Finite Group Databasebeta

← #25251194

Subgroups — #25251194

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×#14583339C211yesmaximal, characteristic, complemented
2#19147698C211yesmaximal, characteristic, complemented
3C2×#14583174C211yesmaximal, characteristic, complemented
4#19136723C214yesmaximal, complemented
5#19136718C214yesmaximal, complemented
6#19136389C211yesmaximal, characteristic, complemented
7#19136344C211yesmaximal, characteristic, complemented
8C2×#14582714C211yesmaximal, characteristic, complemented
9C43×#3067C211yesmaximal, characteristic
10C2×#13063355—21no—
11C22×Dic172C2211yescharacteristic
12#14583339—22no—
13#14583339—22no—
14C2×#13063271C2212yescomplemented
15C2×#13063269C2212yescomplemented
16#14583316—22no—
17#14583316C2214yes—
18C2×#13063265—22no—
19C2×#13063265C2211yescharacteristic
20C2×#13063265C2211yescharacteristic
21#14583174—22no—
22#14583174C2214yes—
23C2×#13063261C2211yescharacteristic
24C2×#13063243—21no—
25#14582728C2214yescomplemented
26#14582715C2212yescomplemented
27#14582714C2214yescomplemented
28#14582712C2212yescomplemented
29C43×#575—21no—
30C2×#135×C43C2211yescharacteristic
31C2×#131×C43C2211yescharacteristic
32C43×#473C2212yes—
33C43×#472C2212yes—
34C43×#471—22no—
35C2×#108×C43C2211yescharacteristic
36C43×#413—21no—
37C22×Dic86—21no—
38#13063355—24no—
39#13063355—42no—
40C2×Dic172—21no—
41C2×Dic172—21no—
42C2×Dic172—21no—
43C2×Dic172—21no—
44C2×Dic172—21no—
45C2×Dic172C2312yes—
46C2×#10621885—41no—
47C2×#10621883—41no—
48C2×#10621877—21no—
49#13063271—24no—
50#13063269—24no—
51#13063265—21no—
52#13063265—24no—
53#13063265D412yes—
54#13063265D412yes—
55#13063265C2312yes—
56C2×C43⋊C16—21no—
57C2×C43⋊C16—24no—
58C2×C43⋊C16C2312yes—
59#13063261—21no—
60#13063261C2312yes—
61#13063243—24no—
62C2×#41×C43—21no—
63C2×#41×C43D411yescharacteristic
64#137×C43—22no—
65#137×C43—41no—
66AGL(1,ℤ/8)×C43—22no—
67AGL(1,ℤ/8)×C43—41no—
68#135×C43—21no—
69#135×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72#135×C43—42no—
73C2×Q16×C43C2311yescharacteristic
74C2×SD16×C43—21no—
75C2×D8×C43C2311yescharacteristic
76#131×C43—21no—
77#131×C43—21no—
78#131×C43D412yes—
79#131×C43C2312yes—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43D411yescharacteristic
83C22×C8×C43—21no—
84C22×C8×C43C2311yescharacteristic
85#108×C43—21no—
86#108×C43C2312yes—
87#101×C43—22no—
88#100×C43—22no—
89#41×C43—21no—
90#41×C43—21no—
91#41×C43—41no—
92#41×C43—41no—
93#41×C43—41no—
94#41×C43—41no—
95#41×C43D812yes—
96#41×C43C2×D412yes—
97C2×Q8×C43—21no—
98C2×Q8×C43D811yescharacteristic
99C2×D4×C43—21no—
100C2×D4×C43—21no—
101C2×D4×C43—41no—
102C2×D4×C43D811yescharacteristic
103C22×C4×C43—21no—
104C22×C4×C43—41no—
105C22×C4×C43C2×D411yescharacteristic
106C22×Dic43—41no—
107C2×Dic86—22no—
108C2×Dic86—41no—
109C2×Dic86—41no—
110C2×Dic86—41no—
111C2×Dic86—41no—
112C2×Dic86—41no—
113Q16×C43—21no—
114Q16×C43—21no—
115Q16×C43—42no—
116SD16×C43—42no—
117SD16×C43—42no—
118SD16×C43—41no—
119SD16×C43—41no—
120D8×C43—21no—
121D8×C43—21no—
122D8×C43—42no—
123M16×C43—21no—
124M16×C43—22no—
125M16×C43—22no—
126M16×C43—22no—
127M16×C43—41no—
128M16×C43C2×D412yes—
129C2×C8×C43—21no—
130C2×C8×C43—22no—
131C2×C8×C43—22no—
132C2×C8×C43—41no—
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43#4111yescharacteristic
137C2×C8×C43#4111yescharacteristic
138C2×C8×C43C2411yescharacteristic
139#10621885—44no—
140#10621883—44no—
141#10621877—22no—
142#10621877—41no—
143C2×C43⋊C8—41no—
144Dic172—22no—
145Dic172—22no—
146Dic172—41no—
147Dic172—41no—
148C43⋊C16—22no—
149C43⋊C16C2×D414yes—
150C23×C43—21no—
151C23×C43—41no—
152C23×C43#13511yescharacteristic
153Q8×C43—21no—
154Q8×C43—41no—
155Q8×C43—41no—
156Q8×C43C2×D812yes—
157D4×C43—22no—
158D4×C43—22no—
159D4×C43—21no—
160D4×C43—41no—
161D4×C43—41no—
162D4×C43—81no—
163D4×C43—81no—
164D4×C43C2×D812yes—
165C2×C4×C43—21no—
166C2×C4×C43—22no—
167C2×C4×C43—22no—
168C2×C4×C43—41no—
169C2×C4×C43—81no—
170C2×C4×C43—81no—
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43C2×D811yescharacteristic
174C2×C4×C43C2×D811yescharacteristic
175C2×C4×C43#13511yescharacteristic
176C2×C4×C43C22×D411yescharacteristic
177C2×Dic43—42no—
178C2×Dic43—81no—
179C2×Dic43—81no—
180Dic86—42no—
181Dic86—42no—
182Dic86—81no—
183Dic86—81no—
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—81no—
196C22×C43—161no—
197C22×C43#46611yescharacteristic
198C22×C43#46611yescharacteristic
199C22×C43C2×#13511yescharacteristic
200C4×C43—22no—
201C4×C43—81no—
202C4×C43#46611yescharacteristic
203C4×C43#46611yescharacteristic
204C4×C43C2×#12111yescharacteristic
205C4×C43C22×D811yescharacteristic
206Dic43—82no—
207C2×#510—431no—
208#3407—431no—
209#3067D4311yescharacteristic
210C2×#473—431no—
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×C43—161no—
221C2×C43C2×#46611yescharacteristic
222#575—21no—
223C2×#137—861no—
224C2×#135C2×D4311yescharacteristic
225C22×Q16—431no—
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—434no—
237#473—862no—
238#473C2×D4312yes—
239#472C2×D4312yes—
240#471—22no—
241C2×#108—431no—
242C2×#108C2×D4311yescharacteristic
243#413—21no—
244C2×#101—861no—
245#368—434no—
246#362—432no—
247#362—434no—
248#361—432no—
249C43#3361911yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C2×#41C22⋊D4311yescharacteristic
252C22×Q8—861no—
253#137—22no—
254#137—41no—
255#137—864no—
256#137—1722no—
257AGL(1,ℤ/8)—22no—
258AGL(1,ℤ/8)—41no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—21no—
263#135—42no—
264C2×Q16—432no—
265C2×Q16—861no—
266C2×Q16—861no—
267C2×Q16—861no—
268C2×Q16—861no—
269C2×Q16—861no—
270C2×Q16—1721no—
271C2×Q16C22×D4311yescharacteristic
272C2×SD16—21no—
273C2×SD16—1721no—
274C2×D8C22×D4311yescharacteristic
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—22no—
300#101—864no—
301#100—22no—
302#41—21no—
303#41—21no—
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41#1062188212yes—
309#41C2×C22⋊D4312yes—
310C2×Q8—21no—
311C2×Q8—862no—
312C2×Q8—1721no—
313C2×Q8—1721no—
314C2×Q8—1721no—
315C2×Q8—1721no—
316C2×Q8—1721no—
317C2×Q8#1062188211yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4#1062188211yescharacteristic
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—1721no—
325C22×C4C2×C22⋊D4311yescharacteristic
326Q16—21no—
327Q16—21no—
328Q16—42no—
329Q16—862no—
330Q16—862no—
331Q16—1724no—
332Q16—1721no—
333Q16—1721no—
334SD16—42no—
335SD16—42no—
336SD16—41no—
337SD16—41no—
338SD16—1724no—
339D8—21no—
340D8—21no—
341D8—42no—
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—41no—
365C23#1306334511yescharacteristic
366Q8—21no—
367Q8—41no—
368Q8—41no—
369Q8—3441no—
370Q8—3441no—
371Q8—1722no—
372Q8—1722no—
373Q8C2×#1062188212yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4C2×#1062188212yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—3441no—
389C2×C4—3441no—
390C2×C4—1722no—
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—81no—
408C22—161no—
409C22#1458313311yescharacteristic
410C22#1458313311yescharacteristic
411C22C2×#1306334511yescharacteristic
412C4—22no—
413C4—81no—
414C4—3442no—
415C4#1458313311yescharacteristic
416C4#1458313311yescharacteristic
417C4C2×#1306329711yescharacteristic
418C4C22×#1062188211yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—161no—
424C2C2×#1458313311yescharacteristic
subgroupG/H
centerC2C2×#14583133
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalC43×#3067C2
socleC2×C43C2×#466
hypercenter#3067D43
hypocenterC43#33619
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. C2×#14583339C2semidirect
2. #19147698C2semidirect
3. C2×#14583174C2semidirect
4. #19136723C2semidirect
5. #19136718C2semidirect
6. #19136389C2semidirect
7. #19136344C2semidirect
8. C2×#14582714C2semidirect
14. C2×#13063271C22semidirect
15. C2×#13063269C22semidirect
25. #14582728C22semidirect
26. #14582715C22semidirect
27. #14582714C22semidirect
28. #14582712C22semidirect
249. C43#33619semidirect

Maximal subgroups

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

subgroupindex
C2×#145833392
#191476982
C2×#145831742
#191367232
#191367182
#191363892
#191363442
C2×#145827142
C43×#30672
#3361943