Finite Group Databasebeta

← #25013752

Subgroups — #25013752

Order 11008.

486 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583339C211yesmaximal, characteristic
2C2×#14582709C211yesmaximal, characteristic
3#19136314C211yesmaximal, characteristic, complemented
4#19135466C211yesmaximal, characteristic, complemented
5#19132700C211yesmaximal, characteristic, complemented
6#19132679C211yesmaximal, characteristic, complemented
7C43×#2943C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9#14583339—22no—
10#14583339C414yescomplemented
11C2×#13063271—21no—
12C2×#13063269—21no—
13C2×#13063265C2211yescharacteristic
14C2×#13063265C2211yescharacteristic
15C2×#13063257C2211yescharacteristic
16C2×#13063250—21no—
17#14582805—21no—
18#14582709—22no—
19#14582702—22no—
20C2×#135×C43C2211yescharacteristic
21C4×#41×C43—21no—
22C43×#442—21no—
23C43×#441—21no—
24C43×#440—22no—
25C43×#427C2211yescharacteristic
26C43×#416—21no—
27C2×#97×C43C2211yescharacteristic
28C22×Dic86—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172—21no—
33C2×Dic172—21no—
34C2×Dic172C2×C412yescomplemented
35C2×C4⋊Dic43—21no—
36#13063271—24no—
37#13063269—24no—
38#13063265—21no—
39#13063265—21no—
40#13063265—21no—
41#13063265C2×C412yescomplemented
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44#13063257—21no—
45#13063257—21no—
46#13063250—42no—
47C43⋊#95—42no—
48C2×#41×C43—21no—
49#135×C43—21no—
50#135×C43—21no—
51#135×C43C2×C412yes—
52#135×C43D412yes—
53C2×Q16×C43D411yescharacteristic
54C2×SD16×C43—21no—
55C2×D8×C43D411yescharacteristic
56C22×C8×C43D411yescharacteristic
57C22×C8×C43C2311yescharacteristic
58C4×Q8×C43—22no—
59C4×D4×C43—22no—
60C4×D4×C43—42no—
61#117×C43—21no—
62#117×C43—41no—
63C2×C42×C43—41no—
64C2×C42×C43D411yescharacteristic
65#107×C43D412yes—
66#106×C43—21no—
67#103×C43—22no—
68#102×C43—22no—
69#97×C43—21no—
70#97×C43—21no—
71#41×C43—22no—
72#41×C43—22no—
73#41×C43—41no—
74#41×C43—41no—
75C2×Q8×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—41no—
78C22×C4×C43—42no—
79C22×C4×C43—41no—
80C22×C4×C43D812yes—
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—41no—
83C22×Dic43—41no—
84C2×Dic86—22no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×Dic86—41no—
88C2×Dic86—41no—
89C2×Dic86—41no—
90Q16×C43—21no—
91Q16×C43C22⋊C412yes—
92SD16×C43—22no—
93SD16×C43—22no—
94D8×C43—21no—
95D8×C43C22⋊C412yes—
96C2×C8×C43—21no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43C22×C411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C2×C8×C43#4111yescharacteristic
105C4⋊C4×C43—22no—
106C4⋊C4×C43—42no—
107C22⋊C4×C43—42no—
108C22⋊C4×C43—41no—
109C42×C43—21no—
110C42×C43—21no—
111C42×C43—42no—
112C42×C43—41no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115Dic172—22no—
116Dic172—22no—
117Dic172—41no—
118Dic172—41no—
119C43⋊C16—22no—
120C43⋊C16—41no—
121C23×C43—41no—
122C23×C43C2×D811yescharacteristic
123Q8×C43—22no—
124Q8×C43—41no—
125D4×C43—22no—
126D4×C43—42no—
127D4×C43—42no—
128D4×C43—41no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—84no—
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×Dic43—42no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145C2×Dic43—82no—
146C2×Dic43—81no—
147Dic86—42no—
148Dic86—42no—
149Dic86—81no—
150Dic86—81no—
151C8×C43—41no—
152C8×C43C2×C22⋊C411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12311yescharacteristic
156#13026—431nomaximal, Sylow
157C22×C43—22no—
158C22×C43—42no—
159C22×C43—82no—
160C22×C43C4×D811yescharacteristic
161C22×C43#44711yescharacteristic
162C22×C43#45911yescharacteristic
163C4×C43—42no—
164C4×C43—42no—
165C4×C43—82no—
166C4×C43#38611yescharacteristic
167C4×C43#44211yescharacteristic
168C4×C43#44911yescharacteristic
169C4×C43#46311yescharacteristic
170Dic43—82no—
171Dic43—161no—
172C2×#510—431no—
173#2943D4311yescharacteristic
174C2×#360—431no—
175#2141—431no—
176#1971—431no—
177#1386—431no—
178#1377—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—82no—
182C2×C43#187911yescharacteristic
183C2×C43#219112yes—
184C2×#135C2×D4311yescharacteristic
185C22×Q16—431no—
186C4×#41—21no—
187#510—434no—
188#510—862no—
189C2×Q32—861no—
190C2×SD32—861no—
191C2×M32—431no—
192C2×M32—431no—
193#442—21no—
194#441—21no—
195#440—22no—
196#427C2×D4311yescharacteristic
197C2×#106—431no—
198#416—21no—
199C2×#103—861no—
200C2×#97C2×D4311yescharacteristic
201#391—861no—
202#360—862no—
203#358—862no—
204C43#1302611yescharacteristic, complemented, Sylow
205C2×#41—21no—
206C22×Q8—861no—
207#135—21no—
208#135—21no—
209#135C4×D4312yes—
210#135D17212yes—
211C2×Q16—432no—
212C2×Q16—861no—
213C2×Q16—861no—
214C2×Q16—861no—
215C2×Q16—861no—
216C2×Q16—861no—
217C2×Q16C22⋊D4311yescharacteristic
218C2×SD16—21no—
219C2×D8C22⋊D4311yescharacteristic
220C22×C8C22⋊D4311yescharacteristic
221C22×C8C22×D4311yescharacteristic
222C4×Q8—22no—
223C4×D4—22no—
224C4×D4—42no—
225#117—21no—
226#117—41no—
227C2×C4⋊C4—861no—
228C2×C42—41no—
229C2×C42C22⋊D4311yescharacteristic
230Q32—864no—
231SD32—864no—
232M32—432no—
233M32—861no—
234M32—861no—
235M32—861no—
236C2×C16—861no—
237C2×C16—861no—
238#107C22⋊D4312yes—
239#106—21no—
240#106—861no—
241#106—861no—
242#103—22no—
243#103—1722no—
244#102—22no—
245#97—21no—
246#97—21no—
247#95—1722no—
248#41—22no—
249#41—22no—
250#41—41no—
251#41—41no—
252C2×Q8—21no—
253C2×Q8—862no—
254C2×Q8—1721no—
255C2×Q8—1721no—
256C2×Q8—1721no—
257C2×Q8—1721no—
258C2×Q8—1721no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—1721no—
264C22×C4—1721no—
265C22×C4#1062188212yes—
266C22×C4C2×C22⋊D4311yescharacteristic
267Q16—21no—
268Q16—862no—
269Q16—862no—
270Q16—1721no—
271Q16—1721no—
272Q16(C2×D43)⋊C412yes—
273SD16—22no—
274SD16—22no—
275D8—21no—
276D8(C2×D43)⋊C412yes—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8C2×C4×D4311yescharacteristic
281C2×C8C2×D17211yescharacteristic
282C2×C8#1062189811yescharacteristic
283C2×C8#1062189811yescharacteristic
284C2×C8C2×C22⋊D4311yescharacteristic
285C2×C8C2×C22⋊D4311yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—42no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C42—21no—
293C42—21no—
294C42—42no—
295C42—41no—
296C16—862no—
297C16—1721no—
298C23—41no—
299C23C2×#1062188211yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—3441no—
303Q8—3441no—
304Q8—1722no—
305Q8—1722no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—84no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3442no—
320C2×C4—3441no—
321C2×C4—1722no—
322C2×C4C4×C22⋊D4311yescharacteristic
323C2×C4#1306329411yescharacteristic
324C2×C4#1306329911yescharacteristic
325C2×C4#1306334511yescharacteristic
326C2×C4#1306335011yescharacteristic
327C2×C4#1306335111yescharacteristic
328C8—41no—
329C8C2×(C2×D43)⋊C411yescharacteristic
330C8C4×C22⋊D4311yescharacteristic
331C8#1306329911yescharacteristic
332C8#1306330811yescharacteristic
333C22—22no—
334C22—42no—
335C22—82no—
336C22C4×#1062188211yescharacteristic
337C22#1458303311yescharacteristic
338C22#1458309411yescharacteristic
339C4—42no—
340C4—42no—
341C4—82no—
342C4—3442no—
343C4—6881no—
344C4#1458277811yescharacteristic
345C4#1458300911yescharacteristic
346C4#1458304411yescharacteristic
347C4#1458311411yescharacteristic
348C2—21no—
349C2—21no—
350C2—82no—
351C2#1913494311yescharacteristic
352C2#1913654612yes—
subgroupG/H
centerC22#14583033
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2943C2
socleC22×C43#447
prime radicalC2×#135×C43C22
cosocleC22×C8×C43C23
hypercenter#2943D43
hypocenterC43#13026
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #2943

Complements

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

NH ≅ G/Ntype
3. #19136314C2semidirect
4. #19135466C2semidirect
5. #19132700C2semidirect
6. #19132679C2semidirect
10. #14583339C4semidirect
34. C2×Dic172C2×C4semidirect
41. #13063265C2×C4semidirect
204. C43#13026semidirect

Maximal subgroups

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

subgroupindex
C2×#145833392
C2×#145827092
#191363142
#191354662
#191327002
#191326792
C43×#29432
#1302643