Finite Group Databasebeta

← #25013522

Subgroups — #25013522

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147697C211yesmaximal, characteristic, complemented
2#19143298C211yesmaximal, characteristic
3#19136215C211yesmaximal, characteristic, complemented
4C2×#14582681C211yesmaximal, characteristic, complemented
5#19132682C211yesmaximal, characteristic, complemented
6#19132680C211yesmaximal, characteristic, complemented
7C2×C43×#349C211yesmaximal, characteristic, complemented
8C2×#13063331C2211yescharacteristic
9#14583410C411yescharacteristic
10#14583317—22no—
11#14583315—22no—
12C2×#13063265C2211yescharacteristic
13C2×#13063265C2211yescharacteristic
14M32×D43—22no—
15#14582975—22no—
16#14582968—22no—
17#14582925C411yescharacteristic
18#14582865C411yescharacteristic
19#14582863C411yescharacteristic
20#14582854C2211yescharacteristic
21#14582681—22no—
22#14582680—22no—
23C22×M16×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×M32×C43C2211yescharacteristic
26C43×#349—22no—
27C2×#10621898C2×C411yescharacteristic
28#13063331—21no—
29#13063331—21no—
30#13063331—21no—
31#13063331—21no—
32C2×#10621877C2×C411yescharacteristic
33C2×#10621877C2×C411yescharacteristic
34C2×#10621872D412yes—
35C2×C8×D43D412yes—
36#13063308C812yes—
37#13063304—21no—
38#13063299—21no—
39#13063294C812yes—
40C4×C22⋊D43—22no—
41#13063284C2×C411yescharacteristic
42#13063265—21no—
43#13063265—21no—
44#13063265—21no—
45#13063265D412yescomplemented
46#13063264—24no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16—21no—
49C16×D43—24no—
50Dic43⋊C8—22no—
51C22⋊(C43⋊C8)—22no—
52(C2×D43)⋊C8—22no—
53#13063235—21no—
54C8×Dic43—21no—
55C23×C4×C43C2×C411yescharacteristic
56C2×M16×C43—21no—
57C2×M16×C43—21no—
58C2×M16×C43—21no—
59C2×M16×C43—21no—
60C2×M16×C43—21no—
61C2×M16×C43—21no—
62C22×C8×C43C2×C411yescharacteristic
63C22×C8×C43C2311yescharacteristic
64M32×C43—21no—
65M32×C43—21no—
66M32×C43—21no—
67M32×C43D412yescomplemented
68C2×C16×C43—21no—
69C2×C16×C43—21no—
70C24×C43C2×C811yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43C2×C811yescharacteristic
78C22×C4×C43C22×C411yescharacteristic
79C2×C22⋊D43—22no—
80C2×C22⋊D43C2×C812yes—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898—21no—
85C2×D172M1611yescharacteristic
86C2×C4×D43C22⋊C412yes—
87C2×Dic86M1611yescharacteristic
88M16×C43—41no—
89M16×C43—41no—
90M16×C43—41no—
91M16×C43—41no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C22⋊Dic43—22no—
102C22⋊Dic43C2×C812yes—
103(C2×D43)⋊C4—22no—
104C4⋊Dic43—21no—
105Dic43⋊C4—22no—
106C4×Dic43—21no—
107#10621877—21no—
108#10621877—21no—
109#10621877—21no—
110#10621877—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8C22⋊C412yes—
113#10621872—22no—
114#10621872—22no—
115C8×D43—22no—
116C8×D43—22no—
117C16×C43—22no—
118C16×C43—41no—
119C43⋊C16—22no—
120C43⋊C16—41no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43—81no—
125C23×C43C22×C811yescharacteristic
126C22×D43C22⋊C812yes—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C2×M1611yescharacteristic
138C2×C4×C43#13111yescharacteristic
139C2×C4×C43#13111yescharacteristic
140C22⋊D43—22no—
141C22⋊D43—22no—
142C22⋊D43—82no—
143C2×Dic43—22no—
144C2×Dic43C22⋊C812yes—
145D172—21no—
146D172—21no—
147C4×D43—22no—
148C4×D43—22no—
149Dic86—21no—
150Dic86—21no—
151C8×C43—41no—
152C8×C43#12011yescharacteristic
153C8×C43#12111yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12311yescharacteristic
156C43⋊C8—22no—
157C43⋊C8—41no—
158#12989—431nomaximal, Sylow
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—81no—
164C22×C43—81no—
165C22×C43C2×C22⋊C811yescharacteristic
166C22×C43C8×D411yescharacteristic
167C22×C43C8×D411yescharacteristic
168C2×D43—22no—
169C2×D43—42no—
170C4×C43—41no—
171C4×C43#38611yescharacteristic
172C4×C43#40811yescharacteristic
173C4×C43#43511yescharacteristic
174C4×C43#43511yescharacteristic
175Dic43—22no—
176Dic43—42no—
177#3407—431no—
178#2930—431no—
179#2115—431no—
180C2×#349—431no—
181C2×#349D4311yescharacteristic, complemented
182#1378—431no—
183#1378—431no—
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43—81no—
188C2×C43#186911yescharacteristic
189D43—42no—
190C2×#131—431no—
191C22×M16C2×D4311yescharacteristic
192#525—431no—
193#504—862no—
194#504—862no—
195C2×M32—431no—
196C2×M32—431no—
197C2×M32—862no—
198C2×M32C2×D4311yescharacteristic
199C2×M32C2×D4311yescharacteristic
200#436—862no—
201#435—862no—
202#424—431no—
203#408—431no—
204#407—431no—
205#405—431no—
206#349—22no—
207#349—862no—
208#349—862no—
209C43#1298911yescharacteristic, complemented, Sylow
210C2×#41—431no—
211C23×C4C4×D4311yescharacteristic
212#131—861no—
213#131—861no—
214#131—861no—
215#131—861no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—431no—
223C2×M16—432no—
224C2×M16—431no—
225C22×C8—432no—
226C22×C8C4×D4311yescharacteristic
227C22×C8C22×D4311yescharacteristic
228#123—432no—
229C22⋊Q8—861no—
230#121—861no—
231#120—432no—
232C4×D4—862no—
233#117—431no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—432no—
238M32—864no—
239M32—861no—
240M32—861no—
241M32—861no—
242M32C22⋊D4312yescomplemented
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—864no—
246C2×C16—861no—
247C2×C16—861no—
248C4⋊C8—862no—
249C22⋊C8—862no—
250C22⋊C8—862no—
251#97—861no—
252C4×C8—861no—
253C24C8×D4311yescharacteristic
254#41—861no—
255#41—861no—
256#41—861no—
257#41—861no—
258C2×Q8—431no—
259C2×D4—432no—
260C2×D4—431no—
261C2×D4—862no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—432no—
269C22×C4C8×D4311yescharacteristic
270C22×C4C2×C4×D4311yescharacteristic
271M16—41no—
272M16—41no—
273M16—41no—
274M16—41no—
275M16—861no—
276M16—861no—
277M16—862no—
278M16—862no—
279M16—861no—
280M16—861no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—432no—
285C2×C8—862no—
286C2×C8—862no—
287C2×C8—861no—
288C2×C8#1062189811yescharacteristic
289C2×C8D4×D4311yescharacteristic
290C2×C8D4×D4311yescharacteristic
291C2×C8D4×D4311yescharacteristic
292C2×C8#1062190011yescharacteristic
293C2×C8C2×C22⋊D4311yescharacteristic
294C4⋊C4—862no—
295C4⋊C4—861no—
296C22⋊C4—432no—
297C22⋊C4—862no—
298C22⋊C4—862no—
299C42—861no—
300C16—22no—
301C16—41no—
302C16—862no—
303C16—1721no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—81no—
308C23—432no—
309C23C2×C8×D4311yescharacteristic
310Q8—861no—
311Q8—861no—
312D4—862no—
313D4—862no—
314D4—861no—
315D4—861no—
316D4—3442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—432no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4C22⋊C4×D4311yescharacteristic
329C2×C4(C22⋊D43)⋊C411yescharacteristic
330C2×C4C4×C22⋊D4311yescharacteristic
331C2×C4M16×D4311yescharacteristic
332C2×C4#1306333111yescharacteristic
333C2×C4#1306333311yescharacteristic
334C8—41no—
335C8—862no—
336C8—1721no—
337C8#1306329311yescharacteristic
338C8#1306329611yescharacteristic
339C8#1306329811yescharacteristic
340C8#1306330711yescharacteristic
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—862no—
348C22—1722no—
349C22C22⋊C8×D4311yescharacteristic
350C22(C22⋊D43)⋊C811yescharacteristic
351C22C8×C22⋊D4311yescharacteristic
352C4—41no—
353C4—862no—
354C4—1722no—
355C4#1458277511yescharacteristic
356C4#1458286411yescharacteristic
357C4#1458296811yescharacteristic
358C4#1458297311yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—1722no—
364C2#1913488411yescharacteristic
subgroupG/H
centerC4#14582775
commutatorC23×C43C22×C8
FrattiniC22×C8C22×D43
FittingC2×C43×#349C2
socleC2×C43#1869
prime radical#14583410C4
cosocleC22×C8×C43C23
hypercenterC2×#349D43
hypocenterC43#12989
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
1. #19147697C2semidirect
3. #19136215C2semidirect
4. C2×#14582681C2semidirect
5. #19132682C2semidirect
6. #19132680C2semidirect
7. C2×C43×#349C2semidirect
45. #13063265D4semidirect
67. M32×C43D4semidirect
181. C2×#349D43semidirect
209. C43#12989semidirect
242. M32C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191476972
#191432982
#191362152
C2×#145826812
#191326822
#191326802
C2×C43×#3492
#1298943