Finite Group Databasebeta

← #25008907

Subgroups — #25008907

Order 11008.

394 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 59 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#19133614C211yesmaximal, characteristic
3#19133580C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic, complemented
5#19132595C211yesmaximal, characteristic, complemented
6#19132543C211yesmaximal, characteristic, complemented
7C43×#2834C211yesmaximal, characteristic, complemented
8#14583461C2211yescharacteristic
9#14583217—21no—
10#14583212—21no—
11C2×#13063239—21no—
12#14582778—21no—
13#14582666C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C43×#401—21no—
19C43×#399C2211yescharacteristic
20C43×#398—21no—
21C43×#398—21no—
22C43×#398—21no—
23C43×#397—21no—
24C43×#397C2211yescharacteristic
25C43×#385—21no—
26C43×#385C2211yescharacteristic
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#13063256—41no—
36#13063245—41no—
37#13063245—41no—
38#13063239—42no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C43⋊#95—41no—
42C23×C4×C43D411yescharacteristic
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43C2311yescharacteristic
54#95×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62#95×C43D411yescharacteristic
63C24×C43C2×D411yescharacteristic
64C23×D43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—41no—
72C22×C4×C43—81no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C2×C22⋊D43—41no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C22×Dic43—21no—
82C22×Dic43—41no—
83C2×D172—21no—
84C2×D172—21no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—81no—
88C4⋊C4×C43—81no—
89C4⋊C4×C43—81no—
90C4⋊C4×C43—81no—
91C4⋊C4×C43—81no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—81no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—82no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43#12011yescharacteristic
112C23×C43#13511yescharacteristic
113C23×C43AGL(1,ℤ/8)11yescharacteristic
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—81no—
118C22×D43—81no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
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—42no—
134C2×C4×C43—41no—
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—81no—
143C22⋊D43—81no—
144C22⋊D43—81no—
145C22⋊D43—81no—
146C22⋊D43—81no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153D172—81no—
154D172—81no—
155C43⋊C8—81no—
156C43⋊C8—81no—
157#12138—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—81no—
167C22×C43#44911yescharacteristic
168C22×C43#45411yescharacteristic
169C22×C43B(4,𝔽2)11yescharacteristic
170C2×D43—82no—
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—161no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—81no—
178C4×C43—81no—
179C4×C43—81no—
180C4×C43—81no—
181C4×C43—81no—
182C4×C43—81no—
183Dic43—81no—
184Dic43—161no—
185#2834D4311yescharacteristic, complemented
186#2044—431no—
187#1613—431no—
188#1607—431no—
189#1352—431no—
190#1344—431no—
191#1326—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—41no—
195C2×C43—41no—
196C2×C43#159711yescharacteristic
197C2×C43#220011yescharacteristic
198C2×C43#220111yescharacteristic
199D43—161no—
200#534—431no—
201#481—861no—
202#480—861no—
203C2×#99—861no—
204#401—21no—
205#399C2×D4311yescharacteristic
206#398—21no—
207#398—21no—
208#398—21no—
209#397—21no—
210#397C2×D4311yescharacteristic
211#386—861no—
212#385—21no—
213#385C2×D4311yescharacteristic
214#342—431no—
215#327—861no—
216#327—861no—
217#323—431no—
218#323—431no—
219C43#1213811yescharacteristic, complemented, Sylow
220C22×D4—861no—
221C23×C4C22⋊D4311yescharacteristic
222#123—1721no—
223#121—861no—
224#121—861no—
225#120—1721no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C22⋊D4311yescharacteristic
232C2×C4⋊C4C22⋊D4311yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4—1721no—
237C2×C22⋊C4C22⋊D4311yescharacteristic
238C2×C22⋊C4C22×D4311yescharacteristic
239#107—1721no—
240#106—1721no—
241#102—1721no—
242#102—1721no—
243#99—1722no—
244C22⋊C8—861no—
245C22⋊C8—861no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—1721no—
254#95C22⋊D4311yescharacteristic
255#95C22⋊D4311yescharacteristic
256C24—861no—
257C24C2×C22⋊D4311yescharacteristic
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—1721no—
261C2×D4—1721no—
262C2×D4—1721no—
263C2×D4—1721no—
264C2×D4—1721no—
265C2×D4—1721no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—81no—
274C22×C4—861no—
275C22×C4—1721no—
276C22×C4C2×C22⋊D4311yescharacteristic
277C22×C4C2×C22⋊D4311yescharacteristic
278C2×C8—1721no—
279C2×C8—1721no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—81no—
295C22⋊C4—3442no—
296C22⋊C4—1721no—
297C22⋊C4—1721no—
298C22⋊C4—1721no—
299C22⋊C4—1721no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—3441no—
305C23—3441no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23#1306329411yescharacteristic
310C23#1306334511yescharacteristic
311C23#1306335011yescharacteristic
312D4—3441no—
313D4—3441no—
314D4—3441no—
315D4—3441no—
316D4—3441no—
317D4—3441no—
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—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—3441no—
343C2×C4—3441no—
344C2×C4—3441no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C8—3441no—
349C8—3441no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—3442no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—6881no—
364C22#1458304411yescharacteristic
365C22#1458307211yescharacteristic
366C22#1458308611yescharacteristic
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—3441no—
376C4—6881no—
377C2—21no—
378C2—21no—
379C2—41no—
380C2—41no—
381C2—6881no—
382C2#1913352411yescharacteristic
383C2#1913660211yescharacteristic
384C2#1913660811yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2834C2
socleC22×C43B(4,𝔽2)
prime radical#14583461C22
hypercenter#2834D43
hypocenterC43#12138
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2834

Complements

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

NH ≅ G/Ntype
4. #19132619C2semidirect
5. #19132595C2semidirect
6. #19132543C2semidirect
7. C43×#2834C2semidirect
185. #2834D43semidirect
219. C43#12138semidirect

Maximal subgroups

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

subgroupindex
#191358462
#191336142
#191335802
#191326192
#191325952
#191325432
C43×#28342
#1213843