Finite Group Databasebeta

← #25012659

Subgroups — #25012659

Order 11008.

422 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063347C211yesmaximal, characteristic
2C2×#14582707C212yesmaximal
3#19134767C211yesmaximal, characteristic, complemented
4#19132691C212yesmaximal, complemented
5C2×C43×C4⋊C16C211yesmaximal, characteristic, complemented
6C2×#13063347C2211yescharacteristic
7C4×#10621898—21no—
8C4×Dic172C411yescharacteristic
9C4×Dic172C411yescharacteristic
10C4×#10621873—21no—
11C4×#10621873—21no—
12C4×D344C411yescharacteristic
13C4×D344C411yescharacteristic
14C2×#13063261—21no—
15C2×#13063261C2212yes—
16#14582937C2211yescharacteristic
17#14582923—21no—
18#14582896—21no—
19#14582707—24no—
20C22×C16×C43C2212yes—
21C2×C4×C8×C43C2211yescharacteristic
22C43×C4⋊C16—21no—
23C43×C4⋊C16—21no—
24C2×#10621898—21no—
25#13063347—21no—
26#13063347—21no—
27#13063347D412yes—
28#13063347Q812yes—
29C2×Dic172C2×C411yescharacteristic
30C2×#10621873—21no—
31C2×D344C2×C411yescharacteristic
32C2×#10621877—22no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×D172—21no—
36C4×D172—21no—
37C4×C22⋊D43—41no—
38C4×C22⋊D43—41no—
39#13063284—21no—
40#13063282—41no—
41C42×D43—41no—
42#13063261—22no—
43#13063261—22no—
44#13063261—42no—
45#13063259C2×C411yescharacteristic
46#13063259C2×C411yescharacteristic
47#13063257—21no—
48C4⋊(C43⋊C8)—41no—
49C4⋊(C43⋊C8)—41no—
50#13063250—21no—
51#13063250—21no—
52#13063247—21no—
53#13063247—21no—
54C22×C8×C43D411yescharacteristic
55C22×C8×C43C2311yescharacteristic
56C2×C42×C43D411yescharacteristic
57C2×C16×C43—22no—
58C2×C16×C43—22no—
59C2×C16×C43—22no—
60C4×C8×C43C2×C411yescharacteristic
61C4×C8×C43C2×C411yescharacteristic
62C4×C8×C43D411yescharacteristic
63C4×C8×C43D411yescharacteristic
64C22×C4×C43SD1611yescharacteristic
65C22×C4×C43SD1611yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C2×C22⋊D43—41no—
68#10621898—22no—
69#10621898—22no—
70#10621898—41no—
71#10621898—41no—
72C2×D172—21no—
73C2×C4×D43—41no—
74C2×C4×D43—41no—
75C2×C4×D43—41no—
76C2×Dic86—21no—
77C2×C8×C43—21no—
78C2×C8×C43—21no—
79C2×C8×C43C22⋊C411yescharacteristic
80C2×C8×C43C22⋊C411yescharacteristic
81C2×C8×C43C22×C411yescharacteristic
82C2×C8×C43C2×D411yescharacteristic
83C2×C8×C43C2×D411yescharacteristic
84C2×C8×C43C2×Q811yescharacteristic
85C2×C8×C43#4111yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C42×C43C22⋊C411yescharacteristic
88C42×C43C22⋊C411yescharacteristic
89C42×C43D811yescharacteristic
90C42×C43D811yescharacteristic
91C22⋊Dic43—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98C4×Dic43—41no—
99C4×Dic43—41no—
100C4×Dic43—41no—
101#10621877—42no—
102#10621877—42no—
103C2×C43⋊C8—42no—
104Dic172—21no—
105Dic172C4⋊C412yes—
106D344—21no—
107D344C4⋊C412yes—
108#10621873—22no—
109#10621873—22no—
110C16×C43—42no—
111C23×C43C2×SD1611yescharacteristic
112C22×D43—41no—
113C2×C4×C43—22no—
114C2×C4×C43—41no—
115C2×C4×C43#10211yescharacteristic
116C2×C4×C43#10211yescharacteristic
117C2×C4×C43#10211yescharacteristic
118C2×C4×C43#10211yescharacteristic
119C2×C4×C43C2×C22⋊C411yescharacteristic
120C2×C4×C43#12111yescharacteristic
121C2×C4×C43C22⋊Q811yescharacteristic
122C2×C4×C43C2×D811yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C22⋊D43—42no—
126C22⋊D43—42no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130D172—22no—
131D172—41no—
132C4×D43—42no—
133C4×D43—42no—
134C4×D43—82no—
135C4×D43—82no—
136Dic86—22no—
137Dic86—41no—
138C8×C43—21no—
139C8×C43—21no—
140C8×C43C2×C4⋊C411yescharacteristic
141C8×C43#11711yescharacteristic
142C8×C43#12111yescharacteristic
143C8×C43C22⋊Q811yescharacteristic
144C43⋊C8—82no—
145#12815—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43C2×#10211yescharacteristic
149C22×C43#46111yescharacteristic
150C22×C43#47611yescharacteristic
151C2×D43—42no—
152C2×D43—81no—
153C2×D43—81no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43#35912yescomplemented
158C4×C43#38011yescharacteristic
159C4×C43#41711yescharacteristic
160C4×C43#45911yescharacteristic
161C4×C43#47411yescharacteristic
162Dic43—42no—
163Dic43—81no—
164Dic43—81no—
165C4×#135—431no—
166C2×C4⋊C16D4311yescharacteristic, complemented
167C2×#359—432no—
168#1848—431no—
169#1382—432no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43#180211yescharacteristic
173C2×C43C2×#35911yescharacteristic
174C2×C43#214311yescharacteristic
175D43—82no—
176C2×#135—431no—
177C4×#41—861no—
178C22×C16C2×D4312yes—
179C4×Q16—431no—
180C4×Q16—431no—
181C4×SD16—861no—
182C4×SD16—861no—
183C4×D8—431no—
184C4×D8—431no—
185C2×#108—432no—
186C2×#108—861no—
187#427—431no—
188#423—861no—
189#416—861no—
190C2×C4×C8C2×D4311yescharacteristic
191C4⋊C16—21no—
192C4⋊C16—21no—
193#359—864no—
194C43#1281511yescharacteristic, complemented, Sylow
195C2×#41—861no—
196#135—432no—
197#135—432no—
198#135—861no—
199#135—861no—
200C2×Q16—431no—
201C2×SD16—861no—
202C2×D8—431no—
203C2×M16—862no—
204C22×C8D17211yescharacteristic
205C22×C8C22×D4311yescharacteristic
206C4×Q8—861no—
207C4×Q8—861no—
208C4×D4—861no—
209C4×D4—861no—
210C4×D4—1721no—
211C4×D4—1721no—
212#117—861no—
213#117—1721no—
214C2×C42—1721no—
215C2×C42D17211yescharacteristic
216C2×C16—22no—
217C2×C16—22no—
218C2×C16—22no—
219#108—862no—
220#108—862no—
221#108—1722no—
222#107—431no—
223#107—431no—
224#106—861no—
225C4⋊C8—1721no—
226C4⋊C8—1721no—
227#103—861no—
228#103—861no—
229#102—861no—
230#102—861no—
231C4×C8C4×D4311yescharacteristic
232C4×C8C4×D4311yescharacteristic
233C4×C8C22⋊D4311yescharacteristic
234C4×C8C22⋊D4311yescharacteristic
235#41—862no—
236#41—862no—
237#41—1721no—
238#41—1721no—
239C2×Q8—861no—
240C2×D4—861no—
241C2×D4—1721no—
242C22×C4—1721no—
243C22×C4—1721no—
244C22×C4—1721no—
245C22×C4#1062187311yescharacteristic
246C22×C4#1062187311yescharacteristic
247C22×C4C2×D17211yescharacteristic
248Q16—432no—
249Q16—861no—
250SD16—862no—
251SD16—862no—
252D8—432no—
253D8—861no—
254M16—1722no—
255M16—1722no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—1722no—
259C2×C8(C2×D43)⋊C411yescharacteristic
260C2×C8(C2×D43)⋊C411yescharacteristic
261C2×C8C2×C4×D4311yescharacteristic
262C2×C8D4×D4311yescharacteristic
263C2×C8#1062190011yescharacteristic
264C2×C8Q8×D4311yescharacteristic
265C2×C8#1062190211yescharacteristic
266C2×C8C2×C22⋊D4311yescharacteristic
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C22⋊C4—1721no—
272C22⋊C4—1721no—
273C22⋊C4—1721no—
274C42—1721no—
275C42—1721no—
276C42—1721no—
277C42D34411yescharacteristic
278C42D34411yescharacteristic
279C42(C2×D43)⋊C411yescharacteristic
280C42(C2×D43)⋊C411yescharacteristic
281C16—42no—
282C23—1721no—
283C23C2×#1062187311yescharacteristic
284Q8—862no—
285Q8—1721no—
286D4—862no—
287D4—1722no—
288D4—1722no—
289D4—1721no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—3442no—
293C2×C4—3442no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1722no—
298C2×C4—1722no—
299C2×C4#1306324711yescharacteristic
300C2×C4#1306324711yescharacteristic
301C2×C4#1306324711yescharacteristic
302C2×C4#1306324711yescharacteristic
303C2×C4C2×(C2×D43)⋊C411yescharacteristic
304C2×C4#1306330011yescharacteristic
305C2×C4#1306330511yescharacteristic
306C2×C4C2×D34411yescharacteristic
307C2×C4#1306335311yescharacteristic
308C2×C4#1306335811yescharacteristic
309C8—21no—
310C8—21no—
311C8—3442no—
312C8C4⋊C4×D4311yescharacteristic
313C8#1306328311yescharacteristic
314C8#1306329611yescharacteristic
315C8#1306330111yescharacteristic
316C22—21no—
317C22—21no—
318C22—3441no—
319C22—3441no—
320C22—1722no—
321C22C2×#1306324711yescharacteristic
322C22#1458310511yescharacteristic
323C22#1458319011yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—3441no—
328C4—3441no—
329C4—1722no—
330C4#1458270712yescomplemented
331C4#1458275611yescharacteristic
332C4#1458290111yescharacteristic
333C4#1458309511yescharacteristic
334C4#1458318011yescharacteristic
335C2—21no—
336C2—21no—
337C2—3442no—
338C2#1913459611yescharacteristic
339C2C2×#1458270711yescharacteristic
340C2#1913632411yescharacteristic
subgroupG/H
centerC2×C4C2×D344
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×C4⋊C16C2
socleC22×C43C2×#102
prime radicalC2×#13063347C22
cosocleC22×C8×C43C23
hypercenterC2×C4⋊C16D43
hypocenterC43#12815
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
3. #19134767C2semidirect
4. #19132691C2semidirect
5. C2×C43×C4⋊C16C2semidirect
157. C4×C43#359semidirect
166. C2×C4⋊C16D43semidirect
194. C43#12815semidirect
330. C4#14582707semidirect

Maximal subgroups

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

subgroupindex
C4×#130633472
C2×#145827072
#191347672
#191326912
C2×C43×C4⋊C162
#1281543