Finite Group Databasebeta

← #25008671

Subgroups — #25008671

Order 11008.

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

normal subgroups only

This group has 476 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#19135641C211yesmaximal, characteristic, complemented
2#19133597C211yesmaximal, characteristic, complemented
3#19133529C211yesmaximal, characteristic
4#19132601C211yesmaximal, characteristic, complemented
5#19132598C211yesmaximal, characteristic, complemented
6#19132529C211yesmaximal, characteristic, complemented
7C43×#2728C211yesmaximal, characteristic, complemented
8C2×#13063356—21no—
9#14583480C2211yescharacteristic
10#14583212—21no—
11#14583033—21no—
12C2×#13063253—21no—
13#14582668C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C2×C22⋊Q8×C43—21no—
19C43×#400—21no—
20C43×#398C2211yescharacteristic
21C43×#397—21no—
22C43×#394C2211yescharacteristic
23C43×#391C2211yescharacteristic
24C43×#388—21no—
25C43×#386—21no—
26C43×#385—21no—
27C2×#10621898—21no—
28#13063356—42no—
29#13063356—42no—
30C2×#10621885—41no—
31C2×#10621884—41no—
32C2×#10621882—41no—
33C2×#10621877—21no—
34#13063305—41no—
35#13063300—41no—
36#13063299—21no—
37#13063299—21no—
38#13063258—41no—
39#13063253—42no—
40#13063246—41no—
41#13063245—41no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C22×Q8×C43D411yescharacteristic
45C22×D4×C43D411yescharacteristic
46C23×C4×C43—21no—
47C22⋊Q8×C43—42no—
48C22⋊Q8×C43—42no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43C2311yescharacteristic
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43D411yescharacteristic
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43—21no—
64#95×C43—21no—
65#95×C43D411yescharacteristic
66#95×C43D411yescharacteristic
67C24×C43—21no—
68C2×Q8×C43—21no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43D812yescomplemented
72C2×D4×C43—42no—
73C2×D4×C43—41no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—42no—
80C22×C4×C43—81no—
81C22×C4×C43—81no—
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C2×C22⋊D43—41no—
86#10621898—41no—
87#10621898—41no—
88#10621898—41no—
89#10621898—41no—
90C2×D172—21no—
91C2×D172—21no—
92C2×D172—21no—
93C2×C4×D43—41no—
94C2×Dic86—21no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—42no—
98C4⋊C4×C43—42no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C22⋊C4×C43—42no—
102C22⋊C4×C43—42no—
103C22⋊C4×C43—42no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—81no—
107C42×C43—41no—
108#10621885—44no—
109#10621884—44no—
110#10621882—82no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—41no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115#10621877—22no—
116#10621877—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C23×C43—22no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43#12011yescharacteristic
128C22×D43—41no—
129Q8×C43—42no—
130Q8×C43—81no—
131D4×C43—42no—
132D4×C43—81no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—22no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
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—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—84no—
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C22⋊D43—81no—
158C22⋊D43—81no—
159C2×Dic43—41no—
160D172—41no—
161D172—41no—
162D172—81no—
163D172—81no—
164C4×D43—81no—
165C4×D43—81no—
166Dic86—41no—
167Dic86—41no—
168C43⋊C8—42no—
169C43⋊C8—81no—
170C43⋊C8—81no—
171#12098—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43#44711yescharacteristic
182C22×C43#45311yescharacteristic
183C22×C43B(4,𝔽2)11yescharacteristic
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—42no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—81no—
193C4×C43—81no—
194C4×C43—81no—
195C4×C43—81no—
196Dic43—81no—
197#2728D4311yescharacteristic, complemented
198#2007—431no—
199#1610—431no—
200#1598—431no—
201#1346—431no—
202#1345—431no—
203#1319—431no—
204C2×C43—21no—
205C2×C43—21no—
206C2×C43—82no—
207C2×C43#159511yescharacteristic
208C2×C43#219711yescharacteristic
209C2×C43#220311yescharacteristic
210D43—161no—
211C2×#137—861no—
212#537—431no—
213C2×C22⋊Q8—21no—
214#480—861no—
215#447—861no—
216C2×#104—861no—
217#400—21no—
218#398C2×D4311yescharacteristic
219#397—21no—
220#394C2×D4311yescharacteristic
221#391C2×D4311yescharacteristic
222#388—21no—
223#386—21no—
224#385—21no—
225#343—431no—
226#327—861no—
227#327—861no—
228#324—431no—
229#324—431no—
230C43#1209811yescharacteristic, complemented, Sylow
231C2×#41—861no—
232C22×Q8C22⋊D4311yescharacteristic
233C22×D4C22⋊D4311yescharacteristic
234C23×C4—21no—
235#137—1722no—
236#137—1722no—
237C2×Q16—1721no—
238C2×SD16—1721no—
239C2×D8—1721no—
240C2×M16—861no—
241C22⋊Q8—42no—
242C22⋊Q8—42no—
243C22⋊Q8—1721no—
244#121—861no—
245#121—861no—
246#121—1721no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C22⋊D4311yescharacteristic
251C2×C4⋊C4C22×D4311yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C42C22⋊D4311yescharacteristic
258#107—1721no—
259#104—1722no—
260#102—1721no—
261#102—1721no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95C22⋊D4311yescharacteristic
270#95C22⋊D4311yescharacteristic
271C24—21no—
272#41—1721no—
273#41—1721no—
274#41—1721no—
275#41—1721no—
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—861no—
280C2×Q8#1062188212yescomplemented
281C2×D4—41no—
282C2×D4—42no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—1721no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—81no—
294C22×C4—81no—
295C22×C4—1721no—
296C22×C4C2×C22⋊D4311yescharacteristic
297C22×C4C2×C22⋊D4311yescharacteristic
298C22×C4C2×C22⋊D4311yescharacteristic
299Q16—1724no—
300SD16—1724no—
301D8—3442no—
302M16—862no—
303M16—1721no—
304C2×C8—1721no—
305C2×C8—1721no—
306C2×C8—1721no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—81no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C42—41no—
324C23—22no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—1721no—
332C23#1306329411yescharacteristic
333Q8—42no—
334Q8—81no—
335Q8—1721no—
336Q8—1721no—
337D4—42no—
338D4—81no—
339D4—3441no—
340D4—3441no—
341D4—3441no—
342D4—3441no—
343D4—1721no—
344D4—1721no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—84no—
367C2×C4—3441no—
368C2×C4—3441no—
369C2×C4—1721no—
370C2×C4C2×#1062188211yescharacteristic
371C2×C4#1306335111yescharacteristic
372C8—3441no—
373C8—3441no—
374C8—1722no—
375C22—21no—
376C22—21no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—3441no—
385C22—3441no—
386C22—3441no—
387C22#1458303311yescharacteristic
388C22#1458306711yescharacteristic
389C22#1458308611yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—3441no—
400C2—21no—
401C2—21no—
402C2—82no—
403C2—6881no—
404C2#1913351311yescharacteristic
405C2#1913658511yescharacteristic
406C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2728C2
socleC22×C43B(4,𝔽2)
prime radical#19133529C2
hypercenter#2728D43
hypocenterC43#12098
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2728

Complements

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

NH ≅ G/Ntype
1. #19135641C2semidirect
2. #19133597C2semidirect
4. #19132601C2semidirect
5. #19132598C2semidirect
6. #19132529C2semidirect
7. C43×#2728C2semidirect
71. C2×Q8×C43D8semidirect
197. #2728D43semidirect
230. C43#12098semidirect
280. C2×Q8#10621882semidirect

Maximal subgroups

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

subgroupindex
#191356412
#191335972
#191335292
#191326012
#191325982
#191325292
C43×#27282
#1209843