Finite Group Databasebeta

← #25013555

Subgroups — #25013555

Order 11008.

476 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#19144315C211yesmaximal, characteristic
2#19136322C211yesmaximal, characteristic, complemented
3C2×#14582705C211yesmaximal, characteristic, complemented
4C2×#14582683C211yesmaximal, characteristic, complemented
5#19132706C211yesmaximal, characteristic, complemented
6#19132688C211yesmaximal, characteristic, complemented
7C43×#2916C211yesmaximal, characteristic, complemented
8#14583697—21no—
9C2×#13063347C2211yescharacteristic
10C2×#13063265C2211yescharacteristic
11C22×C43⋊C16C2211yescharacteristic
12#14583174C412yes—
13#14583169C412yes—
14#14583162—22no—
15C2×#13063261C2211yescharacteristic
16#14582881—21no—
17#14582705—22no—
18#14582705—22no—
19#14582683—22no—
20C43×#568—21no—
21C2×#131×C43C2211yescharacteristic
22C43×#430—21no—
23C43×#430—22no—
24C2×#108×C43—22no—
25C2×#108×C43C2211yescharacteristic
26C2×#108×C43C2211yescharacteristic
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—21no—
42#13063265—21no—
43C2×C43⋊C16—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47#13063261—21no—
48#13063261C2×C412yes—
49#13063243—22no—
50#13063241—22no—
51C2×#41×C43D411yescharacteristic
52#131×C43—21no—
53#131×C43—21no—
54#131×C43—42no—
55#131×C43—42no—
56#131×C43C2×C412yes—
57#131×C43D412yes—
58C2×M16×C43—21no—
59C2×M16×C43—24no—
60C2×M16×C43—21no—
61C2×M16×C43—21no—
62C2×M16×C43D411yescharacteristic
63C22×C8×C43—21no—
64C22×C8×C43C2311yescharacteristic
65#108×C43—24no—
66#108×C43—21no—
67#108×C43—21no—
68#108×C43D412yes—
69#108×C43D412yes—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43C22⋊C412yes—
73#41×C43D812yes—
74C2×Q8×C43SD1611yescharacteristic
75C2×D4×C43—21no—
76C2×D4×C43SD1611yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43C2×D411yescharacteristic
79C2×C22⋊D43—41no—
80#10621898—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84C2×D172—21no—
85C2×C4×D43—41no—
86C2×Dic86—21no—
87M16×C43—21no—
88M16×C43—22no—
89M16×C43—22no—
90M16×C43—22no—
91M16×C43—22no—
92M16×C43—44no—
93M16×C43—41no—
94M16×C43—41no—
95M16×C43C22⋊C412yes—
96C2×C8×C43—21no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—44no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C2×C8×C43C22×C411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43#4111yescharacteristic
107C2×C8×C43#4111yescharacteristic
108#10621885—42no—
109#10621884—42no—
110#10621883—42no—
111#10621882—42no—
112#10621877—22no—
113#10621877—41no—
114C2×C43⋊C8—41no—
115Dic172—21no—
116Dic172—21no—
117D344—21no—
118D344—21no—
119#10621873—41no—
120#10621873—41no—
121C43⋊C16—41no—
122C43⋊C16—41no—
123C23×C43—21no—
124C23×C43#13711yescharacteristic
125C22×D43—41no—
126Q8×C43—21no—
127Q8×C43#10212yes—
128D4×C43—22no—
129D4×C43—22no—
130D4×C43—21no—
131D4×C43#10212yes—
132C2×C4×C43—21no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
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—42no—
152C8×C43—42no—
153C8×C43C4×D411yescharacteristic
154C8×C43C4×D411yescharacteristic
155C8×C43#12111yescharacteristic
156C8×C43#12111yescharacteristic
157C43⋊C8—42no—
158#12995—431nomaximal, Sylow
159C22×C43—22no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43#41711yescharacteristic
163C22×C43#44811yescharacteristic
164C22×C43#48011yescharacteristic
165C2×D43—81no—
166C2×D43—161no—
167C4×C43—22no—
168C4×C43#38611yescharacteristic
169C4×C43C2×#10211yescharacteristic
170C4×C43#44711yescharacteristic
171C4×C43#48111yescharacteristic
172Dic43—81no—
173#3067—431no—
174#2916D4311yescharacteristic, complemented
175#2143—431no—
176C2×#359—431no—
177C2×#350—431no—
178#1388—431no—
179#1381—431no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—42no—
184C2×C43#187411yescharacteristic
185D43—161no—
186#575—861no—
187C2×#135—431no—
188#568—21no—
189C2×#131C2×D4311yescharacteristic
190C2×M32—431no—
191C22×C16—431no—
192#473—432no—
193#472—432no—
194#471—862no—
195#430—21no—
196#430—22no—
197C2×#108—22no—
198C2×#108—431no—
199C2×#108C2×D4311yescharacteristic
200C2×#108C2×D4311yescharacteristic
201#413—861no—
202#359—862no—
203#359—862no—
204#350—862no—
205C43#1299511yescharacteristic, 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#131—42no—
223#131—42no—
224#131C4×D4312yes—
225#131D17212yes—
226C2×M16—21no—
227C2×M16—24no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—861no—
231C2×M16C22⋊D4311yescharacteristic
232C22×C8—21no—
233C22×C8C22×D4311yescharacteristic
234M32—861no—
235M32—861no—
236C2×C16—861no—
237C2×C16—861no—
238C2×C16—861no—
239C2×C16—861no—
240#108—24no—
241#108—21no—
242#108—21no—
243#108—432no—
244#108—861no—
245#108C22⋊D4312yes—
246#108C22⋊D4312yes—
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#1062188212yes—
257C2×Q8—861no—
258C2×Q8#1062188411yescharacteristic
259C2×D4—21no—
260C2×D4—861no—
261C2×D4—1721no—
262C2×D4#1062188411yescharacteristic
263C22×C4—21no—
264C22×C4—1721no—
265C22×C4C2×C22⋊D4311yescharacteristic
266Q16—861no—
267Q16—861no—
268Q16—1722no—
269SD16—1722no—
270SD16—1722no—
271SD16—1721no—
272SD16—1721no—
273D8—861no—
274D8—861no—
275D8—1722no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—44no—
282M16—41no—
283M16—41no—
284M16—862no—
285M16—1721no—
286M16(C2×D43)⋊C412yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—44no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—1721no—
294C2×C8C2×C4×D4311yescharacteristic
295C2×C8C2×D17211yescharacteristic
296C2×C8#1062189811yescharacteristic
297C2×C8#1062189811yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C2×C8C2×C22⋊D4311yescharacteristic
300C16—1721no—
301C16—1721no—
302C23—21no—
303C23—1721no—
304C23#1306335611yescharacteristic
305Q8—21no—
306Q8—1721no—
307Q8—1721no—
308Q8#1306324512yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—3441no—
313D4—3441no—
314D4—1721no—
315D4—1721no—
316D4#1306324512yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4C2×(C2×D43)⋊C411yescharacteristic
324C2×C4#1306329411yescharacteristic
325C2×C4#1306330811yescharacteristic
326C2×C4C2×#1062188211yescharacteristic
327C2×C4C2×#1062188411yescharacteristic
328C2×C4#1306335111yescharacteristic
329C8—22no—
330C8—42no—
331C8—42no—
332C8—1722no—
333C8C4×C22⋊D4311yescharacteristic
334C8C4×C22⋊D4311yescharacteristic
335C8#1306329911yescharacteristic
336C8#1306329911yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—3441no—
341C22—6881no—
342C22#1458289811yescharacteristic
343C22#1458303811yescharacteristic
344C22#1458321211yescharacteristic
345C4—22no—
346C4—3441no—
347C4#1458277811yescharacteristic
348C4C2×#1306324511yescharacteristic
349C4#1458303311yescharacteristic
350C4#1458321711yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—6881no—
356C2#1913491211yescharacteristic
subgroupG/H
centerC4#14583033
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2916C2
socleC2×C43#1874
prime radical#19144315C2
cosocleC22×C8×C43C23
hypercenter#2916D43
hypocenterC43#12995
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #2916

Complements

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

NH ≅ G/Ntype
2. #19136322C2semidirect
3. C2×#14582705C2semidirect
4. C2×#14582683C2semidirect
5. #19132706C2semidirect
6. #19132688C2semidirect
7. C43×#2916C2semidirect
174. #2916D43semidirect
205. C43#12995semidirect

Maximal subgroups

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

subgroupindex
#191443152
#191363222
C2×#145827052
C2×#145826832
#191327062
#191326882
C43×#29162
#1299543