Finite Group Databasebeta

← #25014025

Subgroups — #25014025

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144315C211yesmaximal, characteristic
2#19136332C211yesmaximal, characteristic, complemented
3C2×#14582707C211yesmaximal, characteristic, complemented
4#19134649C211yesmaximal, characteristic, complemented
5#19132707C211yesmaximal, characteristic, complemented
6#19132691C211yesmaximal, characteristic, complemented
7C2×C43×#504C211yesmaximal, characteristic, complemented
8#14583697—21no—
9C2×#13063347C2211yescharacteristic
10#14583174C412yescomplemented
11#14583169C412yescomplemented
12#14583162—22no—
13C2×#13063261C2211yescharacteristic
14C2×#13063261C2211yescharacteristic
15#14582937C2211yescharacteristic
16#14582916—21no—
17#14582881—21no—
18#14582710—22no—
19#14582707—21no—
20#14582707—21no—
21#14582671—21no—
22C2×#131×C43C2211yescharacteristic
23C43×#504—22no—
24C43×#504—22no—
25C2×M32×C43—21no—
26C2×M32×C43C2211yescharacteristic
27C22×C16×C43—21no—
28C22×C16×C43C2211yescharacteristic
29C2×#10621898—21no—
30#13063356—41no—
31#13063355—22no—
32#13063351—41no—
33#13063350—22no—
34#13063347—21no—
35#13063347—21no—
36#13063347—21no—
37#13063347—21no—
38#13063345—42no—
39C2×Dic172C2×C411yescharacteristic
40C2×#10621873—21no—
41C2×D344C2×C411yescharacteristic
42C2×#10621877—21no—
43C2×#10621877—21no—
44#13063284—21no—
45#13063261—21no—
46#13063261—21no—
47#13063261—21no—
48#13063261C2×C412yes—
49#13063259—21no—
50#13063257—21no—
51#13063252—42no—
52#13063243—22no—
53#13063241—22no—
54C2×#41×C43D411yescharacteristic
55#131×C43—21no—
56#131×C43—21no—
57#131×C43C2×C412yes—
58#131×C43D412yes—
59C2×M16×C43—21no—
60C2×M16×C43D411yescharacteristic
61C22×C8×C43—21no—
62C22×C8×C43C2311yescharacteristic
63M32×C43—24no—
64M32×C43—21no—
65M32×C43D412yes—
66C2×C16×C43—24no—
67C2×C16×C43—21no—
68C2×C16×C43—21no—
69C2×C16×C43—21no—
70C2×C16×C43D411yescharacteristic
71C2×C16×C43D411yescharacteristic
72#41×C43—21no—
73#41×C43—21no—
74#41×C43C22⋊C412yes—
75#41×C43D812yes—
76C2×Q8×C43SD1611yescharacteristic
77C2×D4×C43—21no—
78C2×D4×C43SD1611yescharacteristic
79C22×C4×C43—21no—
80C22×C4×C43C2×D411yescharacteristic
81C2×C22⋊D43—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86C2×D172—21no—
87C2×C4×D43—41no—
88C2×Dic86—21no—
89M16×C43—21no—
90M16×C43—22no—
91M16×C43—22no—
92M16×C43C22⋊C412yes—
93C2×C8×C43—21no—
94C2×C8×C43—22no—
95C2×C8×C43—22no—
96C2×C8×C43C22×C411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C22⋊Dic43—41no—
103#10621885—42no—
104#10621884—42no—
105#10621883—42no—
106#10621882—42no—
107C4⋊Dic43—41no—
108C4×Dic43—41no—
109#10621877—22no—
110#10621877—41no—
111#10621877—41no—
112#10621877—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115Dic172—21no—
116Dic172—21no—
117D344—21no—
118D344—21no—
119#10621873—41no—
120#10621873—41no—
121C16×C43—21no—
122C16×C43—22no—
123C16×C43—21no—
124C23×C43—21no—
125C23×C43#13511yescharacteristic
126C22×D43—41no—
127Q8×C43—21no—
128Q8×C43#10212yes—
129D4×C43—22no—
130D4×C43—22no—
131D4×C43—21no—
132D4×C43#10212yes—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43C2×D811yescharacteristic
140C2×C4×C43C2×SD1611yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—41no—
145C2×Dic43—81no—
146D172—41no—
147D172—41no—
148C4×D43—81no—
149C4×D43—81no—
150Dic86—41no—
151Dic86—41no—
152C8×C43—22no—
153C8×C43C4×D411yescharacteristic
154C8×C43C4×D411yescharacteristic
155C8×C43#12011yescharacteristic
156C8×C43#12311yescharacteristic
157C43⋊C8—42no—
158C43⋊C8—81no—
159#13071—431nomaximal, Sylow
160C22×C43—22no—
161C22×C43—41no—
162C22×C43—42no—
163C22×C43#41611yescharacteristic
164C22×C43#46511yescharacteristic
165C22×C43#46611yescharacteristic
166C2×D43—81no—
167C2×D43—161no—
168C4×C43—22no—
169C4×C43#38611yescharacteristic
170C4×C43C2×#10211yescharacteristic
171C4×C43#46511yescharacteristic
172C4×C43#46611yescharacteristic
173Dic43—81no—
174Dic43—161no—
175C2×#504D4311yescharacteristic, complemented
176#3067—431no—
177#2145—431no—
178C2×#359—431no—
179#1814—431no—
180#1388—431no—
181#1382—431no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—42no—
186C2×C43#189311yescharacteristic
187D43—161no—
188#575—861no—
189C2×#135—431no—
190C2×#131C2×D4311yescharacteristic
191#504—22no—
192#504—22no—
193C2×M32—21no—
194C2×M32C2×D4311yescharacteristic
195C22×C16—21no—
196C22×C16C2×D4311yescharacteristic
197#473—432no—
198#472—432no—
199#471—862no—
200C2×#108—431no—
201C2×#108—431no—
202#427—431no—
203#421—861no—
204#413—861no—
205#360—862no—
206#359—861no—
207#359—861no—
208#344—861no—
209C43#1307111yescharacteristic, complemented, Sylow
210C2×#41—861no—
211C2×#41D17211yescharacteristic
212#137—862no—
213#137—1721no—
214AGL(1,ℤ/8)—862no—
215AGL(1,ℤ/8)—1721no—
216#135—861no—
217#135—861no—
218#135—861no—
219#135—861no—
220#135—1722no—
221C2×Q16—431no—
222C2×SD16—861no—
223C2×D8—431no—
224#131—21no—
225#131—21no—
226#131C4×D4312yes—
227#131C22⋊D4312yes—
228C2×M16—21no—
229C2×M16—861no—
230C2×M16—861no—
231C2×M16D17211yescharacteristic
232C22×C8—21no—
233C22×C8C22×D4311yescharacteristic
234#117—861no—
235M32—24no—
236M32—21no—
237M32C22⋊D4312yes—
238C2×C16—24no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16C22⋊D4311yescharacteristic
243C2×C16C22⋊D4311yescharacteristic
244#108—432no—
245#108—861no—
246#108—861no—
247#108—861no—
248#107—861no—
249#106—861no—
250#104—1722no—
251#101—862no—
252#100—862no—
253#41—21no—
254#41—21no—
255#41—1721no—
256#41—1721no—
257#41—1721no—
258#41—1721no—
259#41D34412yes—
260#41(C2×D43)⋊C412yes—
261C2×Q8—861no—
262C2×Q8#1062187311yescharacteristic
263C2×D4—21no—
264C2×D4—861no—
265C2×D4—1721no—
266C2×D4#1062187311yescharacteristic
267C22×C4—21no—
268C22×C4—1721no—
269C22×C4C2×D17211yescharacteristic
270Q16—861no—
271Q16—861no—
272Q16—1722no—
273SD16—1722no—
274SD16—1722no—
275SD16—1721no—
276SD16—1721no—
277D8—861no—
278D8—861no—
279D8—1722no—
280M16—21no—
281M16—22no—
282M16—22no—
283M16—862no—
284M16—1721no—
285M16—1721no—
286M16—1721no—
287M16(C2×D43)⋊C412yes—
288C2×C8—21no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8C2×C4×D4311yescharacteristic
294C2×C8#1062189811yescharacteristic
295C2×C8#1062189811yescharacteristic
296C2×C8C2×C22⋊D4311yescharacteristic
297C2×C8C2×C22⋊D4311yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C4⋊C4—1721no—
300C22⋊C4—1721no—
301C42—1721no—
302C16—21no—
303C16—22no—
304C16—21no—
305C23—21no—
306C23—1721no—
307C23#1306334711yescharacteristic
308Q8—21no—
309Q8—1721no—
310Q8—1721no—
311Q8#1306324712yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—3441no—
316D4—3441no—
317D4—1721no—
318D4—1721no—
319D4#1306324712yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—3441no—
324C2×C4—3441no—
325C2×C4—3441no—
326C2×C4—1721no—
327C2×C4C2×(C2×D43)⋊C411yescharacteristic
328C2×C4#1306329911yescharacteristic
329C2×C4#1306329911yescharacteristic
330C2×C4C2×D34411yescharacteristic
331C2×C4C2×#1062187311yescharacteristic
332C2×C4#1306334711yescharacteristic
333C8—22no—
334C8—3441no—
335C8—1722no—
336C8C4×C22⋊D4311yescharacteristic
337C8C4×C22⋊D4311yescharacteristic
338C8#1306329411yescharacteristic
339C8#1306330811yescharacteristic
340C22—22no—
341C22—41no—
342C22—42no—
343C22—3441no—
344C22—6881no—
345C22#1458289611yescharacteristic
346C22#1458312811yescharacteristic
347C22#1458313511yescharacteristic
348C4—22no—
349C4—3441no—
350C4—6881no—
351C4#1458277811yescharacteristic
352C4C2×#1306324711yescharacteristic
353C4#1458312811yescharacteristic
354C4#1458313511yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—6881no—
360C2#1913502311yescharacteristic
subgroupG/H
centerC4#14583135
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#504C2
socleC2×C43#1893
prime radical#19144315C2
cosocleC22×C8×C43C23
hypercenterC2×#504D43
hypocenterC43#13071
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. #19136332C2semidirect
3. C2×#14582707C2semidirect
4. #19134649C2semidirect
5. #19132707C2semidirect
6. #19132691C2semidirect
7. C2×C43×#504C2semidirect
10. #14583174C4semidirect
11. #14583169C4semidirect
175. C2×#504D43semidirect
209. C43#13071semidirect

Maximal subgroups

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

subgroupindex
#191443152
#191363322
C2×#145827072
#191346492
#191327072
#191326912
C2×C43×#5042
#1307143