Finite Group Databasebeta

← #24993771

Subgroups — #24993771

Order 11008.

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

normal subgroups only

This group has 500 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#19144544C211yesmaximal, characteristic
2#19137482C211yesmaximal, characteristic
3#19135579C211yesmaximal, characteristic
4#19134692C211yesmaximal, characteristic
5#19133116C211yesmaximal, characteristic
6#19132480C211yesmaximal, characteristic
7C43×#1305C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10#14583241—22no—
11#14583235—21no—
12#14583230—21no—
13#14582941C412yescomplemented
14#14582909C412yescomplemented
15#14582795—21no—
16#14582793—22no—
17#14582763—21no—
18C4⋊C4×Dic43—21no—
19C4×C22⋊Dic43C2211yescharacteristic
20C4×C22⋊Dic43C2211yescharacteristic
21#14582744—21no—
22#14582665—22no—
23#14582660—22no—
24#14582637—21no—
25#14582637—21no—
26C43×#407C2211yescharacteristic
27C43×#407C2211yescharacteristic
28C43×#380C2211yescharacteristic
29C22×Dic86C2×C411yescharacteristic
30#13063304—21no—
31#13063304—21no—
32#13063304—21no—
33#13063304—21no—
34#13063284—21no—
35#13063284—21no—
36#13063284C2×C412yes—
37#13063284D412yes—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—22no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—22no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—21no—
51#13063259—22no—
52#13063257—22no—
53#13063250—22no—
54#13063250—22no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—21no—
58C43⋊#95D411yescharacteristic
59C43⋊#95D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C2×M16×C43—21no—
62C2×M16×C43C2×C412yes—
63C2×C4⋊C4×C43—21no—
64C2×C22⋊C4×C43D412yes—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69#95×C43—21no—
70C24×C43C2×D411yescharacteristic
71C22×C4×C43—22no—
72C22×C4×C43—42no—
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—41no—
86C2×Dic86—21no—
87C2×Dic86—21no—
88C2×Dic86—42no—
89M16×C43—42no—
90M16×C43—42no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C4⋊C4×C43—42no—
94C22⋊C4×C43—42no—
95C22⋊Dic43—22no—
96C22⋊Dic43—22no—
97C22⋊Dic43—22no—
98C22⋊Dic43—41no—
99C22⋊Dic43—42no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C4⋊Dic43—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43C22⋊C412yes—
107C4⋊Dic43C22⋊C412yes—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—82no—
111C4×Dic43—22no—
112C4×Dic43—22no—
113C4×Dic43—44no—
114C4×Dic43—42no—
115C4×Dic43—42no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43C4×D411yescharacteristic
121C23×C43#12011yescharacteristic
122C23×C43#12111yescharacteristic
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—22no—
139C2×Dic43—41no—
140C2×Dic43—42no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—42no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154Dic86—42no—
155Dic86—81no—
156C8×C43—42no—
157C8×C43—81no—
158#9363—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—81no—
168C22×C43—81no—
169C22×C43#38611yescharacteristic
170C22×C43#45511yescharacteristic
171C22×C43#45611yescharacteristic
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—82no—
176C4×C43#41012yes—
177Dic43—42no—
178Dic43—42no—
179Dic43—42no—
180Dic43—81no—
181Dic43—82no—
182Dic43—81no—
183Dic43—81no—
184#3095—431no—
185#2346—431no—
186#1996—431no—
187#1826—431no—
188#1508—431no—
189#1305D4311yescharacteristic
190#1297—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43—41no—
194C2×C43—41no—
195C2×C43#188211yescharacteristic
196C2×C43#189911yescharacteristic
197C2×C43#190611yescharacteristic
198C2×C22⋊Q8—431no—
199C2×#117—431no—
200#485—862no—
201#484—861no—
202#483—861no—
203#428—432no—
204#419—432no—
205#407C2×D4311yescharacteristic
206#407C2×D4311yescharacteristic
207#389—861no—
208#388—862no—
209#382—861no—
210#380C2×D4311yescharacteristic
211C4×C4⋊C4—861no—
212C4×C22⋊C4—431no—
213C4×C22⋊C4—431no—
214#376—861no—
215#342—862no—
216#339—862no—
217#328—861no—
218#328—861no—
219C43#936311yescharacteristic, complemented, Sylow
220C22×Q8—431no—
221C23×C4C22×D4311yescharacteristic
222C2×M16—21no—
223C2×M16C4×D4312yes—
224C22⋊Q8—861no—
225C22⋊Q8—861no—
226C22⋊Q8—861no—
227C22⋊Q8—861no—
228#117—432no—
229#117—432no—
230#117—861no—
231#117—861no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4D17212yes—
243C2×C42—861no—
244C2×C42—862no—
245C2×C42—861no—
246C2×C42—861no—
247#107—862no—
248#106—862no—
249#103—862no—
250#103—862no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255#95—21no—
256#95—431no—
257#95—431no—
258#95—862no—
259#95—862no—
260#95—861no—
261C24C2×D17211yescharacteristic
262C2×Q8—861no—
263C2×Q8—861no—
264C2×Q8—1722no—
265C22×C4—22no—
266C22×C4—42no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—1721no—
274C22×C4C2×C4×D4311yescharacteristic
275C22×C4#1062189811yescharacteristic
276C22×C4D4×D4311yescharacteristic
277C22×C4D4×D4311yescharacteristic
278C22×C4D4×D4311yescharacteristic
279C22×C4#1062190211yescharacteristic
280M16—42no—
281M16—42no—
282C2×C8—22no—
283C2×C8—41no—
284C4⋊C4—42no—
285C4⋊C4—432no—
286C4⋊C4—432no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C4⋊C4—3442no—
292C4⋊C4—1721no—
293C4⋊C4—1721no—
294C22⋊C4—42no—
295C22⋊C4—862no—
296C22⋊C4—862no—
297C22⋊C4—862no—
298C22⋊C4—1722no—
299C22⋊C4—1721no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C42—862no—
303C42—862no—
304C42—1722no—
305C42—1722no—
306C42—1724no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23C4×D17211yescharacteristic
312C23#1306329511yescharacteristic
313C23#1306330011yescharacteristic
314Q8—3441no—
315Q8—1722no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—3441no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—1721no—
333C2×C4—1722no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1722no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4C22⋊C4×D4311yescharacteristic
344C2×C4#1306328711yescharacteristic
345C2×C4#1306329811yescharacteristic
346C2×C4#1306331011yescharacteristic
347C8—42no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22#1458277711yescharacteristic
360C22#1458307911yescharacteristic
361C22#1458308411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—3441no—
367C4—3442no—
368C4—3441no—
369C4—3441no—
370C4—1722no—
371C4—1722no—
372C4—1722no—
373C4#1458287112yes—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1913496311yescharacteristic
379C2#1913505211yescharacteristic
380C2#1913509711yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1305C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1305D43
hypocenterC43#9363
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
13. #14582941C4semidirect
14. #14582909C4semidirect
219. C43#9363semidirect

Maximal subgroups

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

subgroupindex
#191445442
#191374822
#191355792
#191346922
#191331162
#191324802
C43×#13052
#936343