Finite Group Databasebeta

← #25013775

Subgroups — #25013775

Order 11008.

512 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583016C211yesmaximal, characteristic, complemented
2C2×#14582712C211yesmaximal, characteristic, complemented
3#19136307C211yesmaximal, characteristic, complemented
4#19135462C211yesmaximal, characteristic, complemented
5#19132704C211yesmaximal, characteristic, complemented
6#19132676C211yesmaximal, characteristic, complemented
7C2×C43×#509C211yesmaximal, characteristic
8C2×#13063332—21no—
9C2×#13063265C2211yescharacteristic
10#14583016—22no—
11#14583016—22no—
12C2×#13063261C2211yescharacteristic
13C2×#13063259C2211yescharacteristic
14C2×#13063252—21no—
15C2×#13063246—21no—
16C2×C8×Dic43C2211yescharacteristic
17#14582802—21no—
18#14582712—22no—
19#14582703—21no—
20#14582700—21no—
21C2×#135×C43C2211yescharacteristic
22C22×D8×C43C2211yescharacteristic
23C43×#509—22no—
24C43×#509C414yescomplemented
25C2×SD32×C43—21no—
26C2×D16×C43—21no—
27C2×M32×C43C2211yescharacteristic
28#13063332—24no—
29#13063332—42no—
30C2×#10621877—21no—
31C2×#10621877—41no—
32C22×C43⋊C8—41no—
33C22×C43⋊C8D411yescharacteristic
34C2×C4⋊Dic43—21no—
35C2×C22⋊Dic43—42no—
36C2×C4×Dic43D411yescharacteristic
37#13063265—21no—
38#13063265—21no—
39C2×C43⋊C16—21no—
40#13063261—21no—
41#13063261D412yes—
42#13063259—21no—
43#13063259—21no—
44#13063252—24no—
45#13063246—41no—
46#13063246—41no—
47C8×Dic43—21no—
48C8×Dic43—21no—
49C2×#41×C43—21no—
50C22×D4×C43—21no—
51#135×C43—21no—
52#135×C43—21no—
53#135×C43C2×C412yes—
54#135×C43D412yes—
55C2×Q16×C43D411yescharacteristic
56C2×SD16×C43—21no—
57C2×D8×C43—21no—
58C2×D8×C43—21no—
59C2×D8×C43—21no—
60C2×D8×C43—21no—
61C2×D8×C43—21no—
62C2×D8×C43C2×C412yes—
63C2×D8×C43D411yescharacteristic
64C22×C8×C43C2311yescharacteristic
65SD32×C43—24no—
66D16×C43—24no—
67M32×C43—21no—
68M32×C43C2×C412yes—
69C2×C16×C43—21no—
70C24×C43—41no—
71#41×C43—22no—
72#41×C43—22no—
73#41×C43—41no—
74#41×C43—41no—
75C2×Q8×C43—21no—
76C2×D4×C43—22no—
77C2×D4×C43—21no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—41no—
88Q16×C43—21no—
89Q16×C43C22⋊C412yescomplemented
90SD16×C43—22no—
91SD16×C43—22no—
92D8×C43—22no—
93D8×C43—22no—
94D8×C43—21no—
95D8×C43—41no—
96D8×C43—41no—
97D8×C43C22⋊C412yescomplemented
98C2×C8×C43C22×C411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C22⋊Dic43—84no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C4×Dic43—21no—
108C4×Dic43—21no—
109#10621877—22no—
110#10621877—44no—
111#10621877—41no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—44no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8D811yescharacteristic
117C2×C43⋊C8D811yescharacteristic
118C16×C43—22no—
119C43⋊C16—41no—
120C23×C43—41no—
121C23×C43—42no—
122C23×C43—82no—
123C23×C43—82no—
124C23×C43—81no—
125C23×C43—81no—
126C23×C43AGL(1,ℤ/8)11yescharacteristic
127Q8×C43—22no—
128Q8×C43—41no—
129D4×C43—22no—
130D4×C43—42no—
131D4×C43—42no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—41no—
135D4×C43—81no—
136D4×C43—81no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43#12011yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43C2×D811yescharacteristic
144C2×C4×C43#13511yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×Dic43—22no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—82no—
150C2×Dic43—81no—
151C8×C43C2×C22⋊C411yescharacteristic
152C8×C43C4×D411yescharacteristic
153C8×C43#12111yescharacteristic
154C8×C43#12311yescharacteristic
155C43⋊C8—21no—
156C43⋊C8—21no—
157C43⋊C8—42no—
158#13029—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—42no—
162C22×C43—84no—
163C22×C43—81no—
164C22×C43—81no—
165C22×C43—82no—
166C22×C43—162no—
167C22×C43—161no—
168C22×C43—161no—
169C22×C43#44211yescharacteristic
170C22×C43#44911yescharacteristic
171C22×C43#45911yescharacteristic
172C4×C43—42no—
173C4×C43#38611yescharacteristic
174C4×C43C4×D811yescharacteristic
175C4×C43#44711yescharacteristic
176C4×C43#46311yescharacteristic
177Dic43—42no—
178Dic43—161no—
179C2×#509D4311yescharacteristic
180C2×#443—431no—
181C2×#361—431no—
182#2139—431no—
183#1970—431no—
184#1387—431no—
185#1376—431no—
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—82no—
189C2×C43—162no—
190C2×C43#187911yescharacteristic
191C2×C43#221211yescharacteristic
192C2×C43#221311yescharacteristic
193C2×#135C2×D4311yescharacteristic
194C22×D8C2×D4311yescharacteristic
195C2×#131—861no—
196#509—22no—
197#509Dic4314yescomplemented
198C2×SD32—21no—
199C2×D16—21no—
200C2×M32—431no—
201C2×M32C2×D4311yescharacteristic
202#443—862no—
203#443—862no—
204C2×#108—431no—
205C2×#107—431no—
206C2×#104—861no—
207C2×#102—861no—
208C2×C4×C8—431no—
209#390—861no—
210#361—862no—
211#358—861no—
212#357—861no—
213C43#1302911yescharacteristic, complemented, Sylow
214C2×#41—21no—
215C22×D4—21no—
216#135—21no—
217#135—21no—
218#135C2×Dic4312yes—
219#135C22⋊D4312yes—
220C2×Q16C22⋊D4311yescharacteristic
221C2×SD16—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8C2×Dic4312yes—
228C2×D8C22⋊D4311yescharacteristic
229#131—864no—
230#131—1722no—
231C2×M16—861no—
232C2×M16—1721no—
233C22×C8—431no—
234C22×C8—1721no—
235C22×C8C22×D4311yescharacteristic
236C2×C4⋊C4—861no—
237C2×C22⋊C4—1722no—
238C2×C42—431no—
239SD32—24no—
240D16—24no—
241M32—21no—
242M32—861no—
243M32—861no—
244M32C2×Dic4312yes—
245C2×C16—21no—
246C2×C16—861no—
247#108—432no—
248#108—861no—
249#107—861no—
250#107—861no—
251#104—864no—
252#102—1721no—
253#102—1721no—
254C4×C8—861no—
255C4×C8—861no—
256C24—41no—
257#41—22no—
258#41—22no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—41no—
271C22×C4—861no—
272C22×C4—1721no—
273C22×C4D4×D4311yescharacteristic
274Q16—21no—
275Q16C22⋊Dic4312yescomplemented
276SD16—22no—
277SD16—22no—
278D8—22no—
279D8—22no—
280D8—21no—
281D8—41no—
282D8—41no—
283D8C22⋊Dic4312yescomplemented
284M16—862no—
285M16—1724no—
286M16—1721no—
287C2×C8—431no—
288C2×C8—431no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—1724no—
292C2×C8—1721no—
293C2×C8D4×D4311yescharacteristic
294C2×C8#1062190011yescharacteristic
295C2×C8#1062190011yescharacteristic
296C2×C8C22×Dic4311yescharacteristic
297C2×C8C2×C22⋊D4311yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C22⋊C4—3444no—
302C42—861no—
303C42—861no—
304C16—22no—
305C16—1721no—
306C23—41no—
307C23—42no—
308C23—82no—
309C23—82no—
310C23—81no—
311C23—81no—
312C23#1306334911yescharacteristic
313Q8—22no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—42no—
320D4—42no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—862no—
327C2×C4—3442no—
328C2×C4—3441no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4D4×Dic4311yescharacteristic
332C2×C4#1306329311yescharacteristic
333C2×C4#1306329711yescharacteristic
334C2×C4D8×D4311yescharacteristic
335C2×C4#1306334411yescharacteristic
336C2×C4#1306334911yescharacteristic
337C8—861no—
338C8—861no—
339C8—1722no—
340C8C2×C22⋊Dic4311yescharacteristic
341C8D4×Dic4311yescharacteristic
342C8#1306329711yescharacteristic
343C8#1306330611yescharacteristic
344C22—21no—
345C22—21no—
346C22—42no—
347C22—84no—
348C22—81no—
349C22—81no—
350C22—82no—
351C22—162no—
352C22—161no—
353C22—161no—
354C22#1458301111yescharacteristic
355C22#1458304111yescharacteristic
356C22#1458309211yescharacteristic
357C4—42no—
358C4—1722no—
359C4—6881no—
360C4#1458277911yescharacteristic
361C4D8×Dic4311yescharacteristic
362C4#1458303111yescharacteristic
363C4#1458311211yescharacteristic
364C2—21no—
365C2—21no—
366C2—82no—
367C2—162no—
368C2#1913494511yescharacteristic
369C2#1913666211yescharacteristic
370C2#1913666911yescharacteristic
subgroupG/H
centerC22#14583092
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC2×C43×#509C2
socleC22×C43#459
cosocleC22×C8×C43C23
hypercenterC2×#509D43
hypocenterC43#13029
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#14583016C2semidirect
2. C2×#14582712C2semidirect
3. #19136307C2semidirect
4. #19135462C2semidirect
5. #19132704C2semidirect
6. #19132676C2semidirect
24. C43×#509C4semidirect
89. Q16×C43C22⋊C4semidirect
97. D8×C43C22⋊C4semidirect
197. #509Dic43semidirect
213. C43#13029semidirect
275. Q16C22⋊Dic43semidirect
283. D8C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830162
C2×#145827122
#191363072
#191354622
#191327042
#191326762
C2×C43×#5092
#1302943