Finite Group Databasebeta

← #24997322

Subgroups — #24997322

Order 11008.

510 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 87 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#19145416C211yesmaximal, characteristic
2C2×#14583232C211yesmaximal, characteristic
3C2×#14583230C211yesmaximal, characteristic
4#19134673C211yesmaximal, characteristic
5#19132960C211yesmaximal, characteristic
6#19132483C211yesmaximal, characteristic
7C43×#1472C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10#14583232—22no—
11#14583232—22no—
12#14583230—22no—
13#14583230—22no—
14#14583229—21no—
15#14583227—21no—
16#14583155—22no—
17#14583055—21no—
18#14583054—21no—
19C2×#13063258—21no—
20C2×#13063257—21no—
21C2×#13063250—21no—
22C2×#13063249—21no—
23#14582863C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582667—22no—
26#14582624—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#324—22no—
31C22×Dic86D411yescharacteristic
32C23×Dic43—21no—
33C2×#10621885—22no—
34C2×#10621877D412yes—
35C22×C43⋊C8—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D412yes—
46C2×C4⋊Dic43D411yescharacteristic
47C2×Dic43⋊C4—21no—
48C2×C22⋊Dic43—21no—
49#13063258—24no—
50#13063257—24no—
51#13063256—22no—
52#13063250—24no—
53#13063249—22no—
54#13063249—24no—
55#13063248—22no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)D412yes—
60C22×Q8×C43D411yescharacteristic
61C23×C4×C43C2311yescharacteristic
62C2×M16×C43—21no—
63C22×C8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C22⋊Q8×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43D412yes—
75C24×C43#4111yescharacteristic
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—42no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—42no—
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—22no—
91C22×Dic43—41no—
92C22×Dic43—41no—
93C22×Dic43—82no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96C2×Dic86—42no—
97M16×C43—42no—
98C2×C8×C43—22no—
99C2×C8×C43—42no—
100C2×C8×C43—41no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
109#10621885—82no—
110C4⋊Dic43—21no—
111C4⋊Dic43—22no—
112C4⋊Dic43—22no—
113C4⋊Dic43—21no—
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118#10621877—42no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—42no—
122C23×C43—22no—
123C23×C43—22no—
124C23×C43—41no—
125C23×C43#12111yescharacteristic
126C23×C43#12111yescharacteristic
127C23×C43#12111yescharacteristic
128Q8×C43—42no—
129Q8×C43—42no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—81no—
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12011yescharacteristic
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12711yescharacteristic
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—82no—
149C2×Dic43—82no—
150C2×Dic43—81no—
151C2×Dic43—82no—
152Dic86—42no—
153Dic86—42no—
154C8×C43—42no—
155C8×C43—81no—
156C43⋊C8—42no—
157C43⋊C8—42no—
158#9995—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—44no—
167C22×C43#39211yescharacteristic
168C22×C43#47112yes—
169C22×C43#47312yes—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—81no—
174C4×C43—81no—
175C4×C43#45812yes—
176Dic43—82no—
177Dic43—81no—
178Dic43—81no—
179#3195—431no—
180C2×#484—431no—
181C2×#483—431no—
182#1821—431no—
183#1472—431no—
184#1472D4311yescharacteristic
185#1298—431no—
186C2×C43—22no—
187C2×C43—22no—
188C2×C43—41no—
189C2×C43#201911yescharacteristic
190C2×C43#202011yescharacteristic
191C2×C43#202211yescharacteristic
192C2×C22⋊Q8—431no—
193C2×C22⋊Q8C2×D4311yescharacteristic
194C22×C4⋊C4—431no—
195#484—862no—
196#484—862no—
197#483—862no—
198#483—861no—
199#483—861no—
200#483—862no—
201#470—862no—
202#451—861no—
203#451—861no—
204C2×#107—861no—
205C2×#106—861no—
206C2×#103—861no—
207C2×#103—861no—
208#407—431no—
209#407C2×D4311yescharacteristic
210C2×C22⋊C8—431no—
211C2×C22⋊C8C2×D4311yescharacteristic
212#343—862no—
213#324—22no—
214#324—862no—
215C43#999511yescharacteristic, complemented, Sylow
216C22×Q8—431no—
217C22×Q8D17211yescharacteristic
218C23×C4—861no—
219C23×C4C22×D4311yescharacteristic
220C2×Q16—862no—
221C2×M16—21no—
222C2×M16—432no—
223C22×C8—21no—
224C22×C8—861no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—861no—
230C22⋊Q8—861no—
231C22⋊Q8—861no—
232C22⋊Q8—861no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—432no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4D17211yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—861no—
245#107—864no—
246#106—862no—
247#106—864no—
248#103—862no—
249#103—864no—
250#103—864no—
251#103—862no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—432no—
256C22⋊C8—861no—
257C22⋊C8—861no—
258C22⋊C8—861no—
259C22⋊C8C22⋊D4312yes—
260C24#1062189811yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—42no—
264C2×Q8—861no—
265C2×Q8—861no—
266C2×Q8—1722no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—861no—
271C22×C4—862no—
272C22×C4—861no—
273C22×C4—3442no—
274C22×C4—1721no—
275C22×C4—1721no—
276C22×C4C2×D17211yescharacteristic
277C22×C4D4×D4311yescharacteristic
278C22×C4D4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281C22×C4C2×C22⋊D4311yescharacteristic
282Q16—3442no—
283M16—42no—
284M16—1722no—
285C2×C8—22no—
286C2×C8—42no—
287C2×C8—41no—
288C2×C8—862no—
289C2×C8—862no—
290C2×C8—1722no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—862no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—862no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C4⋊C4—1721no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23#1306329811yescharacteristic
311C23#1306329811yescharacteristic
312C23#1306329911yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—1722no—
316Q8—1722no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—3442no—
328C2×C4—3442no—
329C2×C4—3442no—
330C2×C4—3441no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4#1306329311yescharacteristic
336C2×C4#1306329511yescharacteristic
337C2×C4#1306329511yescharacteristic
338C2×C4#1306332111yescharacteristic
339C8—42no—
340C8—81no—
341C8—1722no—
342C8—1722no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1458280811yescharacteristic
352C22#1458316212yes—
353C22#1458317312yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—81no—
359C4—3442no—
360C4—3441no—
361C4—3441no—
362C4#1458309012yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1913571011yescharacteristic
367C2#1913571511yescharacteristic
368C2#1913572511yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1472C2
socleC22×C43#392
prime radicalC24×C43#41
hypercenter#1472D43
hypocenterC43#9995
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
215. C43#9995semidirect

Maximal subgroups

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

subgroupindex
#191454162
C2×#145832322
C2×#145832302
#191346732
#191329602
#191324832
C43×#14722
#999543