Finite Group Databasebeta

← #25009694

Subgroups — #25009694

Order 11008.

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

normal subgroups only

This group has 438 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#19135762C211yesmaximal, characteristic, complemented
2#19133551C211yesmaximal, characteristic, complemented
3#19133517C211yesmaximal, characteristic
4#19132616C211yesmaximal, characteristic, complemented
5#19132592C211yesmaximal, characteristic
6#19132525C211yesmaximal, characteristic, complemented
7C43×#2760C211yesmaximal, characteristic
8#14583525C2211yescharacteristic
9#14583055—21no—
10#14583050—21no—
11#14582762—21no—
12#14582666C2211yescharacteristic
13#14582665—21no—
14#14582635—21no—
15#14582635—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C43×#401—21no—
19C43×#393—21no—
20C43×#393C2211yescharacteristic
21C43×#392C2211yescharacteristic
22C43×#386—21no—
23C43×#386—21no—
24C43×#386—21no—
25C43×#381—21no—
26C43×#381C2211yescharacteristic
27C2×#10621885—41no—
28C2×#10621883—41no—
29#13063304—21no—
30#13063304—21no—
31#13063302—41no—
32#13063302—41no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35#13063249—41no—
36#13063246—41no—
37C22⋊(C43⋊C8)—21no—
38C22⋊(C43⋊C8)—21no—
39C43⋊#95—41no—
40C43⋊#95—41no—
41C22×Q8×C43D411yescharacteristic
42C22×D4×C43—21no—
43C22×D4×C43D411yescharacteristic
44C23×C4×C43—21no—
45C23×C4×C43D411yescharacteristic
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C22⋊C4×C43C2311yescharacteristic
53#95×C43—21no—
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×C43D411yescharacteristic
61#95×C43D411yescharacteristic
62C24×C43—21no—
63C24×C43C2×D411yescharacteristic
64C2×Q8×C43—41no—
65C2×Q8×C43—81no—
66C2×D4×C43—42no—
67C2×D4×C43—42no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—81no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43—42no—
82C22×C4×C43—81no—
83C22×C4×C43—81no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—41no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—81no—
94C22⋊C4×C43—81no—
95C22⋊C4×C43—81no—
96C22⋊C4×C43—81no—
97C22⋊C4×C43—81no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102#10621885—82no—
103#10621883—82no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106Dic43⋊C4—41no—
107Dic43⋊C4—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—22no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43#12011yescharacteristic
122C23×C43#13511yescharacteristic
123C23×C43#13711yescharacteristic
124Q8×C43—42no—
125Q8×C43—81no—
126D4×C43—42no—
127D4×C43—81no—
128D4×C43—82no—
129D4×C43—82no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
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—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—84no—
151C2×C4×C43—81no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159Dic86—81no—
160Dic86—81no—
161C43⋊C8—81no—
162C43⋊C8—81no—
163#12263—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—42no—
171C22×C43—42no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—42no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43#45211yescharacteristic
181C22×C43#45511yescharacteristic
182C22×C43B(4,𝔽2)11yescharacteristic
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—81no—
186C4×C43—81no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43—81no—
190Dic43—81no—
191Dic43—81no—
192Dic43—161no—
193#2760D4311yescharacteristic
194#2030—431no—
195#1602—431no—
196#1596—431no—
197#1351—431no—
198#1343—431no—
199#1317—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43—41no—
203C2×C43—41no—
204C2×C43—82no—
205C2×C43#160611yescharacteristic
206C2×C43#219711yescharacteristic
207C2×C43#220011yescharacteristic
208#543—431no—
209#451—861no—
210#450—861no—
211#401—21no—
212#393—21no—
213#393C2×D4311yescharacteristic
214#392C2×D4311yescharacteristic
215#386—21no—
216#386—21no—
217#386—21no—
218#381—21no—
219#381—861no—
220#381C2×D4311yescharacteristic
221#342—431no—
222#342—861no—
223#328—861no—
224#328—861no—
225#323—431no—
226#323—431no—
227C43#1226311yescharacteristic, complemented, Sylow
228C22×Q8C22⋊D4311yescharacteristic
229C22×D4—21no—
230C22×D4C22⋊D4311yescharacteristic
231C23×C4—21no—
232C23×C4C22⋊D4311yescharacteristic
233C2×Q16—1721no—
234C2×SD16—1721no—
235C22⋊Q8—861no—
236C22⋊Q8—861no—
237C22⋊Q8—1721no—
238C22⋊Q8—1721no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4C22⋊D4311yescharacteristic
247C2×C22⋊C4C22×D4311yescharacteristic
248#103—1721no—
249#102—1721no—
250C22⋊C8—861no—
251C22⋊C8—861no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—1721no—
260#95—1721no—
261#95C22⋊D4311yescharacteristic
262#95C22⋊D4311yescharacteristic
263C24—21no—
264C24C2×C22⋊D4311yescharacteristic
265C2×Q8—41no—
266C2×Q8—81no—
267C2×Q8—861no—
268C2×Q8—861no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—81no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—81no—
286C22×C4—81no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—1721no—
290C22×C4C2×C22⋊D4311yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292Q16—3442no—
293SD16—3442no—
294C2×C8—1721no—
295C2×C8—1721no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C22⋊C4—1721no—
310C22⋊C4—1721no—
311C23—21no—
312C23—21no—
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23#1306329411yescharacteristic
323C23#1306334511yescharacteristic
324C23#1306335511yescharacteristic
325Q8—42no—
326Q8—81no—
327Q8—3441no—
328Q8—3441no—
329D4—42no—
330D4—81no—
331D4—82no—
332D4—82no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—84no—
354C2×C4—81no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—1721no—
361C2×C4—1721no—
362C8—3441no—
363C8—3441no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22#1458306111yescharacteristic
381C22#1458307711yescharacteristic
382C22#1458308611yescharacteristic
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—3441no—
391C4—3441no—
392C4—6881no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—82no—
398C2#1913357511yescharacteristic
399C2#1913658511yescharacteristic
400C2#1913660211yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2760C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#392C22
hypercenter#2760D43
hypocenterC43#12263
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2760

Complements

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

NH ≅ G/Ntype
1. #19135762C2semidirect
2. #19133551C2semidirect
4. #19132616C2semidirect
6. #19132525C2semidirect
227. C43#12263semidirect

Maximal subgroups

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

subgroupindex
#191357622
#191335512
#191335172
#191326162
#191325922
#191325252
C43×#27602
#1226343