Finite Group Databasebeta

← #25007127

Subgroups — #25007127

Order 11008.

462 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 73 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#19139971C211yesmaximal, characteristic
2#343×D43C211yesmaximal, characteristic
3#19132923C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063301C411yescharacteristic
10C2×C4⋊C4×D43C2211yescharacteristic
11#14582861—21no—
12#14582831C411yescharacteristic
13#14582829C2211yescharacteristic
14#14582818C411yescharacteristic
15#14582796—21no—
16#14582795—21no—
17#14582773—21no—
18#14582770—21no—
19#14582746C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621877—21no—
31C2×#10621872—41no—
32C2×#10621872—41no—
33M16×D43—24no—
34M16×D43—42no—
35C2×C8×D43—41no—
36#13063301—41no—
37#13063301—41no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4C2×C411yescharacteristic
45C2×Dic43⋊C4D411yescharacteristic
46C4⋊C4×D43—41no—
47C4⋊C4×D43—41no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×C4×Dic43—21no—
51C22⋊(C43⋊C8)—21no—
52(C2×D43)⋊C8—41no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C22×Q8×C43C2×C411yescharacteristic
58C2×M16×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C2×Q8×C43—41no—
66C2×Q8×C43—81no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—22no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—81no—
87C2×C4×D43—81no—
88M16×C43—22no—
89M16×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—81no—
94(C2×D43)⋊C4—24no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97C4⋊Dic43—41no—
98C4⋊Dic43—42no—
99C4⋊Dic43—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—42no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—81no—
106C4×Dic43—81no—
107#10621877—22no—
108#10621877—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111#10621872—44no—
112#10621872—82no—
113C8×D43—44no—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—22no—
118C22×D43—41no—
119C22×D43#9911yescharacteristic
120C22×D43#9911yescharacteristic
121Q8×C43—82no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
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×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—22no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43#10412yes—
149C4×D43—22no—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—22no—
153C4×D43—42no—
154C4×D43—81no—
155C4×D43—81no—
156C4×D43—81no—
157C8×C43—42no—
158C8×C43—81no—
159C43⋊C8—42no—
160C43⋊C8—81no—
161#11768—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43C2×#9911yescharacteristic
165C22×C43#41711yescharacteristic
166C22×C43C2×#10411yescharacteristic
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—42no—
173C2×D43—42no—
174C2×D43#35612yes—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—42no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—81no—
181Dic43—22no—
182Dic43—42no—
183Dic43—41no—
184Dic43—41no—
185Dic43—81no—
186#2583—431no—
187C2×#343—431no—
188#1463—431no—
189#1354—431no—
190#1354D4311yescharacteristic, complemented
191#1346—431no—
192#1346—431no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43#150411yescharacteristic
196C2×C43#212111yescharacteristic
197C2×C43C2×#35611yescharacteristic
198D43—22no—
199D43—41no—
200C22×M16—861no—
201C2×C22⋊Q8—431no—
202C22×C4⋊C4—431no—
203#407—861no—
204#398—431no—
205#398—431no—
206#395—431no—
207#395C2×D4311yescharacteristic
208#389—861no—
209#389—861no—
210#385—861no—
211#385—861no—
212C4×C22⋊C4—431no—
213#343—431no—
214#343—861no—
215#343C2×D4311yescharacteristic
216#324—431no—
217#324—861no—
218#324C2×D4311yescharacteristic
219C43#1176811yescharacteristic, complemented, Sylow
220C22×Q8C4×D4311yescharacteristic
221C23×C4—431no—
222C23×C4—431no—
223C23×C4—431no—
224C2×M16—21no—
225C2×M16—864no—
226C2×M16—861no—
227C2×M16—1721no—
228C2×M16—1721no—
229C2×M16—1722no—
230C22×C8—1721no—
231C22⋊Q8—1721no—
232C22⋊Q8—1721no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—1721no—
243C2×C4⋊C4—1721no—
244C2×C4⋊C4C22×D4311yescharacteristic
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C42—861no—
248C22⋊C8—21no—
249C22⋊C8—861no—
250C22⋊C8—1721no—
251#95—21no—
252#95—431no—
253#95—861no—
254#95—861no—
255#95—861no—
256#95C4×D4311yescharacteristic
257C24—431no—
258C2×Q8—41no—
259C2×Q8—81no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—431no—
265C22×C4—862no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—3441no—
277C22×C4—3441no—
278C22×C4C2×C4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281M16—22no—
282M16—41no—
283M16—862no—
284M16—3442no—
285M16—1724no—
286M16—1721no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—1724no—
290C2×C8—1721no—
291C2×C8—1721no—
292C4⋊C4—41no—
293C4⋊C4—81no—
294C4⋊C4—3441no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1722no—
300C4⋊C4—1722no—
301C4⋊C4—1721no—
302C4⋊C4—1721no—
303C22⋊C4—864no—
304C22⋊C4—1721no—
305C22⋊C4—1721no—
306C42—3441no—
307C23—431no—
308C23—431no—
309C23—862no—
310C23—861no—
311C23—861no—
312C23—1721no—
313C23C22⋊C4×D4311yescharacteristic
314Q8—82no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—432no—
328C2×C4—862no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—862no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—3441no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—1722no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4#1306335211yescharacteristic
349C2×C4#1306335711yescharacteristic
350C8—42no—
351C8—81no—
352C8—3441no—
353C8—1722no—
354C22—21no—
355C22—21no—
356C22—432no—
357C22—861no—
358C22—861no—
359C22—861no—
360C22—861no—
361C22—861no—
362C22—1722no—
363C22—1722no—
364C22#99×D4311yescharacteristic
365C22#1458289911yescharacteristic
366C22#104×D4311yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—862no—
374C4—3441no—
375C4—1722no—
376C4—1721no—
377C4—1721no—
378C2—21no—
379C2—21no—
380C2—862no—
381C2—1721no—
382C2#1913309811yescharacteristic
383C2#1913623811yescharacteristic
384C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11768
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132602C2semidirect
6. #19132600C2semidirect
7. C43×#1354C2semidirect
190. #1354D43semidirect
219. C43#11768semidirect

Maximal subgroups

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

subgroupindex
#191399712
#343×D432
#191329232
#191326252
#191326022
#191326002
C43×#13542
#1176843