Finite Group Databasebeta

← #25007199

Subgroups — #25007199

Order 11008.

460 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 71 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#19139948C211yesmaximal, characteristic
2#19134382C211yesmaximal, characteristic
3#19132930C211yesmaximal, characteristic
4#19132620C211yesmaximal, characteristic, complemented
5#19132618C211yesmaximal, characteristic, complemented
6#19132616C211yesmaximal, characteristic, complemented
7C43×#1351C211yesmaximal, characteristic, complemented
8C2×Q8×Dic43C411yescharacteristic, complemented
9C2×(C22⋊D43)⋊C4C2211yescharacteristic
10C2×#13063239—21no—
11#14582861—21no—
12#14582836C411yescharacteristic, complemented
13#14582835C2211yescharacteristic
14#14582810C411yescharacteristic, complemented
15#14582799—21no—
16#14582796—21no—
17#14582774—21no—
18#14582773—21no—
19#14582763C411yescharacteristic, complemented
20C22⋊C4×Dic43—21no—
21#14582666C2211yescharacteristic
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#393C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621872—41no—
31Q8×Dic43—41no—
32Q8×Dic43—41no—
33(C22⋊D43)⋊C4—41no—
34(C22⋊D43)⋊C4—41no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4D411yescharacteristic
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4C2×C411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43—41no—
48C2×C4×Dic43C2×C411yescharacteristic
49#13063239—24no—
50C22⋊(C43⋊C8)—21no—
51(C2×D43)⋊C8—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—41no—
55C43⋊#95C2×C411yescharacteristic
56C22×Q8×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63C24×C43C2×D411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C2×Q8×C43—42no—
66C2×Q8×C43—41no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—22no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—21no—
75C2×C22⋊D43—41no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—41no—
81C22×Dic43—81no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—81no—
88C2×C8×C43—41no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—42no—
92C22⋊C4×C43—41no—
93C22⋊Dic43—22no—
94C22⋊Dic43—41no—
95C22⋊Dic43—81no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—81no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101C4⋊Dic43—41no—
102C4⋊Dic43—81no—
103Dic43⋊C4—41no—
104Dic43⋊C4—42no—
105Dic43⋊C4—81no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43—42no—
109C4×Dic43—82no—
110C2×C43⋊C8—41no—
111#10621872—82no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43C2×C22⋊C411yescharacteristic
117C23×C43#13711yescharacteristic
118C23×C43#13711yescharacteristic
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—41no—
123C22×D43—41no—
124Q8×C43—42no—
125Q8×C43—42no—
126C2×C4×C43—22no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C22⋊D43—42no—
140C22⋊D43—42no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—41no—
145C2×Dic43—42no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—42no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157C2×Dic43#9911yescharacteristic
158C2×Dic43#9911yescharacteristic
159C2×Dic43#10412yes—
160C4×D43—42no—
161C4×D43—81no—
162C8×C43—81no—
163C43⋊C8—81no—
164#11784—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—81no—
174C22×C43C2×#9911yescharacteristic
175C22×C43#41911yescharacteristic
176C22×C43C2×#10411yescharacteristic
177C2×D43—42no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—81no—
182C4×C43—42no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—81no—
186C4×C43—82no—
187Dic43—21no—
188Dic43—21no—
189Dic43—22no—
190Dic43—41no—
191Dic43—81no—
192Dic43—82no—
193Dic43—81no—
194#2580—431no—
195C4×#99—431no—
196#1465—431no—
197#1352—431no—
198#1352—431no—
199#1351—431no—
200#1351D4311yescharacteristic, complemented
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—41no—
204C2×C43—41no—
205C2×C43#150811yescharacteristic
206C2×C43#212011yescharacteristic
207C2×C43#212711yescharacteristic
208D43—81no—
209C2×C4×Q8—431no—
210C2×C4×D4—431no—
211C2×#99—861no—
212#407—861no—
213#399—431no—
214#399—431no—
215#393—431no—
216#393C2×D4311yescharacteristic
217#390—861no—
218#389—861no—
219#385—861no—
220#385—861no—
221#382—431no—
222C4×C22⋊C4—861no—
223#342—431no—
224#342C2×D4311yescharacteristic
225#324—861no—
226#323—431no—
227#323C2×D4311yescharacteristic
228C43#1178411yescharacteristic, complemented, Sylow
229C22×Q8C4×D4311yescharacteristic
230C22×D4—431no—
231C23×C4—431no—
232C23×C4—431no—
233C2×M16—1721no—
234C4×Q8—1721no—
235C4×Q8—1721no—
236C4×D4—1721no—
237C4×D4—1721no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—431no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4C22×D4311yescharacteristic
252C2×C42—431no—
253C2×C42—861no—
254C2×C42—1721no—
255#99—864no—
256C22⋊C8—21no—
257C22⋊C8—861no—
258C22⋊C8—1721no—
259#95—21no—
260#95—431no—
261#95—861no—
262#95—861no—
263#95—1721no—
264#95C4×D4311yescharacteristic
265C24—431no—
266C24D4×D4311yescharacteristic
267C2×Q8—42no—
268C2×Q8—41no—
269C2×D4—862no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—1721no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—3441no—
286C22×C4—3441no—
287C22×C4—1721no—
288C22×C4C2×C4×D4311yescharacteristic
289C22×C4D4×D4311yescharacteristic
290M16—3442no—
291C2×C8—41no—
292C2×C8—1721no—
293C4⋊C4—3441no—
294C4⋊C4—3441no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1722no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—862no—
305C22⋊C4—3441no—
306C22⋊C4—3441no—
307C22⋊C4—1721no—
308C22⋊C4—1722no—
309C22⋊C4—1721no—
310C42—861no—
311C42—861no—
312C42—3442no—
313C42—1722no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23—1721no—
322C23—1721no—
323C23C22⋊C4×D4311yescharacteristic
324C23#1306335411yescharacteristic
325C23#1306335711yescharacteristic
326Q8—42no—
327Q8—42no—
328D4—1722no—
329D4—1722no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—431no—
344C2×C4—431no—
345C2×C4—432no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—1722no—
354C2×C4—1721no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C8—81no—
365C8—3441no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—3441no—
376C22—1722no—
377C22—1721no—
378C22—1721no—
379C22—1721no—
380C22#99×D4311yescharacteristic
381C22#1458290611yescharacteristic
382C22#104×D4311yescharacteristic
383C4—41no—
384C4—42no—
385C4—41no—
386C4—81no—
387C4—82no—
388C4—861no—
389C4—861no—
390C4—862no—
391C4—3441no—
392C4—3442no—
393C4—3441no—
394C4—1721no—
395C2—21no—
396C2—21no—
397C2—41no—
398C2—41no—
399C2—3441no—
400C2#1913311311yescharacteristic
401C2#1913623311yescharacteristic
402C2#1913626311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1351C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1351D43
hypocenterC43#11784
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
4. #19132620C2semidirect
5. #19132618C2semidirect
6. #19132616C2semidirect
7. C43×#1351C2semidirect
8. C2×Q8×Dic43C4semidirect
12. #14582836C4semidirect
14. #14582810C4semidirect
19. #14582763C4semidirect
200. #1351D43semidirect
228. C43#11784semidirect

Maximal subgroups

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

subgroupindex
#191399482
#191343822
#191329302
#191326202
#191326182
#191326162
C43×#13512
#1178443