Finite Group Databasebeta

← #28372572

Subgroups — #28372572

Order 13952.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812723C211yesmaximal, characteristic, complemented
2C2×#16812720C211yesmaximal, characteristic, complemented
3#20295594C211yesmaximal, characteristic, complemented
4#20295505C211yesmaximal, characteristic, complemented
5#20295251C211yesmaximal, characteristic, complemented
6#20295245C211yesmaximal, characteristic, complemented
7#20295243C211yesmaximal, characteristic, complemented
8#20295227C211yesmaximal, characteristic, complemented
9#20295225C211yesmaximal, characteristic, complemented
10#20295221C211yesmaximal, characteristic, complemented
11#20295219C211yesmaximal, characteristic, complemented
12#20295051C211yesmaximal, characteristic, complemented
13#20295026C211yesmaximal, characteristic, complemented
14#102×D109C211yesmaximal, characteristic, complemented
15#463×C109C211yesmaximal, characteristic, complemented
16C2×#13182030C2211yescharacteristic
17C2×#13182028C2211yescharacteristic
18C2×D4×D109C2211yescharacteristic
19#16812723—24no—
20#16812720—24no—
21C2×#13182019C2211yescharacteristic, complemented
22C2×#13182018C2211yescharacteristic
23C2×#13182018C2211yescharacteristic, complemented
24C2×#13182017C2211yescharacteristic
25C2×#13182014C2211yescharacteristic
26C2×#13182014C2211yescharacteristic, complemented
27C2×#13182012C2211yescharacteristic
28C2×C8×D109C2211yescharacteristic
29#16812696C2211yescharacteristic
30#16812695C2211yescharacteristic
31#16812688C2211yescharacteristic
32#16812672—21no—
33#16812672—21no—
34#16812669—21no—
35#16812669—21no—
36C4×Dic218C2211yescharacteristic, complemented
37#16812664C2211yescharacteristic, complemented
38D4×Dic109C2211yescharacteristic, complemented
39C4×C22⋊D109—21no—
40#16812659—21no—
41#16812656C2211yescharacteristic
42#16812655—21no—
43C2×#13182008—21no—
44C4⋊C4×D109C2211yescharacteristic
45C4⋊#11724784C2211yescharacteristic, complemented
46#16812628C2211yescharacteristic, complemented
47#16812628C2211yescharacteristic, complemented
48#16812623C2211yescharacteristic, complemented
49#16812621C2211yescharacteristic
50#16812621C2211yescharacteristic, complemented
51#16812620C2211yescharacteristic
52#16812619C2211yescharacteristic
53#16812619C2211yescharacteristic, complemented
54C2×SD16×C109C2211yescharacteristic, complemented
55C2×D8×C109C2211yescharacteristic
56#124×C109C2211yescharacteristic
57C4×D4×C109C2211yescharacteristic, complemented
58C4⋊C8×C109C2211yescharacteristic, complemented
59#103×C109C2211yescharacteristic, complemented
60#102×C109C2211yescharacteristic
61C23×D109—21no—
62#13182030—22no—
63#13182030—22no—
64#13182028—22no—
65#13182028D414yescomplemented
66C2×Dic218C2311yescharacteristic
67C2×D436—21no—
68C2×D436—21no—
69C2×D436—21no—
70C2×D436C2311yescharacteristic
71C2×D436C2311yescharacteristic
72C2×C22⋊D109—21no—
73C2×C22⋊D109—21no—
74C2×C22⋊D109—21no—
75C2×C22⋊D109—21no—
76D4×D109—22no—
77D4×D109—22no—
78C22×Dic109—21no—
79C22×Dic109—21no—
80C2×C4×D109—21no—
81C2×C4×D109—21no—
82C2×C4×D109C2311yescharacteristic
83#13182019—22no—
84#13182018—22no—
85#13182018—22no—
86#13182017—22no—
87#13182014—22no—
88#13182014—22no—
89#13182012—22no—
90C2×#11724784C2311yescharacteristic
91C2×#11724784C2311yescharacteristic
92C8×D109—22no—
93C4⋊Dic109C2311yescharacteristic
94#13182008—21no—
95#13182008—21no—
96#13182008—21no—
97#13182008D411yescharacteristic
98#13182008D411yescharacteristic
99C22⋊Dic109—21no—
100#13182006—21no—
101#13182006—21no—
102#13182006D411yescharacteristic
103#13182006D411yescharacteristic
104C4×Dic109—21no—
105C4×Dic109—21no—
106C4×Dic109C2311yescharacteristic
107C2×Q8×C109C2311yescharacteristic
108C2×D4×C109C2311yescharacteristic
109C2×D4×C109C2311yescharacteristic
110C22×C4×C109—21no—
111SD16×C109—22no—
112D8×C109—22no—
113C2×C8×C109C2311yescharacteristic
114C2×C8×C109C2311yescharacteristic
115C4⋊C4×C109C2311yescharacteristic
116C22⋊C4×C109—21no—
117C22⋊C4×C109—21no—
118C22⋊C4×C109—21no—
119C42×C109C2311yescharacteristic
120C23×C109—21no—
121C23×C109—21no—
122C22×D109—21no—
123C22×D109—21no—
124C22×D109—42no—
125C22×D109—81no—
126C22×D109—81no—
127C22×D109C2×D411yescharacteristic
128Q8×C109—21no—
129Q8×C109—21no—
130D4×C109—21no—
131D4×C109—21no—
132D4×C109—21no—
133D4×C109C2×D412yes—
134C2×C4×C109—21no—
135C2×C4×C109—21no—
136C2×C4×C109—81no—
137C2×C4×C109C2×D411yescharacteristic
138C2×C4×C109C2×D411yescharacteristic
139C2×C4×C109C2411yescharacteristic
140C22⋊D109—24no—
141C22⋊D109—42no—
142C22⋊D109—81no—
143C22⋊D109—81no—
144C2×Dic109—21no—
145C2×Dic109—24no—
146C2×Dic109—21no—
147C2×Dic109—81no—
148C2×Dic109C2×D411yescharacteristic
149C2×Dic109C2×D411yescharacteristic
150C2×Dic109C2×D411yescharacteristic
151D436—21no—
152D436—21no—
153D436—21no—
154D436—21no—
155D436—42no—
156D436—81no—
157D436—81no—
158C4×D109—42no—
159C4×D109—81no—
160C4×D109C2×D412yes—
161C4×D109#4112yes—
162Dic218—21no—
163Dic218C2×D412yes—
164C8×C109—21no—
165C8×C109—21no—
166#11724784—21no—
167#11724784—21no—
168C22×C109—22no—
169C22×C109—41no—
170C22×C109—41no—
171C22×C109—41no—
172C22×C109—41no—
173C22×C109—41no—
174C22×C109C22×D411yescharacteristic
175C2×D109—21no—
176C2×D109—21no—
177C2×D109—41no—
178C2×D109—41no—
179C2×D109—41no—
180C2×D109—41no—
181C2×D109—41no—
182C2×D109—41no—
183C2×D109—84no—
184C2×D109#12112yes—
185C4×C109—21no—
186C4×C109—21no—
187C4×C109—41no—
188C4×C109—41no—
189C4×C109C22×D411yescharacteristic
190C4×C109C2×#4111yescharacteristic
191Dic109—22no—
192Dic109—21no—
193Dic109—21no—
194Dic109—41no—
195Dic109#12112yes—
196C2×C109—42no—
197C2×C109—81no—
198C2×C109C2×#12111yescharacteristic
199C2×C109#57611yescharacteristic
200C2×C109#57711yescharacteristic
201D109—22no—
202D109—81no—
203D109—81no—
204#3045—1091nomaximal, Sylow
205C109#304511yescharacteristic, complemented, Sylow
206C2×AGL(1,ℤ/8)—1091no—
207C2×#135—1091no—
208#535—1091no—
209#520—1091no—
210#464—1091no—
211#464—1091no—
212#463—1091no—
213#463D10911yescharacteristic, complemented
214#460—1091no—
215#460—1091no—
216#459—1091no—
217#459—1091no—
218#424—1091no—
219#417—1091no—
220C2×#102—1091no—
221C2×#41—1091no—
222C2×#41—1091no—
223C22×D4—1091no—
224AGL(1,ℤ/8)—2184no—
225#135—2184no—
226C2×Q16—1091no—
227C2×SD16—1091no—
228C2×SD16—1091no—
229C2×SD16—1091no—
230C2×SD16C2×D10911yescharacteristic, complemented
231C2×D8—1091no—
232C2×D8—1091no—
233C2×D8C2×D10911yescharacteristic
234C2×M16—1091no—
235C22×C8—1091no—
236#127—1091no—
237#127—1091no—
238#124—1091no—
239#124C2×D10911yescharacteristic
240#121—2181no—
241#121—2181no—
242#120—2181no—
243#120—2181no—
244C4×Q8—1091no—
245C4×Q8—1091no—
246C4×D4—1091no—
247C4×D4—2181no—
248C4×D4—2181no—
249C4×D4C2×D10911yescharacteristic, complemented
250#117—1091no—
251#117—2181no—
252C2×C4⋊C4—1091no—
253C2×C4⋊C4—2181no—
254C4⋊C8—1091no—
255C4⋊C8—1091no—
256C4⋊C8—1091no—
257C4⋊C8C2×D10911yescharacteristic, complemented
258#103—1091no—
259#103C2×D10911yescharacteristic, complemented
260#102—1091no—
261#102—1091no—
262#102—1091no—
263#102—1091no—
264#102—1091no—
265#102C2×D10911yescharacteristic
266C24—2181no—
267#41—1094no—
268#41—2182no—
269#41—2182no—
270#41—2182no—
271C2×Q8—1091no—
272C2×Q8C22×D10911yescharacteristic
273C2×D4—1091no—
274C2×D4—1091no—
275C2×D4—2181no—
276C2×D4—2182no—
277C2×D4—2182no—
278C2×D4—2181no—
279C2×D4—2181no—
280C2×D4—2181no—
281C2×D4—2181no—
282C2×D4—2181no—
283C2×D4—2181no—
284C2×D4C22×D10911yescharacteristic
285C2×D4C22×D10911yescharacteristic
286C22×C4—21no—
287C22×C4—1091no—
288C22×C4—2181no—
289C22×C4—2181no—
290C22×C4—2181no—
291C22×C4—2181no—
292Q16—2182no—
293SD16—22no—
294SD16—2182no—
295SD16—2182no—
296SD16—2182no—
297D8—22no—
298D8—2182no—
299D8—2182no—
300M16—2182no—
301C2×C8—1091no—
302C2×C8—1091no—
303C2×C8—2182no—
304C2×C8C22×D10911yescharacteristic
305C2×C8C22×D10911yescharacteristic
306C4⋊C4—1091no—
307C4⋊C4—1091no—
308C4⋊C4—1091no—
309C4⋊C4—2181no—
310C4⋊C4—2181no—
311C4⋊C4—2181no—
312C4⋊C4C22×D10911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—1091no—
317C22⋊C4—1091no—
318C22⋊C4—2181no—
319C22⋊C4—2181no—
320C22⋊C4—2181no—
321C42—1091no—
322C42—2181no—
323C42—2181no—
324C42C22×D10911yescharacteristic
325C23—21no—
326C23—21no—
327C23—8721no—
328C23—8721no—
329C23—1091no—
330C23—4362no—
331C23—2181no—
332C23—2181no—
333Q8—21no—
334Q8—21no—
335Q8—1092no—
336Q8—2181no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—8721no—
341D4—8721no—
342D4—8721no—
343D4—8721no—
344D4—4362no—
345D4—4362no—
346D4—2184no—
347D4—2181no—
348D4—2181no—
349D4—2181no—
350D4—2181no—
351D4D4×D10912yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—81no—
355C2×C4—8721no—
356C2×C4—8721no—
357C2×C4—1091no—
358C2×C4—1092no—
359C2×C4—1092no—
360C2×C4—1091no—
361C2×C4—1091no—
362C2×C4—4362no—
363C2×C4—2184no—
364C2×C4—2181no—
365C2×C4—2181no—
366C2×C4D4×D10911yescharacteristic
367C2×C4D4×D10911yescharacteristic
368C2×C4C23×D10911yescharacteristic
369C8—21no—
370C8—21no—
371C8—2181no—
372C8—2181no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—8724no—
380C22—1092no—
381C22—4361no—
382C22—4361no—
383C22—4361no—
384C22—4361no—
385C22—4361no—
386C22—4361no—
387C22—2181no—
388C22—2181no—
389C22C2×D4×D10911yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—1092no—
395C4—4361no—
396C4—2182no—
397C4—2181no—
398C4—2181no—
399C4C2×D4×D10911yescharacteristic
400C4#41×D10911yescharacteristic
401C2—42no—
402C2—81no—
403C2—8721no—
404C2—8721no—
405C2—2182no—
406C2#121×D10911yescharacteristic
407C2#2029583011yescharacteristic
408C2#2029583311yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#463×C109C2
socleC22×C109C22×D4
hypercenter#463D109
hypocenterC109#3045
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#16812723C2semidirect
2. C2×#16812720C2semidirect
3. #20295594C2semidirect
4. #20295505C2semidirect
5. #20295251C2semidirect
6. #20295245C2semidirect
7. #20295243C2semidirect
8. #20295227C2semidirect
9. #20295225C2semidirect
10. #20295221C2semidirect
11. #20295219C2semidirect
12. #20295051C2semidirect
13. #20295026C2semidirect
14. #102×D109C2semidirect
15. #463×C109C2semidirect
21. C2×#13182019C22semidirect
23. C2×#13182018C22semidirect
26. C2×#13182014C22semidirect
36. C4×Dic218C22semidirect
37. #16812664C22semidirect
38. D4×Dic109C22semidirect
45. C4⋊#11724784C22semidirect
46. #16812628C22semidirect
47. #16812628C22semidirect
48. #16812623C22semidirect
50. #16812621C22semidirect
53. #16812619C22semidirect
54. C2×SD16×C109C22semidirect
57. C4×D4×C109C22semidirect
58. C4⋊C8×C109C22semidirect
59. #103×C109C22semidirect
65. #13182028D4semidirect
205. C109#3045semidirect
213. #463D109semidirect
230. C2×SD16C2×D109semidirect
249. C4×D4C2×D109semidirect
257. C4⋊C8C2×D109semidirect
259. #103C2×D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127232
C2×#168127202
#202955942
#202955052
#202952512
#202952452
#202952432
#202952272
#202952252
#202952212
#202952192
#202950512
#202950262
#102×D1092
#463×C1092
#3045109