Finite Group Databasebeta

← #25009413

Subgroups — #25009413

Order 11008.

370 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 57 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#19142857C211yesmaximal, characteristic
2#19135763C211yesmaximal, characteristic
3#19133619C211yesmaximal, characteristic
4#19133554C211yesmaximal, characteristic
5#19132615C211yesmaximal, characteristic
6#19132524C211yesmaximal, characteristic
7C43×#1352C211yesmaximal, characteristic
8#14583525C2211yescharacteristic
9#14583234—21no—
10#14583057—21no—
11#14582840—21no—
12#14582832—21no—
13#14582829—21no—
14#14582822—21no—
15#14582819—21no—
16#14582811C2211yescharacteristic
17#14582760—21no—
18#14582760C2211yescharacteristic
19#14582757—21no—
20#14582665—21no—
21#14582637—21no—
22#14582635—21no—
23#14582623C2211yescharacteristic
24C43×#399C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C2×Dic172—41no—
30#13063304—21no—
31#13063304—21no—
32#13063302—41no—
33#13063302—41no—
34C2×C4⋊Dic43—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43D411yescharacteristic
42#13063258—41no—
43#13063250—41no—
44#13063248—41no—
45C22⋊(C43⋊C8)—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—41no—
53C43⋊#95—41no—
54C43⋊#95D411yescharacteristic
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43D411yescharacteristic
62C24×C43C2×D411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—41no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—41no—
76C22×Dic43—41no—
77C22×Dic43Q1612yescomplemented
78C2×Dic86—21no—
79C2×Dic86—21no—
80C2×Dic86—41no—
81C2×Dic86—81no—
82C2×C8×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—81no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—81no—
89C22⋊Dic43—41no—
90C22⋊Dic43—41no—
91C22⋊Dic43—41no—
92C22⋊Dic43—81no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43—81no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99Dic43⋊C4—81no—
100Dic43⋊C4—81no—
101Dic43⋊C4—81no—
102C2×C43⋊C8—41no—
103Dic172—82no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43#12011yescharacteristic
109C23×C43C2×Q1611yescharacteristic
110C23×C43#13711yescharacteristic
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43—81no—
124C2×Dic43—22no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—42no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142Dic86—42no—
143Dic86—81no—
144Dic86—81no—
145Dic86—81no—
146C8×C43—81no—
147C43⋊C8—81no—
148#12219—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—81no—
158C22×C43#45111yescharacteristic
159C22×C43#45511yescharacteristic
160C22×C43B(4,𝔽2)11yescharacteristic
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43—161no—
166Dic43—42no—
167Dic43—81no—
168Dic43—81no—
169Dic43—81no—
170Dic43—81no—
171Dic43—81no—
172#2841—431no—
173#2030—431no—
174#1614—431no—
175#1602—431no—
176#1352D4311yescharacteristic
177#1351—431no—
178#1317—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—41no—
182C2×C43—41no—
183C2×C43#160211yescharacteristic
184C2×C43#220011yescharacteristic
185C2×C43#220111yescharacteristic
186#543—431no—
187#484—861no—
188#451—861no—
189#400—861no—
190#399C2×D4311yescharacteristic
191#398—861no—
192#398—861no—
193#396—861no—
194#395—861no—
195#393—431no—
196#381—431no—
197#381—861no—
198#380—861no—
199#342—861no—
200#342C2×D4311yescharacteristic
201#328—861no—
202#328—861no—
203#323—431no—
204#323C2×D4311yescharacteristic
205C43#1221911yescharacteristic, complemented, Sylow
206C22×Q8—431no—
207C23×C4—431no—
208C2×Q16—1721no—
209C22⋊Q8—861no—
210C22⋊Q8—861no—
211C22⋊Q8—1721no—
212C22⋊Q8—1721no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4D17211yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—431no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—861no—
225C2×C22⋊C4C22×D4311yescharacteristic
226#107—1721no—
227#103—1721no—
228#103—1721no—
229C22⋊C8—21no—
230C22⋊C8—861no—
231#95—431no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—1721no—
239#95—1721no—
240#95D17211yescharacteristic
241C24D4×D4311yescharacteristic
242C2×Q8—861no—
243C2×Q8—861no—
244C2×Q8—3441no—
245C2×Q8—1721no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—432no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—1721no—
258C22×C4—1721no—
259C22×C4C2×D17211yescharacteristic
260C22×C4D4×D4311yescharacteristic
261Q16—3442no—
262C2×C8—41no—
263C2×C8—1721no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—3441no—
269C4⋊C4—3441no—
270C4⋊C4—3441no—
271C4⋊C4—3441no—
272C4⋊C4—3441no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—81no—
279C22⋊C4—3441no—
280C22⋊C4—1721no—
281C22⋊C4—1721no—
282C22⋊C4—1721no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23#1306329511yescharacteristic
288C23Q16×D4311yescharacteristic
289C23#1306335411yescharacteristic
290Q8—3441no—
291Q8—3441no—
292Q8—3441no—
293Q8—1722no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—862no—
308C2×C4—3441no—
309C2×C4—3441no—
310C2×C4—3441no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1722no—
325C8—81no—
326C8—3441no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22#1458305611yescharacteristic
337C22#1458307811yescharacteristic
338C22#1458308711yescharacteristic
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—161no—
344C4—3441no—
345C4—3441no—
346C4—3441no—
347C4—3441no—
348C4—3441no—
349C4—1722no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2#1913355311yescharacteristic
355C2#1913660511yescharacteristic
356C2#1913660911yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1352C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#1352D43
hypocenterC43#12219
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
77. C22×Dic43Q16semidirect
205. C43#12219semidirect

Maximal subgroups

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

subgroupindex
#191428572
#191357632
#191336192
#191335542
#191326152
#191325242
C43×#13522
#1221943