Finite Group Databasebeta

← #24993115

Subgroups — #24993115

Order 11008.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145725C211yesmaximal, characteristic
2#19143338C211yesmaximal, characteristic
3#19135583C211yesmaximal, characteristic, complemented
4#19133273C211yesmaximal, characteristic
5C2×#14582644C211yesmaximal, characteristic, complemented
6#19132444C211yesmaximal, characteristic, complemented
7C43×#1301C211yesmaximal, characteristic, complemented
8C2×#13063331—21no—
9#14583449C2211yescharacteristic
10C2×#13063325C2211yescharacteristic
11#14583297—21no—
12#14583246—21no—
13#14583218C414yes—
14#14583190—22no—
15#14582976—21no—
16#14582969—22no—
17#14582964—21no—
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19#14582865—21no—
20C4×#10621877C2211yescharacteristic
21#14582667—21no—
22#14582667—21no—
23#14582646—21no—
24#14582644—21no—
25#14582644—21no—
26#14582642—21no—
27C43×#431C2211yescharacteristic
28C43×#423C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#10621898—21no—
31C22×Dic86—21no—
32#13063331—42no—
33#13063331—42no—
34C2×#10621877D411yescharacteristic
35C2×#10621877D411yescharacteristic
36C2×#10621872—22no—
37C22×C43⋊C8—21no—
38C2×C8×D43—22no—
39#13063325—21no—
40#13063325—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325D411yescharacteristic
44#13063322D411yescharacteristic
45#13063313—21no—
46#13063299—21no—
47#13063299C2×C412yes—
48C4×D172—21no—
49C4×D172D412yes—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43C2×C412yes—
52#13063257—24no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55#13063247—24no—
56(C2×D43)⋊C8—22no—
57(C2×D43)⋊C8—22no—
58#13063236—21no—
59C4×C43⋊C8—21no—
60C2×M16×C43—21no—
61C22×C8×C43—21no—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43D411yescharacteristic
68C4⋊C8×C43D411yescharacteristic
69C22⋊C8×C43C2×C412yes—
70C4×C8×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43#4111yescharacteristic
74C2×C22⋊D43—22no—
75C22×Dic43—22no—
76#10621898—41no—
77#10621898—41no—
78#10621898—41no—
79#10621898—41no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172C22⋊C412yes—
83C2×C4×D43—22no—
84C2×Dic86—21no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×Dic86—81no—
88C2×Dic86—81no—
89M16×C43—41no—
90M16×C43—41no—
91C2×C8×C43—22no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101(C2×D43)⋊C4—22no—
102(C2×D43)⋊C4—22no—
103C4⋊Dic43—21no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43C22⋊C412yes—
109#10621877—21no—
110#10621877—21no—
111#10621877—21no—
112#10621877SD1612yes—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—81no—
117#10621872—44no—
118C8×D43—44no—
119C23×C43C4×D411yescharacteristic
120C22×D43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43C4×D411yescharacteristic
126C2×C4×C43#12011yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12311yescharacteristic
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C22⋊D43—42no—
135C22⋊D43—42no—
136C2×Dic43—22no—
137C2×Dic43—42no—
138C2×Dic43—82no—
139D172—42no—
140D172—41no—
141D172—41no—
142D172—41no—
143D172—41no—
144C4×D43—42no—
145C4×D43—42no—
146Dic86—41no—
147Dic86—41no—
148Dic86—82no—
149Dic86—81no—
150Dic86—81no—
151C8×C43—42no—
152C8×C43—41no—
153C8×C43—41no—
154C8×C43—81no—
155C43⋊C8—22no—
156C43⋊C8—41no—
157C43⋊C8—81no—
158#9269—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43#38611yescharacteristic
162C22×C43C4×SD1611yescharacteristic
163C22×C43#44011yescharacteristic
164C2×D43—42no—
165C2×D43—42no—
166C2×D43—42no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43#45011yescharacteristic
171C4×C43#45211yescharacteristic
172C4×C43#46111yescharacteristic
173C4×C43#46311yescharacteristic
174C4×C43#47111yescharacteristic
175C4×C43#47211yescharacteristic
176Dic43—42no—
177Dic43—82no—
178#3227—431no—
179#2935—431no—
180#1997—431no—
181#1547—431no—
182C2×#332—431no—
183#1301D4311yescharacteristic, complemented
184#1283—431no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43#187711yescharacteristic
188C2×C43#190711yescharacteristic
189C2×C43#191511yescharacteristic
190D43—82no—
191C2×#131—861no—
192#532—431no—
193C2×C4⋊Q8—431no—
194#498—861no—
195#486—861no—
196#481—434no—
197#476—862no—
198#436—861no—
199#435—862no—
200C8×D4—861no—
201#431C2×D4311yescharacteristic
202#423C2×D4311yescharacteristic
203C2×C4⋊C8—431no—
204C2×C4⋊C8C2×D4311yescharacteristic
205#408—861no—
206C4×M16—431no—
207#343—861no—
208#343—861no—
209#332—861no—
210#332—861no—
211#332—861no—
212#331—861no—
213C43#926911yescharacteristic, complemented, Sylow
214C2×#41—861no—
215C22×Q8—861no—
216#131—1722no—
217#131—1722no—
218C2×M16—21no—
219C2×M16—431no—
220C2×M16—431no—
221C2×M16—862no—
222C22×C8—21no—
223C22×C8—862no—
224C22×C8—861no—
225C4⋊Q8—431no—
226C4⋊Q8—861no—
227C4⋊Q8—861no—
228C4⋊Q8—861no—
229C4⋊Q8—861no—
230#127—431no—
231#124—861no—
232#121—432no—
233#121—861no—
234C4×D4—432no—
235C4×D4—861no—
236C2×C4⋊C4—432no—
237C2×C4⋊C4—861no—
238C2×C42C22×D4311yescharacteristic
239#106—864no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246C4⋊C8D17211yescharacteristic
247C4⋊C8D17211yescharacteristic
248#102—864no—
249C22⋊C8—862no—
250C22⋊C8—862no—
251C22⋊C8C4×D4312yes—
252#97—861no—
253C4×C8—21no—
254C4×C8—861no—
255#41—1721no—
256#41—1721no—
257#41—1721no—
258#41—1721no—
259C2×Q8—861no—
260C2×Q8—3441no—
261C2×Q8—3441no—
262C2×Q8—1721no—
263C2×Q8—1721no—
264C2×D4—432no—
265C2×D4—862no—
266C2×D4—861no—
267C2×D4—861no—
268C22×C4—862no—
269C22×C4—862no—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4#1062190211yescharacteristic
273M16—41no—
274M16—41no—
275M16—432no—
276M16—861no—
277M16—861no—
278M16—861no—
279M16—1724no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—861no—
287C2×C8—861no—
288C2×C8—3441no—
289C2×C8—1724no—
290C2×C8—1721no—
291C4⋊C4—432no—
292C4⋊C4—861no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C22⋊C4—862no—
298C22⋊C4—862no—
299C42C2×D17211yescharacteristic
300C42#1062189811yescharacteristic
301C42D4×D4311yescharacteristic
302C42D4×D4311yescharacteristic
303C23—862no—
304C23#1306328711yescharacteristic
305Q8—3442no—
306Q8—3441no—
307Q8—3441no—
308Q8—1721no—
309Q8—1721no—
310D4—1722no—
311D4—1722no—
312D4—1722no—
313D4—1721no—
314D4—1721no—
315D4—1721no—
316D4—1721no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—862no—
321C2×C4—3442no—
322C2×C4—1722no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4C22⋊C4×D4311yescharacteristic
326C2×C4C4×D17211yescharacteristic
327C2×C4#1306329511yescharacteristic
328C2×C4#1306329811yescharacteristic
329C2×C4#1306330011yescharacteristic
330C2×C4#1306331011yescharacteristic
331C2×C4SD16×D4311yescharacteristic
332C2×C4#1306334611yescharacteristic
333C2×C4#1306334911yescharacteristic
334C2×C4#1306335711yescharacteristic
335C8—42no—
336C8—41no—
337C8—41no—
338C8—81no—
339C8—862no—
340C8—3441no—
341C8—1721no—
342C22—21no—
343C22—21no—
344C22—1722no—
345C22—1722no—
346C22—1722no—
347C22#1458277711yescharacteristic
348C22#1458298611yescharacteristic
349C22#1458299811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—3442no—
354C4—1722no—
355C4#1458305111yescharacteristic
356C4#1458306411yescharacteristic
357C4#1458310311yescharacteristic
358C4#1458311311yescharacteristic
359C4#1458316311yescharacteristic
360C4#1458317011yescharacteristic
361C2—21no—
362C2—21no—
363C2—3442no—
364C2#1913493011yescharacteristic
365C2#1913510211yescharacteristic
366C2#1913514611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1301C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1301D43
hypocenterC43#9269
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #19135583C2semidirect
5. C2×#14582644C2semidirect
6. #19132444C2semidirect
7. C43×#1301C2semidirect
183. #1301D43semidirect
213. C43#9269semidirect

Maximal subgroups

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

subgroupindex
#191457252
#191433382
#191355832
#191332732
C2×#145826442
#191324442
C43×#13012
#926943