Finite Group Databasebeta

← #25251192

Subgroups — #25251192

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×#14583342C211yesmaximal, characteristic, complemented
2#19144315C211yesmaximal, characteristic
3C2×#14583174C211yesmaximal, characteristic, complemented
4#19136725C214yesmaximal, complemented
5#19136720C214yesmaximal, complemented
6#19136390C211yesmaximal, characteristic, complemented
7#19136345C211yesmaximal, characteristic, complemented
8C2×#14582716C211yesmaximal, characteristic, complemented
9C43×#3407C211yesmaximal, characteristic, complemented
10#14583697—21no—
11C2×#13063355—21no—
12C2×#13063347C2211yescharacteristic
13C22×Dic172C2211yescharacteristic
14#14583342—22no—
15#14583342—22no—
16C2×Dic344C2212yescomplemented
17C2×#13063270C2212yescomplemented
18#14583174—22no—
19#14583174C2214yes—
20#14583174C2212yes—
21#14583169C2212yes—
22#14583162—22no—
23C2×#13063261C2211yescharacteristic
24C2×#13063261C2211yescharacteristic
25#14582881—21no—
26C2×#13063243—21no—
27#14582729C2214yescomplemented
28#14582716C2214yescomplemented
29#14582716C2212yescomplemented
30#14582713C2212yescomplemented
31C2×#131×C43C2211yescharacteristic
32C43×#504—22no—
33C43×#504C2214yes—
34C2×M32×C43—22no—
35C2×M32×C43C2211yescharacteristic
36C2×M32×C43C2211yescharacteristic
37C2×#10621898—21no—
38C22×Dic86—21no—
39#13063356—41no—
40#13063355—22no—
41#13063355—24no—
42#13063355—42no—
43#13063351—41no—
44#13063350—22no—
45#13063347—21no—
46#13063347—21no—
47#13063347—21no—
48#13063347—21no—
49#13063345—42no—
50C2×Dic172—21no—
51C2×Dic172—21no—
52C2×Dic172—21no—
53C2×Dic172—21no—
54C2×Dic172—21no—
55C2×Dic172C2312yes—
56C2×Dic172C2311yescharacteristic
57C2×#10621885—41no—
58C2×#10621873—21no—
59C2×#10621883—41no—
60C2×D344C2311yescharacteristic
61C2×#10621877—21no—
62C2×#10621877—21no—
63Dic344—24no—
64#13063270—24no—
65#13063261—21no—
66#13063261—21no—
67#13063261C2312yes—
68#13063261C2312yes—
69#13063243—24no—
70#13063243—22no—
71#13063241—22no—
72C2×#41×C43D411yescharacteristic
73#131×C43—21no—
74#131×C43—21no—
75#131×C43D412yes—
76#131×C43C2312yes—
77C2×M16×C43—21no—
78C2×M16×C43D411yescharacteristic
79C22×C8×C43—21no—
80C22×C8×C43C2311yescharacteristic
81M32×C43—21no—
82M32×C43—24no—
83M32×C43D412yes—
84M32×C43D412yes—
85M32×C43C2312yes—
86C2×C16×C43—21no—
87C2×C16×C43—24no—
88C2×C16×C43C2312yes—
89#41×C43—21no—
90#41×C43—21no—
91#41×C43D812yes—
92#41×C43C2×D412yes—
93C2×Q8×C43D811yescharacteristic
94C2×D4×C43—21no—
95C2×D4×C43D811yescharacteristic
96C22×C4×C43—21no—
97C22×C4×C43C2×D411yescharacteristic
98C2×C22⋊D43—41no—
99C22×Dic43—41no—
100#10621898—41no—
101#10621898—41no—
102#10621898—41no—
103#10621898—41no—
104C2×D172—21no—
105C2×C4×D43—41no—
106C2×Dic86—21no—
107C2×Dic86—22no—
108C2×Dic86—41no—
109C2×Dic86—41no—
110C2×Dic86—41no—
111C2×Dic86—41no—
112C2×Dic86—41no—
113M16×C43—21no—
114M16×C43—22no—
115M16×C43—22no—
116M16×C43C2×D412yes—
117C2×C8×C43—21no—
118C2×C8×C43—22no—
119C2×C8×C43—22no—
120C2×C8×C43C2×D411yescharacteristic
121C2×C8×C43C2×D411yescharacteristic
122C2×C8×C43C2×D411yescharacteristic
123C2×C8×C43#4111yescharacteristic
124C2×C8×C43#4111yescharacteristic
125C2×C8×C43C2411yescharacteristic
126#10621885—44no—
127#10621885—42no—
128#10621884—42no—
129#10621883—44no—
130#10621883—42no—
131#10621882—42no—
132#10621877—22no—
133#10621877—22no—
134#10621877—41no—
135#10621877—41no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138Dic172—22no—
139Dic172—21no—
140Dic172—22no—
141Dic172—21no—
142Dic172—41no—
143Dic172—41no—
144D344—21no—
145D344—21no—
146#10621873—41no—
147#10621873—41no—
148C16×C43—22no—
149C16×C43C2×D414yes—
150C23×C43—21no—
151C23×C43#13511yescharacteristic
152C22×D43—41no—
153Q8×C43—21no—
154Q8×C43C2×D812yes—
155D4×C43—22no—
156D4×C43—22no—
157D4×C43—21no—
158D4×C43C2×D812yes—
159C2×C4×C43—21no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43C2×D811yescharacteristic
165C2×C4×C43C2×D811yescharacteristic
166C2×C4×C43#13511yescharacteristic
167C2×C4×C43C22×D411yescharacteristic
168C22⋊D43—81no—
169C22⋊D43—81no—
170C2×Dic43—42no—
171C2×Dic43—41no—
172C2×Dic43—81no—
173C2×Dic43—81no—
174D172—41no—
175D172—41no—
176C4×D43—81no—
177C4×D43—81no—
178Dic86—41no—
179Dic86—42no—
180Dic86—42no—
181Dic86—41no—
182Dic86—81no—
183Dic86—81no—
184C8×C43—22no—
185C8×C43#12111yescharacteristic
186C8×C43#12111yescharacteristic
187C8×C43C22×D411yescharacteristic
188C8×C43C2×#4111yescharacteristic
189C43⋊C8—42no—
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#46611yescharacteristic
202C4×C43#46611yescharacteristic
203C4×C43C2×#12111yescharacteristic
204C4×C43C22×D811yescharacteristic
205Dic43—82no—
206Dic43—81no—
207C2×#510—431no—
208#3407D4311yescharacteristic, complemented
209#3067—431no—
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×C43C2×#46611yescharacteristic
221D43—161no—
222#575—861no—
223C2×#137—861no—
224C2×#135—431no—
225C22×Q16—431no—
226C2×#131C2×D4311yescharacteristic
227#510—862no—
228#510—862no—
229C2×Q32—432no—
230C2×SD32—432no—
231#504—22no—
232#504C2×D4314yes—
233C2×M32—22no—
234C2×M32C2×D4311yescharacteristic
235C2×M32C2×D4311yescharacteristic
236#473—432no—
237#473—434no—
238#473—862no—
239#472—432no—
240#471—862no—
241C2×#108—431no—
242C2×#108—431no—
243#413—861no—
244C2×#101—861no—
245#368—434no—
246#362—434no—
247#362—432no—
248#361—432no—
249C43#3361911yescharacteristic, complemented, Sylow
250C2×#41—861no—
251C2×#41D17211yescharacteristic
252C22×Q8—861no—
253#137—864no—
254#137—862no—
255#137—1722no—
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—432no—
265C2×Q16—431no—
266C2×Q16—861no—
267C2×Q16—861no—
268C2×Q16—861no—
269C2×Q16—861no—
270C2×Q16—861no—
271C2×Q16—1721no—
272C2×SD16—861no—
273C2×SD16—1721no—
274C2×D8—431no—
275#131—21no—
276#131—21no—
277#131D17212yes—
278#131C22×D4312yes—
279C2×M16—21no—
280C2×M16—861no—
281C2×M16—861no—
282C2×M16D17211yescharacteristic
283C22×C8—21no—
284C22×C8C22×D4311yescharacteristic
285Q32—864no—
286SD32—864no—
287M32—21no—
288M32—24no—
289M32C22⋊D4312yes—
290M32C22⋊D4312yes—
291M32C22×D4312yes—
292C2×C16—21no—
293C2×C16—24no—
294C2×C16C22×D4312yes—
295#108—432no—
296#108—432no—
297#108—861no—
298#108—861no—
299#101—864no—
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#41D34412yes—
309#41C2×D17212yes—
310C2×Q8—861no—
311C2×Q8—862no—
312C2×Q8—1721no—
313C2×Q8—1721no—
314C2×Q8—1721no—
315C2×Q8—1721no—
316C2×Q8—1721no—
317C2×Q8D34411yescharacteristic
318C2×D4—21no—
319C2×D4—861no—
320C2×D4—1721no—
321C2×D4D34411yescharacteristic
322C22×C4—21no—
323C22×C4—1721no—
324C22×C4—1721no—
325C22×C4C2×D17211yescharacteristic
326Q16—862no—
327Q16—861no—
328Q16—862no—
329Q16—861no—
330Q16—1724no—
331Q16—1722no—
332Q16—1721no—
333Q16—1721no—
334SD16—1722no—
335SD16—1724no—
336SD16—1722no—
337SD16—1721no—
338SD16—1721no—
339D8—861no—
340D8—861no—
341D8—1722no—
342M16—21no—
343M16—22no—
344M16—22no—
345M16—862no—
346M16—862no—
347M16—1721no—
348M16—1721no—
349M16C2×D17212yes—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—1721no—
354C2×C8—1721no—
355C2×C8C2×D17211yescharacteristic
356C2×C8#1062189811yescharacteristic
357C2×C8#1062189811yescharacteristic
358C2×C8C2×C22⋊D4311yescharacteristic
359C2×C8C2×C22⋊D4311yescharacteristic
360C2×C8C23×D4311yescharacteristic
361C16—22no—
362C16C2×C22⋊D4314yes—
363C23—21no—
364C23—1721no—
365C23#1306334711yescharacteristic
366Q8—21no—
367Q8—3441no—
368Q8—3441no—
369Q8—1721no—
370Q8—1722no—
371Q8—1722no—
372Q8—1721no—
373Q8C2×D34412yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—3441no—
378D4—3441no—
379D4—1721no—
380D4—1721no—
381D4C2×D34412yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—3441no—
386C2×C4—3441no—
387C2×C4—3441no—
388C2×C4—3441no—
389C2×C4—1721no—
390C2×C4—1722no—
391C2×C4#1306329911yescharacteristic
392C2×C4#1306329911yescharacteristic
393C2×C4C2×D34411yescharacteristic
394C2×C4C2×D34411yescharacteristic
395C2×C4#1306334711yescharacteristic
396C2×C4C22×D17211yescharacteristic
397C8—22no—
398C8—1722no—
399C8—1722no—
400C8#1306329911yescharacteristic
401C8#1306329911yescharacteristic
402C8C22×C22⋊D4311yescharacteristic
403C8C2×#1062189811yescharacteristic
404C22—22no—
405C22—41no—
406C22—81no—
407C22—3441no—
408C22—6881no—
409C22#1458313511yescharacteristic
410C22#1458313511yescharacteristic
411C22C2×#1306334711yescharacteristic
412C4—22no—
413C4—3441no—
414C4—3442no—
415C4#1458313511yescharacteristic
416C4#1458313511yescharacteristic
417C4C2×#1306329911yescharacteristic
418C4C22×D34411yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—6881no—
424C2C2×#1458313511yescharacteristic
subgroupG/H
centerC2C2×#14583135
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3407C2
socleC2×C43C2×#466
prime radical#19144315C2
hypercenter#3407D43
hypocenterC43#33619
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
1. C2×#14583342C2semidirect
3. C2×#14583174C2semidirect
4. #19136725C2semidirect
5. #19136720C2semidirect
6. #19136390C2semidirect
7. #19136345C2semidirect
8. C2×#14582716C2semidirect
9. C43×#3407C2semidirect
16. C2×Dic344C22semidirect
17. C2×#13063270C22semidirect
27. #14582729C22semidirect
28. #14582716C22semidirect
29. #14582716C22semidirect
30. #14582713C22semidirect
208. #3407D43semidirect
249. C43#33619semidirect

Maximal subgroups

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

subgroupindex
C2×#145833422
#191443152
C2×#145831742
#191367252
#191367202
#191363902
#191363452
C2×#145827162
C43×#34072
#3361943