Finite Group Databasebeta

← #24988226

Subgroups — #24988226

Order 11008.

744 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#14583622C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic, complemented
3#19133194C212yesmaximal
4#19133041C212yesmaximal, complemented
5C43×#1467C211yesmaximal, characteristic, complemented
6#14583622—24no—
7#14583622—24no—
8C2×#13063325C411yescharacteristic
9C2×#13063320—21no—
10C2×#13063320—21no—
11C2×#13063313C411yescharacteristic
12C2×#13063313C2211yescharacteristic
13C2×#13063301—21no—
14C2×C4×Dic86C411yescharacteristic
15C2×C4×Dic86C2211yescharacteristic
16C2×C4×D172C411yescharacteristic
17C2×#13063283—21no—
18C2×#13063244—21no—
19C4×#10621877C2212yes—
20#14582668—21no—
21#14582638—24no—
22#14582629—24no—
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#432C2212yes—
25C43×#324—21no—
26C43×#324—21no—
27C22×Dic86C2×C411yescharacteristic
28C22×Dic86C2×C411yescharacteristic
29C22×D172C2×C411yescharacteristic
30C22×C4×D43—21no—
31C2×#10621877—22no—
32#13063325—22no—
33#13063325—22no—
34#13063320—28no—
35#13063320—28no—
36#13063313—22no—
37#13063313—22no—
38#13063313—22no—
39#13063313D414yes—
40#13063301—28no—
41C4×Dic86—22no—
42C4×Dic86—22no—
43C4×Dic86—22no—
44C4×Dic86D414yes—
45C4×D172—22no—
46C4×D172—22no—
47#13063283—28no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43C2×C411yescharacteristic
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×C4×Dic43—21no—
59C2×C4×Dic43—21no—
60#13063244—24no—
61#13063236—22no—
62C4×C43⋊C8—22no—
63C22×Q8×C43D411yescharacteristic
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C42×C43C2×C411yescharacteristic
70C2×C42×C43C2×C411yescharacteristic
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—22no—
73C22⋊C8×C43—22no—
74#97×C43—22no—
75C23×D43—21no—
76C2×Q8×C43—22no—
77C2×Q8×C43—22no—
78C2×Q8×C43—41no—
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C2×D172—21no—
90C2×D172—42no—
91C2×D172C22⋊C412yes—
92C2×C4×D43—24no—
93C2×C4×D43—42no—
94C2×C4×D43—42no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86—42no—
98C2×Dic86—42no—
99C2×Dic86C22⋊C412yes—
100C2×Dic86C22⋊C412yes—
101C2×C8×C43—42no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C42×C43—21no—
106C42×C43—21no—
107C42×C43—21no—
108C42×C43—21no—
109C42×C43C2×D412yes—
110C42×C43C2×D412yes—
111(C2×D43)⋊C4—24no—
112(C2×D43)⋊C4—24no—
113(C2×D43)⋊C4—24no—
114(C2×D43)⋊C4—24no—
115(C2×D43)⋊C4—24no—
116C4⋊Dic43—24no—
117C4⋊Dic43—24no—
118C4⋊Dic43—21no—
119C4⋊Dic43C22⋊C412yes—
120Dic43⋊C4—24no—
121Dic43⋊C4—24no—
122C4×Dic43—24no—
123C4×Dic43—24no—
124#10621877—24no—
125#10621877—42no—
126C2×C43⋊C8—42no—
127C23×C43C2×C22⋊C411yescharacteristic
128C22×D43—22no—
129C22×D43—42no—
130C22×D43—42no—
131C22×D43—41no—
132C22×D43—41no—
133Q8×C43—44no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—22no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43#10412yes—
148C2×C4×C43C2×C22⋊C411yescharacteristic
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43#12012yes—
151C2×C4×C43#12012yes—
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159D172—42no—
160D172—42no—
161C4×D43—48no—
162Dic86—24no—
163Dic86—42no—
164Dic86—42no—
165Dic86—42no—
166C8×C43—82no—
167C43⋊C8—44no—
168#8368—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43#37911yescharacteristic
172C22×C43C2×#10411yescharacteristic
173C22×C43#42111yescharacteristic
174C2×D43—42no—
175C2×D43—42no—
176C2×D43—42no—
177C2×D43—82no—
178C2×D43—82no—
179C4×C43—22no—
180C4×C43—21no—
181C4×C43—22no—
182C4×C43—22no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43#41312yes—
187Dic43—42no—
188Dic43—42no—
189Dic43—42no—
190C2×#556—431no—
191C4×#101—431no—
192#1527—432no—
193#1491—432no—
194#1467D4311yescharacteristic, complemented
195C2×C43—21no—
196C2×C43—21no—
197C2×C43#178511yescharacteristic
198C2×C43#178911yescharacteristic
199C2×C43#179611yescharacteristic
200D43—82no—
201#556—864no—
202#556—864no—
203C2×C4⋊Q8—431no—
204C2×#126—861no—
205C2×#126—861no—
206C2×#124—431no—
207C2×#124—431no—
208C2×C22⋊Q8—861no—
209C2×C4×Q8—431no—
210C2×C4×Q8—431no—
211C2×C4×Q8C2×D4311yescharacteristic
212C2×C4×D4—431no—
213C2×#117—861no—
214#432C2×D4312yes—
215C2×#101—861no—
216C4×M16—432no—
217#343—861no—
218#329—864no—
219Q8⋊C8—864no—
220#324—21no—
221#324—21no—
222C43#836811yescharacteristic, complemented, Sylow
223C22×Q8—431no—
224C22×Q8—431no—
225C22×Q8D17211yescharacteristic
226C22×D4—431no—
227C23×C4—861no—
228C2×M16—862no—
229C4⋊Q8—862no—
230C4⋊Q8—862no—
231#126—868no—
232#126—868no—
233#124—434no—
234#124—862no—
235#124—862no—
236#124—862no—
237C22⋊Q8—868no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×Q8—434no—
241C4×Q8—862no—
242C4×Q8—862no—
243C4×Q8—862no—
244C4×D4—862no—
245C4×D4—862no—
246#117—868no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4D17211yescharacteristic
253C2×C4⋊C4C22⋊D4311yescharacteristic
254C2×C4⋊C4C22⋊D4311yescharacteristic
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C42—861no—
261C2×C42—861no—
262C2×C42C4×D4311yescharacteristic
263C2×C42C4×D4311yescharacteristic
264C2×C42C22×D4311yescharacteristic
265C4⋊C8—22no—
266#101—864no—
267C22⋊C8—22no—
268#97—22no—
269#97—862no—
270C4×C8—862no—
271C24—861no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—432no—
276C2×Q8—432no—
277C2×Q8—861no—
278C2×Q8—861no—
279C2×Q8—1722no—
280C2×Q8—1722no—
281C2×D4—432no—
282C2×D4—861no—
283C2×D4—1722no—
284C22×C4—864no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—1722no—
289C22×C4—1722no—
290C22×C4(C2×D43)⋊C411yescharacteristic
291C22×C4(C2×D43)⋊C411yescharacteristic
292C22×C4(C2×D43)⋊C411yescharacteristic
293C22×C4(C2×D43)⋊C411yescharacteristic
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4C2×D17211yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297M16—864no—
298M16—1722no—
299C2×C8—42no—
300C2×C8—1722no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—432no—
305C4⋊C4—864no—
306C4⋊C4—864no—
307C4⋊C4—864no—
308C4⋊C4—861no—
309C4⋊C4—864no—
310C22⋊C4—864no—
311C22⋊C4—864no—
312C22⋊C4—864no—
313C22⋊C4—864no—
314C22⋊C4—864no—
315C42—21no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—864no—
320C42—864no—
321C42D4×D4312yes—
322C42D4×D4312yes—
323C23—862no—
324C23—1722no—
325C23—1722no—
326C23—1721no—
327C23—1721no—
328C23C2×(C2×D43)⋊C411yescharacteristic
329Q8—44no—
330Q8—864no—
331Q8—1722no—
332Q8—1722no—
333Q8—1722no—
334D4—1722no—
335D4—1722no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—1728no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4#1306325112yes—
358C2×C4C22⋊C4×D4311yescharacteristic
359C2×C4C22⋊C4×D4311yescharacteristic
360C2×C4#1306329312yes—
361C2×C4#1306329512yes—
362C8—82no—
363C8—1724no—
364C22—21no—
365C22—21no—
366C22—3442no—
367C22—3442no—
368C22—1722no—
369C22—1722no—
370C22—1722no—
371C22#1458275411yescharacteristic
372C22C2×#1306325111yescharacteristic
373C22#1458291511yescharacteristic
374C4—21no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—1722no—
382C4—1722no—
383C4—1722no—
384C4#1458288212yes—
385C2—21no—
386C2—21no—
387C2—3442no—
388C2#1913452211yescharacteristic
389C2#1913453811yescharacteristic
390C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1467C2
socleC22×C43#379
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1467D43
hypocenterC43#8368
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. C4×#13063244C2semidirect
4. #19133041C2semidirect
5. C43×#1467C2semidirect
194. #1467D43semidirect
222. C43#8368semidirect

Maximal subgroups

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

subgroupindex
C2×#145836222
C4×#130632442
#191331942
#191330412
C43×#14672
#836843