Finite Group Databasebeta

← #24993140

Subgroups — #24993140

Order 11008.

560 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145510C211yesmaximal, characteristic
2#19143339C211yesmaximal, characteristic, complemented
3#19135434C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132445C211yesmaximal, characteristic, complemented
7C43×#1547C211yesmaximal, characteristic, complemented
8C2×#13063332—21no—
9C2×#13063322C2211yescharacteristic
10#14583275—21no—
11#14583247—21no—
12#14583094—22no—
13#14583032C414yes—
14#14582977—21no—
15#14582971—22no—
16D4×C43⋊C8—21no—
17#14582952C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×#13063241—21no—
20C2×#13063241—21no—
21#14582866—21no—
22C4×#10621877C2211yescharacteristic
23#14582642—21no—
24#14582642—21no—
25C43×#532C2211yescharacteristic
26C43×#423C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C43×#332—21no—
29C43×#331—21no—
30C22×D172—21no—
31C22×D172—21no—
32C22×D172C2×C412yes—
33C2×#10621882—24no—
34#13063332—42no—
35#13063332—42no—
36C2×#10621877—22no—
37C2×#10621877D411yescharacteristic
38C2×#10621877D411yescharacteristic
39C22×C43⋊C8—22no—
40C22×C43⋊C8—21no—
41#13063322—21no—
42#13063322—21no—
43#13063322—21no—
44#13063322—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)D411yescharacteristic
48C4⋊(C43⋊C8)D411yescharacteristic
49#13063245—24no—
50#13063241—42no—
51#13063241—42no—
52C22⋊(C43⋊C8)—22no—
53C22⋊(C43⋊C8)—22no—
54C22⋊(C43⋊C8)C2×C412yes—
55#13063236—21no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8—21no—
58C2×#41×C43—21no—
59C2×M16×C43—21no—
60C22×C8×C43—21no—
61C4⋊Q8×C43D411yescharacteristic
62#127×C43D411yescharacteristic
63#124×C43—21no—
64#121×C43—21no—
65#121×C43C2×C412yes—
66C4×D4×C43—21no—
67C4×D4×C43D412yes—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C23×D43—22no—
74#41×C43—41no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78C2×Q8×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—22no—
82C2×D4×C43C22⋊C412yes—
83C22×C4×C43—22no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×D172—22no—
88C2×D172—22no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—81no—
98C2×D172—81no—
99C2×D172—82no—
100M16×C43—41no—
101M16×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43—81no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43C22⋊C412yes—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—22no—
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113#10621882—84no—
114#10621877—21no—
115#10621877—21no—
116#10621877—21no—
117#10621877—44no—
118#10621877D812yescomplemented
119C2×C43⋊C8—21no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—44no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C23×C43—22no—
128C23×C43C4×D411yescharacteristic
129C22×D43—42no—
130C22×D43—42no—
131C22×D43—42no—
132C22×D43—82no—
133C22×D43—82no—
134Q8×C43—41no—
135Q8×C43—41no—
136D4×C43—42no—
137D4×C43—42no—
138D4×C43—42no—
139D4×C43—41no—
140D4×C43—41no—
141D4×C43—41no—
142D4×C43—41no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159D172—44no—
160D172—82no—
161D172—82no—
162D172—81no—
163D172—81no—
164D172—81no—
165D172—81no—
166D172—81no—
167D172—81no—
168C8×C43—81no—
169C8×C43—81no—
170C43⋊C8—22no—
171C43⋊C8—42no—
172C43⋊C8—41no—
173C43⋊C8—41no—
174C43⋊C8—41no—
175#9273—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43#38611yescharacteristic
182C22×C43C4×D811yescharacteristic
183C22×C43#44211yescharacteristic
184C2×D43—82no—
185C2×D43—82no—
186C2×D43—82no—
187C2×D43—162no—
188C2×D43—162no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—42no—
193C4×C43#44711yescharacteristic
194C4×C43#44911yescharacteristic
195C4×C43#45911yescharacteristic
196C4×C43#46311yescharacteristic
197C4×C43#47111yescharacteristic
198C4×C43#47211yescharacteristic
199#3205—431no—
200#2935—431no—
201#1965—431no—
202#1547D4311yescharacteristic, complemented
203C2×#331—431no—
204#1301—431no—
205#1283—431no—
206C2×C43—21no—
207C2×C43—21no—
208C2×C43—82no—
209C2×C43#187911yescharacteristic
210C2×C43#190711yescharacteristic
211C2×C43#191411yescharacteristic
212D43—162no—
213C2×#131—861no—
214#532C2×D4311yescharacteristic
215C2×#127—431no—
216#493—861no—
217#486—861no—
218#459—862no—
219#447—434no—
220#436—861no—
221#435—862no—
222C8×D4—861no—
223#431—431no—
224#423C2×D4311yescharacteristic
225C2×C4⋊C8—431no—
226C2×C4⋊C8C2×D4311yescharacteristic
227C2×#100—861no—
228C2×#100—861no—
229#408—861no—
230C4×M16—431no—
231#332—21no—
232#331—21no—
233#331—861no—
234#331—861no—
235C43#927311yescharacteristic, complemented, Sylow
236C2×#41—21no—
237C22×D4—432no—
238C22×D4—861no—
239C22×D4—861no—
240C2×D8—864no—
241#131—1722no—
242#131—1722no—
243C2×M16—21no—
244C2×M16—431no—
245C2×M16—431no—
246C2×M16—862no—
247C22×C8—21no—
248C22×C8—862no—
249C22×C8—861no—
250C4⋊Q8C22⋊D4311yescharacteristic
251#127—861no—
252#127—861no—
253#127—861no—
254#127—861no—
255#127C22⋊D4311yescharacteristic
256#124—21no—
257#121—21no—
258#121C4×D4312yes—
259C4×D4—21no—
260C4×D4D17212yes—
261C2×C42C22×D4311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—431no—
267C4⋊C8—431no—
268C4⋊C8—861no—
269C4⋊C8—861no—
270#102—864no—
271#100—1722no—
272#100—1722no—
273C22⋊C8—432no—
274C22⋊C8—862no—
275C22⋊C8—862no—
276#97—861no—
277C4×C8—861no—
278C4×C8—861no—
279C24—862no—
280#41—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284C2×Q8—21no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—862no—
289C2×D4—862no—
290C2×D4—3441no—
291C2×D4—3441no—
292C2×D4—3442no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1721no—
298C2×D4—1721no—
299C2×D4—1721no—
300C2×D4—1721no—
301C2×D4(C2×D43)⋊C412yes—
302C22×C4—22no—
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305C22×C4#1062190011yescharacteristic
306D8—3444no—
307M16—41no—
308M16—41no—
309M16—432no—
310M16—861no—
311M16—861no—
312M16—861no—
313M16—1724no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—81no—
317C2×C8—861no—
318C2×C8—862no—
319C2×C8—861no—
320C2×C8—861no—
321C2×C8—861no—
322C2×C8—1724no—
323C2×C8—1721no—
324C2×C8—1721no—
325C4⋊C4—21no—
326C4⋊C4(C2×D43)⋊C412yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C42C2×D17211yescharacteristic
330C42D4×D4311yescharacteristic
331C42#1062190011yescharacteristic
332C42C2×C22⋊D4311yescharacteristic
333C23—22no—
334C23—3442no—
335C23—3442no—
336C23—1722no—
337C23—1722no—
338C23—1722no—
339C23(C22⋊D43)⋊C411yescharacteristic
340Q8—41no—
341Q8—41no—
342D4—42no—
343D4—42no—
344D4—42no—
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—3442no—
350D4—3442no—
351D4—3441no—
352D4—3441no—
353D4—3441no—
354D4—3441no—
355D4—3441no—
356D4—3441no—
357D4—1724no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4C2×(C2×D43)⋊C411yescharacteristic
365C2×C4(C22⋊D43)⋊C411yescharacteristic
366C2×C4#1306329511yescharacteristic
367C2×C4#1306329711yescharacteristic
368C2×C4#1306329711yescharacteristic
369C2×C4#1306330911yescharacteristic
370C2×C4D8×D4311yescharacteristic
371C2×C4#1306334611yescharacteristic
372C2×C4#1306334911yescharacteristic
373C2×C4#1306335211yescharacteristic
374C8—81no—
375C8—81no—
376C8—862no—
377C8—1722no—
378C8—1721no—
379C8—1721no—
380C8—1721no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—3442no—
387C22—3442no—
388C22—3442no—
389C22—6882no—
390C22—6882no—
391C22#1458277611yescharacteristic
392C22#1458297911yescharacteristic
393C22#1458300811yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4#1458303411yescharacteristic
399C4#1458304511yescharacteristic
400C4#1458309211yescharacteristic
401C4#1458311611yescharacteristic
402C4#1458316411yescharacteristic
403C4#1458316711yescharacteristic
404C2—21no—
405C2—21no—
406C2—82no—
407C2—6882no—
408C2#1913494111yescharacteristic
409C2#1913510111yescharacteristic
410C2#1913514011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1547C2
socleC22×C43#386
prime radical#19145510C2
cosocleC2×C42×C43C23
hypercenter#1547D43
hypocenterC43#9273
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #19143339C2semidirect
3. #19135434C2semidirect
4. C2×#14582642C2semidirect
5. #19132490C2semidirect
6. #19132445C2semidirect
7. C43×#1547C2semidirect
118. #10621877D8semidirect
202. #1547D43semidirect
235. C43#9273semidirect

Maximal subgroups

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

subgroupindex
#191455102
#191433392
#191354342
C2×#145826422
#191324902
#191324452
C43×#15472
#927343