Finite Group Databasebeta

← #24997305

Subgroups — #24997305

Order 11008.

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

normal subgroups only

This group has 536 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#19145397C211yesmaximal, characteristic
2C2×#14583218C211yesmaximal, characteristic
3C2×#14583227C211yesmaximal, characteristic, complemented
4#19134673C211yesmaximal, characteristic, complemented
5#19132956C211yesmaximal, characteristic
6#19132483C211yesmaximal, characteristic, complemented
7C43×#1472C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10#14583232—21no—
11#14583227—22no—
12#14583227—22no—
13#14583218—22no—
14#14583218—22no—
15#14583212—21no—
16#14583147—22no—
17#14583049—21no—
18#14583038—21no—
19C2×#13063257—21no—
20C2×#13063256—21no—
21C2×#13063249—21no—
22C2×#13063247—21no—
23#14582863C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582667—22no—
26#14582622—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#324—22no—
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C23×Dic43—21no—
34C2×#10621884—22no—
35C2×#10621877D412yes—
36C22×C43⋊C8—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43D412yes—
47C2×C4⋊Dic43D411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49#13063258—22no—
50#13063257—24no—
51#13063256—24no—
52#13063249—24no—
53#13063249—22no—
54#13063247—24no—
55#13063245—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
76C23×D43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—42no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—42no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—41no—
90C2×C22⋊D43—41no—
91C2×C22⋊D43—82no—
92C22×Dic43—21no—
93C22×Dic43—22no—
94C22×Dic43—41no—
95C22×Dic43—41no—
96C22×Dic43—82no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—42no—
100M16×C43—42no—
101C2×C8×C43—22no—
102C2×C8×C43—42no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110#10621884—82no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—41no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—41no—
118C4⋊Dic43—41no—
119#10621877—42no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—42no—
123C23×C43—22no—
124C23×C43—22no—
125C23×C43—41no—
126C23×C43#12111yescharacteristic
127C23×C43#12111yescharacteristic
128C23×C43#12111yescharacteristic
129C22×D43—41no—
130C22×D43—42no—
131C22×D43—81no—
132C22×D43—81no—
133Q8×C43—42no—
134Q8×C43—42no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—81no—
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12711yescharacteristic
149C22⋊D43—82no—
150C22⋊D43—82no—
151C2×Dic43—42no—
152C2×Dic43—41no—
153C2×Dic43—82no—
154C2×Dic43—82no—
155C2×Dic43—82no—
156C2×Dic43—81no—
157D172—42no—
158D172—42no—
159C8×C43—42no—
160C8×C43—81no—
161C43⋊C8—42no—
162C43⋊C8—42no—
163#9993—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—44no—
172C22×C43#39211yescharacteristic
173C22×C43#47112yes—
174C22×C43#47112yes—
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—162no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43#45812yes—
185Dic43—82no—
186Dic43—81no—
187#3193—431no—
188C2×#481—431no—
189C2×#483—431no—
190#1821—431no—
191#1472D4311yescharacteristic, complemented
192#1471—431no—
193#1298—431no—
194C2×C43—22no—
195C2×C43—22no—
196C2×C43—41no—
197C2×C43#201911yescharacteristic
198C2×C43#201911yescharacteristic
199C2×C43#202211yescharacteristic
200D43—161no—
201C2×C22⋊Q8C2×D4311yescharacteristic
202C2×#121—431no—
203C22×C4⋊C4—431no—
204#484—861no—
205#483—862no—
206#483—862no—
207#481—862no—
208#481—862no—
209#480—861no—
210#468—862no—
211#450—861no—
212#448—861no—
213C2×#106—861no—
214C2×#106—861no—
215C2×#103—861no—
216C2×#102—861no—
217#407—431no—
218#407C2×D4311yescharacteristic
219C2×C22⋊C8—431no—
220C2×C22⋊C8C2×D4311yescharacteristic
221#343—862no—
222#324—22no—
223#323—862no—
224C43#999311yescharacteristic, complemented, Sylow
225C22×Q8D17211yescharacteristic
226C22×D4—431no—
227C22×D4—861no—
228C23×C4—861no—
229C23×C4C22×D4311yescharacteristic
230C2×SD16—862no—
231C2×M16—21no—
232C2×M16—432no—
233C22×C8—21no—
234C22×C8—861no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239#121—861no—
240#121—861no—
241#121—861no—
242#121—861no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—432no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4D17211yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—861no—
254#107—862no—
255#106—864no—
256#106—864no—
257#103—864no—
258#103—862no—
259#102—862no—
260#102—864no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—432no—
265C22⋊C8—861no—
266C22⋊C8—861no—
267C22⋊C8—861no—
268C22⋊C8C22⋊D4312yes—
269C24—861no—
270C24#1062189811yescharacteristic
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—3442no—
277C2×D4—1722no—
278C2×D4—1721no—
279C2×D4—1721no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—42no—
283C22×C4—861no—
284C22×C4—862no—
285C22×C4—3442no—
286C22×C4—1721no—
287C22×C4—1721no—
288C22×C4C2×D17211yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4D4×D4311yescharacteristic
293C22×C4C2×C22⋊D4311yescharacteristic
294SD16—3442no—
295M16—42no—
296M16—1722no—
297C2×C8—22no—
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—862no—
301C2×C8—862no—
302C2×C8—1722no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—862no—
308C4⋊C4—861no—
309C4⋊C4—862no—
310C4⋊C4—861no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23—3441no—
321C23—3441no—
322C23—1721no—
323C23—1722no—
324C23#1306329811yescharacteristic
325C23#1306329811yescharacteristic
326C23#1306329911yescharacteristic
327Q8—42no—
328Q8—42no—
329D4—3442no—
330D4—3442no—
331D4—1722no—
332D4—1722no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—3442no—
344C2×C4—3442no—
345C2×C4—3442no—
346C2×C4—3441no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4#1306329311yescharacteristic
350C2×C4#1306329511yescharacteristic
351C2×C4#1306329511yescharacteristic
352C2×C4#1306332111yescharacteristic
353C8—42no—
354C8—81no—
355C8—1722no—
356C8—1722no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—44no—
365C22—3441no—
366C22—3441no—
367C22—3441no—
368C22—6882no—
369C22#1458280811yescharacteristic
370C22#1458316212yes—
371C22#1458316512yes—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—81no—
376C4—81no—
377C4—3442no—
378C4—3441no—
379C4#1458309012yes—
380C2—22no—
381C2—22no—
382C2—41no—
383C2—6881no—
384C2#1913570811yescharacteristic
385C2#1913571011yescharacteristic
386C2#1913572511yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1472C2
socleC22×C43#392
prime radicalC2×#13063299C22
hypercenter#1472D43
hypocenterC43#9993
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
3. C2×#14583227C2semidirect
4. #19134673C2semidirect
6. #19132483C2semidirect
7. C43×#1472C2semidirect
191. #1472D43semidirect
224. C43#9993semidirect

Maximal subgroups

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

subgroupindex
#191453972
C2×#145832182
C2×#145832272
#191346732
#191329562
#191324832
C43×#14722
#999343