Finite Group Databasebeta

← #25013780

Subgroups — #25013780

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#19147729C211yesmaximal, characteristic
2#19136331C211yesmaximal, characteristic, complemented
3C2×#14582708C211yesmaximal, characteristic, complemented
4#19135493C211yesmaximal, characteristic, complemented
5#19132702C211yesmaximal, characteristic, complemented
6#19132681C211yesmaximal, characteristic, complemented
7C43×#2952C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583340—21no—
10#14583339C412yescomplemented
11#14583335—21no—
12#14583334C412yescomplemented
13#14583329—22no—
14C2×#13063265C2211yescharacteristic
15C2×#13063265C2211yescharacteristic
16#14582937C2211yescharacteristic
17#14582915—21no—
18#14582872—21no—
19#14582709—22no—
20#14582708—22no—
21C2×#135×C43C2211yescharacteristic
22C43×#520—21no—
23C43×#442—21no—
24C43×#441—21no—
25C4×SD16×C43—22no—
26C2×#106×C43C2211yescharacteristic
27C43×#417—21no—
28C43×#405C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347—21no—
33#13063347—21no—
34C2×Dic172C2×C411yescharacteristic, complemented
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic, complemented
37#13063284—21no—
38#13063271—22no—
39#13063269—22no—
40#13063268—22no—
41#13063266—22no—
42#13063265—21no—
43#13063265—21no—
44#13063265—21no—
45#13063265C2×C412yescomplemented
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48#13063259—21no—
49#13063257—21no—
50#13063251—42no—
51#13063239—42no—
52C2×#41×C43—21no—
53#135×C43—21no—
54#135×C43—21no—
55#135×C43C2×C412yes—
56#135×C43D412yes—
57C2×Q16×C43D411yescharacteristic
58C2×SD16×C43—21no—
59C2×D8×C43D411yescharacteristic
60C2×M16×C43D411yescharacteristic
61C22×C8×C43C2311yescharacteristic
62C4×Q8×C43—22no—
63C4×D4×C43—22no—
64C4×D4×C43—42no—
65#117×C43—41no—
66#117×C43D411yescharacteristic
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—41no—
69#106×C43—21no—
70#106×C43D412yes—
71#103×C43—22no—
72#102×C43—22no—
73#97×C43—21no—
74C4×C8×C43—21no—
75#41×C43—22no—
76#41×C43—22no—
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—41no—
82C22×C4×C43—42no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C2×C22⋊D43—41no—
87#10621898—41no—
88#10621898—41no—
89#10621898—41no—
90#10621898—41no—
91C2×D172—21no—
92C2×C4×D43—41no—
93C2×Dic86—21no—
94Q16×C43—21no—
95Q16×C43C22⋊C412yes—
96SD16×C43—22no—
97SD16×C43—22no—
98D8×C43—21no—
99D8×C43C22⋊C412yes—
100M16×C43—21no—
101M16×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43C22×C411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C4⋊C4×C43—21no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—42no—
114C22⋊C4×C43D812yes—
115C42×C43—21no—
116C42×C43—42no—
117C22⋊Dic43—41no—
118C4⋊Dic43—41no—
119C4×Dic43—41no—
120Dic172—21no—
121Dic172—21no—
122D344—21no—
123D344—21no—
124#10621873—41no—
125#10621873—41no—
126C43⋊C16—22no—
127C43⋊C16—41no—
128C23×C43—41no—
129C23×C43C2×D811yescharacteristic
130C22×D43—41no—
131Q8×C43—22no—
132Q8×C43—41no—
133D4×C43—22no—
134D4×C43—42no—
135D4×C43—42no—
136D4×C43—41no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—162no—
143C2×C4×C43—161no—
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#13511yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—41no—
153C2×Dic43—81no—
154D172—41no—
155D172—41no—
156C4×D43—81no—
157C4×D43—81no—
158Dic86—41no—
159Dic86—41no—
160C8×C43—41no—
161C8×C43C2×C22⋊C411yescharacteristic
162C8×C43C4×D411yescharacteristic
163C8×C43#12111yescharacteristic
164C8×C43#12311yescharacteristic
165#13030—431nomaximal, Sylow
166C22×C43—41no—
167C22×C43—42no—
168C22×C43—81no—
169C22×C43—81no—
170C22×C43C4×D811yescharacteristic
171C22×C43#44711yescharacteristic
172C22×C43#45911yescharacteristic
173C2×D43—81no—
174C2×D43—161no—
175C4×C43—42no—
176C4×C43—42no—
177C4×C43—82no—
178C4×C43#38611yescharacteristic
179C4×C43#44211yescharacteristic
180C4×C43#44911yescharacteristic
181C4×C43#46311yescharacteristic
182Dic43—81no—
183Dic43—161no—
184#3414—431no—
185#2952D4311yescharacteristic, complemented
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#187911yescharacteristic
196D43—161no—
197C2×#135—431no—
198C2×#135C2×D4311yescharacteristic
199#520—21no—
200#510—432no—
201#510—861no—
202#509—432no—
203#509—861no—
204#508—862no—
205C2×M32—431no—
206C2×M32—431no—
207#442—21no—
208#441—21no—
209C4×SD16—22no—
210#427—431no—
211C2×#106C2×D4311yescharacteristic
212#421—861no—
213#417—21no—
214#410—861no—
215#405C2×D4311yescharacteristic
216#360—862no—
217#360—862no—
218C43#1303011yescharacteristic, complemented, Sylow
219C2×#41—21no—
220C2×#41—861no—
221#135—21no—
222#135—21no—
223#135—861no—
224#135—861no—
225#135—861no—
226#135—861no—
227#135C4×D4312yes—
228#135D17212yes—
229C2×Q16—431no—
230C2×Q16C22⋊D4311yescharacteristic
231C2×SD16—21no—
232C2×SD16—861no—
233C2×D8—431no—
234C2×D8C22⋊D4311yescharacteristic
235C2×M16C22⋊D4311yescharacteristic
236C22×C8C22×D4311yescharacteristic
237C4×Q8—22no—
238C4×D4—22no—
239C4×D4—42no—
240#117—41no—
241#117—861no—
242#117C22⋊D4311yescharacteristic
243C2×C4⋊C4—21no—
244C2×C4⋊C4—41no—
245Q32—862no—
246SD32—862no—
247SD32—862no—
248D16—862no—
249M32—432no—
250M32—861no—
251M32—861no—
252M32—861no—
253C2×C16—861no—
254C2×C16—861no—
255#107—861no—
256#106—21no—
257#106—861no—
258#106C22⋊D4312yes—
259#104—1722no—
260#103—22no—
261#102—22no—
262#99—1722no—
263#97—21no—
264C4×C8—21no—
265#41—22no—
266#41—22no—
267#41—41no—
268#41—41no—
269#41—1721no—
270#41—1721no—
271#41—1721no—
272#41—1721no—
273C2×Q8—21no—
274C2×Q8—861no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—861no—
278C2×D4—1721no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—1721no—
283C22×C4C2×C22⋊D4311yescharacteristic
284Q16—21no—
285Q16—861no—
286Q16—861no—
287Q16(C2×D43)⋊C412yes—
288SD16—22no—
289SD16—22no—
290SD16—1721no—
291SD16—1721no—
292D8—21no—
293D8—861no—
294D8—861no—
295D8(C2×D43)⋊C412yes—
296M16—21no—
297M16—21no—
298C2×C8—21no—
299C2×C8C2×C4×D4311yescharacteristic
300C2×C8C2×D17211yescharacteristic
301C2×C8#1062189811yescharacteristic
302C2×C8#1062189811yescharacteristic
303C2×C8C2×C22⋊D4311yescharacteristic
304C2×C8C2×C22⋊D4311yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—1721no—
310C22⋊C4—42no—
311C22⋊C4—1721no—
312C22⋊C4#1062188212yes—
313C42—21no—
314C42—42no—
315C42—1721no—
316C16—862no—
317C16—1721no—
318C23—41no—
319C23—1721no—
320C23C2×#1062188211yescharacteristic
321Q8—22no—
322Q8—41no—
323Q8—1721no—
324Q8—1721no—
325D4—22no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—3441no—
330D4—3441no—
331D4—1721no—
332D4—1721no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—162no—
339C2×C4—161no—
340C2×C4—3441no—
341C2×C4—3441no—
342C2×C4—3441no—
343C2×C4—1721no—
344C2×C4C4×C22⋊D4311yescharacteristic
345C2×C4#1306329411yescharacteristic
346C2×C4#1306329911yescharacteristic
347C2×C4#1306334511yescharacteristic
348C2×C4#1306335011yescharacteristic
349C2×C4#1306335111yescharacteristic
350C8—41no—
351C8C2×(C2×D43)⋊C411yescharacteristic
352C8C4×C22⋊D4311yescharacteristic
353C8#1306329911yescharacteristic
354C8#1306330811yescharacteristic
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—3441no—
360C22—6881no—
361C22C4×#1062188211yescharacteristic
362C22#1458303311yescharacteristic
363C22#1458309411yescharacteristic
364C4—42no—
365C4—42no—
366C4—82no—
367C4—3441no—
368C4—6881no—
369C4#1458277811yescharacteristic
370C4#1458300911yescharacteristic
371C4#1458304411yescharacteristic
372C4#1458311411yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—6881no—
378C2#1913494311yescharacteristic
subgroupG/H
centerC2#19134943
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2952C2
socleC2×C43#1879
prime radical#19147729C2
cosocleC22×C8×C43C23
hypercenter#2952D43
hypocenterC43#13030
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2952

Complements

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

NH ≅ G/Ntype
2. #19136331C2semidirect
3. C2×#14582708C2semidirect
4. #19135493C2semidirect
5. #19132702C2semidirect
6. #19132681C2semidirect
7. C43×#2952C2semidirect
10. #14583339C4semidirect
12. #14583334C4semidirect
34. C2×Dic172C2×C4semidirect
36. C2×D344C2×C4semidirect
45. #13063265C2×C4semidirect
185. #2952D43semidirect
218. C43#13030semidirect

Maximal subgroups

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

subgroupindex
#191477292
#191363312
C2×#145827082
#191354932
#191327022
#191326812
C43×#29522
#1303043