Finite Group Databasebeta

← #24993125

Subgroups — #24993125

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#19145716C211yesmaximal, characteristic
2#19143338C211yesmaximal, characteristic
3#19135440C211yesmaximal, characteristic, complemented
4#19133270C211yesmaximal, characteristic
5#19132492C211yesmaximal, characteristic, complemented
6#19132445C211yesmaximal, characteristic, complemented
7C2×C43×#332C211yesmaximal, characteristic, complemented
8C2×#13063331—21no—
9#14583449C2211yescharacteristic
10#14583302—21no—
11#14583247—21no—
12#14583212C414yes—
13#14583176—22no—
14#14582976—21no—
15#14582969—22no—
16#14582964—21no—
17#14582952C2211yescharacteristic
18#14582923C2211yescharacteristic
19C2×#13063244—21no—
20C2×#13063244—21no—
21#14582865—21no—
22C4×#10621877C2211yescharacteristic
23#14582644—21no—
24#14582642—21no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C43×#332—21no—
29C43×#332—21no—
30C2×#10621898—21no—
31#13063331—42no—
32#13063331—42no—
33C2×#10621877—21no—
34C2×#10621877D411yescharacteristic
35C2×#10621877D411yescharacteristic
36C2×#10621872—22no—
37C2×C8×D43—22no—
38#13063325D411yescharacteristic
39#13063322D411yescharacteristic
40#13063313—21no—
41#13063299—21no—
42#13063299C2×C412yes—
43C4×D172—21no—
44C4×D172D412yes—
45#13063258—24no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49#13063245—24no—
50#13063244—42no—
51#13063244—42no—
52C22⋊(C43⋊C8)C2×C412yes—
53(C2×D43)⋊C8—22no—
54(C2×D43)⋊C8—22no—
55#13063236—21no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8—21no—
58C22×Q8×C43—21no—
59C22×C8×C43—21no—
60C22×C8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43C2×C412yes—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43D411yescharacteristic
72C4⋊C8×C43D411yescharacteristic
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C22×C4×C43—22no—
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C2×C22⋊D43—22no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87#10621898—41no—
88C2×D172—21no—
89C2×D172—21no—
90C2×D172C22⋊C412yes—
91C2×C4×D43—22no—
92C2×Dic86—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—81no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109C4⋊Dic43—21no—
110C4⋊Dic43C22⋊C412yes—
111#10621877—21no—
112#10621877—21no—
113#10621877—21no—
114#10621877—41no—
115#10621877—41no—
116#10621877D812yes—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—41no—
121#10621872—44no—
122C8×D43—44no—
123C23×C43C4×D411yescharacteristic
124C22×D43—22no—
125Q8×C43—81no—
126Q8×C43—81no—
127Q8×C43—81no—
128Q8×C43—81no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×C4×C43C2×D811yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C22⋊D43—42no—
146C22⋊D43—42no—
147C2×Dic43—22no—
148D172—42no—
149D172—41no—
150D172—41no—
151D172—41no—
152D172—41no—
153C4×D43—42no—
154C4×D43—42no—
155Dic86—41no—
156Dic86—41no—
157C8×C43—41no—
158C8×C43—41no—
159C8×C43—81no—
160C43⋊C8—22no—
161C43⋊C8—42no—
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—82no—
177C4×C43#44711yescharacteristic
178C4×C43#44911yescharacteristic
179C4×C43#45911yescharacteristic
180C4×C43#46311yescharacteristic
181C4×C43#47111yescharacteristic
182C4×C43#47311yescharacteristic
183Dic43—42no—
184#3226—431no—
185#2935—431no—
186#1966—431no—
187#1547—431no—
188C2×#332D4311yescharacteristic, complemented
189#1301—431no—
190#1283—431no—
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⋊Q8C2×D4311yescharacteristic
200#500—861no—
201#486—861no—
202#480—434no—
203#474—862no—
204#436—861no—
205#435—862no—
206C8×D4—861no—
207#431—431no—
208#423—431no—
209C2×C4⋊C8C2×D4311yescharacteristic
210C2×C4⋊C8C2×D4311yescharacteristic
211C2×#101—861no—
212C2×#101—861no—
213#408—861no—
214C4×M16—431no—
215#332—21no—
216#332—21no—
217#332—861no—
218#331—861no—
219C43#927111yescharacteristic, complemented, Sylow
220C2×#41—861no—
221C22×Q8—21no—
222#131—1722no—
223#131—1722no—
224C2×M16—431no—
225C2×M16—431no—
226C2×M16—862no—
227C2×M16—861no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—862no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—431no—
236#127—431no—
237#124—861no—
238#121—432no—
239#121—861no—
240C4×D4—432no—
241C4×D4—861no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C4×D4312yes—
244C2×C42C22×D4311yescharacteristic
245#107—864no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—861no—
250C4⋊C8—861no—
251C4⋊C8—861no—
252C4⋊C8C22⋊D4311yescharacteristic
253C4⋊C8C22⋊D4311yescharacteristic
254#102—864no—
255#101—1722no—
256#101—1722no—
257C22⋊C8—432no—
258C22⋊C8—862no—
259C22⋊C8—862no—
260#97—861no—
261C4×C8—861no—
262C4×C8—861no—
263#41—1721no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—861no—
274C2×D4—432no—
275C2×D4—862no—
276C2×D4—861no—
277C2×D4—861no—
278C22×C4—22no—
279C22×C4—862no—
280C22×C4C2×C4×D4311yescharacteristic
281C22×C4D4×D4311yescharacteristic
282C22×C4#1062190011yescharacteristic
283M16—432no—
284M16—861no—
285M16—861no—
286M16—861no—
287M16—1724no—
288M16—1721no—
289M16—1721no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—81no—
296C2×C8—861no—
297C2×C8—862no—
298C2×C8—861no—
299C2×C8—1724no—
300C2×C8—1721no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—432no—
306C4⋊C4—861no—
307C22⋊C4—862no—
308C22⋊C4—862no—
309C42#1062189811yescharacteristic
310C42D4×D4311yescharacteristic
311C42D4×D4311yescharacteristic
312C42C2×C22⋊D4311yescharacteristic
313C23—862no—
314C23(C22⋊D43)⋊C411yescharacteristic
315Q8—81no—
316Q8—81no—
317Q8—81no—
318Q8—81no—
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—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—862no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4C22⋊C4×D4311yescharacteristic
338C2×C4C4×C22⋊D4311yescharacteristic
339C2×C4#1306329311yescharacteristic
340C2×C4#1306329611yescharacteristic
341C2×C4#1306329811yescharacteristic
342C2×C4#1306330711yescharacteristic
343C2×C4D8×D4311yescharacteristic
344C2×C4#1306334611yescharacteristic
345C2×C4#1306334911yescharacteristic
346C2×C4#1306335211yescharacteristic
347C8—41no—
348C8—41no—
349C8—81no—
350C8—862no—
351C8—3441no—
352C8—1722no—
353C8—1721no—
354C22—21no—
355C22—21no—
356C22—1722no—
357C22—1722no—
358C22—1722no—
359C22#1458277511yescharacteristic
360C22#1458297911yescharacteristic
361C22#1458300811yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—1722no—
367C4#1458303111yescharacteristic
368C4#1458304311yescharacteristic
369C4#1458309311yescharacteristic
370C4#1458311311yescharacteristic
371C4#1458315911yescharacteristic
372C4#1458317111yescharacteristic
373C2—21no—
374C2—21no—
375C2—3442no—
376C2#1913494011yescharacteristic
377C2#1913511311yescharacteristic
378C2#1913514411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenterC2×#332D43
hypocenterC43#9271
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #19135440C2semidirect
5. #19132492C2semidirect
6. #19132445C2semidirect
7. C2×C43×#332C2semidirect
188. C2×#332D43semidirect
219. C43#9271semidirect

Maximal subgroups

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

subgroupindex
#191457162
#191433382
#191354402
#191332702
#191324922
#191324452
C2×C43×#3322
#927143