Finite Group Databasebeta

← #24993127

Subgroups — #24993127

Order 11008.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145718C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic
3#19135439C211yesmaximal, characteristic, complemented
4#19133270C211yesmaximal, characteristic
5C2×#14582644C211yesmaximal, characteristic, complemented
6#19132491C211yesmaximal, characteristic, complemented
7C43×#1283C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9#14583449C2211yescharacteristic
10C2×#13063325C2211yescharacteristic
11#14583304—21no—
12#14583246—21no—
13#14583213C414yes—
14#14583180—22no—
15#14582978—21no—
16#14582972—22no—
17C8×D172—21no—
18#14582923C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063243—21no—
21C2×#13063243—21no—
22#14582867—21no—
23#14582644—21no—
24#14582644—21no—
25#14582644—21no—
26#14582642—21no—
27C43×#431C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C2×#10621898—21no—
31C22×Dic86—21no—
32#13063333—42no—
33#13063333—42no—
34C2×#10621877—21no—
35C2×#10621872—22no—
36C22×C43⋊C8—21no—
37C2×C8×D43—22no—
38#13063325—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325—21no—
42#13063325D411yescharacteristic
43#13063322D411yescharacteristic
44#13063313—21no—
45#13063299—21no—
46#13063299C2×C412yes—
47C4×D172—21no—
48C4×D172D412yes—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43C2×C412yes—
51#13063259—24no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)D411yescharacteristic
56C4⋊(C43⋊C8)D411yescharacteristic
57#13063247—24no—
58#13063243—42no—
59#13063243—42no—
60(C2×D43)⋊C8—22no—
61(C2×D43)⋊C8—22no—
62C2×M16×C43D411yescharacteristic
63C2×M16×C43D411yescharacteristic
64C22×C8×C43—21no—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C22⋊C8×C43C2×C412yes—
70#97×C43—21no—
71C4×C8×C43—21no—
72C4×C8×C43—21no—
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C2×C22⋊D43—22no—
77C22×Dic43—22no—
78#10621898—41no—
79#10621898—41no—
80#10621898—41no—
81#10621898—41no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172C22⋊C412yes—
85C2×C4×D43—22no—
86C2×Dic86—21no—
87C2×Dic86—41no—
88C2×Dic86—41no—
89C2×Dic86—41no—
90C2×Dic86—41no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93M16×C43—21no—
94M16×C43—21no—
95M16×C43—21no—
96M16×C43D812yes—
97C2×C8×C43—21no—
98C2×C8×C43—22no—
99C2×C8×C43—21no—
100C2×C8×C43—41no—
101C2×C8×C43—81no—
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108C4⋊Dic43—21no—
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43—41no—
112C4⋊Dic43—41no—
113C4⋊Dic43C22⋊C412yes—
114#10621877—41no—
115#10621877—41no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121#10621872—44no—
122C8×D43—44no—
123C23×C43C4×D411yescharacteristic
124C22×D43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C2×C4×C43C2×D811yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C22⋊D43—42no—
139C22⋊D43—42no—
140C2×Dic43—22no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144D172—42no—
145D172—41no—
146D172—41no—
147D172—41no—
148D172—41no—
149C4×D43—42no—
150C4×D43—42no—
151Dic86—41no—
152Dic86—41no—
153Dic86—81no—
154Dic86—81no—
155Dic86—81no—
156Dic86—81no—
157C8×C43—22no—
158C8×C43—42no—
159C8×C43—41no—
160C8×C43—81no—
161C43⋊C8—41no—
162C43⋊C8—41no—
163C43⋊C8—81no—
164#9271—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43#38611yescharacteristic
168C22×C43C4×D811yescharacteristic
169C22×C43#44211yescharacteristic
170C2×D43—42no—
171C2×D43—42no—
172C2×D43—42no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43#44711yescharacteristic
177C4×C43#44911yescharacteristic
178C4×C43#45911yescharacteristic
179C4×C43#46311yescharacteristic
180C4×C43#47111yescharacteristic
181C4×C43#47311yescharacteristic
182Dic43—42no—
183Dic43—82no—
184#3226—431no—
185#2935—431no—
186#1966—431no—
187#1547—431no—
188C2×#332—431no—
189#1301—431no—
190#1283D4311yescharacteristic, complemented
191C2×C43—21no—
192C2×C43—21no—
193C2×C43#187911yescharacteristic
194C2×C43#190811yescharacteristic
195C2×C43#191511yescharacteristic
196D43—82no—
197C2×#131—861no—
198#532—431no—
199C2×C4⋊Q8—431no—
200#500—861no—
201#486—861no—
202#480—434no—
203#474—862no—
204#436—861no—
205#435—862no—
206C8×D4—861no—
207#431C2×D4311yescharacteristic
208#423—431no—
209C2×C4⋊C8—431no—
210C2×C4⋊C8C2×D4311yescharacteristic
211C2×#101—861no—
212C2×#101—861no—
213#408—861no—
214C4×M16C2×D4311yescharacteristic
215#332—861no—
216#332—861no—
217#332—861no—
218#331—861no—
219C43#927111yescharacteristic, complemented, Sylow
220C2×#41—861no—
221C22×Q8—861no—
222#131—1722no—
223#131—1722no—
224C2×M16—862no—
225C2×M16—861no—
226C2×M16D17211yescharacteristic
227C2×M16D17211yescharacteristic
228C22×C8—21no—
229C22×C8—862no—
230C22×C8—861no—
231C4⋊Q8—431no—
232C4⋊Q8—861no—
233C4⋊Q8—861no—
234C4⋊Q8—861no—
235C4⋊Q8—861no—
236#127—431no—
237#124—861no—
238#121—432no—
239#121—861no—
240C4×D4—432no—
241C4×D4—861no—
242C2×C4⋊C4—432no—
243C2×C4⋊C4—861no—
244C2×C42C22×D4311yescharacteristic
245#107—864no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—431no—
250C4⋊C8—431no—
251C4⋊C8—861no—
252C4⋊C8—861no—
253C4⋊C8—861no—
254#102—864no—
255#101—1722no—
256#101—1722no—
257C22⋊C8—862no—
258C22⋊C8—862no—
259C22⋊C8C4×D4312yes—
260#97—21no—
261C4×C8—21no—
262C4×C8—21no—
263#41—1721no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267C2×Q8—861no—
268C2×Q8—1721no—
269C2×Q8—1721no—
270C2×Q8—1721no—
271C2×Q8—1721no—
272C2×Q8—1721no—
273C2×Q8—1721no—
274C2×D4—432no—
275C2×D4—862no—
276C2×D4—861no—
277C2×D4—861no—
278C22×C4—862no—
279C22×C4—862no—
280C22×C4C2×C4×D4311yescharacteristic
281C22×C4C2×D17211yescharacteristic
282C22×C4#1062189811yescharacteristic
283M16—21no—
284M16—21no—
285M16—21no—
286M16—1724no—
287M16—1721no—
288M16—1721no—
289M16D34412yes—
290C2×C8—21no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—81no—
295C2×C8—861no—
296C2×C8—861no—
297C2×C8—1724no—
298C2×C8—1721no—
299C2×C8—1721no—
300C2×C8—1721no—
301C4⋊C4—432no—
302C4⋊C4—861no—
303C4⋊C4—862no—
304C4⋊C4—862no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C22⋊C4—862no—
308C22⋊C4—862no—
309C42D4×D4311yescharacteristic
310C42D4×D4311yescharacteristic
311C42D4×D4311yescharacteristic
312C42#1062190211yescharacteristic
313C23—862no—
314C23C4×D17211yescharacteristic
315Q8—3441no—
316Q8—3441no—
317Q8—3441no—
318Q8—3441no—
319Q8—1721no—
320Q8—1721no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324D4—1721no—
325D4—1721no—
326D4—1721no—
327D4—1721no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—862no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4C22⋊C4×D4311yescharacteristic
338C2×C4#1306328711yescharacteristic
339C2×C4#1306329511yescharacteristic
340C2×C4#1306329811yescharacteristic
341C2×C4#1306330011yescharacteristic
342C2×C4#1306331011yescharacteristic
343C2×C4C2×D34411yescharacteristic
344C2×C4#1306334711yescharacteristic
345C2×C4#1306335311yescharacteristic
346C2×C4#1306335311yescharacteristic
347C8—22no—
348C8—42no—
349C8—41no—
350C8—81no—
351C8—3441no—
352C8—1721no—
353C8—1721no—
354C22—21no—
355C22—21no—
356C22—1722no—
357C22—1722no—
358C22—1722no—
359C22#1458277711yescharacteristic
360C22C4×D34411yescharacteristic
361C22#1458301211yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—3442no—
366C4—1722no—
367C4#1458303511yescharacteristic
368C4#1458304611yescharacteristic
369C4#1458309511yescharacteristic
370C4#1458311511yescharacteristic
371C4#1458316111yescharacteristic
372C4#1458317311yescharacteristic
373C2—21no—
374C2—21no—
375C2—3442no—
376C2#1913494211yescharacteristic
377C2#1913511111yescharacteristic
378C2#1913514611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1283C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1283D43
hypocenterC43#9271
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
3. #19135439C2semidirect
5. C2×#14582644C2semidirect
6. #19132491C2semidirect
7. C43×#1283C2semidirect
190. #1283D43semidirect
219. C43#9271semidirect

Maximal subgroups

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

subgroupindex
#191457182
#191433412
#191354392
#191332702
C2×#145826442
#191324912
C43×#12832
#927143