Finite Group Databasebeta

← #24994049

Subgroups — #24994049

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#19139754C211yesmaximal, characteristic
2#19137190C211yesmaximal, characteristic
3#19133115C211yesmaximal, characteristic, complemented
4#19132921C211yesmaximal, characteristic
5#19132481C211yesmaximal, characteristic, complemented
6#19132480C211yesmaximal, characteristic, complemented
7C43×#1508C211yesmaximal, characteristic, complemented
8C22×(C2×D43)⋊C4C2211yescharacteristic
9#14582863C2211yescharacteristic
10#14582825C412yescomplemented
11#14582810C412yescomplemented
12#14582790—22no—
13#14582789—22no—
14#14582788—22no—
15#14582760—21no—
16#14582757—21no—
17#14582754—21no—
18#14582754—21no—
19C4×C22⋊Dic43C2211yescharacteristic
20C4×C22⋊Dic43C2211yescharacteristic
21#14582636—22no—
22#14582622—22no—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C43×#328—22no—
27C24×D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C2×#10621877—21no—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—22no—
38C2×(C2×D43)⋊C4—22no—
39C2×(C2×D43)⋊C4—22no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4C2×C412yes—
42C2×(C2×D43)⋊C4D412yes—
43C2×C4×Dic43—21no—
44C2×C4×Dic43—21no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47C43⋊#95—22no—
48C43⋊#95—22no—
49C43⋊#95—22no—
50C43⋊#95C2×C412yes—
51C43⋊#95D412yes—
52C22×Q8×C43C2×C411yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C2×M16×C43—21no—
55C22⋊Q8×C43—21no—
56C22⋊Q8×C43—21no—
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C42×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43D412yes—
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C23×D43—21no—
70C23×D43—42no—
71C23×D43—42no—
72C23×D43—81no—
73C23×D43C22⋊C412yes—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—81no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—81no—
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×Dic43—22no—
88C22×Dic43—21no—
89C22×Dic43—22no—
90C22×Dic43—21no—
91C22×Dic43—42no—
92C22×Dic43C22⋊C412yes—
93M16×C43—81no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C22⋊C4×C43—42no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—41no—
102C42×C43—81no—
103C22⋊Dic43—42no—
104C22⋊Dic43—42no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—44no—
110(C2×D43)⋊C4—82no—
111(C2×D43)⋊C4—82no—
112(C2×D43)⋊C4—82no—
113Dic43⋊C4—82no—
114C4×Dic43—81no—
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—
136Q8×C43—81no—
137Q8×C43—81no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×Dic43—22no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—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—81no—
192C4×C43—81no—
193Dic43—42no—
194Dic43—82no—
195Dic43—82no—
196#2561—431no—
197#2312—431no—
198#1508—431no—
199#1508D4311yescharacteristic, complemented
200#1462—431no—
201#1297—431no—
202#1297—431no—
203C2×C43—22no—
204C2×C43—22no—
205C2×C43—41no—
206C2×C43#188511yescharacteristic
207C2×C43#189711yescharacteristic
208C2×C43#191311yescharacteristic
209D43—82no—
210C2×C22⋊Q8C2×D4311yescharacteristic
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⋊C4—431no—
225C4×C22⋊C4C2×D4311yescharacteristic
226#328—22no—
227#328—862no—
228#323—862no—
229C43#941111yescharacteristic, complemented, Sylow
230C25—431no—
231C22×Q8C4×D4311yescharacteristic
232C23×C4—431no—
233C23×C4C22×D4311yescharacteristic
234C2×M16—21no—
235C2×M16—861no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—862no—
242C2×C4⋊C4C4×D4311yescharacteristic
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—861no—
259C2×C42—861no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264#95—432no—
265#95—432no—
266#95—862no—
267#95—862no—
268#95—862no—
269#95C22⋊D4312yes—
270C24—432no—
271C24—861no—
272C24—861no—
273C24—3441no—
274C24—1722no—
275C24—1722no—
276C24D4×D4311yescharacteristic
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—81no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—81no—
284C22×C4—432no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—862no—
288C22×C4—862no—
289C22×C4—1722no—
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4#1062189811yescharacteristic
292C22×C4D4×D4311yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4#1062190011yescharacteristic
295C22×C4C2×C22⋊D4311yescharacteristic
296M16—81no—
297M16—3441no—
298C2×C8—41no—
299C2×C8—1721no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—3442no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—862no—
309C22⋊C4—862no—
310C22⋊C4—862no—
311C22⋊C4—862no—
312C22⋊C4—3442no—
313C22⋊C4—3442no—
314C22⋊C4—3442no—
315C22⋊C4—1724no—
316C22⋊C4—1722no—
317C22⋊C4—1722no—
318C42—81no—
319C42—3441no—
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#1306329311yescharacteristic
338C23#1306330711yescharacteristic
339Q8—81no—
340Q8—81no—
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—41no—
353C2×C4—41no—
354C2×C4—862no—
355C2×C4—3441no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4(C22⋊D43)⋊C411yescharacteristic
365C2×C4C4×C22⋊D4311yescharacteristic
366C2×C4#1306329611yescharacteristic
367C2×C4#1306329811yescharacteristic
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#1458277511yescharacteristic
386C22#1458291412yes—
387C22#1458307512yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—81no—
394C4—81no—
395C4—3442no—
396C4—3442no—
397C4—1722no—
398C2—22no—
399C2—22no—
400C2—41no—
401C2—3442no—
402C2#1913498011yescharacteristic
403C2#1913504011yescharacteristic
404C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1508C2
socleC22×C43#386
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1508D43
hypocenterC43#9411
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
3. #19133115C2semidirect
5. #19132481C2semidirect
6. #19132480C2semidirect
7. C43×#1508C2semidirect
10. #14582825C4semidirect
11. #14582810C4semidirect
199. #1508D43semidirect
229. C43#9411semidirect

Maximal subgroups

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

subgroupindex
#191397542
#191371902
#191331152
#191329212
#191324812
#191324802
C43×#15082
#941143