Finite Group Databasebeta

← #24994051

Subgroups — #24994051

Order 11008.

606 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 93 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#19139748C211yesmaximal, characteristic
2#19137190C211yesmaximal, characteristic
3#19133116C211yesmaximal, characteristic, complemented
4#19133114C211yesmaximal, characteristic, complemented
5#19132921C211yesmaximal, characteristic
6#19132481C211yesmaximal, characteristic, complemented
7C43×#1297C211yesmaximal, characteristic, complemented
8C2×#13063304C2211yescharacteristic
9C22×(C2×D43)⋊C4C2211yescharacteristic
10#14582863C2211yescharacteristic
11#14582826C412yescomplemented
12#14582812C412yescomplemented
13#14582790—22no—
14#14582790—22no—
15#14582788—22no—
16#14582760—21no—
17#14582757—21no—
18#14582754—21no—
19#14582754—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21#14582637—22no—
22#14582635—22no—
23#14582622—22no—
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C24×D43D411yescharacteristic
28C22×Dic86C2×C411yescharacteristic
29C23×Dic43D411yescharacteristic
30C2×#10621877—21no—
31#13063304—21no—
32#13063304—21no—
33#13063304—21no—
34#13063304—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—22no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4—22no—
48C2×(C2×D43)⋊C4C2×C412yes—
49C2×(C2×D43)⋊C4D412yes—
50C2×C4×Dic43—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95D412yes—
57C23×C4×C43C2311yescharacteristic
58C2×M16×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C42×C43—21no—
62C2×C42×C43—21no—
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65#95×C43C2×C412yes—
66#95×C43D412yes—
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C23×D43—21no—
70C23×D43—42no—
71C23×D43—42no—
72C23×D43—81no—
73C23×D43C22⋊C412yes—
74C22×C4×C43—22no—
75C22×C4×C43—22no—
76C22×C4×C43—81no—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—42no—
89C22×Dic43C22⋊C412yes—
90C2×Dic86—21no—
91C2×Dic86—21no—
92C2×Dic86—81no—
93M16×C43—81no—
94C2×C8×C43—41no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—42no—
97C42×C43—81no—
98C42×C43—81no—
99C22⋊Dic43—42no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102(C2×D43)⋊C4—22no—
103(C2×D43)⋊C4—22no—
104(C2×D43)⋊C4—22no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—44no—
107(C2×D43)⋊C4—82no—
108(C2×D43)⋊C4—82no—
109(C2×D43)⋊C4—82no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114Dic43⋊C4—82no—
115C4×Dic43—81no—
116#10621877—81no—
117C2×C43⋊C8—41no—
118C23×C43—22no—
119C23×C43—22no—
120C23×C43—41no—
121C23×C43C2×C22⋊C411yescharacteristic
122C23×C43#12011yescharacteristic
123C23×C43#12311yescharacteristic
124C22×D43—22no—
125C22×D43—22no—
126C22×D43—22no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—42no—
130C22×D43—42no—
131C22×D43—42no—
132C22×D43—42no—
133C22×D43—81no—
134C22×D43—81no—
135C22×D43—88no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×Dic43—22no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—81no—
163Dic86—81no—
164Dic86—81no—
165C8×C43—81no—
166C43⋊C8—81no—
167#9411—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—44no—
176C22×C43#38611yescharacteristic
177C22×C43#42112yes—
178C22×C43#45512yes—
179C2×D43—44no—
180C2×D43—42no—
181C2×D43—42no—
182C2×D43—42no—
183C2×D43—84no—
184C2×D43—84no—
185C2×D43—82no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—82no—
191C4×C43—82no—
192Dic43—42no—
193Dic43—82no—
194Dic43—81no—
195Dic43—81no—
196#2561—431no—
197#2312—431no—
198#1508—431no—
199#1508—431no—
200#1462—431no—
201#1297—431no—
202#1297D4311yescharacteristic, complemented
203C2×C43—22no—
204C2×C43—22no—
205C2×C43—41no—
206C2×C43#188511yescharacteristic
207C2×C43#189711yescharacteristic
208C2×C43#191311yescharacteristic
209D43—82no—
210C2×C22⋊Q8—431no—
211C22×C22⋊C4—431no—
212#407—431no—
213#407C2×D4311yescharacteristic
214#397—432no—
215#393—432no—
216#388—862no—
217#388—862no—
218#388—862no—
219#381—861no—
220#380—861no—
221#379—861no—
222#379—861no—
223C4×C22⋊C4—431no—
224C4×C22⋊C4C2×D4311yescharacteristic
225C4×C22⋊C4C2×D4311yescharacteristic
226#328—862no—
227#328—862no—
228#323—862no—
229C43#941111yescharacteristic, complemented, Sylow
230C25—431no—
231C22×Q8—431no—
232C23×C4—431no—
233C23×C4C22×D4311yescharacteristic
234C2×M16—21no—
235C2×M16—861no—
236C22⋊Q8—861no—
237C22⋊Q8—861no—
238C22⋊Q8—861no—
239C22⋊Q8—861no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—862no—
242C2×C4⋊C4—861no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—432no—
246C2×C22⋊C4—432no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—862no—
252C2×C22⋊C4—862no—
253C2×C22⋊C4—862no—
254C2×C22⋊C4—862no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—861no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264#95—432no—
265#95—862no—
266#95—862no—
267#95—862no—
268#95C4×D4312yes—
269#95D17212yes—
270C24—432no—
271C24—861no—
272C24—861no—
273C24—3441no—
274C24—1722no—
275C24—1722no—
276C24D4×D4311yescharacteristic
277C2×Q8—861no—
278C2×Q8—861no—
279C2×Q8—3441no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—81no—
283C22×C4—432no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—862no—
289C22×C4—1722no—
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4C2×D17211yescharacteristic
292C22×C4#1062189811yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4D4×D4311yescharacteristic
295C22×C4#1062190211yescharacteristic
296M16—81no—
297M16—3441no—
298C2×C8—41no—
299C2×C8—1721no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—3442no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—862no—
308C22⋊C4—862no—
309C22⋊C4—862no—
310C22⋊C4—862no—
311C22⋊C4—3442no—
312C22⋊C4—3442no—
313C22⋊C4—3442no—
314C22⋊C4—1724no—
315C22⋊C4—1722no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C42—81no—
319C42—81no—
320C42—3441no—
321C23—22no—
322C23—22no—
323C23—41no—
324C23—862no—
325C23—862no—
326C23—862no—
327C23—3441no—
328C23—3441no—
329C23—3448no—
330C23—1722no—
331C23—1722no—
332C23—1722no—
333C23—1722no—
334C23—1722no—
335C23—1722no—
336C23C22⋊C4×D4311yescharacteristic
337C23#1306329511yescharacteristic
338C23#1306331011yescharacteristic
339Q8—3441no—
340Q8—3441no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—862no—
354C2×C4—3441no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4#1306328711yescharacteristic
365C2×C4C4×D17211yescharacteristic
366C2×C4#1306329811yescharacteristic
367C2×C4#1306330011yescharacteristic
368C8—81no—
369C8—3441no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—44no—
378C22—3442no—
379C22—3444no—
380C22—3444no—
381C22—1724no—
382C22—1722no—
383C22—1722no—
384C22—1722no—
385C22#1458277711yescharacteristic
386C22#1458291412yes—
387C22#1458307812yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—82no—
394C4—3442no—
395C4—3441no—
396C4—3441no—
397C4—1722no—
398C2—22no—
399C2—22no—
400C2—41no—
401C2—3442no—
402C2#1913498211yescharacteristic
403C2#1913504211yescharacteristic
404C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1297C2
socleC22×C43#386
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1297D43
hypocenterC43#9411
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
3. #19133116C2semidirect
4. #19133114C2semidirect
6. #19132481C2semidirect
7. C43×#1297C2semidirect
11. #14582826C4semidirect
12. #14582812C4semidirect
202. #1297D43semidirect
229. C43#9411semidirect

Maximal subgroups

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

subgroupindex
#191397482
#191371902
#191331162
#191331142
#191329212
#191324812
C43×#12972
#941143