Finite Group Databasebeta

← #25013503

Subgroups — #25013503

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147697C211yesmaximal, characteristic, complemented
2C2×#14583019C211yesmaximal, characteristic
3#19136222C211yesmaximal, characteristic, complemented
4#19136216C211yesmaximal, characteristic, complemented
5#19132678C211yesmaximal, characteristic, complemented
6#19132674C211yesmaximal, characteristic, complemented
7C43×#2117C211yesmaximal, characteristic, complemented
8C2×#13063345C411yescharacteristic
9C2×#13063331C2211yescharacteristic
10#14583317—22no—
11#14583315—22no—
12C2×#13063265C2211yescharacteristic
13C2×#13063265C2211yescharacteristic
14M32×D43—22no—
15#14583019—22no—
16#14583019—22no—
17C2×#13063260C411yescharacteristic
18C2×#13063252C411yescharacteristic
19C2×#13063251C411yescharacteristic
20C2×#13063235C2211yescharacteristic
21#14582682—22no—
22#14582681—22no—
23C2×#131×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C43×#350—22no—
27C2×#10621898C2×C411yescharacteristic
28#13063345—22no—
29#13063345—22no—
30C2×#10621885C811yescharacteristic
31C2×#10621883C811yescharacteristic
32C2×#10621884C811yescharacteristic
33C2×#10621882C811yescharacteristic
34#13063331—21no—
35#13063331—21no—
36#13063331D412yes—
37#13063331D412yes—
38C2×#10621877C2×C411yescharacteristic
39C2×#10621872—21no—
40C22×C43⋊C8C2×C411yescharacteristic
41C2×C8×D43—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43#13063265—21no—
44#13063265—21no—
45#13063265—21no—
46#13063265D412yes—
47#13063264—24no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16—21no—
50C16×D43—24no—
51#13063260—22no—
52#13063252—22no—
53#13063251—22no—
54#13063235—21no—
55#13063235—21no—
56C2×#41×C43C2×C411yescharacteristic
57#131×C43—21no—
58#131×C43—21no—
59#131×C43—21no—
60#131×C43—21no—
61C2×M16×C43—21no—
62C2×M16×C43C2×C411yescharacteristic
63C22×C8×C43—21no—
64C22×C8×C43C2311yescharacteristic
65M32×C43—21no—
66M32×C43—21no—
67M32×C43—21no—
68M32×C43—21no—
69C2×C16×C43—21no—
70C2×C16×C43D412yes—
71#41×C43—21no—
72#41×C43—21no—
73#41×C43—21no—
74#41×C43—21no—
75C2×Q8×C43C2×C811yescharacteristic
76C2×D4×C43—21no—
77C2×D4×C43C2×C811yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43C22×C411yescharacteristic
80C2×C22⋊D43—21no—
81C22×Dic43—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898C22⋊C412yes—
85#10621898M1612yes—
86C2×D172C2×C811yescharacteristic
87C2×C4×D43—21no—
88C2×Dic86C2×C811yescharacteristic
89M16×C43—21no—
90M16×C43—21no—
91M16×C43—41no—
92M16×C43—41no—
93C2×C8×C43—21no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43#4111yescharacteristic
102#10621885—22no—
103#10621884—22no—
104#10621883—22no—
105#10621882—22no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108#10621877—21no—
109#10621877C22⋊C412yes—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8C2×C811yescharacteristic
114C2×C43⋊C8C2×C811yescharacteristic
115#10621872—22no—
116#10621872—22no—
117C8×D43—22no—
118C8×D43—22no—
119C16×C43—22no—
120C16×C43—41no—
121C43⋊C16—22no—
122C43⋊C16—41no—
123C23×C43—21no—
124C23×C43#13111yescharacteristic
125C22×D43—21no—
126Q8×C43—21no—
127Q8×C43—21no—
128D4×C43—21no—
129D4×C43—21no—
130D4×C43—41no—
131D4×C43—41no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C22×C811yescharacteristic
139C2×C4×C43C2×M1611yescharacteristic
140C2×C4×C43#13111yescharacteristic
141C22⋊D43—22no—
142C22⋊D43—22no—
143C2×Dic43—21no—
144C2×Dic43—41no—
145C2×Dic43—81no—
146D172—21no—
147D172C22⋊C812yes—
148C4×D43—22no—
149C4×D43—22no—
150Dic86—21no—
151Dic86C22⋊C812yes—
152C8×C43—41no—
153C8×C43#12011yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12111yescharacteristic
156C8×C43#12311yescharacteristic
157C43⋊C8—22no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160#12986—431nomaximal, Sylow
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—81no—
164C22×C43#40811yescharacteristic
165C22×C43C8×D411yescharacteristic
166C22×C43#43511yescharacteristic
167C2×D43—22no—
168C2×D43—81no—
169C4×C43—41no—
170C4×C43#38611yescharacteristic
171C4×C43C2×C22⋊C811yescharacteristic
172C4×C43C8×D411yescharacteristic
173C4×C43#43511yescharacteristic
174Dic43—22no—
175Dic43—81no—
176#3407—431no—
177C2×#444—431no—
178#2117—431no—
179#2117D4311yescharacteristic, complemented
180#2115—431no—
181#1377—431no—
182#1375—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—81no—
187C2×C43#186911yescharacteristic
188D43—42no—
189C2×#135—431no—
190C2×#131—431no—
191C2×#131C2×D4311yescharacteristic
192#504—862no—
193#504—862no—
194C2×M32—431no—
195C2×M32—431no—
196C2×M32—862no—
197C2×M32C2×D4311yescharacteristic
198C2×M32C2×D4311yescharacteristic
199#444—862no—
200#444—862no—
201C2×#108—431no—
202C2×#104—431no—
203C2×#104—431no—
204C2×#97—431no—
205#350—22no—
206#350—862no—
207#349—862no—
208C43#1298611yescharacteristic, complemented, Sylow
209C2×#41—431no—
210C2×#41C4×D4311yescharacteristic
211#135—862no—
212#135—862no—
213C2×Q16—431no—
214C2×SD16—431no—
215C2×SD16—431no—
216C2×D8—431no—
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221#131—432no—
222#131—432no—
223#131—861no—
224#131—861no—
225C2×M16—21no—
226C2×M16—431no—
227C2×M16—861no—
228C2×M16C4×D4311yescharacteristic
229C22×C8—21no—
230C22×C8—431no—
231C22×C8—861no—
232C22×C8C22×D4311yescharacteristic
233C2×C42—431no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—432no—
239M32—864no—
240M32—861no—
241M32—861no—
242M32—861no—
243C2×C16—21no—
244C2×C16—864no—
245C2×C16—861no—
246C2×C16—861no—
247C2×C16C22⋊D4312yes—
248#108—862no—
249#104—862no—
250#104—862no—
251#97—861no—
252#97—861no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—432no—
258#41—432no—
259#41—861no—
260#41—861no—
261C2×Q8—431no—
262C2×Q8C8×D4311yescharacteristic
263C2×D4—21no—
264C2×D4—431no—
265C2×D4—861no—
266C2×D4C8×D4311yescharacteristic
267C22×C4—21no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4C2×C4×D4311yescharacteristic
271Q16—862no—
272SD16—862no—
273SD16—862no—
274D8—862no—
275M16—21no—
276M16—21no—
277M16—41no—
278M16—41no—
279M16—432no—
280M16—861no—
281M16—862no—
282M16—862no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—862no—
292C2×C8—862no—
293C2×C8#1062189811yescharacteristic
294C2×C8D4×D4311yescharacteristic
295C2×C8D4×D4311yescharacteristic
296C2×C8D4×D4311yescharacteristic
297C2×C8#1062190011yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C42—861no—
300C42—861no—
301C16—22no—
302C16—41no—
303C16—862no—
304C16—1721no—
305C23—21no—
306C23—861no—
307C23#1306333311yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—432no—
311Q8—861no—
312D4—21no—
313D4—21no—
314D4—41no—
315D4—41no—
316D4—432no—
317D4—862no—
318D4—862no—
319D4—861no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—861no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—3441no—
327C2×C4—1721no—
328C2×C4C22⋊C4×D4311yescharacteristic
329C2×C4(C22⋊D43)⋊C411yescharacteristic
330C2×C4C4×C22⋊D4311yescharacteristic
331C2×C4C2×C8×D4311yescharacteristic
332C2×C4M16×D4311yescharacteristic
333C2×C4#1306333111yescharacteristic
334C8—41no—
335C8—861no—
336C8—861no—
337C8—862no—
338C8#1306329311yescharacteristic
339C8#1306329611yescharacteristic
340C8#1306329811yescharacteristic
341C8#1306330711yescharacteristic
342C22—41no—
343C22—41no—
344C22—81no—
345C22—862no—
346C22—3441no—
347C22#1458286411yescharacteristic
348C22(C22⋊D43)⋊C811yescharacteristic
349C22#1458296811yescharacteristic
350C4—41no—
351C4—862no—
352C4—3441no—
353C4#1458277511yescharacteristic
354C4C22⋊C8×D4311yescharacteristic
355C4C8×C22⋊D4311yescharacteristic
356C4#1458297311yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—1722no—
362C2#1913488411yescharacteristic
subgroupG/H
centerC4#14582775
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#2117C2
socleC2×C43#1869
prime radicalC2×#13063345C4
cosocleC22×C8×C43C23
hypercenter#2117D43
hypocenterC43#12986
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #19147697C2semidirect
3. #19136222C2semidirect
4. #19136216C2semidirect
5. #19132678C2semidirect
6. #19132674C2semidirect
7. C43×#2117C2semidirect
179. #2117D43semidirect
208. C43#12986semidirect

Maximal subgroups

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

subgroupindex
#191476972
C2×#145830192
#191362222
#191362162
#191326782
#191326742
C43×#21172
#1298643