Finite Group Databasebeta

← #24995807

Subgroups — #24995807

Order 11008.

414 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic
2C4×#13063261C211yesmaximal, characteristic, complemented
3#19133189C211yesmaximal, characteristic, complemented
4#19133186C211yesmaximal, characteristic
5#19133015C211yesmaximal, characteristic, complemented
6#19133011C211yesmaximal, characteristic
7C43×#1451C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583297C411yescharacteristic
11#14583272C411yescharacteristic
12#14583250C411yescharacteristic
13#14583246C411yescharacteristic
14#14583128—21no—
15#14583128—21no—
16C4×#10621873—21no—
17C4×#10621873—21no—
18C2×#13063261—21no—
19C4×#10621877C2211yescharacteristic
20C4×#10621877C2211yescharacteristic
21#14582664—21no—
22#14582640—22no—
23#14582638—22no—
24#14582629—22no—
25#14582626—22no—
26C43×#431C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C2×C4×C8×C43C2211yescharacteristic
29C43×#322—21no—
30C43×#322—21no—
31C2×#10621898—21no—
32C2×#10621873—21no—
33C2×#10621873—21no—
34C2×#10621877—21no—
35C2×#10621877—21no—
36#13063325C2×C411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063325C2×C411yescharacteristic
39#13063322C2×C411yescharacteristic
40#13063317—21no—
41#13063313—21no—
42#13063304—21no—
43#13063304—21no—
44#13063299—21no—
45#13063299—21no—
46C4×Dic86—21no—
47C4×Dic86—21no—
48C4×D172—21no—
49C4×D172—21no—
50#13063284—21no—
51#13063261—24no—
52#13063257—21no—
53#13063257—21no—
54#13063250—21no—
55#13063250—21no—
56#13063247—21no—
57#13063247—21no—
58#13063236—21no—
59#13063236—21no—
60C4×C43⋊C8—21no—
61C4×C43⋊C8—21no—
62C2×M16×C43—21no—
63C22×C8×C43D411yescharacteristic
64C22×C8×C43D411yescharacteristic
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43D412yes—
67C22⋊C8×C43—21no—
68#97×C43D412yes—
69C4×C8×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43D411yescharacteristic
74C4×C8×C43D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—41no—
79#10621898—82no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172—21no—
83C2×C4×D43—41no—
84C2×Dic86—21no—
85C2×Dic86—21no—
86C2×Dic86—21no—
87M16×C43—42no—
88C2×C8×C43—22no—
89C2×C8×C43—22no—
90C2×C8×C43—22no—
91C2×C8×C43—41no—
92C2×C8×C43C22⋊C411yescharacteristic
93C2×C8×C43C22⋊C411yescharacteristic
94C2×C8×C43C22⋊C411yescharacteristic
95C2×C8×C43C22⋊C411yescharacteristic
96C42×C43C22×C411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C22⋊Dic43—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109Dic43⋊C4—41no—
110Dic43⋊C4—41no—
111C4×Dic43—41no—
112#10621877—22no—
113#10621877—22no—
114#10621877—41no—
115#10621877—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118#10621873—42no—
119#10621873—42no—
120C23×C43#12411yescharacteristic
121C22×D43—41no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12711yescharacteristic
132C22⋊D43—82no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136D172—41no—
137D172—41no—
138D172—42no—
139D172—81no—
140C4×D43—82no—
141Dic86—41no—
142Dic86—41no—
143Dic86—42no—
144Dic86—81no—
145C8×C43—21no—
146C8×C43—21no—
147C8×C43—21no—
148C8×C43—42no—
149C8×C43—42no—
150C8×C43#10412yes—
151C43⋊C8—42no—
152C43⋊C8—42no—
153#9728—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43#39011yescharacteristic
158C2×D43—81no—
159C2×D43—81no—
160C2×D43—81no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43C2×#10411yescharacteristic
165C4×C43#42111yescharacteristic
166C4×C43#44412yes—
167C4×C43#47112yes—
168Dic43—81no—
169Dic43—81no—
170Dic43—81no—
171#3167—431no—
172C4×#108—431no—
173#1526—431no—
174#1525—431no—
175#1485—431no—
176#1484—431no—
177#1451D4311yescharacteristic, complemented
178C2×C43—41no—
179C2×C43#197511yescharacteristic
180C2×C43#197711yescharacteristic
181C2×C43#198011yescharacteristic
182D43—161no—
183#533—431no—
184#532—431no—
185#498—431no—
186#492—431no—
187#487—431no—
188#486—431no—
189#465—861no—
190#465—861no—
191C4×SD16—861no—
192C4×SD16—861no—
193#431C2×D4311yescharacteristic
194C2×#108—861no—
195C4×M16—431no—
196C4×M16—431no—
197C4×M16C2×D4311yescharacteristic
198C2×C4×C8C2×D4311yescharacteristic
199#341—861no—
200#330—862no—
201#329—862no—
202Q8⋊C8—862no—
203D4⋊C8—862no—
204#322—21no—
205#322—21no—
206C43#972811yescharacteristic, complemented, Sylow
207C2×#41—861no—
208C2×SD16—861no—
209C2×SD16—861no—
210C2×M16—21no—
211C2×M16—861no—
212C2×M16—861no—
213C22×C8D17211yescharacteristic
214C22×C8D17211yescharacteristic
215C4⋊Q8—431no—
216C4⋊Q8—431no—
217C4⋊Q8—431no—
218#127—431no—
219#125—861no—
220#124—861no—
221C22⋊Q8—861no—
222C22⋊Q8—861no—
223#121—861no—
224#121—861no—
225C4×Q8—861no—
226C4×Q8—861no—
227C4×D4—861no—
228C4×D4—861no—
229#117—861no—
230C2×C42C22×D4311yescharacteristic
231#108—864no—
232#106—861no—
233#106—861no—
234C4⋊C8D17212yes—
235#103—861no—
236#103—861no—
237#102—861no—
238#102—861no—
239C22⋊C8—21no—
240#97—861no—
241#97—861no—
242#97D17212yes—
243C4×C8—21no—
244C4×C8—21no—
245C4×C8—861no—
246C4×C8—861no—
247C4×C8C4×D4311yescharacteristic
248C4×C8C4×D4311yescharacteristic
249C4×C8C22⋊D4311yescharacteristic
250C4×C8C22⋊D4311yescharacteristic
251#41—3442no—
252C2×Q8—861no—
253C2×Q8—861no—
254C2×Q8—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—1721no—
259C22×C4—1721no—
260C22×C4C2×D17211yescharacteristic
261C22×C4#1062189811yescharacteristic
262C22×C4#1062189811yescharacteristic
263SD16—1722no—
264SD16—1722no—
265M16—42no—
266M16—862no—
267M16—862no—
268M16—1721no—
269M16—1721no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—1721no—
275C2×C8—1721no—
276C2×C8(C2×D43)⋊C411yescharacteristic
277C2×C8(C2×D43)⋊C411yescharacteristic
278C2×C8(C2×D43)⋊C411yescharacteristic
279C2×C8(C2×D43)⋊C411yescharacteristic
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C22⋊C4—1721no—
289C22⋊C4—1721no—
290C22⋊C4—1721no—
291C42—1721no—
292C42C2×C4×D4311yescharacteristic
293C42C2×D17211yescharacteristic
294C42C2×D17211yescharacteristic
295C42C2×C22⋊D4311yescharacteristic
296C23—1721no—
297C23#1306331311yescharacteristic
298Q8—3441no—
299Q8—1721no—
300Q8—1721no—
301Q8—1722no—
302D4—3441no—
303D4—3442no—
304D4—1721no—
305D4—1721no—
306D4—1722no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—3442no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4C2×(C2×D43)⋊C411yescharacteristic
316C2×C4C4×D17211yescharacteristic
317C2×C4C4×D17211yescharacteristic
318C2×C4#1306329911yescharacteristic
319C2×C4#1306329911yescharacteristic
320C2×C4#1306332211yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—42no—
325C8—42no—
326C8—1722no—
327C8—1722no—
328C8#1306325112yes—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—3441no—
333C22—3441no—
334C22—3441no—
335C22#1458280111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—3441no—
340C4—3441no—
341C4—3441no—
342C4C2×#1306325111yescharacteristic
343C4#1458291511yescharacteristic
344C4#1458302212yes—
345C4#1458316212yes—
346C2—41no—
347C2—6881no—
348C2#1913548811yescharacteristic
349C2#1913549811yescharacteristic
350C2#1913551411yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1451C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1451D43
hypocenterC43#9728
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. C4×#13063261C2semidirect
3. #19133189C2semidirect
5. #19133015C2semidirect
7. C43×#1451C2semidirect
177. #1451D43semidirect
206. C43#9728semidirect

Maximal subgroups

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

subgroupindex
#191451542
C4×#130632612
#191331892
#191331862
#191330152
#191330112
C43×#14512
#972843