Finite Group Databasebeta

← #24992428

Subgroups — #24992428

Order 11008.

458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144718C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19134428C211yesmaximal, characteristic, complemented
4#19133207C211yesmaximal, characteristic
5#19133089C211yesmaximal, characteristic
6#19132493C211yesmaximal, characteristic, complemented
7C43×#1285C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583213—21no—
11#14583195C411yescharacteristic, complemented
12#14583195C411yescharacteristic, complemented
13#14583100C411yescharacteristic, complemented
14#14583100C411yescharacteristic, complemented
15#14583040—21no—
16#14583027—22no—
17#14583026—21no—
18#14583023—21no—
19#14583001—21no—
20#14583001—21no—
21#14582953—21no—
22#14582952C2211yescharacteristic
23#14582949—21no—
24C2×#13063248—21no—
25C2×#13063236C2211yescharacteristic
26#14582661—21no—
27#14582638—22no—
28#14582632—21no—
29#14582632—21no—
30C43×#432C2211yescharacteristic
31C43×#432C2211yescharacteristic
32C4×C4⋊C4×C43C2211yescharacteristic
33C2×#10621898—21no—
34C22×Dic86D411yescharacteristic
35C2×#10621873—21no—
36C2×#10621873—21no—
37C22×C43⋊C8—21no—
38#13063325C2×C411yescharacteristic
39#13063322C2×C411yescharacteristic
40#13063313—21no—
41#13063299—21no—
42#13063299—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45C4×Dic86C2×C411yescharacteristic
46C4×Dic86C2×C411yescharacteristic
47C4×Dic86D411yescharacteristic
48C4×Dic86D411yescharacteristic
49C4×D172—21no—
50C4×D172—21no—
51C2×C4⋊Dic43D411yescharacteristic
52C2×Dic43⋊C4—21no—
53C2×C4×Dic43—21no—
54#13063259—21no—
55#13063259—21no—
56C4⋊(C43⋊C8)—21no—
57Dic43⋊C8—22no—
58Dic43⋊C8—22no—
59#13063250—21no—
60#13063250—21no—
61#13063248—24no—
62#13063247—21no—
63#13063247—21no—
64C22⋊(C43⋊C8)D411yescharacteristic
65C22⋊(C43⋊C8)D411yescharacteristic
66#13063236—21no—
67#13063236—21no—
68#13063235—22no—
69C4×C43⋊C8—21no—
70C8×Dic43—22no—
71C2×C4⋊C4×C43—21no—
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C4⋊C8×C43C2×C411yescharacteristic
76C4⋊C8×C43C2×C411yescharacteristic
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79#97×C43—21no—
80#97×C43D412yes—
81#95×C43—21no—
82C22×C4×C43—41no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C2×C22⋊D43—41no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89#10621898—81no—
90#10621898—81no—
91C2×D172—21no—
92C2×D172—21no—
93C2×D172—21no—
94C2×C4×D43—41no—
95C2×Dic86—22no—
96C2×Dic86—21no—
97C2×Dic86—21no—
98C2×Dic86—41no—
99C2×Dic86C22⋊C411yescharacteristic
100C2×Dic86C22⋊C411yescharacteristic
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—41no—
106C42×C43—81no—
107C42×C43C22×C411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43#4111yescharacteristic
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—41no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43C22⋊C411yescharacteristic
117C4⋊Dic43C22⋊C411yescharacteristic
118Dic43⋊C4—21no—
119Dic43⋊C4—21no—
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131#10621873—42no—
132#10621873—42no—
133C23×C43#12111yescharacteristic
134C22×D43—41no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C2×C4×C43C2×C22⋊C411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C22⋊D43—81no—
150C22⋊D43—81no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—42no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159D172—41no—
160D172—41no—
161D172—81no—
162D172—81no—
163C4×D43—82no—
164Dic86—21no—
165Dic86—21no—
166Dic86—21no—
167Dic86—42no—
168Dic86—81no—
169Dic86#10412yes—
170C8×C43—42no—
171C8×C43—41no—
172C8×C43—41no—
173C43⋊C8—41no—
174C43⋊C8—41no—
175C43⋊C8—42no—
176#9164—431nomaximal, Sylow
177C22×C43—21no—
178C22×C43—21no—
179C22×C43#38611yescharacteristic
180C22×C43#47111yescharacteristic
181C22×C43#47211yescharacteristic
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—82no—
191C4×C43C2×#10411yescharacteristic
192C4×C43#42111yescharacteristic
193Dic43—22no—
194Dic43—41no—
195Dic43—41no—
196Dic43—41no—
197Dic43—81no—
198#3112—431no—
199#2984—431no—
200#1763—431no—
201#1530—431no—
202#1502—431no—
203#1302—431no—
204#1285D4311yescharacteristic, complemented
205C2×C43—21no—
206C2×C43—21no—
207C2×C43#187111yescharacteristic
208C2×C43#190511yescharacteristic
209C2×C43#190711yescharacteristic
210D43—161no—
211#532—431no—
212C2×C4×Q8—431no—
213#480—861no—
214#477—431no—
215#477—431no—
216#460—431no—
217#460—431no—
218#448—861no—
219#446—861no—
220#446—862no—
221C8×Q8—861no—
222#440—861no—
223#440—861no—
224#432—861no—
225#432C2×D4311yescharacteristic
226#432C2×D4311yescharacteristic
227#431—431no—
228#431—861no—
229C2×#103—861no—
230C2×#97—431no—
231C4×C4⋊C4C2×D4311yescharacteristic
232#340—861no—
233#329—862no—
234#327—861no—
235#327—861no—
236C43#916411yescharacteristic, complemented, Sylow
237C2×#41—861no—
238C22×Q8—431no—
239C2×SD16—861no—
240C2×SD16—861no—
241C22×C8—861no—
242C4⋊Q8—431no—
243#127—431no—
244#124—861no—
245#121—861no—
246#121—861no—
247C4×Q8—431no—
248C4×Q8—431no—
249C4×Q8—431no—
250C4×Q8—431no—
251C4×Q8—861no—
252C4×Q8—861no—
253C4×D4—861no—
254C4×D4—861no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—861no—
258C2×C42—21no—
259C2×C42—861no—
260C2×C42C22×D4311yescharacteristic
261#107—861no—
262#107—861no—
263C4⋊C8—21no—
264C4⋊C8—862no—
265C4⋊C8—862no—
266C4⋊C8—861no—
267C4⋊C8C4×D4311yescharacteristic
268C4⋊C8C4×D4311yescharacteristic
269#103—864no—
270#103—861no—
271#103—861no—
272#102—861no—
273#102—861no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—431no—
277C22⋊C8—431no—
278#97—21no—
279#97—862no—
280#97—861no—
281#97—861no—
282#97D17212yes—
283C4×C8—862no—
284C4×C8—861no—
285#95—21no—
286#41—3441no—
287#41—3441no—
288C2×Q8—431no—
289C2×Q8—431no—
290C2×Q8—862no—
291C2×Q8—861no—
292C2×Q8—861no—
293C2×Q8—1721no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—1721no—
298C22×C4—41no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—1721no—
302C22×C4#1062189811yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305SD16—1722no—
306SD16—1722no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—862no—
311C2×C8—861no—
312C2×C8—861no—
313C2×C8—1721no—
314C2×C8—1721no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—431no—
318C4⋊C4—431no—
319C4⋊C4—861no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C42—81no—
329C42—861no—
330C42—861no—
331C42—861no—
332C42—861no—
333C42C2×C4×D4311yescharacteristic
334C42C2×D17211yescharacteristic
335C42D4×D4311yescharacteristic
336C42#1062190211yescharacteristic
337C23—1721no—
338C23#1306329811yescharacteristic
339Q8—432no—
340Q8—861no—
341Q8—861no—
342Q8—861no—
343Q8—3441no—
344Q8—1722no—
345D4—3441no—
346D4—3441no—
347D4—3441no—
348D4—3441no—
349D4—1721no—
350D4—1721no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—3442no—
364C2×C4—1722no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4C22⋊C4×D4311yescharacteristic
369C2×C4#1306328711yescharacteristic
370C2×C4C4×D17211yescharacteristic
371C2×C4#1306329511yescharacteristic
372C2×C4#1306330011yescharacteristic
373C2×C4#1306331011yescharacteristic
374C8—42no—
375C8—41no—
376C8—41no—
377C8—1722no—
378C8—1721no—
379C8—1721no—
380C22—21no—
381C22—21no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22#1458277711yescharacteristic
386C22#1458316511yescharacteristic
387C22#1458316811yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—82no—
394C4—862no—
395C4—3441no—
396C4—1721no—
397C4—1721no—
398C4—1721no—
399C4#104×D4311yescharacteristic
400C4#1458291411yescharacteristic
401C2—21no—
402C2—21no—
403C2—6881no—
404C2#1913489611yescharacteristic
405C2#1913509011yescharacteristic
406C2#1913510411yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1285C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1285D43
hypocenterC43#9164
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19134428C2semidirect
6. #19132493C2semidirect
7. C43×#1285C2semidirect
11. #14583195C4semidirect
12. #14583195C4semidirect
13. #14583100C4semidirect
14. #14583100C4semidirect
204. #1285D43semidirect
236. C43#9164semidirect

Maximal subgroups

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

subgroupindex
#191447182
#191436852
#191344282
#191332072
#191330892
#191324932
C43×#12852
#916443