Finite Group Databasebeta

← #25251003

Subgroups — #25251003

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147729C211yesmaximal, characteristic
2C2×#14583340C211yesmaximal, characteristic, complemented
3#19143513C211yesmaximal, characteristic, complemented
4#19136673C214yesmaximal, complemented
5#19136661C214yesmaximal, complemented
6#19136361C211yesmaximal, characteristic, complemented
7#19136344C211yesmaximal, characteristic, complemented
8C2×#14582715C211yesmaximal, characteristic, complemented
9C43×#3156C211yesmaximal, characteristic, complemented
10C2×#13063347C2211yescharacteristic
11#14583665—21no—
12#14583340—22no—
13#14583340C2214yes—
14#14583340C2212yes—
15#14583339—21no—
16#14583335C2212yes—
17#14583334—21no—
18#14583329—22no—
19C2×#13063271—21no—
20C2×#13063268—21no—
21C2×#13063265C2211yescharacteristic
22C2×#13063265C2211yescharacteristic
23#14583022—22no—
24#14583017C2214yes—
25C2×#13063261C2211yescharacteristic
26#14582917—21no—
27#14582720C2214yescomplemented
28#14582715C2214yescomplemented
29#14582715C2212yescomplemented
30#14582712C2212yescomplemented
31C2×#137×C43—21no—
32C2×#135×C43C2211yescharacteristic
33C22×Q16×C43C2211yescharacteristic
34C43×#536—21no—
35C43×#497—22no—
36C43×#495C2212yescomplemented
37C43×#494C2212yescomplemented
38C43×#405C2211yescharacteristic
39C2×#10621898—21no—
40#13063347—21no—
41#13063347—21no—
42#13063347D412yes—
43#13063347C2312yes—
44C2×Dic172D411yescharacteristic
45C2×#10621873—21no—
46C2×D344D411yescharacteristic
47#13063333—42no—
48#13063331—24no—
49C2×#10621877—21no—
50M16×D43—42no—
51#13063271—24no—
52#13063271—22no—
53#13063269—22no—
54#13063268—24no—
55#13063268—22no—
56#13063266—22no—
57#13063265—21no—
58#13063265—21no—
59#13063265C2312yes—
60#13063265C2312yes—
61C2×C43⋊C16—21no—
62C2×C43⋊C16—21no—
63#13063261—21no—
64#13063261C2312yes—
65#13063253—24no—
66C2×#41×C43—21no—
67C22×Q8×C43—21no—
68#137×C43—42no—
69#137×C43—42no—
70#135×C43—21no—
71#135×C43—21no—
72#135×C43—21no—
73#135×C43—21no—
74C2×Q16×C43—21no—
75C2×Q16×C43—21no—
76C2×Q16×C43—21no—
77C2×Q16×C43—22no—
78C2×Q16×C43—21no—
79C2×Q16×C43—21no—
80C2×Q16×C43C2312yes—
81C2×Q16×C43C2311yescharacteristic
82C2×SD16×C43—21no—
83C2×SD16×C43—22no—
84C2×D8×C43C2311yescharacteristic
85C2×M16×C43D411yescharacteristic
86C22×C8×C43C2311yescharacteristic
87C4⋊Q8×C43—22no—
88#124×C43—22no—
89#123×C43—42no—
90C22⋊Q8×C43—42no—
91#117×C43D411yescharacteristic
92#97×C43D412yes—
93C4×C8×C43C2312yes—
94#41×C43—41no—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—41no—
98C2×Q8×C43—22no—
99C2×Q8×C43—21no—
100C2×Q8×C43—41no—
101C2×Q8×C43—41no—
102C2×Q8×C43—41no—
103C2×Q8×C43—41no—
104C2×Q8×C43—41no—
105C2×D4×C43—21no—
106C2×D4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43C2×D411yescharacteristic
110C2×C22⋊D43—41no—
111#10621898—22no—
112#10621898—22no—
113#10621898—41no—
114#10621898—41no—
115C2×D172—21no—
116C2×C4×D43—41no—
117C2×Dic86—21no—
118Q16×C43—22no—
119Q16×C43—21no—
120Q16×C43—22no—
121Q16×C43—21no—
122Q16×C43—41no—
123Q16×C43—41no—
124Q16×C43—44no—
125SD16×C43—41no—
126SD16×C43—41no—
127SD16×C43—44no—
128D8×C43—21no—
129D8×C43—21no—
130M16×C43D812yes—
131M16×C43D812yes—
132C2×C8×C43C2×D411yescharacteristic
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D412yes—
136C2×C8×C43#4111yescharacteristic
137C2×C8×C43#4111yescharacteristic
138C2×C8×C43C2411yescharacteristic
139C4⋊C4×C43—21no—
140C4⋊C4×C43—44no—
141C22⋊C4×C43—21no—
142C22⋊C4×C43—44no—
143C42×C43C2×D412yes—
144#10621877—22no—
145#10621877—41no—
146C2×C43⋊C8—41no—
147Dic172—21no—
148Dic172C2×D412yes—
149D344—21no—
150D344C2×D412yes—
151#10621873—22no—
152#10621873—22no—
153#10621872—44no—
154C8×D43—44no—
155C43⋊C16—22no—
156C43⋊C16—22no—
157C23×C43—41no—
158C23×C43AGL(1,ℤ/8)11yescharacteristic
159C22×D43—41no—
160Q8×C43—41no—
161Q8×C43—42no—
162Q8×C43—42no—
163Q8×C43—41no—
164Q8×C43—81no—
165Q8×C43—81no—
166D4×C43—41no—
167D4×C43—41no—
168D4×C43—81no—
169D4×C43—81no—
170C2×C4×C43—22no—
171C2×C4×C43—42no—
172C2×C4×C43—41no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43C2×D811yescharacteristic
180C2×C4×C43C2×D811yescharacteristic
181C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C22⋊D43—42no—
184C22⋊D43—42no—
185C2×Dic43—41no—
186D172—22no—
187D172—41no—
188C4×D43—42no—
189C4×D43—42no—
190Dic86—22no—
191Dic86—41no—
192C8×C43#12111yescharacteristic
193C8×C43#12111yescharacteristic
194C8×C43C2×D814yes—
195C8×C43C22×D411yescharacteristic
196C8×C43C2×#4111yescharacteristic
197C43⋊C8—42no—
198#33596—431nomaximal, Sylow
199C22×C43—41no—
200C22×C43—82no—
201C22×C43—81no—
202C22×C43#45911yescharacteristic
203C22×C43#45911yescharacteristic
204C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
205C2×D43—42no—
206C2×D43—161no—
207C4×C43—42no—
208C4×C43—81no—
209C4×C43—82no—
210C4×C43#45911yescharacteristic
211C4×C43#45911yescharacteristic
212C4×C43C2×#12111yescharacteristic
213C4×C43C22×D811yescharacteristic
214Dic43—42no—
215#3414—431no—
216C2×#510—431no—
217#3156D4311yescharacteristic, complemented
218#2957—431no—
219#2214—434no—
220#2212—434no—
221#2153—431no—
222#2148—431no—
223C2×#362—431no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—161no—
228C2×C43C2×#45911yescharacteristic
229D43—82no—
230C2×#137—21no—
231C2×#135—431no—
232C2×#135C2×D4311yescharacteristic
233C22×Q16C2×D4311yescharacteristic
234#568—861no—
235#536—21no—
236#510—434no—
237#510—432no—
238#510—862no—
239#510—861no—
240#509—432no—
241#509—861no—
242#508—862no—
243C2×Q32—861no—
244C2×SD32—861no—
245C2×M32—431no—
246C2×M32—431no—
247#497—22no—
248#495C2×D4312yescomplemented
249#494C2×D4312yescomplemented
250#444—862no—
251#443—434no—
252C2×#108—431no—
253#421—861no—
254#405C2×D4311yescharacteristic
255#364—434no—
256#362—434no—
257#362—432no—
258#361—432no—
259C43#3359611yescharacteristic, complemented, Sylow
260C2×#41—21no—
261C2×#41—861no—
262C22×Q8—21no—
263#137—42no—
264#137—42no—
265#135—21no—
266#135—21no—
267#135—21no—
268#135—21no—
269#135—432no—
270#135—432no—
271#135—861no—
272#135—861no—
273C2×Q16—21no—
274C2×Q16—21no—
275C2×Q16—21no—
276C2×Q16—21no—
277C2×Q16—21no—
278C2×Q16—22no—
279C2×Q16—431no—
280C2×Q16C22×D4312yes—
281C2×Q16C22×D4311yescharacteristic
282C2×SD16—21no—
283C2×SD16—22no—
284C2×SD16—861no—
285C2×D8—431no—
286C2×D8C22×D4311yescharacteristic
287#131—864no—
288#131—1722no—
289C2×M16—861no—
290C2×M16—1722no—
291C2×M16C22⋊D4311yescharacteristic
292C22×C8C22×D4311yescharacteristic
293C4⋊Q8—22no—
294#124—22no—
295#123—42no—
296C22⋊Q8—42no—
297#117C22⋊D4311yescharacteristic
298Q32—864no—
299Q32—862no—
300SD32—862no—
301SD32—864no—
302SD32—862no—
303D16—862no—
304M32—432no—
305M32—432no—
306M32—861no—
307M32—861no—
308C2×C16—861no—
309C2×C16—861no—
310#108—432no—
311#108—861no—
312#104—864no—
313#97C22⋊D4312yes—
314C4×C8C22×D4312yes—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41—862no—
320#41—862no—
321#41—1721no—
322#41—1721no—
323C2×Q8—22no—
324C2×Q8—21no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—41no—
330C2×Q8—861no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—861no—
334C2×D4—1721no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—1721no—
338C22×C4C2×C22⋊D4311yescharacteristic
339Q16—22no—
340Q16—21no—
341Q16—22no—
342Q16—21no—
343Q16—41no—
344Q16—41no—
345Q16—44no—
346Q16—432no—
347Q16—861no—
348SD16—41no—
349SD16—41no—
350SD16—44no—
351SD16—862no—
352SD16—862no—
353D8—21no—
354D8—21no—
355D8—432no—
356D8—861no—
357M16—862no—
358M16—1721no—
359M16—1724no—
360M16#1062188212yes—
361M16#1062188212yes—
362C2×C8—1721no—
363C2×C8—1724no—
364C2×C8D4×D4311yescharacteristic
365C2×C8D4×D4311yescharacteristic
366C2×C8#1062190011yescharacteristic
367C2×C8#1062190011yescharacteristic
368C2×C8C2×C22⋊D4311yescharacteristic
369C2×C8C2×C22⋊D4312yes—
370C2×C8C23×D4311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—44no—
373C22⋊C4—21no—
374C22⋊C4—44no—
375C42C2×C22⋊D4312yes—
376C16—862no—
377C16—862no—
378C23—41no—
379C23—1721no—
380C23#1306335111yescharacteristic
381Q8—41no—
382Q8—42no—
383Q8—42no—
384Q8—41no—
385Q8—81no—
386Q8—81no—
387Q8—862no—
388Q8—1721no—
389D4—41no—
390D4—41no—
391D4—81no—
392D4—81no—
393D4—862no—
394D4—1722no—
395D4—1722no—
396D4—1721no—
397C2×C4—22no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—1721no—
405C2×C4—1722no—
406C2×C4—1722no—
407C2×C4#1306329611yescharacteristic
408C2×C4#1306329611yescharacteristic
409C2×C4C2×#1062188211yescharacteristic
410C2×C4C2×#1062188211yescharacteristic
411C2×C4#1306335111yescharacteristic
412C2×C4C22×C22⋊D4311yescharacteristic
413C8—1722no—
414C8#1306329611yescharacteristic
415C8#1306329611yescharacteristic
416C8C2×#1062188214yes—
417C8C2×D4×D4311yescharacteristic
418C8C2×#1062190011yescharacteristic
419C22—41no—
420C22—82no—
421C22—81no—
422C22—1722no—
423C22—6881no—
424C22#1458309111yescharacteristic
425C22#1458309111yescharacteristic
426C22C2×#1306335111yescharacteristic
427C4—42no—
428C4—81no—
429C4—82no—
430C4—1722no—
431C4#1458309111yescharacteristic
432C4#1458309111yescharacteristic
433C4C2×#1306329611yescharacteristic
434C4C22×#1062188211yescharacteristic
435C2—21no—
436C2—21no—
437C2—21no—
438C2—161no—
439C2—3442no—
440C2C2×#1458309111yescharacteristic
subgroupG/H
centerC2C2×#14583091
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3156C2
socleC2×C43C2×#459
prime radical#19147729C2
hypercenter#3156D43
hypocenterC43#33596
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #3156

Complements

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

NH ≅ G/Ntype
2. C2×#14583340C2semidirect
3. #19143513C2semidirect
4. #19136673C2semidirect
5. #19136661C2semidirect
6. #19136361C2semidirect
7. #19136344C2semidirect
8. C2×#14582715C2semidirect
9. C43×#3156C2semidirect
27. #14582720C22semidirect
28. #14582715C22semidirect
29. #14582715C22semidirect
30. #14582712C22semidirect
36. C43×#495C22semidirect
37. C43×#494C22semidirect
217. #3156D43semidirect
248. #495C2×D43semidirect
249. #494C2×D43semidirect
259. C43#33596semidirect

Maximal subgroups

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

subgroupindex
#191477292
C2×#145833402
#191435132
#191366732
#191366612
#191363612
#191363442
C2×#145827152
C43×#31562
#3359643