Finite Group Databasebeta

← #25007479

Subgroups — #25007479

Order 11008.

432 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 69 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#19140283C211yesmaximal, characteristic
2#19134671C211yesmaximal, characteristic, complemented
3#19132906C211yesmaximal, characteristic, complemented
4#19132616C211yesmaximal, characteristic, complemented
5#19132593C211yesmaximal, characteristic
6#19132591C211yesmaximal, characteristic
7C43×#1351C211yesmaximal, characteristic, complemented
8C2×#13063314C411yescharacteristic, complemented
9C2×#13063281C2211yescharacteristic
10#14582949—21no—
11#14582818C411yescharacteristic, complemented
12#14582817C411yescharacteristic, complemented
13#14582808C2211yescharacteristic
14#14582799—21no—
15#14582788—21no—
16#14582788—21no—
17#14582776—21no—
18#14582760—21no—
19#14582744C411yescharacteristic, complemented
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#393C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C23×Dic43D411yescharacteristic
30#13063314—41no—
31#13063314—41no—
32#13063281—41no—
33#13063281—41no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4C2×C411yescharacteristic
36C2×Dic43⋊C4D411yescharacteristic
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43D411yescharacteristic
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47Dic43⋊C8—41no—
48C22⋊(C43⋊C8)—21no—
49C8×Dic43—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—41no—
53C43⋊#95—41no—
54C43⋊#95C2×C411yescharacteristic
55C22×Q8×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43C2311yescharacteristic
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43C2×C411yescharacteristic
62C24×C43C2×D411yescharacteristic
63C23×D43—21no—
64C2×Q8×C43—41no—
65C2×Q8×C43—81no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—41no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C2×C22⋊D43—42no—
72C2×C22⋊D43—41no—
73C2×C22⋊D43—41no—
74C2×C22⋊D43—81no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—41no—
81C22×Dic43—41no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C2×D172—41no—
87C2×D172—81no—
88C2×C8×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—81no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—81no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104Dic43⋊C4—81no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43—21no—
109C4×Dic43—42no—
110C2×C43⋊C8—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C23×C43#13511yescharacteristic
117C23×C43#13511yescharacteristic
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125Q8×C43—82no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C22⋊D43—82no—
140C22⋊D43—82no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—22no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159C2×Dic43—81no—
160C2×Dic43#9911yescharacteristic
161C2×Dic43#9911yescharacteristic
162D172—82no—
163C8×C43—81no—
164C43⋊C8—81no—
165#11844—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—81no—
175C22×C43C2×#9911yescharacteristic
176C22×C43#41611yescharacteristic
177C22×C43#42111yescharacteristic
178C2×D43—81no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43—161no—
190Dic43—21no—
191Dic43—21no—
192Dic43—42no—
193Dic43—41no—
194Dic43—41no—
195Dic43—41no—
196Dic43—161no—
197#2610—431no—
198#1820—431no—
199#1458—431no—
200#1351—431no—
201#1351D4311yescharacteristic, complemented
202#1343—431no—
203#1343—431no—
204C2×C43—21no—
205C2×C43—21no—
206C2×C43—41no—
207C2×C43—41no—
208C2×C43#151611yescharacteristic
209C2×C43#212211yescharacteristic
210C2×C43#212611yescharacteristic
211D43—161no—
212C2×#124—431no—
213C2×#117—431no—
214#431—861no—
215#395—431no—
216#394—431no—
217#393C2×D4311yescharacteristic
218#392—431no—
219#390—861no—
220#388—861no—
221#388—861no—
222#386—861no—
223#381—861no—
224#376—431no—
225#342—431no—
226#342—861no—
227#342C2×D4311yescharacteristic
228#324—861no—
229#323—431no—
230#323C2×D4311yescharacteristic
231C43#1184411yescharacteristic, complemented, Sylow
232C22×Q8C4×D4311yescharacteristic
233C22×D4—431no—
234C22×D4—861no—
235C23×C4—431no—
236#124—1721no—
237#124—1721no—
238#117—1721no—
239#117—1721no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—861no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—431no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4C22×D4311yescharacteristic
253C2×C42—431no—
254C2×C42—431no—
255C2×C42—861no—
256C4⋊C8—1721no—
257C22⋊C8—21no—
258C22⋊C8—861no—
259C4×C8—1721no—
260#95—21no—
261#95—431no—
262#95—861no—
263#95—861no—
264#95—1721no—
265#95—1721no—
266#95C4×D4311yescharacteristic
267C24—861no—
268C24D4×D4311yescharacteristic
269C2×Q8—41no—
270C2×Q8—81no—
271C2×D4—3441no—
272C2×D4—3441no—
273C2×D4—1721no—
274C2×D4—1722no—
275C2×D4—1721no—
276C2×D4—1721no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—1721no—
290C22×C4—1721no—
291C22×C4C2×C4×D4311yescharacteristic
292C22×C4D4×D4311yescharacteristic
293C2×C8—41no—
294C2×C8—1721no—
295C4⋊C4—3441no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—81no—
302C22⋊C4—3441no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C22⋊C4—1722no—
306C22⋊C4—1722no—
307C22⋊C4—1722no—
308C22⋊C4—1721no—
309C22⋊C4—1721no—
310C22⋊C4—1721no—
311C42—861no—
312C42—861no—
313C42—861no—
314C42—861no—
315C42—1722no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—1721no—
321C23—1721no—
322C23—1721no—
323C23—1721no—
324C23—1721no—
325C23—1721no—
326C23—1721no—
327C23C22⋊C4×D4311yescharacteristic
328C23#1306334611yescharacteristic
329C23#1306334811yescharacteristic
330Q8—82no—
331D4—3442no—
332D4—3442no—
333D4—3442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—431no—
348C2×C4—431no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—862no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C8—81no—
369C8—3441no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—3441no—
380C22—3441no—
381C22—3441no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22—3441no—
386C22#99×D4311yescharacteristic
387C22#1458289411yescharacteristic
388C22#1458291411yescharacteristic
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4—161no—
394C4—861no—
395C4—861no—
396C4—1722no—
397C4—1721no—
398C4—1721no—
399C4—1721no—
400C4—6881no—
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2—6881no—
406C2#1913315011yescharacteristic
407C2#1913624311yescharacteristic
408C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1351C2
socleC22×C43C2×#99
prime radical#14582808C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1351D43
hypocenterC43#11844
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
2. #19134671C2semidirect
3. #19132906C2semidirect
4. #19132616C2semidirect
7. C43×#1351C2semidirect
8. C2×#13063314C4semidirect
11. #14582818C4semidirect
12. #14582817C4semidirect
19. #14582744C4semidirect
201. #1351D43semidirect
231. C43#11844semidirect

Maximal subgroups

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

subgroupindex
#191402832
#191346712
#191329062
#191326162
#191325932
#191325912
C43×#13512
#1184443