Finite Group Databasebeta

← #25014016

Subgroups — #25014016

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147698C211yesmaximal, characteristic, complemented
2#19144315C211yesmaximal, characteristic
3C2×#14582708C211yesmaximal, characteristic, complemented
4#19136322C211yesmaximal, characteristic, complemented
5#19132708C211yesmaximal, characteristic, complemented
6#19132693C211yesmaximal, characteristic, complemented
7C43×#1815C211yesmaximal, characteristic, complemented
8#14583697—21no—
9C2×#13063347C2211yescharacteristic
10#14583316—22no—
11#14583316—22no—
12C2×#13063265—22no—
13C2×#13063265C2211yescharacteristic
14C2×#13063265C2211yescharacteristic
15#14583174C412yescomplemented
16#14583169C412yescomplemented
17#14583162—22no—
18C2×#13063261C2211yescharacteristic
19#14582881—21no—
20#14582708—22no—
21#14582705—22no—
22C2×#131×C43C2211yescharacteristic
23C2×#108×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C43×#417—21no—
26C43×#343—21no—
27C2×#10621898—21no—
28#13063356—41no—
29#13063355—22no—
30#13063351—41no—
31#13063350—22no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063345—42no—
37C2×Dic172C2×C411yescharacteristic
38C2×#10621873—21no—
39C2×D344C2×C411yescharacteristic
40C2×#10621877—21no—
41#13063265—24no—
42#13063265—21no—
43#13063265—21no—
44#13063265—21no—
45#13063265D412yes—
46C2×C43⋊C16—24no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16D412yes—
49#13063261—21no—
50#13063261C2×C412yes—
51#13063243—22no—
52#13063241—22no—
53C2×#41×C43D411yescharacteristic
54#131×C43—21no—
55#131×C43—21no—
56#131×C43C2×C412yes—
57#131×C43D412yes—
58C2×M16×C43—21no—
59C2×M16×C43—21no—
60C2×M16×C43D411yescharacteristic
61C22×C8×C43—21no—
62C22×C8×C43C2311yescharacteristic
63C2×C4⋊C4×C43—21no—
64#108×C43—21no—
65#108×C43—21no—
66#106×C43—21no—
67#106×C43—21no—
68#103×C43—41no—
69#102×C43—41no—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43C22⋊C412yes—
73#41×C43SD1612yes—
74C2×Q8×C43D811yescharacteristic
75C2×D4×C43—21no—
76C2×D4×C43D811yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C2×C22⋊D43—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85C2×D172—21no—
86C2×C4×D43—41no—
87C2×Dic86—21no—
88M16×C43—21no—
89M16×C43—22no—
90M16×C43—22no—
91M16×C43—41no—
92M16×C43—41no—
93M16×C43C22⋊C412yes—
94C2×C8×C43—21no—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43—41no—
98C2×C8×C43C22×C411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106#10621885—42no—
107#10621884—42no—
108#10621883—42no—
109#10621882—42no—
110#10621877—22no—
111#10621877—41no—
112C2×C43⋊C8—41no—
113Dic172—21no—
114Dic172—21no—
115D344—21no—
116D344—21no—
117#10621873—41no—
118#10621873—41no—
119C43⋊C16—22no—
120C43⋊C16—22no—
121C23×C43—21no—
122C23×C43#13511yescharacteristic
123C22×D43—41no—
124Q8×C43—21no—
125Q8×C43#10212yes—
126D4×C43—22no—
127D4×C43—22no—
128D4×C43—21no—
129D4×C43#10212yes—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—81no—
134C2×C4×C43—161no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C22⋊D43—81no—
142C22⋊D43—81no—
143C2×Dic43—41no—
144D172—41no—
145D172—41no—
146C4×D43—81no—
147C4×D43—81no—
148Dic86—41no—
149Dic86—41no—
150C8×C43—22no—
151C8×C43—81no—
152C8×C43C4×D411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12011yescharacteristic
155C8×C43#12311yescharacteristic
156C43⋊C8—42no—
157#13070—431nomaximal, Sylow
158C22×C43—22no—
159C22×C43—41no—
160C22×C43—81no—
161C22×C43#41611yescharacteristic
162C22×C43#46511yescharacteristic
163C22×C43#46611yescharacteristic
164C2×D43—81no—
165C2×D43—161no—
166C4×C43—22no—
167C4×C43—161no—
168C4×C43#38611yescharacteristic
169C4×C43C2×#10211yescharacteristic
170C4×C43#46511yescharacteristic
171C4×C43#46611yescharacteristic
172Dic43—81no—
173#3407—431no—
174#3067—431no—
175C2×#360—431no—
176#2143—431no—
177#1815D4311yescharacteristic, complemented
178#1388—431no—
179#1383—431no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—42no—
184C2×C43#189311yescharacteristic
185D43—161no—
186#575—861no—
187C2×#135—431no—
188C2×#131C2×D4311yescharacteristic
189#504—862no—
190#504—862no—
191C2×M32—431no—
192C2×M32—431no—
193C2×M32—862no—
194#473—432no—
195#472—432no—
196#471—862no—
197C2×#108—431no—
198C2×#108C2×D4311yescharacteristic
199C2×#106C2×D4311yescharacteristic
200#417—21no—
201#413—861no—
202#360—862no—
203#359—862no—
204#343—21no—
205C43#1307011yescharacteristic, complemented, Sylow
206C2×#41—861no—
207C2×#41C22⋊D4311yescharacteristic
208#137—862no—
209#137—1721no—
210AGL(1,ℤ/8)—862no—
211AGL(1,ℤ/8)—1721no—
212#135—861no—
213#135—861no—
214#135—861no—
215#135—861no—
216#135—1722no—
217C2×Q16—431no—
218C2×SD16—861no—
219C2×D8—431no—
220#131—21no—
221#131—21no—
222#131C4×D4312yes—
223#131D17212yes—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—861no—
227C2×M16C22⋊D4311yescharacteristic
228C22×C8—21no—
229C22×C8C22×D4311yescharacteristic
230C2×C4⋊C4—21no—
231M32—432no—
232M32—864no—
233M32—861no—
234M32—861no—
235M32—861no—
236C2×C16—432no—
237C2×C16—864no—
238C2×C16—861no—
239#108—21no—
240#108—21no—
241#108—432no—
242#108—861no—
243#106—21no—
244#106—21no—
245#103—41no—
246#102—41no—
247#101—862no—
248#100—862no—
249#41—21no—
250#41—21no—
251#41—1721no—
252#41—1721no—
253#41—1721no—
254#41—1721no—
255#41(C2×D43)⋊C412yes—
256#41#1062188412yes—
257C2×Q8—861no—
258C2×Q8#1062188211yescharacteristic
259C2×D4—21no—
260C2×D4—861no—
261C2×D4—1721no—
262C2×D4#1062188211yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—1721no—
266C22×C4C2×C22⋊D4311yescharacteristic
267Q16—861no—
268Q16—861no—
269Q16—1722no—
270SD16—1722no—
271SD16—1722no—
272SD16—1721no—
273SD16—1721no—
274D8—861no—
275D8—861no—
276D8—1722no—
277M16—21no—
278M16—22no—
279M16—22no—
280M16—41no—
281M16—41no—
282M16—862no—
283M16—1721no—
284M16(C2×D43)⋊C412yes—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—1721no—
290C2×C8C2×C4×D4311yescharacteristic
291C2×C8C2×D17211yescharacteristic
292C2×C8D4×D4311yescharacteristic
293C2×C8D4×D4311yescharacteristic
294C2×C8#1062190011yescharacteristic
295C2×C8#1062190011yescharacteristic
296C4⋊C4—41no—
297C4⋊C4—41no—
298C16—862no—
299C16—862no—
300C23—21no—
301C23—1721no—
302C23#1306334511yescharacteristic
303Q8—21no—
304Q8—1721no—
305Q8—1721no—
306Q8#1306324512yes—
307D4—22no—
308D4—22no—
309D4—21no—
310D4—3441no—
311D4—3441no—
312D4—1721no—
313D4—1721no—
314D4#1306324512yes—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—81no—
319C2×C4—161no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4C2×(C2×D43)⋊C411yescharacteristic
324C2×C4#1306329711yescharacteristic
325C2×C4#1306329711yescharacteristic
326C2×C4C2×#1062188211yescharacteristic
327C2×C4C2×#1062188411yescharacteristic
328C2×C4#1306334511yescharacteristic
329C8—22no—
330C8—81no—
331C8—1722no—
332C8(C22⋊D43)⋊C411yescharacteristic
333C8(C22⋊D43)⋊C411yescharacteristic
334C8#1306329511yescharacteristic
335C8#1306330911yescharacteristic
336C22—22no—
337C22—41no—
338C22—81no—
339C22—3441no—
340C22—6881no—
341C22#1458289311yescharacteristic
342C22#1458313011yescharacteristic
343C22#1458313311yescharacteristic
344C4—22no—
345C4—161no—
346C4—3441no—
347C4#1458277611yescharacteristic
348C4C2×#1306324511yescharacteristic
349C4#1458313011yescharacteristic
350C4#1458313311yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—6881no—
356C2#1913502111yescharacteristic
subgroupG/H
centerC2#19135021
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1815C2
socleC2×C43#1893
prime radical#19144315C2
cosocleC22×C8×C43C23
hypercenter#1815D43
hypocenterC43#13070
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #1815

Complements

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

NH ≅ G/Ntype
1. #19147698C2semidirect
3. C2×#14582708C2semidirect
4. #19136322C2semidirect
5. #19132708C2semidirect
6. #19132693C2semidirect
7. C43×#1815C2semidirect
15. #14583174C4semidirect
16. #14583169C4semidirect
177. #1815D43semidirect
205. C43#13070semidirect

Maximal subgroups

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

subgroupindex
#191476982
#191443152
C2×#145827082
#191363222
#191327082
#191326932
C43×#18152
#1307043