Finite Group Databasebeta

← #24991480

Subgroups — #24991480

Order 11008.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic
3#19133050C211yesmaximal, characteristic, complemented
4#19132975C211yesmaximal, characteristic
5#19132491C211yesmaximal, characteristic, complemented
6#19132429C211yesmaximal, characteristic, complemented
7C43×#1481C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583203—21no—
10#14583196—21no—
11#14583191C411yescharacteristic
12#14583186C411yescharacteristic
13#14583181C411yescharacteristic
14#14583176C411yescharacteristic
15#14582959—22no—
16#14582955—21no—
17#14582951—21no—
18#14582935—21no—
19#14582923C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21#14582893—21no—
22#14582865—21no—
23#14582854—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25Q8⋊(C43⋊C8)—22no—
26#14582629—21no—
27#14582626—21no—
28C43×#533C2211yescharacteristic
29C43×#431C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C43×Q8⋊C8—21no—
32C43×Q8⋊C8—21no—
33C2×#10621898D411yescharacteristic
34C2×#10621877—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C4×Dic86C2×C411yescharacteristic
38C4×Dic86D411yescharacteristic
39C4×D172C2×C411yescharacteristic
40C4×D172D411yescharacteristic
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43#13063284D411yescharacteristic
44#13063282—21no—
45C42×D43—21no—
46#13063258—21no—
47#13063258—21no—
48#13063256—21no—
49#13063256—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)C2×C411yescharacteristic
53C4⋊(C43⋊C8)C2×C411yescharacteristic
54C4⋊(C43⋊C8)D412yes—
55#13063248—21no—
56#13063248—21no—
57#13063245—21no—
58#13063245—21no—
59(C2×D43)⋊C8—22no—
60(C2×D43)⋊C8—22no—
61#13063235—22no—
62C4×C43⋊C8—21no—
63C4×C43⋊C8—21no—
64C8×Dic43—22no—
65C22×C8×C43—21no—
66C4⋊Q8×C43C2×C411yescharacteristic
67C4⋊Q8×C43C2×C411yescharacteristic
68#125×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73#117×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C4⋊C8×C43—21no—
77C4⋊C8×C43D411yescharacteristic
78C4⋊C8×C43D411yescharacteristic
79C22⋊C8×C43—21no—
80C4×C8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C2×C22⋊D43—21no—
87#10621898—21no—
88#10621898—21no—
89#10621898—21no—
90#10621898—21no—
91C2×D172C22⋊C411yescharacteristic
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×Dic86C22⋊C411yescharacteristic
96C2×C8×C43—21no—
97C2×C8×C43—21no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C42×C43—41no—
109C42×C43C22×C411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C22⋊Dic43—21no—
114(C2×D43)⋊C4—21no—
115(C2×D43)⋊C4—21no—
116C4⋊Dic43C22⋊C411yescharacteristic
117C4⋊Dic43C22⋊C411yescharacteristic
118Dic43⋊C4—21no—
119Dic43⋊C4—21no—
120C4×Dic43—21no—
121C4×Dic43—21no—
122C4×Dic43—21no—
123#10621877—41no—
124#10621877—41no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133C23×C43#12311yescharacteristic
134C22×D43—21no—
135Q8×C43—42no—
136Q8×C43—41no—
137Q8×C43—41no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43C2×C22⋊C411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43#13711yescharacteristic
152C2×C4×C43#13711yescharacteristic
153C22⋊D43—41no—
154C22⋊D43—41no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158D172—21no—
159D172—21no—
160C4×D43—41no—
161C4×D43—41no—
162C4×D43—41no—
163C4×D43—41no—
164C4×D43—81no—
165Dic86—21no—
166Dic86—21no—
167C8×C43—41no—
168C8×C43—41no—
169C8×C43—81no—
170C43⋊C8—42no—
171C43⋊C8—41no—
172C43⋊C8—41no—
173C43⋊C8—42no—
174#8994—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43#38611yescharacteristic
178C22×C43#48511yescharacteristic
179C22×C43#48511yescharacteristic
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—81no—
187C4×C43—81no—
188C4×C43#41611yescharacteristic
189C4×C43#41911yescharacteristic
190C4×C43#44311yescharacteristic
191C4×C43#44411yescharacteristic
192C4×C43#45211yescharacteristic
193C4×C43#45211yescharacteristic
194Dic43—41no—
195Dic43—41no—
196Dic43—41no—
197#3076—431no—
198#2925—431no—
199#1493—431no—
200#1481D4311yescharacteristic, complemented
201#1476—431no—
202#1301—431no—
203#1277—431no—
204C2×C43—21no—
205C2×C43—21no—
206C2×C43#187311yescharacteristic
207C2×C43#187611yescharacteristic
208C2×C43#188111yescharacteristic
209D43—81no—
210#533C2×D4311yescharacteristic
211C4×#41—431no—
212#479—861no—
213#478—861no—
214#477—431no—
215#476—431no—
216#475—431no—
217#474—431no—
218#433—862no—
219#432—861no—
220#431—861no—
221#431C2×D4311yescharacteristic
222#427—861no—
223#423—431no—
224C2×C4⋊C8—431no—
225C2×C4⋊C8C2×D4311yescharacteristic
226#416—861no—
227#408—861no—
228#405—861no—
229C2×C4×C8—431no—
230Q8⋊C8—21no—
231Q8⋊C8—21no—
232Q8⋊C8—861no—
233Q8⋊C8—862no—
234D4⋊C8—861no—
235C43#899411yescharacteristic, complemented, Sylow
236C2×#41—431no—
237C2×M16—861no—
238C22×C8—21no—
239C22×C8—861no—
240C22×C8—861no—
241C4⋊Q8C4×D4311yescharacteristic
242C4⋊Q8C4×D4311yescharacteristic
243#125—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—431no—
249C4×Q8—431no—
250C4×D4—431no—
251C4×D4—431no—
252C4×D4—861no—
253C4×D4—861no—
254#117—21no—
255#117—431no—
256#117—861no—
257C2×C42—861no—
258C2×C42C22×D4311yescharacteristic
259#107—861no—
260#107—861no—
261#106—861no—
262#106—861no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—431no—
266C4⋊C8—431no—
267C4⋊C8—432no—
268C4⋊C8—861no—
269C4⋊C8—861no—
270C4⋊C8C22⋊D4311yescharacteristic
271C4⋊C8C22⋊D4311yescharacteristic
272#103—861no—
273#103—861no—
274#102—861no—
275#102—861no—
276C22⋊C8—21no—
277C22⋊C8—862no—
278C22⋊C8—862no—
279#97—862no—
280C4×C8—21no—
281C4×C8—862no—
282C4×C8—861no—
283C4×C8—861no—
284#41—861no—
285#41—861no—
286#41—861no—
287#41—861no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—431no—
291C2×D4—431no—
292C2×D4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4#1062189811yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190011yescharacteristic
299M16—1721no—
300M16—1721no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—862no—
307C2×C8—861no—
308C2×C8—861no—
309C2×C8—862no—
310C2×C8—1721no—
311C2×C8—1721no—
312C2×C8—1721no—
313C2×C8—1721no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—431no—
321C4⋊C4—431no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C22⋊C4—41no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C42—41no—
329C42—861no—
330C42—861no—
331C42—861no—
332C42C2×C4×D4311yescharacteristic
333C42D4×D4311yescharacteristic
334C42D4×D4311yescharacteristic
335C42C2×C22⋊D4311yescharacteristic
336C23—861no—
337C23#1306330711yescharacteristic
338Q8—42no—
339Q8—41no—
340Q8—41no—
341Q8—861no—
342Q8—861no—
343D4—861no—
344D4—861no—
345D4—1721no—
346D4—1721no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—3441no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4C22⋊C4×D4311yescharacteristic
361C2×C4(C22⋊D43)⋊C411yescharacteristic
362C2×C4C4×C22⋊D4311yescharacteristic
363C2×C4#1306329311yescharacteristic
364C2×C4#1306329611yescharacteristic
365C2×C4#1306329811yescharacteristic
366C2×C4#1306334611yescharacteristic
367C2×C4#1306334811yescharacteristic
368C2×C4#1306335411yescharacteristic
369C2×C4#1306335711yescharacteristic
370C8—41no—
371C8—41no—
372C8—81no—
373C8—1722no—
374C8—1722no—
375C8—1721no—
376C8—1721no—
377C22—21no—
378C22—21no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22#1458277511yescharacteristic
383C22#1458323811yescharacteristic
384C22#1458323911yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—1721no—
391C4—1721no—
392C4—1721no—
393C4#1458289411yescharacteristic
394C4#1458290611yescharacteristic
395C4#1458301411yescharacteristic
396C4#1458301911yescharacteristic
397C4#1458305811yescharacteristic
398C4#1458306011yescharacteristic
399C2—21no—
400C2—21no—
401C2—3441no—
402C2#1913490411yescharacteristic
403C2#1913492511yescharacteristic
404C2#1913495411yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1481C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1481D43
hypocenterC43#8994
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #19133050C2semidirect
5. #19132491C2semidirect
6. #19132429C2semidirect
7. C43×#1481C2semidirect
200. #1481D43semidirect
235. C43#8994semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191432602
#191330502
#191329752
#191324912
#191324292
C43×#14812
#899443