Finite Group Databasebeta

← #25013782

Subgroups — #25013782

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143479C211yesmaximal, characteristic, complemented
2#19136331C211yesmaximal, characteristic, complemented
3C2×#14582709C211yesmaximal, characteristic, complemented
4#19135494C211yesmaximal, characteristic, complemented
5#19132701C211yesmaximal, characteristic, complemented
6#19132682C211yesmaximal, characteristic, complemented
7C43×#3414C211yesmaximal, characteristic
8#14583382—21no—
9C2×#13063265C2211yescharacteristic
10#14583011—21no—
11#14583006—21no—
12SD16×Dic43—22no—
13#14582937C2211yescharacteristic
14C2×#13063257C2211yescharacteristic
15#14582916—21no—
16#14582900—21no—
17#14582873—21no—
18#14582854C2211yescharacteristic
19#14582709—22no—
20#14582709—22no—
21C2×#135×C43C2211yescharacteristic
22C2×#135×C43C2211yescharacteristic
23C43×#510—21no—
24C43×#510C412yescomplemented
25C43×#509—21no—
26C43×#509C412yescomplemented
27C43×#508—22no—
28C2×M32×C43C2211yescharacteristic
29C2×#10621877D411yescharacteristic
30Q8×Dic43—22no—
31D4×Dic43—22no—
32D4×Dic43—42no—
33#13063284—21no—
34#13063284—41no—
35#13063284D411yescharacteristic
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—41no—
38#13063265—21no—
39#13063265—21no—
40C2×C43⋊C16—21no—
41#13063259—21no—
42#13063257—21no—
43#13063257—21no—
44#13063257D412yes—
45#13063252—42no—
46#13063249—22no—
47#13063246—22no—
48#13063240—42no—
49#13063235—21no—
50C8×Dic43—21no—
51C2×#41×C43—21no—
52C2×#41×C43—21no—
53#135×C43—21no—
54#135×C43—21no—
55#135×C43—21no—
56#135×C43—21no—
57#135×C43—21no—
58#135×C43—21no—
59#135×C43C2×C412yes—
60#135×C43D412yes—
61C2×Q16×C43C2×C411yescharacteristic, complemented
62C2×Q16×C43D411yescharacteristic
63C2×SD16×C43—21no—
64C2×SD16×C43—21no—
65C2×D8×C43C2×C411yescharacteristic, complemented
66C2×D8×C43D411yescharacteristic
67C22×C8×C43C2311yescharacteristic
68Q32×C43—22no—
69SD32×C43—22no—
70SD32×C43—22no—
71D16×C43—22no—
72M32×C43—21no—
73M32×C43C2×C412yescomplemented
74C2×C16×C43—21no—
75#41×C43—22no—
76#41×C43—22no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82#41×C43—41no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43C2×D411yescharacteristic
92C22×Dic43—42no—
93C22×Dic43—41no—
94Q16×C43—21no—
95Q16×C43—21no—
96Q16×C43—21no—
97Q16×C43C22⋊C412yes—
98SD16×C43—22no—
99SD16×C43—22no—
100SD16×C43—41no—
101SD16×C43—41no—
102D8×C43—21no—
103D8×C43—21no—
104D8×C43—21no—
105D8×C43C22⋊C412yes—
106C2×C8×C43C22×C411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43#4111yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C22⋊Dic43—42no—
113C22⋊Dic43—41no—
114C22⋊Dic43D812yes—
115C4⋊Dic43—21no—
116C4⋊Dic43—22no—
117C4⋊Dic43—42no—
118C4⋊Dic43—41no—
119C4⋊Dic43—41no—
120C4×Dic43—21no—
121C4×Dic43—42no—
122C4×Dic43—41no—
123#10621877—21no—
124#10621877—21no—
125C2×C43⋊C8—21no—
126C16×C43—22no—
127C43⋊C16—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43C2×D811yescharacteristic
131Q8×C43—22no—
132Q8×C43—41no—
133Q8×C43—41no—
134Q8×C43—41no—
135D4×C43—22no—
136D4×C43—42no—
137D4×C43—42no—
138D4×C43—41no—
139D4×C43—41no—
140D4×C43—41no—
141D4×C43—81no—
142D4×C43—81no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×Dic43—22no—
156C2×Dic43—42no—
157C2×Dic43—81no—
158C2×Dic43—162no—
159C2×Dic43—161no—
160C8×C43C2×C22⋊C411yescharacteristic
161C8×C43C4×D411yescharacteristic
162C8×C43#12111yescharacteristic
163C8×C43#12311yescharacteristic
164C43⋊C8—41no—
165#13030—431nomaximal, Sylow
166C22×C43—41no—
167C22×C43—42no—
168C22×C43—81no—
169C22×C43—81no—
170C22×C43—81no—
171C22×C43—161no—
172C22×C43C4×D811yescharacteristic
173C22×C43#44711yescharacteristic
174C22×C43#45911yescharacteristic
175C4×C43—42no—
176C4×C43—81no—
177C4×C43#38611yescharacteristic
178C4×C43#44211yescharacteristic
179C4×C43#44911yescharacteristic
180C4×C43#46311yescharacteristic
181Dic43—42no—
182Dic43—82no—
183Dic43—161no—
184#3414D4311yescharacteristic
185#2952—431no—
186#2145—431no—
187C2×#360—431no—
188#1976—431no—
189#1386—431no—
190#1378—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—82no—
195C2×C43—161no—
196C2×C43#187911yescharacteristic
197C2×#135C2×D4311yescharacteristic
198C2×#135C2×D4311yescharacteristic
199#520—861no—
200#510—21no—
201#510Dic4312yescomplemented
202#509—21no—
203#509Dic4312yescomplemented
204#508—22no—
205C2×M32—431no—
206C2×M32C2×D4311yescharacteristic
207#442—861no—
208#441—861no—
209C4×SD16—862no—
210#427—431no—
211C2×#106—431no—
212#421—861no—
213#417—861no—
214#410—861no—
215#405—431no—
216#360—862no—
217#360—862no—
218C43#1303011yescharacteristic, complemented, Sylow
219C2×#41—21no—
220C2×#41—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135C2×Dic4312yes—
228#135C22⋊D4312yes—
229C2×Q16C2×Dic4311yescharacteristic, complemented
230C2×Q16C22⋊D4311yescharacteristic
231C2×SD16—21no—
232C2×SD16—21no—
233C2×D8C2×Dic4311yescharacteristic, complemented
234C2×D8C22⋊D4311yescharacteristic
235C2×M16—431no—
236C22×C8C22×D4311yescharacteristic
237C4×Q8—862no—
238C4×D4—862no—
239C4×D4—1722no—
240#117—431no—
241#117—861no—
242#117—1721no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—1721no—
245Q32—22no—
246SD32—22no—
247SD32—22no—
248D16—22no—
249M32—21no—
250M32—861no—
251M32—861no—
252M32C2×Dic4312yescomplemented
253C2×C16—21no—
254C2×C16—861no—
255#107—861no—
256#106—432no—
257#106—861no—
258#106—861no—
259#104—1722no—
260#103—862no—
261#102—862no—
262#99—1722no—
263#97—861no—
264C4×C8—861no—
265#41—22no—
266#41—22no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—1722no—
282C22×C4—1721no—
283C22×C4D4×D4311yescharacteristic
284Q16—21no—
285Q16—21no—
286Q16—21no—
287Q16C22⋊Dic4312yes—
288SD16—22no—
289SD16—22no—
290SD16—41no—
291SD16—41no—
292D8—21no—
293D8—21no—
294D8—21no—
295D8C22⋊Dic4312yes—
296M16—861no—
297M16—861no—
298C2×C8—861no—
299C2×C8D4×D4311yescharacteristic
300C2×C8#1062190011yescharacteristic
301C2×C8#1062190011yescharacteristic
302C2×C8C22×Dic4311yescharacteristic
303C2×C8C2×C22⋊D4311yescharacteristic
304C2×C8C2×C22⋊D4311yescharacteristic
305C4⋊C4—861no—
306C4⋊C4—862no—
307C4⋊C4—1722no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C22⋊C4—432no—
311C22⋊C4—1722no—
312C22⋊C4—1721no—
313C42—861no—
314C42—1722no—
315C42—1721no—
316C16—22no—
317C16—1721no—
318C23—41no—
319C23—41no—
320C23D8×D4311yescharacteristic
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325D4—22no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—862no—
340C2×C4—3441no—
341C2×C4—1722no—
342C2×C4—6881no—
343C2×C4—6882no—
344C2×C4D4×Dic4311yescharacteristic
345C2×C4#1306329311yescharacteristic
346C2×C4#1306329711yescharacteristic
347C2×C4#1306334411yescharacteristic
348C2×C4#1306334911yescharacteristic
349C2×C4#1306334911yescharacteristic
350C8—1721no—
351C8C2×C22⋊Dic4311yescharacteristic
352C8D4×Dic4311yescharacteristic
353C8#1306329711yescharacteristic
354C8#1306330611yescharacteristic
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—161no—
361C22D8×Dic4311yescharacteristic
362C22#1458303111yescharacteristic
363C22#1458309211yescharacteristic
364C4—42no—
365C4—81no—
366C4—3442no—
367C4—1722no—
368C4—6881no—
369C4#1458277911yescharacteristic
370C4#1458301111yescharacteristic
371C4#1458304111yescharacteristic
372C4#1458311211yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—161no—
378C2#1913494511yescharacteristic
subgroupG/H
centerC2#19134945
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC43×#3414C2
socleC2×C43#1879
cosocleC22×C8×C43C23
hypercenter#3414D43
hypocenterC43#13030
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #19143479C2semidirect
2. #19136331C2semidirect
3. C2×#14582709C2semidirect
4. #19135494C2semidirect
5. #19132701C2semidirect
6. #19132682C2semidirect
24. C43×#510C4semidirect
26. C43×#509C4semidirect
61. C2×Q16×C43C2×C4semidirect
65. C2×D8×C43C2×C4semidirect
73. M32×C43C2×C4semidirect
201. #510Dic43semidirect
203. #509Dic43semidirect
218. C43#13030semidirect
229. C2×Q16C2×Dic43semidirect
233. C2×D8C2×Dic43semidirect
252. M32C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191434792
#191363312
C2×#145827092
#191354942
#191327012
#191326822
C43×#34142
#1303043