Finite Group Databasebeta

← #25007632

Subgroups — #25007632

Order 11008.

472 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 79 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#19139586C211yesmaximal, characteristic
2#19134582C211yesmaximal, characteristic
3#19132910C211yesmaximal, characteristic
4#19132596C211yesmaximal, characteristic, complemented
5#19132595C211yesmaximal, characteristic, complemented
6#19132594C211yesmaximal, characteristic, complemented
7C43×#1344C211yesmaximal, characteristic, complemented
8C2×#13063324C411yescharacteristic, complemented
9C2×#13063311—21no—
10C2×(C22⋊D43)⋊C4C2211yescharacteristic
11C2×#13063239—21no—
12C22⋊C8×D43—21no—
13#14582826C411yescharacteristic, complemented
14#14582825C411yescharacteristic, complemented
15#14582824C2211yescharacteristic
16#14582803—21no—
17#14582758—21no—
18#14582757—21no—
19#14582757—21no—
20#14582750C411yescharacteristic, complemented
21#14582666C2211yescharacteristic
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#397C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86—21no—
28C22×C22⋊D43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×C8×D43—41no—
32#13063324—41no—
33#13063324—41no—
34#13063311—42no—
35#13063311—42no—
36(C22⋊D43)⋊C4—41no—
37(C22⋊D43)⋊C4—41no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—41no—
42C2×Dic43⋊C4D411yescharacteristic
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4C2×C411yescharacteristic
48C2×C4×Dic43—21no—
49C2×C4×Dic43C2×C411yescharacteristic
50#13063239—42no—
51C22⋊(C43⋊C8)—21no—
52(C2×D43)⋊C8—41no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—41no—
57C43⋊#95C2×C411yescharacteristic
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43C2311yescharacteristic
62C22⋊C8×C43—21no—
63#95×C43—21no—
64#95×C43C2×C411yescharacteristic
65C24×C43C2×D411yescharacteristic
66C23×D43C22⋊C411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—41no—
73C2×C22⋊D43—41no—
74C2×C22⋊D43D812yes—
75C2×C22⋊D43SD1612yes—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—41no—
81C22×Dic43—42no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—42no—
88C2×Dic86—42no—
89C2×Dic86—42no—
90C2×Dic86—42no—
91C2×C8×C43—41no—
92C4⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—42no—
104(C2×D43)⋊C4—42no—
105C4⋊Dic43—41no—
106Dic43⋊C4—41no—
107Dic43⋊C4—42no—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—82no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43—42no—
114C2×C43⋊C8—41no—
115C8×D43—82no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43C2×C22⋊C411yescharacteristic
121C23×C43C2×D811yescharacteristic
122C23×C43C2×SD1611yescharacteristic
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43#10212yes—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
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—41no—
137C2×C4×C43—41no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43—81no—
141C22⋊D43—42no—
142C22⋊D43—42no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—22no—
146C2×Dic43—21no—
147C2×Dic43—42no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159C2×Dic43#9911yescharacteristic
160C2×Dic43#9911yescharacteristic
161C2×Dic43#10212yes—
162C4×D43—42no—
163C4×D43—81no—
164Dic86—84no—
165C8×C43—81no—
166C43⋊C8—81no—
167#11878—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—81no—
177C22×C43C2×#9911yescharacteristic
178C22×C43C2×#10211yescharacteristic
179C22×C43#42111yescharacteristic
180C2×D43—22no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—42no—
184C2×D43—81no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43—161no—
190Dic43—21no—
191Dic43—22no—
192Dic43—41no—
193Dic43—81no—
194Dic43—81no—
195Dic43—161no—
196Dic43#35412yes—
197#2547—431no—
198#1799—431no—
199#1459—431no—
200#1344—431no—
201#1344—431no—
202#1344—431no—
203#1344D4311yescharacteristic, complemented
204C2×C43—21no—
205C2×C43—21no—
206C2×C43—41no—
207C2×C43—41no—
208C2×C43#151911yescharacteristic
209C2×C43#212311yescharacteristic
210C2×C43C2×#35411yescharacteristic
211D43—42no—
212C2×C4⋊Q8—431no—
213C2×#124—861no—
214C2×C4×D4—431no—
215C2×#99—861no—
216C2×C22⋊C8—861no—
217#397—431no—
218#397—431no—
219#397—431no—
220#397C2×D4311yescharacteristic
221#391—861no—
222#380—861no—
223#380—861no—
224#380—861no—
225C4×C4⋊C4—431no—
226#342—431no—
227#342C2×D4311yescharacteristic
228#324—861no—
229#323—431no—
230#323C2×D4311yescharacteristic
231C43#1187811yescharacteristic, complemented, Sylow
232C22×Q8—861no—
233C22×D4—431no—
234C23×C4—431no—
235C23×C4—431no—
236C22×C8—1721no—
237C4⋊Q8—1721no—
238C4⋊Q8—1721no—
239#124—1722no—
240#124—1722no—
241C4×D4—1721no—
242C4×D4—1721no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—1721no—
248C2×C4⋊C4C4×D4311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—431no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4C22×D4311yescharacteristic
257C2×C42—431no—
258C2×C42—861no—
259#99—1722no—
260C22⋊C8—21no—
261C22⋊C8—861no—
262C22⋊C8—1721no—
263#95—21no—
264#95—431no—
265#95—861no—
266#95—861no—
267#95—861no—
268#95—1721no—
269#95C4×D4311yescharacteristic
270C24—431no—
271C24D4×D4311yescharacteristic
272C2×Q8—1722no—
273C2×Q8—1722no—
274C2×Q8—1722no—
275C2×D4—432no—
276C2×D4—432no—
277C2×D4—1721no—
278C2×D4—1721no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—1722no—
292C22×C4—1722no—
293C22×C4—1721no—
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C2×C8—41no—
297C2×C8—3442no—
298C2×C8—1721no—
299C4⋊C4—41no—
300C4⋊C4—3442no—
301C4⋊C4—1721no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1722no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—1721no—
312C22⋊C4—1722no—
313C22⋊C4—1722no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C42—861no—
319C42—861no—
320C42—1722no—
321C23—21no—
322C23—21no—
323C23—41no—
324C23—41no—
325C23—432no—
326C23—861no—
327C23—861no—
328C23—1721no—
329C23—1721no—
330C23C22⋊C4×D4311yescharacteristic
331C23D8×D4311yescharacteristic
332C23SD16×D4311yescharacteristic
333Q8—3444no—
334D4—1722no—
335D4—1722no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—431no—
350C2×C4—431no—
351C2×C4—432no—
352C2×C4—862no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—3441no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C8—81no—
371C8—3441no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—862no—
382C22—3441no—
383C22—1722no—
384C22—1721no—
385C22—1721no—
386C22#99×D4311yescharacteristic
387C22#102×D4311yescharacteristic
388C22#1458291411yescharacteristic
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4—161no—
394C4—432no—
395C4—862no—
396C4—861no—
397C4—3441no—
398C4—3441no—
399C4—1721no—
400C4—6881no—
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2—1722no—
406C2#1913316111yescharacteristic
407C2#1913624711yescharacteristic
408C2#354×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1344C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1344D43
hypocenterC43#11878
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #19132596C2semidirect
5. #19132595C2semidirect
6. #19132594C2semidirect
7. C43×#1344C2semidirect
8. C2×#13063324C4semidirect
13. #14582826C4semidirect
14. #14582825C4semidirect
20. #14582750C4semidirect
203. #1344D43semidirect
231. C43#11878semidirect

Maximal subgroups

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

subgroupindex
#191395862
#191345822
#191329102
#191325962
#191325952
#191325942
C43×#13442
#1187843