Finite Group Databasebeta

← #25251189

Subgroups — #25251189

Order 11008.

636 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583340C211yesmaximal, characteristic, complemented
2#19147698C211yesmaximal, characteristic, complemented
3#19144315C211yesmaximal, characteristic
4#19136727C214yesmaximal, complemented
5#19136718C214yesmaximal, complemented
6#19136389C211yesmaximal, characteristic, complemented
7#19136342C211yesmaximal, characteristic, complemented
8C2×#14582715C211yesmaximal, characteristic, complemented
9C2×C43×#473C211yesmaximal, characteristic, complemented
10#14583697—21no—
11C2×#13063347C2211yescharacteristic
12#14583340—22no—
13#14583340—22no—
14C2×#13063271C2212yescomplemented
15C2×#13063268C2212yescomplemented
16#14583316—22no—
17#14583316C2214yes—
18C2×#13063265—22no—
19C2×#13063265C2211yescharacteristic
20C2×#13063265C2211yescharacteristic
21#14583174C2212yes—
22#14583169C2212yes—
23#14583162—22no—
24C2×#13063261C2211yescharacteristic
25#14582881—21no—
26#14582728C2214yescomplemented
27#14582715C2214yescomplemented
28#14582714C2212yescomplemented
29#14582711C2212yescomplemented
30C2×#137×C43—21no—
31C22×Q16×C43C2211yescharacteristic
32C2×#131×C43C2211yescharacteristic
33C43×#473—22no—
34C43×#473C2214yes—
35C2×#108×C43C2211yescharacteristic
36C2×#101×C43—21no—
37C2×#10621898—21no—
38#13063356—41no—
39#13063355—22no—
40#13063351—41no—
41#13063350—22no—
42#13063347—21no—
43#13063347—21no—
44#13063347—21no—
45#13063347—21no—
46#13063345—42no—
47C2×Dic172C2311yescharacteristic
48C2×#10621873—21no—
49C2×D344C2311yescharacteristic
50C2×#10621877—21no—
51#13063271—24no—
52#13063268—24no—
53#13063265—21no—
54#13063265—24no—
55#13063265D412yes—
56#13063265D412yes—
57#13063265C2312yes—
58C2×C43⋊C16—21no—
59C2×C43⋊C16—24no—
60C2×C43⋊C16C2312yes—
61#13063261—21no—
62#13063261C2312yes—
63#13063243—22no—
64#13063241—22no—
65C2×#41×C43D411yescharacteristic
66C22×Q8×C43—21no—
67#137×C43—24no—
68#137×C43—42no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×Q16×C43—21no—
74C2×Q16×C43—41no—
75C2×Q16×C43C2312yes—
76C2×SD16×C43—41no—
77#131×C43—21no—
78#131×C43—21no—
79#131×C43D412yes—
80#131×C43C2312yes—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43D411yescharacteristic
84C22×C8×C43—21no—
85C22×C8×C43C2311yescharacteristic
86#108×C43—21no—
87#108×C43C2312yes—
88#101×C43—24no—
89#41×C43—21no—
90#41×C43—21no—
91#41×C43D812yes—
92#41×C43C2×D412yes—
93C2×Q8×C43—22no—
94C2×Q8×C43—41no—
95C2×Q8×C43—41no—
96C2×Q8×C43—41no—
97C2×Q8×C43—41no—
98C2×Q8×C43—41no—
99C2×Q8×C43D811yescharacteristic
100C2×D4×C43—21no—
101C2×D4×C43D811yescharacteristic
102C22×C4×C43—21no—
103C22×C4×C43—41no—
104C22×C4×C43C2×D411yescharacteristic
105C2×C22⋊D43—41no—
106#10621898—41no—
107#10621898—41no—
108#10621898—41no—
109#10621898—41no—
110C2×D172—21no—
111C2×C4×D43—41no—
112C2×Dic86—21no—
113Q16×C43—22no—
114Q16×C43—22no—
115Q16×C43—44no—
116Q16×C43—41no—
117Q16×C43—41no—
118SD16×C43—44no—
119M16×C43—21no—
120M16×C43—22no—
121M16×C43—22no—
122M16×C43—22no—
123M16×C43—41no—
124M16×C43C2×D412yes—
125C2×C8×C43—21no—
126C2×C8×C43—22no—
127C2×C8×C43—22no—
128C2×C8×C43—41no—
129C2×C8×C43C2×D411yescharacteristic
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2×D411yescharacteristic
132C2×C8×C43#4111yescharacteristic
133C2×C8×C43#4111yescharacteristic
134C2×C8×C43C2411yescharacteristic
135#10621885—42no—
136#10621884—42no—
137#10621883—42no—
138#10621882—42no—
139#10621877—22no—
140#10621877—41no—
141C2×C43⋊C8—41no—
142Dic172—21no—
143Dic172—21no—
144D344—21no—
145D344—21no—
146#10621873—41no—
147#10621873—41no—
148C43⋊C16—22no—
149C43⋊C16C2×D414yes—
150C23×C43—21no—
151C23×C43#13511yescharacteristic
152C22×D43—41no—
153Q8×C43—21no—
154Q8×C43—42no—
155Q8×C43—42no—
156Q8×C43—81no—
157Q8×C43—81no—
158Q8×C43C2×D812yes—
159D4×C43—22no—
160D4×C43—22no—
161D4×C43—21no—
162D4×C43C2×D812yes—
163C2×C4×C43—21no—
164C2×C4×C43—22no—
165C2×C4×C43—22no—
166C2×C4×C43—42no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43C2×D811yescharacteristic
172C2×C4×C43C2×D811yescharacteristic
173C2×C4×C43#13511yescharacteristic
174C2×C4×C43C22×D411yescharacteristic
175C22⋊D43—81no—
176C22⋊D43—81no—
177C2×Dic43—41no—
178D172—41no—
179D172—41no—
180C4×D43—81no—
181C4×D43—81no—
182Dic86—41no—
183Dic86—41no—
184C8×C43—22no—
185C8×C43—42no—
186C8×C43#12111yescharacteristic
187C8×C43#12111yescharacteristic
188C8×C43C22×D411yescharacteristic
189C8×C43C2×#4111yescharacteristic
190C43⋊C8—42no—
191#33619—431nomaximal, Sylow
192C22×C43—22no—
193C22×C43—41no—
194C22×C43—81no—
195C22×C43#46611yescharacteristic
196C22×C43#46611yescharacteristic
197C22×C43C2×#13511yescharacteristic
198C2×D43—81no—
199C2×D43—161no—
200C4×C43—22no—
201C4×C43—82no—
202C4×C43#46611yescharacteristic
203C4×C43#46611yescharacteristic
204C4×C43C2×#12111yescharacteristic
205C4×C43C22×D811yescharacteristic
206Dic43—81no—
207C2×#510—431no—
208#3407—431no—
209#3067—431no—
210C2×#473D4311yescharacteristic, complemented
211#2223—434no—
212#2222—434no—
213#2161—431no—
214#2148—431no—
215C2×#362—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—42no—
220C2×C43C2×#46611yescharacteristic
221D43—161no—
222#575—861no—
223C2×#137—21no—
224C2×#135—431no—
225C22×Q16C2×D4311yescharacteristic
226C2×#131C2×D4311yescharacteristic
227#510—862no—
228#510—862no—
229C2×Q32—432no—
230C2×SD32—432no—
231#504—434no—
232#504—862no—
233C2×M32—431no—
234C2×M32—431no—
235C2×M32—862no—
236#473—22no—
237#473—432no—
238#473C2×D4314yes—
239#472—432no—
240#471—862no—
241C2×#108—431no—
242C2×#108C2×D4311yescharacteristic
243#413—861no—
244C2×#101—21no—
245#368—434no—
246#362—434no—
247#362—432no—
248#361—432no—
249C43#3361911yescharacteristic, complemented, Sylow
250C2×#41—861no—
251C2×#41C22⋊D4311yescharacteristic
252C22×Q8—21no—
253#137—24no—
254#137—42no—
255#137—862no—
256#137—1721no—
257AGL(1,ℤ/8)—862no—
258AGL(1,ℤ/8)—1721no—
259#135—861no—
260#135—861no—
261#135—861no—
262#135—861no—
263#135—1722no—
264C2×Q16—21no—
265C2×Q16—21no—
266C2×Q16—21no—
267C2×Q16—21no—
268C2×Q16—21no—
269C2×Q16—41no—
270C2×Q16—431no—
271C2×Q16C22×D4312yes—
272C2×SD16—41no—
273C2×SD16—861no—
274C2×D8—431no—
275#131—21no—
276#131—21no—
277#131C22⋊D4312yes—
278#131C22×D4312yes—
279C2×M16—21no—
280C2×M16—21no—
281C2×M16—861no—
282C2×M16C22⋊D4311yescharacteristic
283C22×C8—21no—
284C22×C8C22×D4311yescharacteristic
285Q32—864no—
286SD32—864no—
287M32—432no—
288M32—432no—
289M32—432no—
290M32—864no—
291M32—861no—
292C2×C16—432no—
293C2×C16—864no—
294C2×C16—861no—
295#108—21no—
296#108—432no—
297#108—861no—
298#108C22×D4312yes—
299#101—24no—
300#101—862no—
301#100—862no—
302#41—21no—
303#41—21no—
304#41—1721no—
305#41—1721no—
306#41—1721no—
307#41—1721no—
308#41#1062188212yes—
309#41C2×C22⋊D4312yes—
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—861no—
317C2×Q8#1062188211yescharacteristic
318C2×D4—21no—
319C2×D4—861no—
320C2×D4—1721no—
321C2×D4#1062188211yescharacteristic
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—1721no—
325C22×C4C2×C22⋊D4311yescharacteristic
326Q16—22no—
327Q16—22no—
328Q16—44no—
329Q16—41no—
330Q16—41no—
331Q16—861no—
332Q16—861no—
333Q16—1722no—
334SD16—44no—
335SD16—1722no—
336SD16—1722no—
337SD16—1721no—
338SD16—1721no—
339D8—861no—
340D8—861no—
341D8—1722no—
342M16—21no—
343M16—22no—
344M16—22no—
345M16—22no—
346M16—41no—
347M16—862no—
348M16—1721no—
349M16C2×C22⋊D4312yes—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—41no—
354C2×C8—1721no—
355C2×C8D4×D4311yescharacteristic
356C2×C8D4×D4311yescharacteristic
357C2×C8#1062190011yescharacteristic
358C2×C8#1062190011yescharacteristic
359C2×C8C2×C22⋊D4311yescharacteristic
360C2×C8C23×D4311yescharacteristic
361C16—434no—
362C16—862no—
363C23—21no—
364C23—1721no—
365C23#1306334511yescharacteristic
366Q8—21no—
367Q8—42no—
368Q8—42no—
369Q8—81no—
370Q8—81no—
371Q8—1721no—
372Q8—1721no—
373Q8C2×#1062188212yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—3441no—
378D4—3441no—
379D4—1721no—
380D4—1721no—
381D4C2×#1062188212yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—42no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—3441no—
389C2×C4—3441no—
390C2×C4—1721no—
391C2×C4#1306329711yescharacteristic
392C2×C4#1306329711yescharacteristic
393C2×C4C2×#1062188211yescharacteristic
394C2×C4C2×#1062188211yescharacteristic
395C2×C4#1306334511yescharacteristic
396C2×C4C22×C22⋊D4311yescharacteristic
397C8—22no—
398C8—42no—
399C8—1722no—
400C8#1306329711yescharacteristic
401C8#1306329711yescharacteristic
402C8C2×D4×D4311yescharacteristic
403C8C2×#1062190011yescharacteristic
404C22—22no—
405C22—41no—
406C22—81no—
407C22—3441no—
408C22—6881no—
409C22#1458313311yescharacteristic
410C22#1458313311yescharacteristic
411C22C2×#1306334511yescharacteristic
412C4—22no—
413C4—82no—
414C4—3441no—
415C4#1458313311yescharacteristic
416C4#1458313311yescharacteristic
417C4C2×#1306329711yescharacteristic
418C4C22×#1062188211yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—6881no—
424C2C2×#1458313311yescharacteristic
subgroupG/H
centerC2C2×#14583133
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#473C2
socleC2×C43C2×#466
prime radical#19144315C2
hypercenterC2×#473D43
hypocenterC43#33619
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
1. C2×#14583340C2semidirect
2. #19147698C2semidirect
4. #19136727C2semidirect
5. #19136718C2semidirect
6. #19136389C2semidirect
7. #19136342C2semidirect
8. C2×#14582715C2semidirect
9. C2×C43×#473C2semidirect
14. C2×#13063271C22semidirect
15. C2×#13063268C22semidirect
26. #14582728C22semidirect
27. #14582715C22semidirect
28. #14582714C22semidirect
29. #14582711C22semidirect
210. C2×#473D43semidirect
249. C43#33619semidirect

Maximal subgroups

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

subgroupindex
C2×#145833402
#191476982
#191443152
#191367272
#191367182
#191363892
#191363422
C2×#145827152
C2×C43×#4732
#3361943