Finite Group Databasebeta

← #24997418

Subgroups — #24997418

Order 11008.

528 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 85 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#19145801C211yesmaximal, characteristic, complemented
2#19144694C211yesmaximal, characteristic
3#19135538C211yesmaximal, characteristic, complemented
4#19133197C211yesmaximal, characteristic, complemented
5#19133038C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic, complemented
7C43×#2562C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583309—21no—
10#14583269—21no—
11#14583234—21no—
12#14583234—21no—
13#14583229—21no—
14#14583203—22no—
15#14583179—21no—
16#14583104—21no—
17#14583050—21no—
18#14582999—22no—
19#14582956C2211yescharacteristic
20#14582956C2211yescharacteristic
21C4×#10621877C2211yescharacteristic
22#14582659—22no—
23#14582641—22no—
24D4⋊(C43⋊C8)—22no—
25C2×#125×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C43×#400—21no—
28C43×#394—21no—
29C43×#388—22no—
30C43×#380—21no—
31C43×#380—21no—
32C4×C4⋊C4×C43C2211yescharacteristic
33C2×#10621883—22no—
34C2×#10621877—21no—
35#13063325D411yescharacteristic
36#13063325D411yescharacteristic
37#13063317—21no—
38#13063304—21no—
39#13063304—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42#13063284—21no—
43#13063258—22no—
44#13063258—22no—
45#13063256—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)D412yes—
48#13063248—22no—
49#13063248—22no—
50#13063248—22no—
51#13063246—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55#13063236—21no—
56#13063236D412yes—
57C4×C43⋊C8—21no—
58C22×D4×C43D411yescharacteristic
59C23×C4×C43—21no—
60#125×C43—21no—
61#125×C43—21no—
62#125×C43—21no—
63#125×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—22no—
77C2×C42×C43D412yes—
78C2×C42×C43C2311yescharacteristic
79#95×C43—22no—
80#95×C43—22no—
81#95×C43—21no—
82C24×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—42no—
86C22×C4×C43—21no—
87C22×C4×C43—22no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—42no—
91C22×C4×C43—42no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C2×Dic86—21no—
98C2×Dic86—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—42no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C22⋊C4×C43—44no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—82no—
114C42×C43—42no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119C22⋊Dic43—41no—
120#10621883—44no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127C4×Dic43—41no—
128#10621877—22no—
129#10621877—41no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—41no—
133C23×C43—22no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43#12011yescharacteristic
141D4×C43—22no—
142D4×C43—22no—
143D4×C43—41no—
144D4×C43—41no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—22no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—82no—
161C2×C4×C43—82no—
162C2×C4×C43#12011yescharacteristic
163C2×C4×C43#12011yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#12711yescharacteristic
168C2×Dic43—41no—
169C2×Dic43—41no—
170Dic86—42no—
171Dic86—42no—
172C43⋊C8—42no—
173C43⋊C8—42no—
174C43⋊C8—42no—
175#10009—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43#39211yescharacteristic
186C22×C43#45511yescharacteristic
187C22×C43#45611yescharacteristic
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—82no—
194C4×C43—81no—
195C4×C43—81no—
196C4×C43—81no—
197C4×C43#45412yes—
198Dic43—81no—
199Dic43—81no—
200#3236—431no—
201#3110—431no—
202#2562D4311yescharacteristic
203#1986—431no—
204#1528—431no—
205#1490—431no—
206#1285—431no—
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—82no—
210C2×C43#200311yescharacteristic
211C2×C43#200711yescharacteristic
212C2×C43#201011yescharacteristic
213#533—431no—
214C2×#125C2×D4311yescharacteristic
215C2×C4×D4C2×D4311yescharacteristic
216#501—861no—
217#491—861no—
218#484—861no—
219#484—861no—
220#483—861no—
221#479—862no—
222#474—861no—
223#461—861no—
224#450—861no—
225#440—862no—
226#432—431no—
227#432—431no—
228C4×M16—431no—
229#400—21no—
230#394—21no—
231#388—22no—
232#380—21no—
233#380—21no—
234C4×C4⋊C4C2×D4311yescharacteristic
235#339—862no—
236#330—862no—
237D4⋊C8—862no—
238C43#1000911yescharacteristic, complemented, Sylow
239C22×D4C22⋊D4311yescharacteristic
240C23×C4—21no—
241C2×SD16—862no—
242C2×M16—861no—
243C4⋊Q8—431no—
244C4⋊Q8—431no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—861no—
250C22⋊Q8—861no—
251C22⋊Q8—861no—
252C4×Q8—861no—
253C4×Q8—861no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258#117—861no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C22⋊D4311yescharacteristic
263C2×C4⋊C4C22⋊D4311yescharacteristic
264C2×C4⋊C4C22⋊D4311yescharacteristic
265C2×C22⋊C4—22no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—22no—
268C2×C42C22⋊D4312yes—
269C2×C42C22×D4311yescharacteristic
270#107—862no—
271#107—862no—
272#106—862no—
273C4⋊C8—432no—
274C4⋊C8—861no—
275#103—862no—
276#103—862no—
277#103—862no—
278#102—862no—
279C22⋊C8—861no—
280C22⋊C8—861no—
281#97—432no—
282#97—861no—
283#97—861no—
284C4×C8—861no—
285#95—22no—
286#95—22no—
287#95—21no—
288C24—21no—
289C2×Q8—861no—
290C2×Q8—861no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—42no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×C22⋊D4311yescharacteristic
303C22×C4C2×C22⋊D4311yescharacteristic
304C22×C4C2×C22⋊D4311yescharacteristic
305SD16—1724no—
306M16—862no—
307M16—1721no—
308C2×C8—862no—
309C2×C8—862no—
310C2×C8—1721no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—1721no—
327C4⋊C4—1721no—
328C22⋊C4—44no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—82no—
332C22⋊C4—1721no—
333C42—42no—
334C42—1721no—
335C42D4×D4311yescharacteristic
336C42D4×D4311yescharacteristic
337C42D4×D4311yescharacteristic
338C42#1062190011yescharacteristic
339C23—22no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23#1306329411yescharacteristic
347Q8—1722no—
348Q8—1722no—
349D4—22no—
350D4—22no—
351D4—41no—
352D4—41no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4#1306329311yescharacteristic
373C2×C4#1306329311yescharacteristic
374C2×C4#1306329611yescharacteristic
375C2×C4#1306329711yescharacteristic
376C2×C4#1306329711yescharacteristic
377C2×C4#1306332111yescharacteristic
378C8—1722no—
379C8—1722no—
380C8—1722no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22#1458280711yescharacteristic
391C22#1458307711yescharacteristic
392C22#1458308211yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—3441no—
403C4—3441no—
404C4#1458307112yes—
405C2—21no—
406C2—21no—
407C2—82no—
408C2#1913561711yescharacteristic
409C2#1913564211yescharacteristic
410C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2562C2
socleC22×C43#392
prime radicalC22×D4×C43D4
hypercenter#2562D43
hypocenterC43#10009
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2562

Complements

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

NH ≅ G/Ntype
1. #19145801C2semidirect
3. #19135538C2semidirect
4. #19133197C2semidirect
6. #19132451C2semidirect
238. C43#10009semidirect

Maximal subgroups

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

subgroupindex
#191458012
#191446942
#191355382
#191331972
#191330382
#191324512
C43×#25622
#1000943