋊Q811yescharacteristic
121C2×C4×C43#12411yescharacteristic
122C2×C4×C43C4⋊Q811yescharacteristic
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43#10412yes—
141C8×C43—42no—
142C8×C43—42no—
143C43⋊C8—42no—
144C43⋊C8—42no—
145#9893—431nomaximal, Sylow
146C22×C43#39111yescharacteristic
147C22×C43#41311yescharacteristic
148C22×C43#41311yescharacteristic
149C22×C43C2×#10411yescharacteristic
150C22×C43#42111yescharacteristic
151C22×C43#42111yescharacteristic
152C22×C43#42111yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—81no—
160C4×C43—81no—
161Dic43—22no—
162Dic43—41no—
163Dic43—41no—
164Dic43—41no—
165Dic43—81no—
166Dic43—81no—
167#2864—431no—
168#1767—431no—
169#1745—431no—
170#1295—431no—
171#1295—431no—
172#1295—431no—
173#1295D4311yescharacteristic
174C2×C43#152911yescharacteristic
175C2×C43#153211yescharacteristic
176C2×C43#153511yescharacteristic
177C2×C43#153511yescharacteristic
178C2×C43#198611yescharacteristic
179C2×C43#199511yescharacteristic
180C2×C43#199811yescharacteristic
181C2×C4⋊C8—861no—
182C2×#97—431no—
183C2×#97—431no—
184C2×#97C2×D4311yescharacteristic
185C2×#97C2×D4311yescharacteristic
186#389—431no—
187#389—431no—
188#389—431no—
189#389—431no—
190#387—861no—
191#387—861no—
192#387—861no—
193#387—861no—
194#382—431no—
195#382C2×D4311yescharacteristic
196C43—431no—
197#336—861no—
198#336—861no—
199#336—861no—
200C43#989311yescharacteristic, complemented, Sylow
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—861no—
204C22×C8—861no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4C4×D4311yescharacteristic
212C2×C4⋊C4C4×D4311yescharacteristic
213C2×C42—431no—
214C2×C42—431no—
215C2×C42—431no—
216C2×C42—431no—
217C2×C42—431no—
218C2×C42—431no—
219C2×C42C22×D4311yescharacteristic
220C4⋊C8—864no—
221#97—21no—
222#97—21no—
223#97—21no—
224#97—432no—
225#97—861no—
226#97—861no—
227#97—861no—
228#97Dic8612yes—
229#95—21no—
230#95—21no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—431no—
240C22×C4—431no—
241C22×C4—431no—
242C22×C4—431no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4D4×D4311yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—862no—
255C2×C8—862no—
256C2×C8—1721no—
257C2×C8—1721no—
258C2×C8—1721no—
259C2×C8—1721no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1722no—
265C4⋊C4—1722no—
266C4⋊C4—1722no—
267C4⋊C4—1722no—
268C42—862no—
269C42—1721no—
270C42—1721no—
271C42—1721no—
272C42—1721no—
273C42—1721no—
274C42C2×Dic8611yescharacteristic
275C42#1062189811yescharacteristic
276C42#1062190011yescharacteristic
277C42Q8×D4311yescharacteristic
278C23C22⋊C4×D4311yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—432no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4#1306329011yescharacteristic
310C2×C4C4×Dic8611yescharacteristic
311C2×C4#1306330211yescharacteristic
312C2×C4#1306330311yescharacteristic
313C2×C4#1306331111yescharacteristic
314C2×C4#1306332411yescharacteristic
315C8—42no—
316C8—42no—
317C8—1722no—
318C8—1722no—
319C22#1458280311yescharacteristic
320C22#1458288011yescharacteristic
321C22#1458288211yescharacteristic
322C22#104×D4311yescharacteristic
323C22#1458291411yescharacteristic
324C22#1458291411yescharacteristic
325C22#1458291411yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—862no—
335C4—3441no—
336C4—3441no—
337C4—1721no—
338C4—1721no—
339C4—1721no—
340C2#1913319911yescharacteristic
341C2#1913321411yescharacteristic
342C2#1913322311yescharacteristic
343C2#1913322511yescharacteristic
344C2#1913553711yescharacteristic
345C2#1913557411yescharacteristic
346C2#1913558611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#9893
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
200. C43#9893semidirect

Maximal subgroups

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

subgroupindex
#191429802
#191344492
#191343432
#191324772
#191324762
C43×#12952
#989343