Finite Group Databasebeta

← #25152819

Subgroups — #25152819

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583447C211yesmaximal, characteristic
2C2×#14583268C211yesmaximal, characteristic, complemented
3C2×#14583263C211yesmaximal, characteristic, complemented
4#19142906C211yesmaximal, characteristic, complemented
5#19135835C214yesmaximal, complemented
6#19135414C211yesmaximal, characteristic, complemented
7#19134532C214yesmaximal, complemented
8#19134358C211yesmaximal, characteristic, complemented
9C43×#1961C211yesmaximal, characteristic, complemented
10C22×#10621900C2212yes—
11#14583447—24no—
12#14583447—24no—
13C2×#13063325C2211yescharacteristic
14C2×#13063317C2211yescharacteristic
15C2×#13063312C2212yes—
16C2×#13063296—22no—
17C2×D4×Dic43—22no—
18C2×C42×D43C2211yescharacteristic
19#14583268—24no—
20#14583263—24no—
21C2×#13063250C2214yes—
22C2×#13063248C2214yes—
23C2×#13063246C2214yes—
24C2×(C2×D43)⋊C8C2212yes—
25C2×#13063236C2211yescharacteristic
26#14582798C2212yes—
27#14582784—22no—
28#14582773—22no—
29#14582756C2212yes—
30#14582653C2212yes—
31C2×#127×C43C2211yescharacteristic
32C2×#102×C43C2214yes—
33C2×#97×C43C2211yescharacteristic
34C43×#382C2211yescharacteristic
35C2×#10621900—24no—
36C2×#10621900—28no—
37C2×#10621900—24no—
38C2×#10621900—44no—
39C22×Dic86C2312yes—
40C22×C22⋊D43—22no—
41C23×Dic43—22no—
42C22×C4×D43D412yes—
43C22×C4×D43C2311yescharacteristic
44C22×C43⋊C8C2312yes—
45#13063325—22no—
46#13063325D414yes—
47#13063317—22no—
48#13063317—22no—
49#13063312—24no—
50#13063312—24no—
51#13063296—216no—
52D4×Dic43—216no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43C2312yes—
56C2×Dic43⋊C4—22no—
57C2×C22⋊Dic43—24no—
58C2×(C2×D43)⋊C4—22no—
59C2×C4×Dic43D412yes—
60C2×C4×Dic43C2311yescharacteristic
61C42×D43—22no—
62C42×D43—22no—
63#13063250—28no—
64#13063248—44no—
65#13063246—28no—
66(C2×D43)⋊C8—24no—
67#13063236—22no—
68C43⋊#95—22no—
69C43⋊#95—22no—
70C22×D4×C43—22no—
71C22×D4×C43C2312yes—
72C22×C8×C43C2312yes—
73#127×C43—22no—
74#127×C43D414yes—
75C2×C4⋊C4×C43C2312yes—
76C2×C42×C43C2311yescharacteristic
77#102×C43—44no—
78#97×C43—22no—
79#95×C43—22no—
80C24×C43—22no—
81C23×D43C2×D411yescharacteristic
82C2×D4×C43—28no—
83C2×D4×C43—22no—
84C2×D4×C43—24no—
85C2×D4×C43—24no—
86C2×D4×C43—44no—
87C2×D4×C43—44no—
88C2×D4×C43C2×D414yes—
89C22×C4×C43—22no—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2411yescharacteristic
92C2×C22⋊D43—28no—
93C2×C22⋊D43—44no—
94C2×C22⋊D43—44no—
95C22×Dic43—28no—
96C22×Dic43—22no—
97C22×Dic43—22no—
98C22×Dic43—44no—
99C22×Dic43—44no—
100C22×Dic43C2×D412yes—
101C22×Dic43C2×D411yescharacteristic
102#10621900—416no—
103#10621900—416no—
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—22no—
107C2×C4×D43—24no—
108C2×C4×D43—42no—
109C2×C4×D43—42no—
110C2×C4×D43#4114yes—
111C2×Dic86—24no—
112C2×Dic86—24no—
113C2×Dic86—22no—
114C2×Dic86C2×D414yes—
115C2×C8×C43—22no—
116C2×C8×C43—22no—
117C2×C8×C43—22no—
118C4⋊C4×C43—24no—
119C42×C43C2×D412yes—
120C42×C43C2×D412yes—
121C22⋊Dic43—216no—
122(C2×D43)⋊C4—44no—
123C4⋊Dic43—28no—
124C4⋊Dic43—22no—
125C4⋊Dic43—22no—
126C4⋊Dic43—44no—
127Dic43⋊C4—44no—
128C4×Dic43—24no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—22no—
134C23×C43—24no—
135C23×C43—42no—
136C23×C43—42no—
137C23×C43—44no—
138C23×C43—44no—
139C23×C43C22×D411yescharacteristic
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—22no—
143C22×D43—22no—
144C22×D43#12412yes—
145D4×C43—28no—
146D4×C43—416no—
147D4×C43—44no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43#12014yes—
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C2×#4112yes—
157C2×C4×C43H(5,𝔽2)12yes—
158C22⋊D43—416no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—22no—
162C2×Dic43—24no—
163C2×Dic43—22no—
164C2×Dic43—22no—
165C2×Dic43—416no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43#12412yes—
172C4×D43—24no—
173C4×D43—24no—
174C4×D43—48no—
175Dic86—28no—
176Dic86—44no—
177C8×C43—42no—
178C43⋊C8—42no—
179#25862—431nomaximal, Sylow
180C22×C43—44no—
181C22×C43—48no—
182C22×C43—82no—
183C22×C43—82no—
184C22×C43—84no—
185C22×C43C2×#12011yescharacteristic
186C22×C43C2×#12411yescharacteristic
187C22×C43#53511yescharacteristic
188C22×C43#57512yes—
189C22×C43#57512yes—
190C2×D43—22no—
191C2×D43—22no—
192C2×D43—22no—
193C2×D43—42no—
194C2×D43—42no—
195C4×C43—24no—
196C4×C43—82no—
197C4×C43#54612yes—
198C4×C43#54612yes—
199Dic43—22no—
200Dic43—44no—
201Dic43—42no—
202Dic43—82no—
203C2×#532—431no—
204C2×#491—431no—
205C2×#490—431no—
206#2851—431no—
207#2042—434no—
208#1961D4311yescharacteristic, complemented
209#1960—431no—
210#1788—434no—
211#1749—431no—
212C2×C43—84no—
213C2×C43#243511yescharacteristic
214C2×C43#300512yes—
215C2×C43#313511yescharacteristic
216C2×C43#314211yescharacteristic
217C2×C43#321912yes—
218D43—42no—
219C22×#41—432no—
220#532—864no—
221#532—864no—
222C2×C4⋊Q8—431no—
223C2×#127C2×D4311yescharacteristic
224C2×#125—431no—
225C2×#124—432no—
226C2×#121—862no—
227C2×C4×D4—862no—
228C22×C42—431no—
229#491—864no—
230#490—864no—
231C2×#103—434no—
232C2×#103—434no—
233C2×#102—434no—
234C2×#102C2×D4314yes—
235C2×C22⋊C8—432no—
236C2×#97—431no—
237C2×#97C2×D4311yescharacteristic
238#389—432no—
239#387—862no—
240#385—862no—
241#382C2×D4311yescharacteristic
242#380—432no—
243#336—432no—
244C43#2586211yescharacteristic, complemented, Sylow
245C2×#41—868no—
246C2×#41—864no—
247C2×#41—864no—
248C2×#41—1724no—
249C22×Q8—432no—
250C22×D4—22no—
251C22×D4—862no—
252C22×D4C22×D4312yes—
253C23×C4—431no—
254C23×C4—432no—
255C23×C4—862no—
256C22×C8—432no—
257C22×C8C22×D4312yes—
258C4⋊Q8—434no—
259C4⋊Q8—862no—
260#127—22no—
261#127D17214yes—
262#125—862no—
263#125—862no—
264#124—864no—
265#124—864no—
266#121—8616no—
267C4×D4—8616no—
268C2×C4⋊C4—432no—
269C2×C4⋊C4—862no—
270C2×C4⋊C4—862no—
271C2×C4⋊C4—862no—
272C2×C4⋊C4C22×D4312yes—
273C2×C22⋊C4—864no—
274C2×C22⋊C4—862no—
275C2×C42—432no—
276C2×C42—431no—
277C2×C42—862no—
278C2×C42—862no—
279C2×C42C22×D4311yescharacteristic
280#103—868no—
281#103—1724no—
282#102—44no—
283#102—868no—
284C22⋊C8—864no—
285#97—22no—
286#97—862no—
287#95—22no—
288#95—862no—
289#95—862no—
290C24—22no—
291C24—431no—
292#41—17216no—
293#41—17216no—
294C2×Q8—434no—
295C2×Q8—862no—
296C2×Q8—864no—
297C2×Q8—864no—
298C2×D4—28no—
299C2×D4—22no—
300C2×D4—24no—
301C2×D4—24no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—868no—
305C2×D4—1724no—
306C2×D4—1724no—
307C2×D4C2×D17214yes—
308C22×C4—22no—
309C22×C4—431no—
310C22×C4—434no—
311C22×C4—432no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—862no—
315C22×C4—868no—
316C22×C4—862no—
317C22×C4—864no—
318C22×C4—862no—
319C22×C4—1722no—
320C22×C4—1722no—
321C22×C4—1724no—
322C22×C4—1724no—
323C22×C4D4×D4312yes—
324C22×C4C23×D4311yescharacteristic
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—862no—
329C2×C8—862no—
330C2×C8—862no—
331C4⋊C4—24no—
332C4⋊C4—868no—
333C4⋊C4—862no—
334C4⋊C4—862no—
335C4⋊C4—1724no—
336C4⋊C4—1724no—
337C22⋊C4—8616no—
338C22⋊C4—1724no—
339C42—864no—
340C42—861no—
341C42—861no—
342C42C2×D17212yes—
343C42D4×D4312yes—
344C23—24no—
345C23—42no—
346C23—44no—
347C23—44no—
348C23—42no—
349C23—432no—
350C23—861no—
351C23—862no—
352C23—862no—
353C23—861no—
354C23C2×D4×D4311yescharacteristic
355Q8—868no—
356Q8—1724no—
357D4—28no—
358D4—416no—
359D4—44no—
360D4—17216no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—432no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—864no—
370C2×C4—864no—
371C2×C4—862no—
372C2×C4—864no—
373C2×C4—862no—
374C2×C4—862no—
375C2×C4—1728no—
376C2×C4—17216no—
377C2×C4—1722no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4#1306329514yes—
383C2×C4C2×D4×D4311yescharacteristic
384C2×C4C22×D17211yescharacteristic
385C2×C4#41×D4312yes—
386C2×C4#1306337012yes—
387C8—42no—
388C8—1722no—
389C22—48no—
390C22—44no—
391C22—82no—
392C22—84no—
393C22—82no—
394C22—862no—
395C22—862no—
396C22—862no—
397C22—1722no—
398C22—1722no—
399C22C2×#1306329511yescharacteristic
400C22#124×D4311yescharacteristic
401C22#1458346211yescharacteristic
402C22#1458369512yes—
403C22#1458369512yes—
404C4—24no—
405C4—82no—
406C4—862no—
407C4—3442no—
408C4—1722no—
409C4—1724no—
410C4#1458354412yes—
411C4#1458354612yes—
412C2—84no—
413C2—1722no—
414C2#1913824511yescharacteristic
415C2#1914383912yes—
416C2#1914493911yescharacteristic
417C2#1914499411yescharacteristic
418C2#1914562712yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1961C2
socleC23×C43C22×D4
prime radicalC2×#14583447C2
hypercenter#1961D43
hypocenterC43#25862
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. C2×#14583268C2semidirect
3. C2×#14583263C2semidirect
4. #19142906C2semidirect
5. #19135835C2semidirect
6. #19135414C2semidirect
7. #19134532C2semidirect
8. #19134358C2semidirect
9. C43×#1961C2semidirect
208. #1961D43semidirect
244. C43#25862semidirect

Maximal subgroups

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

subgroupindex
C2×#145834472
C2×#145832682
C2×#145832632
#191429062
#191358352
#191354142
#191345322
#191343582
C43×#19612
#2586243