Finite Group Databasebeta

← #24989785

Subgroups — #24989785

Order 11008.

408 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143551C211yesmaximal, characteristic
2C4×#13063260C211yesmaximal, characteristic, complemented
3#19133353C211yesmaximal, characteristic, complemented
4#19133035C211yesmaximal, characteristic
5#19133032C211yesmaximal, characteristic
6#19132486C211yesmaximal, characteristic, complemented
7C43×#1299C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583023C411yescharacteristic
10#14583023C411yescharacteristic
11#14582964C411yescharacteristic
12#14582964C411yescharacteristic
13(C22⋊D43)⋊C8—21no—
14(C22⋊D43)⋊C8—21no—
15#14582950—21no—
16C2×#13063260—21no—
17#14582923C2211yescharacteristic
18C4×#10621877C2211yescharacteristic
19C2×C4×C43⋊C8C2211yescharacteristic
20C4×C8×D43—21no—
21#14582663—21no—
22#14582651—21no—
23#14582651—21no—
24#14582631—21no—
25#14582629—21no—
26#14582628—21no—
27#14582626—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×M16×C43C2211yescharacteristic
31C2×#10621898Q811yescharacteristic
32C2×#10621877—21no—
33C2×#10621877—21no—
34C22×C43⋊C8D411yescharacteristic
35C22×C43⋊C8D411yescharacteristic
36C2×C8×D43—21no—
37C2×C8×D43—21no—
38C4×Dic86C2×C411yescharacteristic
39C4×Dic86D411yescharacteristic
40C4×D172C2×C411yescharacteristic
41C4×D172D411yescharacteristic
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44#13063284Q811yescharacteristic
45#13063282—21no—
46C42×D43—21no—
47#13063260—24no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50Dic43⋊C8—21no—
51Dic43⋊C8—21no—
52(C2×D43)⋊C8—21no—
53(C2×D43)⋊C8—21no—
54#13063236—21no—
55C4×C43⋊C8—21no—
56C4×C43⋊C8C2×C411yescharacteristic
57C4×C43⋊C8C2×C411yescharacteristic
58C4×C43⋊C8D411yescharacteristic
59C4×C43⋊C8D411yescharacteristic
60C8×Dic43—21no—
61C8×Dic43—21no—
62C2×M16×C43—21no—
63C2×M16×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43C2×C411yescharacteristic
68C4⋊C8×C43C2×C411yescharacteristic
69C22⋊C8×C43—21no—
70#97×C43—21no—
71C4×C8×C43—21no—
72C4×C8×C43—21no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×Q811yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C2×C22⋊D43—21no—
77#10621898—22no—
78#10621898—22no—
79C2×D172C4⋊C411yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×Dic86C4⋊C411yescharacteristic
84M16×C43—22no—
85M16×C43—41no—
86M16×C43—81no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C42×C43C22×C411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43#4111yescharacteristic
95C22⋊Dic43—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43C4⋊C411yescharacteristic
99C4⋊Dic43C4⋊C411yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105#10621877—22no—
106#10621877—41no—
107#10621877—81no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8C22⋊C411yescharacteristic
113C2×C43⋊C8C22⋊C411yescharacteristic
114C2×C43⋊C8C22⋊C411yescharacteristic
115C2×C43⋊C8C22⋊C411yescharacteristic
116C8×D43—42no—
117C8×D43—42no—
118C23×C43C22⋊Q811yescharacteristic
119C22×D43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C2×C4⋊C411yescharacteristic
128C2×C4×C43#11711yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43C22⋊Q811yescharacteristic
132C22⋊D43—24no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136D172—21no—
137D172#10812yescomplemented
138C4×D43—24no—
139C4×D43—41no—
140C4×D43—41no—
141C4×D43—41no—
142C4×D43—41no—
143Dic86—21no—
144Dic86#10812yescomplemented
145C8×C43—42no—
146C8×C43—41no—
147C8×C43—41no—
148C8×C43—81no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C43⋊C8—42no—
153C43⋊C8—81no—
154C43⋊C8#10412yes—
155#8671—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43#38011yescharacteristic
160C2×D43—22no—
161C2×D43—41no—
162C2×D43—41no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43C2×#10411yescharacteristic
167C4×C43#42111yescharacteristic
168C4×C43C2×#10811yescharacteristic
169C4×C43C2×#10811yescharacteristic
170C4×C43#47211yescharacteristic
171C4×C43#47311yescharacteristic
172Dic43—22no—
173Dic43—41no—
174Dic43—41no—
175C8×#41—431no—
176C4×#108—431no—
177#1567—431no—
178#1489—431no—
179#1489—431no—
180#1299—431no—
181#1299D4311yescharacteristic, complemented
182C2×C43—41no—
183C2×C43#180611yescharacteristic
184C2×C43#181011yescharacteristic
185C2×C43#181611yescharacteristic
186D43—42no—
187C4×#41—431no—
188C8×Q8—431no—
189C8×Q8—431no—
190C8×D4—431no—
191C8×D4—431no—
192C8×D4—861no—
193C8×D4—861no—
194#431—861no—
195#431C2×D4311yescharacteristic
196C2×#108—861no—
197#423—431no—
198#423C2×D4311yescharacteristic
199C4×M16—431no—
200C4×M16C2×D4311yescharacteristic
201C2×C4×C8—431no—
202C2×C4×C8—861no—
203#341—861no—
204#335—861no—
205#335—861no—
206Q8⋊C8—861no—
207Q8⋊C8—861no—
208D4⋊C8—861no—
209D4⋊C8—861no—
210C43#867111yescharacteristic, complemented, Sylow
211C2×#41—431no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—861no—
215C2×M16—861no—
216C22×C8—431no—
217C22×C8—431no—
218C22×C8—861no—
219C22×C8—861no—
220C4×Q8—431no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—431no—
224C4×D4—861no—
225C4×D4—861no—
226#117—431no—
227#117—861no—
228C2×C42—861no—
229C2×C42C22×D4311yescharacteristic
230#108—864no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—861no—
234C4⋊C8—861no—
235C4⋊C8—861no—
236C4⋊C8—861no—
237C4⋊C8C4×D4311yescharacteristic
238C4⋊C8C4×D4311yescharacteristic
239C22⋊C8—21no—
240C22⋊C8—861no—
241C22⋊C8—861no—
242#97—21no—
243#97—861no—
244C4×C8—21no—
245C4×C8—21no—
246C4×C8—431no—
247C4×C8—431no—
248C4×C8—431no—
249C4×C8—431no—
250C4×C8—861no—
251C4×C8—861no—
252C4×C8—861no—
253#41—862no—
254#41—862no—
255C2×Q8—431no—
256C2×D4—431no—
257C2×D4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4#1062189811yescharacteristic
262C22×C4D4×D4311yescharacteristic
263C22×C4Q8×D4311yescharacteristic
264M16—22no—
265M16—41no—
266M16—81no—
267M16—862no—
268M16—3441no—
269M16—1721no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—431no—
275C2×C8—431no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—862no—
279C2×C8—1722no—
280C2×C8—1722no—
281C2×C8—1721no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—431no—
285C4⋊C4—431no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C42—861no—
292C42—861no—
293C42—861no—
294C42C2×C4×D4311yescharacteristic
295C42#1062189811yescharacteristic
296C42D4×D4311yescharacteristic
297C42D4×D4311yescharacteristic
298C23—861no—
299C23#1306330311yescharacteristic
300Q8—432no—
301Q8—861no—
302D4—432no—
303D4—864no—
304D4—861no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—864no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4C22⋊C4×D4311yescharacteristic
320C2×C4C4⋊C4×D4311yescharacteristic
321C2×C4#1306328211yescharacteristic
322C2×C4#1306329811yescharacteristic
323C2×C4#1306329811yescharacteristic
324C2×C4#1306330311yescharacteristic
325C8—42no—
326C8—41no—
327C8—41no—
328C8—81no—
329C8—432no—
330C8—861no—
331C8—861no—
332C8—861no—
333C8—3441no—
334C8—1722no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—862no—
339C22—1721no—
340C22—1721no—
341C22#1458275811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—862no—
346C4—1721no—
347C4—1721no—
348C4#104×D4311yescharacteristic
349C4#1458291411yescharacteristic
350C4#108×D4311yescharacteristic
351C4#108×D4311yescharacteristic
352C4#1458316811yescharacteristic
353C4#1458317311yescharacteristic
354C2—41no—
355C2—1722no—
356C2#1913461411yescharacteristic
357C2#1913463211yescharacteristic
358C2#1913465811yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1299C2
socleC22×C43#380
prime radicalC2×#10621898Q8
cosocleC2×C42×C43C23
hypercenter#1299D43
hypocenterC43#8671
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
2. C4×#13063260C2semidirect
3. #19133353C2semidirect
6. #19132486C2semidirect
7. C43×#1299C2semidirect
137. D172#108semidirect
144. Dic86#108semidirect
181. #1299D43semidirect
210. C43#8671semidirect

Maximal subgroups

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

subgroupindex
#191435512
C4×#130632602
#191333532
#191330352
#191330322
#191324862
C43×#12992
#867143