Finite Group Databasebeta

← #25014955

Subgroups — #25014955

Order 11008.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144250C211yesmaximal, characteristic
2#19136289C212yesmaximal
3#19136250C212yesmaximal
4#19134395C211yesmaximal, characteristic
5C43×#1813C211yesmaximal, characteristic
6C22×Dic172C411yescharacteristic, complemented
7#14583470C2212yes—
8#14583157—21no—
9#14583157—21no—
10#14583140—21no—
11#14583140—21no—
12#14582937C411yescharacteristic, complemented
13#14582909C412yescomplemented
14#14582883C2211yescharacteristic
15#14582873C2211yescharacteristic
16#14582854—21no—
17#14582697—24no—
18#14582690—24no—
19#14582670—21no—
20C2×#131×C43C2211yescharacteristic
21C2×#108×C43—21no—
22C43×#413C2212yes—
23C43×#338—21no—
24C22×Dic86C2×C412yes—
25C2×Dic172—21no—
26C2×Dic172—21no—
27C2×Dic172—41no—
28C2×Dic172—41no—
29C2×#10621877—21no—
30#13063323—22no—
31#13063312—22no—
32#13063306—22no—
33#13063306—22no—
34#13063304—22no—
35#13063304—22no—
36#13063284—21no—
37#13063284C2×C412yes—
38#13063259—21no—
39#13063257—21no—
40#13063250—22no—
41#13063250—22no—
42#13063244D412yes—
43#13063242—21no—
44#13063240—21no—
45#13063240D412yes—
46#13063235—41no—
47C8×Dic43—41no—
48C2×#41×C43C2311yescharacteristic
49#131×C43—41no—
50#131×C43—41no—
51C2×M16×C43—22no—
52C2×M16×C43C2×C411yescharacteristic
53C2×M16×C43D411yescharacteristic
54C2×M16×C43D411yescharacteristic
55C22×C8×C43C2×C411yescharacteristic
56C22×C8×C43D411yescharacteristic
57C22×C8×C43D411yescharacteristic
58#108×C43—41no—
59#108×C43—41no—
60#101×C43—22no—
61#100×C43—22no—
62#41×C43—41no—
63#41×C43—41no—
64C2×Q8×C43C2×D411yescharacteristic
65C2×D4×C43C2×D411yescharacteristic
66C2×D4×C43#4111yescharacteristic
67C2×D4×C43#4111yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—22no—
72C2×Dic86—22no—
73C2×Dic86—22no—
74C2×Dic86—42no—
75C2×Dic86—42no—
76M16×C43—41no—
77M16×C43—41no—
78M16×C43—41no—
79M16×C43—42no—
80M16×C43—42no—
81C2×C8×C43—21no—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—42no—
88C2×C8×C43C22⋊C411yescharacteristic
89C2×C8×C43C22⋊C411yescharacteristic
90C2×C8×C43C22⋊C411yescharacteristic
91C2×C8×C43C22⋊C411yescharacteristic
92C22⋊Dic43—22no—
93C22⋊Dic43—22no—
94C22⋊Dic43—42no—
95C22⋊Dic43—42no—
96C4⋊Dic43—22no—
97C4⋊Dic43—41no—
98Dic43⋊C4—42no—
99Dic43⋊C4—42no—
100C4×Dic43—22no—
101C4×Dic43—41no—
102#10621877—22no—
103#10621877—41no—
104C2×C43⋊C8—41no—
105Dic172—42no—
106Dic172—41no—
107Dic172—41no—
108C23×C43C4×D411yescharacteristic
109C23×C43#12111yescharacteristic
110C23×C43#12411yescharacteristic
111Q8×C43—41no—
112D4×C43—41no—
113D4×C43—41no—
114D4×C43—41no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43C2×C22⋊C411yescharacteristic
122C2×C4×C43C4×D411yescharacteristic
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12711yescharacteristic
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128C2×Dic43—82no—
129Dic86—42no—
130Dic86—42no—
131Dic86—82no—
132C8×C43—21no—
133C8×C43—21no—
134C8×C43—21no—
135C8×C43—82no—
136C8×C43#9911yescharacteristic
137C8×C43#9911yescharacteristic
138C43⋊C8—42no—
139#13233—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43#39011yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43C2×#9911yescharacteristic
151C4×C43#41011yescharacteristic
152Dic43—82no—
153Dic43—82no—
154Dic43—82no—
155#3059—431no—
156#2135—432no—
157#2123—432no—
158#1813D4311yescharacteristic
159#1757—431no—
160C2×C43—21no—
161C2×C43—41no—
162C2×C43—41no—
163C2×C43—41no—
164C2×C43#196411yescharacteristic
165C22×Q16—431no—
166C2×#131C2×D4311yescharacteristic
167#536—432no—
168#470—861no—
169#470—861no—
170#467—861no—
171#467—861no—
172C2×#108—21no—
173#427—431no—
174#419—432no—
175#413—431no—
176#413C2×D4312yes—
177#410—431no—
178#405—861no—
179#356—864no—
180#352—864no—
181#344—861no—
182#338—21no—
183C43#1323311yescharacteristic, complemented, Sylow
184C2×#41C22×D4311yescharacteristic
185C22×Q8—432no—
186C2×Q16—861no—
187C2×Q16—861no—
188C2×Q16—1721no—
189C2×Q16—1721no—
190#131—41no—
191#131—41no—
192C2×M16—22no—
193C2×M16—861no—
194C2×M16C4×D4311yescharacteristic
195C2×M16D17211yescharacteristic
196C2×M16C22⋊D4311yescharacteristic
197C22×C8C4×D4311yescharacteristic
198C22×C8D17211yescharacteristic
199C22×C8C22⋊D4311yescharacteristic
200C4⋊Q8—862no—
201#124—862no—
202#123—862no—
203#123—862no—
204C22⋊Q8—862no—
205C22⋊Q8—862no—
206#117—432no—
207#117—861no—
208#108—41no—
209#108—41no—
210#107—861no—
211#106—861no—
212#103—862no—
213#103—862no—
214#101—22no—
215#101—432no—
216#100—22no—
217#100—861no—
218#99—432no—
219#99—861no—
220#97—1721no—
221C4×C8—1721no—
222#41—41no—
223#41—41no—
224C2×Q8—862no—
225C2×Q8—862no—
226C2×Q8—1722no—
227C2×Q8—1722no—
228C2×Q8D4×D4311yescharacteristic
229C2×D4D4×D4311yescharacteristic
230C2×D4#1062190211yescharacteristic
231C2×D4#1062190211yescharacteristic
232C22×C4—862no—
233C22×C4C2×C4×D4311yescharacteristic
234C22×C4C2×D17211yescharacteristic
235C22×C4C2×C22⋊D4311yescharacteristic
236Q16—1722no—
237Q16—1721no—
238Q16—1721no—
239M16—41no—
240M16—41no—
241M16—41no—
242M16—42no—
243M16—42no—
244M16—862no—
245M16—1721no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—42no—
253C2×C8—1721no—
254C2×C8(C2×D43)⋊C411yescharacteristic
255C2×C8(C2×D43)⋊C411yescharacteristic
256C2×C8(C2×D43)⋊C411yescharacteristic
257C2×C8(C2×D43)⋊C411yescharacteristic
258C4⋊C4—862no—
259C4⋊C4—1721no—
260C4⋊C4—1722no—
261C4⋊C4—1722no—
262C22⋊C4—862no—
263C22⋊C4—862no—
264C22⋊C4—1722no—
265C22⋊C4—1722no—
266C42—862no—
267C42—1721no—
268C23#1306328711yescharacteristic
269C23#1306330011yescharacteristic
270C23#1306331411yescharacteristic
271Q8—41no—
272Q8—3442no—
273Q8—1722no—
274Q8—1722no—
275D4—41no—
276D4—41no—
277D4—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—3442no—
285C2×C4—1722no—
286C2×C4—1722no—
287C2×C4—1722no—
288C2×C4C2×(C2×D43)⋊C411yescharacteristic
289C2×C4#1306328711yescharacteristic
290C2×C4#1306330011yescharacteristic
291C2×C4#1306332111yescharacteristic
292C8—21no—
293C8—21no—
294C8—21no—
295C8—82no—
296C8—1722no—
297C8#1306323911yescharacteristic
298C8#1306323911yescharacteristic
299C22—21no—
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22#1458280011yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—3442no—
310C4—3442no—
311C4—3442no—
312C4C2×#1306323911yescharacteristic
313C4#1458287211yescharacteristic
314C2—21no—
315C2—41no—
316C2—41no—
317C2—41no—
318C2#1913543011yescharacteristic
subgroupG/H
centerC2#19135430
commutatorC22×C4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#1813C2
socleC2×C43#1964
prime radical, cosocleC2×#41×C43C23
hypercenter#1813D43
hypocenterC43#13233
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1813

Complements

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

NH ≅ G/Ntype
6. C22×Dic172C4semidirect
12. #14582937C4semidirect
13. #14582909C4semidirect
183. C43#13233semidirect

Maximal subgroups

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

subgroupindex
#191442502
#191362892
#191362502
#191343952
C43×#18132
#1323343