Finite Group Databasebeta

← #25008822

Subgroups — #25008822

Order 11008.

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

normal subgroups only

This group has 440 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#19142852C211yesmaximal, characteristic, complemented
2#19133615C211yesmaximal, characteristic
3#19133547C211yesmaximal, characteristic
4#19132618C211yesmaximal, characteristic, complemented
5#19132615C211yesmaximal, characteristic, complemented
6#19132525C211yesmaximal, characteristic, complemented
7C43×#2022C211yesmaximal, characteristic
8#14583215—21no—
9#14583037—21no—
10#14582841—21no—
11#14582835C2211yescharacteristic
12#14582833—21no—
13#14582831—21no—
14#14582822—21no—
15#14582820—21no—
16#14582811C2211yescharacteristic
17#14582759—21no—
18#14582633—21no—
19#14582633—21no—
20#14582623C2211yescharacteristic
21#14582623C2211yescharacteristic
22C43×#534C2211yescharacteristic
23C2×#123×C43—21no—
24C2×#99×C43—21no—
25C43×#381C2211yescharacteristic
26C43×#342C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621883—41no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38#13063256—41no—
39#13063248—41no—
40#13063246—41no—
41C22⋊(C43⋊C8)—21no—
42C22⋊(C43⋊C8)—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C22×D4×C43—21no—
50C23×C4×C43D411yescharacteristic
51#123×C43—42no—
52#123×C43—41no—
53#123×C43—42no—
54#121×C43—21no—
55#121×C43—21no—
56#120×C43—41no—
57C2×C4⋊C4×C43—41no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—41no—
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43C2311yescharacteristic
62#99×C43—42no—
63#95×C43—21no—
64#95×C43—21no—
65C24×C43—21no—
66C24×C43C2×D411yescharacteristic
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
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—41no—
82C22×C4×C43SD1612yescomplemented
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C2×Dic86—41no—
90C2×Dic86—81no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—44no—
94C22⋊C4×C43—22no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—44no—
100C22⋊C4×C43—41no—
101C22⋊Dic43—81no—
102C22⋊Dic43—81no—
103#10621883—82no—
104C4⋊Dic43—41no—
105C4⋊Dic43—81no—
106C4⋊Dic43—81no—
107C4⋊Dic43—81no—
108Dic43⋊C4—81no—
109Dic43⋊C4—81no—
110Dic43⋊C4—81no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—81no—
121C23×C43—81no—
122C23×C43#12011yescharacteristic
123C23×C43C2×SD1611yescharacteristic
124C23×C43#13711yescharacteristic
125D4×C43—81no—
126D4×C43—81no—
127D4×C43—81no—
128D4×C43—81no—
129D4×C43—81no—
130D4×C43—81no—
131C2×C4×C43—22no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161Dic86—42no—
162Dic86—81no—
163C43⋊C8—81no—
164C43⋊C8—81no—
165#12125—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—81no—
175C22×C43—82no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—161no—
180C22×C43#44811yescharacteristic
181C22×C43#45311yescharacteristic
182C22×C43B(4,𝔽2)11yescharacteristic
183C4×C43—42no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—81no—
187C4×C43—82no—
188C4×C43—81no—
189Dic43—81no—
190Dic43—81no—
191Dic43—81no—
192Dic43—81no—
193#2841—431no—
194#2022D4311yescharacteristic
195#1613—431no—
196#1601—431no—
197#1352—431no—
198#1351—431no—
199#1317—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43—41no—
203C2×C43—41no—
204C2×C43—161no—
205C2×C43#159611yescharacteristic
206C2×C43#220011yescharacteristic
207C2×C43#220111yescharacteristic
208#534C2×D4311yescharacteristic
209C2×#123—21no—
210#481—861no—
211#448—861no—
212C2×#99—21no—
213#400—861no—
214#399—431no—
215#398—861no—
216#398—861no—
217#396—861no—
218#395—861no—
219#393—431no—
220#381C2×D4311yescharacteristic
221#380—861no—
222#342C2×D4311yescharacteristic
223#327—861no—
224#327—861no—
225#323—431no—
226#323—431no—
227C43#1212511yescharacteristic, complemented, Sylow
228C22×Q8—431no—
229C22×D4—21no—
230C23×C4C22⋊D4311yescharacteristic
231C2×SD16—1721no—
232#123—42no—
233#123—41no—
234#123—42no—
235#121—21no—
236#121—21no—
237#120—41no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—861no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—41no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4C22⋊D4311yescharacteristic
251C2×C22⋊C4C22×D4311yescharacteristic
252#106—1721no—
253#103—1721no—
254#102—1721no—
255#99—42no—
256C22⋊C8—861no—
257C22⋊C8—861no—
258#95—21no—
259#95—21no—
260#95—431no—
261#95—431no—
262#95—861no—
263#95—861no—
264#95—861no—
265#95—861no—
266C24—21no—
267C24C2×C22⋊D4311yescharacteristic
268C2×Q8—3441no—
269C2×Q8—1721no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4#1062188312yescomplemented
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292SD16—3442no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—44no—
298C4⋊C4—3441no—
299C4⋊C4—3441no—
300C4⋊C4—3441no—
301C4⋊C4—3441no—
302C4⋊C4—3441no—
303C4⋊C4—3441no—
304C4⋊C4—1721no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—44no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—3441no—
313C22⋊C4—3441no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—81no—
322C23—81no—
323C23#1306329311yescharacteristic
324C23C2×#1062188311yescharacteristic
325C23#1306335511yescharacteristic
326Q8—3441no—
327Q8—1722no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C8—3441no—
365C8—3441no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—82no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—161no—
380C22#1458303711yescharacteristic
381C22#1458306611yescharacteristic
382C22#1458308511yescharacteristic
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—3441no—
390C4—3441no—
391C4—3441no—
392C4—3441no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—161no—
398C2#1913351711yescharacteristic
399C2#1913659911yescharacteristic
400C2#1913660611yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2022C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#534C22
hypercenter#2022D43
hypocenterC43#12125
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #19142852C2semidirect
4. #19132618C2semidirect
5. #19132615C2semidirect
6. #19132525C2semidirect
82. C22×C4×C43SD16semidirect
227. C43#12125semidirect
289. C22×C4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191428522
#191336152
#191335472
#191326182
#191326152
#191325252
C43×#20222
#1212543