Finite Group Databasebeta

← #25008991

Subgroups — #25008991

Order 11008.

432 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135846C211yesmaximal, characteristic
2#19133580C211yesmaximal, characteristic
3#19133580C211yesmaximal, characteristic
4#19132595C211yesmaximal, characteristic, complemented
5#19132595C211yesmaximal, characteristic, complemented
6#19132543C211yesmaximal, characteristic, complemented
7C43×#2722C211yesmaximal, characteristic, complemented
8#14583461C2211yescharacteristic
9#14583212—21no—
10#14583212—21no—
11C2×#13063239—21no—
12#14582778—21no—
13#14582666C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C2×#126×C43—21no—
19C43×#398—21no—
20C43×#398—21no—
21C43×#397C2211yescharacteristic
22C43×#397C2211yescharacteristic
23C43×#389—21no—
24C43×#387—21no—
25C43×#385C2211yescharacteristic
26C43×#380—21no—
27C22×C22⋊D43—21no—
28#13063309—41no—
29#13063299—21no—
30#13063299—21no—
31#13063295—41no—
32C2×C22⋊Dic43—21no—
33C2×(C2×D43)⋊C4—41no—
34#13063258—41no—
35#13063258—41no—
36#13063245—41no—
37#13063245—41no—
38#13063239—42no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C43⋊#95—41no—
42C23×C4×C43D411yescharacteristic
43#126×C43—42no—
44#126×C43—42no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43—21no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43C2311yescharacteristic
57C2×C42×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64#95×C43D411yescharacteristic
65C24×C43C2×D411yescharacteristic
66C23×D43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43—42no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C2×C22⋊D43—41no—
83C22×Dic43—21no—
84C22×Dic43—41no—
85C2×D172—21no—
86C2×D172—21no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—42no—
90C4⋊C4×C43—42no—
91C4⋊C4×C43—42no—
92C4⋊C4×C43—42no—
93C4⋊C4×C43—42no—
94C4⋊C4×C43—81no—
95C22⋊C4×C43—21no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43D812yes—
102C42×C43—42no—
103C22⋊Dic43—41no—
104C22⋊Dic43—41no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—82no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43#12011yescharacteristic
117C23×C43C2×D811yescharacteristic
118C23×C43AGL(1,ℤ/8)11yescharacteristic
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—81no—
123C22×D43—81no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
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—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—81no—
148C22⋊D43—81no—
149C22⋊D43—81no—
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158D172—81no—
159D172—81no—
160C43⋊C8—81no—
161C43⋊C8—81no—
162#12150—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—81no—
172C22×C43#44711yescharacteristic
173C22×C43#45411yescharacteristic
174C22×C43B(4,𝔽2)11yescharacteristic
175C2×D43—82no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—161no—
180C4×C43—42no—
181C4×C43—41no—
182C4×C43—42no—
183C4×C43—41no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43—81no—
187C4×C43—81no—
188Dic43—81no—
189Dic43—161no—
190#2722D4311yescharacteristic, complemented
191#2044—431no—
192#1607—431no—
193#1607—431no—
194#1344—431no—
195#1344—431no—
196#1326—431no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—41no—
200C2×C43—41no—
201C2×C43#159811yescharacteristic
202C2×C43#219711yescharacteristic
203C2×C43#220111yescharacteristic
204D43—161no—
205#534—431no—
206C2×#126—21no—
207#480—861no—
208#480—861no—
209C2×#99—861no—
210#398—21no—
211#398—21no—
212#397C2×D4311yescharacteristic
213#397C2×D4311yescharacteristic
214#389—21no—
215#387—21no—
216#386—861no—
217#385C2×D4311yescharacteristic
218#380—21no—
219#342—431no—
220#327—861no—
221#327—861no—
222#323—431no—
223#323—431no—
224C43#1215011yescharacteristic, complemented, Sylow
225C22×D4—861no—
226C23×C4C22⋊D4311yescharacteristic
227#126—42no—
228#126—42no—
229#123—1721no—
230#121—861no—
231#121—861no—
232#120—1721no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C22⋊D4311yescharacteristic
240C2×C4⋊C4C22⋊D4311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—1721no—
245C2×C22⋊C4C22⋊D4311yescharacteristic
246C2×C22⋊C4C22×D4311yescharacteristic
247C2×C42—21no—
248#107—1721no—
249#107—1721no—
250#102—1721no—
251#102—1721no—
252#99—1722no—
253C22⋊C8—861no—
254C22⋊C8—861no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—1721no—
261#95C22⋊D4311yescharacteristic
262#95C22⋊D4311yescharacteristic
263C24—861no—
264C24C2×C22⋊D4311yescharacteristic
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—1721no—
268C2×D4—1721no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4—1721no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—861no—
282C22×C4—1721no—
283C22×C4C2×C22⋊D4311yescharacteristic
284C22×C4C2×C22⋊D4311yescharacteristic
285C2×C8—1721no—
286C2×C8—1721no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—81no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C22⋊C4—21no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—3442no—
304C22⋊C4—1721no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C22⋊C4—1721no—
308C22⋊C4#1062188212yes—
309C42—42no—
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—3441no—
315C23—3441no—
316C23—1721no—
317C23—1721no—
318C23—1721no—
319C23#1306329411yescharacteristic
320C23C2×#1062188211yescharacteristic
321C23#1306335111yescharacteristic
322D4—3441no—
323D4—3441no—
324D4—3441no—
325D4—3441no—
326D4—3441no—
327D4—3441no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—3441no—
353C2×C4—3441no—
354C2×C4—3441no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C8—3441no—
359C8—3441no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—3442no—
370C22—3441no—
371C22—3441no—
372C22—3441no—
373C22—6881no—
374C22#1458303311yescharacteristic
375C22#1458307211yescharacteristic
376C22#1458308611yescharacteristic
377C4—42no—
378C4—41no—
379C4—42no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—3441no—
386C4—6881no—
387C2—21no—
388C2—21no—
389C2—41no—
390C2—41no—
391C2—6881no—
392C2#1913353011yescharacteristic
393C2#1913658511yescharacteristic
394C2#1913660811yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2722C2
socleC22×C43B(4,𝔽2)
prime radical#14583461C22
hypercenter#2722D43
hypocenterC43#12150
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2722

Complements

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

NH ≅ G/Ntype
4. #19132595C2semidirect
5. #19132595C2semidirect
6. #19132543C2semidirect
7. C43×#2722C2semidirect
190. #2722D43semidirect
224. C43#12150semidirect

Maximal subgroups

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

subgroupindex
#191358462
#191335802
#191325952
#191325432
C43×#27222
#1215043