Finite Group Databasebeta

← #28372709

Subgroups — #28372709

Order 13952.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812723C211yesmaximal, characteristic, complemented
2C2×#16812707C211yesmaximal, characteristic, complemented
3#20295605C211yesmaximal, characteristic, complemented
4#20295592C211yesmaximal, characteristic, complemented
5#20295278C211yesmaximal, characteristic, complemented
6#20295272C211yesmaximal, characteristic, complemented
7#20295271C211yesmaximal, characteristic, complemented
8#20295260C211yesmaximal, characteristic, complemented
9#20295259C211yesmaximal, characteristic, complemented
10#20295256C211yesmaximal, characteristic, complemented
11#20295253C211yesmaximal, characteristic, complemented
12#20295065C211yesmaximal, characteristic, complemented
13#20295019C211yesmaximal, characteristic, complemented
14#102×D109C211yesmaximal, characteristic, complemented
15#469×C109C211yesmaximal, characteristic, complemented
16C2×#13182029C2211yescharacteristic
17C2×#13182028C2211yescharacteristic
18C2×D4×D109C2211yescharacteristic
19#16812723—24no—
20C2×#13182018C2211yescharacteristic
21C2×#13182017C2211yescharacteristic
22C2×#13182014C2211yescharacteristic
23#16812707—24no—
24C2×#13182012C2211yescharacteristic
25C2×#13182012C2211yescharacteristic, complemented
26C22×#11724784C2211yescharacteristic, complemented
27C2×C8×D109C2211yescharacteristic
28C2×C8×D109C2211yescharacteristic, complemented
29#16812695—21no—
30#16812685—21no—
31#16812679C2211yescharacteristic, complemented
32#16812678C2211yescharacteristic, complemented
33#16812676—21no—
34#16812674C2211yescharacteristic
35#16812673C2211yescharacteristic
36#16812672—21no—
37#16812671—21no—
38#16812670—21no—
39#16812670C2211yescharacteristic
40#16812670C2211yescharacteristic, complemented
41#16812669—21no—
42#16812667—21no—
43#16812657C2211yescharacteristic
44C4⋊C4×D109C2211yescharacteristic
45#16812633C2211yescharacteristic, complemented
46#16812632C2211yescharacteristic, complemented
47#16812630C2211yescharacteristic, complemented
48#16812624C2211yescharacteristic, complemented
49#16812622C2211yescharacteristic, complemented
50#16812621C2211yescharacteristic
51#16812620C2211yescharacteristic
52#16812620C2211yescharacteristic, complemented
53#16812619C2211yescharacteristic
54C2×D8×C109C2211yescharacteristic
55C2×M16×C109C2211yescharacteristic, complemented
56#121×C109C2211yescharacteristic
57#121×C109C2211yescharacteristic, complemented
58#106×C109C2211yescharacteristic, complemented
59#102×C109C2211yescharacteristic
60#102×C109C2211yescharacteristic, complemented
61C23×D109—21no—
62#13182029—22no—
63#13182029—22no—
64#13182028—22no—
65#13182028—22no—
66C2×Dic218D411yescharacteristic
67C2×Dic218C2311yescharacteristic
68C2×D436—21no—
69C2×D436D411yescharacteristic
70C2×D436C2311yescharacteristic
71C2×C22⋊D109—21no—
72C2×C22⋊D109—21no—
73C2×C22⋊D109—21no—
74C2×C22⋊D109—21no—
75C2×C22⋊D109—21no—
76C2×C22⋊D109D411yescharacteristic
77C2×C22⋊D109D411yescharacteristic
78D4×D109—22no—
79D4×D109—22no—
80C22×Dic109—21no—
81C2×C4×D109—21no—
82C2×C4×D109C2311yescharacteristic
83C2×C4×D109C2311yescharacteristic
84#13182018—22no—
85#13182017—22no—
86#13182014—22no—
87#13182012—22no—
88#13182012D414yescomplemented
89C2×#11724784—22no—
90C2×#11724784C2311yescharacteristic
91C2×#11724784C2311yescharacteristic
92C8×D109—22no—
93C8×D109—22no—
94C4⋊Dic109—21no—
95C4⋊Dic109C2311yescharacteristic
96C4⋊Dic109C2311yescharacteristic
97#13182008—21no—
98#13182008—21no—
99C22⋊Dic109—21no—
100C22⋊Dic109—21no—
101C22⋊Dic109—21no—
102#13182006—21no—
103#13182006—21no—
104#13182006—21no—
105#13182006—21no—
106C4×Dic109—21no—
107C2×D4×C109—21no—
108C2×D4×C109—21no—
109C2×D4×C109C2311yescharacteristic
110C2×D4×C109C2311yescharacteristic
111C22×C4×C109C2311yescharacteristic
112D8×C109—22no—
113M16×C109—22no—
114C2×C8×C109C2311yescharacteristic
115C2×C8×C109C2311yescharacteristic
116C4⋊C4×C109C2311yescharacteristic
117C4⋊C4×C109C2311yescharacteristic
118C22⋊C4×C109—21no—
119C22⋊C4×C109—21no—
120C23×C109—21no—
121C23×C109—21no—
122C23×C109C2×D411yescharacteristic
123C22×D109—21no—
124C22×D109—42no—
125C22×D109—81no—
126C22×D109—81no—
127C22×D109C2×D411yescharacteristic
128C22×D109C2×D411yescharacteristic
129D4×C109—21no—
130D4×C109—21no—
131D4×C109—21no—
132D4×C109—21no—
133D4×C109—81no—
134D4×C109—81no—
135C2×C4×C109—21no—
136C2×C4×C109—21no—
137C2×C4×C109—21no—
138C2×C4×C109—21no—
139C2×C4×C109C2×D411yescharacteristic
140C2×C4×C109C2411yescharacteristic
141C22⋊D109—22no—
142C22⋊D109—22no—
143C22⋊D109—42no—
144C22⋊D109—42no—
145C22⋊D109—81no—
146C22⋊D109—81no—
147C22⋊D109—81no—
148C2×Dic109—21no—
149C2×Dic109—21no—
150C2×Dic109—21no—
151C2×Dic109—42no—
152C2×Dic109C2×D411yescharacteristic
153C2×Dic109C2×D411yescharacteristic
154D436—22no—
155D436—21no—
156D436—21no—
157D436—81no—
158C4×D109—21no—
159C4×D109—21no—
160C4×D109—81no—
161C4×D109C2×D412yes—
162C4×D109#4112yes—
163Dic218—22no—
164Dic218—21no—
165Dic218—21no—
166C8×C109—21no—
167C8×C109C2×D412yes—
168#11724784—21no—
169#11724784C2×D412yes—
170C22×C109—21no—
171C22×C109—21no—
172C22×C109—21no—
173C22×C109—41no—
174C22×C109—41no—
175C22×C109—41no—
176C22×C109—41no—
177C22×C109—41no—
178C22×C109—41no—
179C22×C109C22×D411yescharacteristic
180C2×D109—21no—
181C2×D109—21no—
182C2×D109—21no—
183C2×D109—21no—
184C2×D109—21no—
185C2×D109—41no—
186C2×D109—41no—
187C2×D109—41no—
188C2×D109—84no—
189C2×D109#12112yes—
190C4×C109—21no—
191C4×C109—41no—
192C4×C109—41no—
193C4×C109C22×D411yescharacteristic
194C4×C109C2×#4111yescharacteristic
195Dic109—21no—
196Dic109—41no—
197Dic109—41no—
198Dic109—41no—
199Dic109#12112yes—
200C2×C109—41no—
201C2×C109—81no—
202C2×C109—81no—
203C2×C109C2×#12111yescharacteristic
204C2×C109#57611yescharacteristic
205C2×C109#57711yescharacteristic
206D109—22no—
207D109—41no—
208D109—81no—
209#3062—1091nomaximal, Sylow
210C109#306211yescharacteristic, complemented, Sylow
211C2×AGL(1,ℤ/8)—1091no—
212C2×#131—1091no—
213#537—1091no—
214#535—1091no—
215#469—1091no—
216#469D10911yescharacteristic, complemented
217#468—1091no—
218#468—1091no—
219#466—1091no—
220#466—1091no—
221#465—1091no—
222#465—1091no—
223#428—1091no—
224#416—1091no—
225C2×#102—1091no—
226C2×#41—1091no—
227C2×#41—1091no—
228C22×D4—1091no—
229AGL(1,ℤ/8)—2184no—
230C2×SD16—1091no—
231C2×SD16—1091no—
232C2×D8—1091no—
233C2×D8C2×D10911yescharacteristic
234#131—2184no—
235C2×M16—1091no—
236C2×M16—1091no—
237C2×M16C2×D10911yescharacteristic, complemented
238C22×C8—1091no—
239C22×C8—1091no—
240C22×C8—1091no—
241#127—2181no—
242#124—2181no—
243C22⋊Q8—1091no—
244C22⋊Q8—1091no—
245C22⋊Q8—2181no—
246#121—1091no—
247#121—1091no—
248#121—1091no—
249#121—1091no—
250#121—2181no—
251#121—2181no—
252#121—2181no—
253#121C2×D10911yescharacteristic
254#121C2×D10911yescharacteristic, complemented
255#120—2181no—
256#120—2181no—
257#117—1091no—
258C2×C4⋊C4—1091no—
259#107—1091no—
260#107—1091no—
261#106—1091no—
262#106C2×D10911yescharacteristic, complemented
263#103—1091no—
264#103—1091no—
265#102—1091no—
266#102—1091no—
267#102—1091no—
268#102—1091no—
269#102C2×D10911yescharacteristic
270#102C2×D10911yescharacteristic, complemented
271C24—2181no—
272#41—2182no—
273#41—2182no—
274#41—2182no—
275#41—2182no—
276C2×Q8—1091no—
277C2×Q8—1091no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—1091no—
281C2×D4—1091no—
282C2×D4—1091no—
283C2×D4—1091no—
284C2×D4—2181no—
285C2×D4—2182no—
286C2×D4—2182no—
287C2×D4—2181no—
288C2×D4—2181no—
289C2×D4—2181no—
290C2×D4—2181no—
291C2×D4—2181no—
292C2×D4C22×D10911yescharacteristic
293C2×D4C22×D10911yescharacteristic
294C22×C4—1091no—
295C22×C4—1091no—
296C22×C4—2181no—
297C22×C4—2181no—
298C22×C4C22×D10911yescharacteristic
299SD16—2182no—
300SD16—2182no—
301D8—22no—
302D8—2182no—
303M16—22no—
304M16—1094no—
305M16—2182no—
306C2×C8—1091no—
307C2×C8—1091no—
308C2×C8—2182no—
309C2×C8—2182no—
310C2×C8—2182no—
311C2×C8C22×D10911yescharacteristic
312C2×C8C22×D10911yescharacteristic
313C4⋊C4—1091no—
314C4⋊C4—1091no—
315C4⋊C4—2181no—
316C4⋊C4—2181no—
317C4⋊C4—2181no—
318C4⋊C4C22×D10911yescharacteristic
319C4⋊C4C22×D10911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—2181no—
323C22⋊C4—2181no—
324C22⋊C4—2181no—
325C22⋊C4—2181no—
326C22⋊C4—2181no—
327C22⋊C4—2181no—
328C22⋊C4—2181no—
329C42—2181no—
330C23—21no—
331C23—21no—
332C23—8721no—
333C23—8721no—
334C23—1091no—
335C23—1091no—
336C23—4362no—
337C23—2181no—
338C23D4×D10911yescharacteristic
339Q8—2182no—
340Q8—2181no—
341Q8—2181no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—81no—
347D4—81no—
348D4—8721no—
349D4—8721no—
350D4—8721no—
351D4—8721no—
352D4—4362no—
353D4—4362no—
354D4—2182no—
355D4—2182no—
356D4—2182no—
357D4—2181no—
358D4—2181no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—8721no—
364C2×C4—1091no—
365C2×C4—1092no—
366C2×C4—1092no—
367C2×C4—1091no—
368C2×C4—4362no—
369C2×C4—2181no—
370C2×C4—2181no—
371C2×C4—2181no—
372C2×C4—2181no—
373C2×C4—2181no—
374C2×C4D4×D10911yescharacteristic
375C2×C4C23×D10911yescharacteristic
376C8—21no—
377C8—1092no—
378C8—2181no—
379C8D4×D10912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—8724no—
390C22—1092no—
391C22—4361no—
392C22—4361no—
393C22—4361no—
394C22—2181no—
395C22—2181no—
396C22—2181no—
397C22—2181no—
398C22—2181no—
399C22C2×D4×D10911yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—1092no—
404C4—4361no—
405C4—4361no—
406C4—4361no—
407C4—2181no—
408C4C2×D4×D10911yescharacteristic
409C4#41×D10911yescharacteristic
410C2—41no—
411C2—81no—
412C2—81no—
413C2—8721no—
414C2—4361no—
415C2—2182no—
416C2#121×D10911yescharacteristic
417C2#2029583011yescharacteristic
418C2#2029583611yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#469×C109C2
socleC22×C109C22×D4
hypercenter#469D109
hypocenterC109#3062
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#16812723C2semidirect
2. C2×#16812707C2semidirect
3. #20295605C2semidirect
4. #20295592C2semidirect
5. #20295278C2semidirect
6. #20295272C2semidirect
7. #20295271C2semidirect
8. #20295260C2semidirect
9. #20295259C2semidirect
10. #20295256C2semidirect
11. #20295253C2semidirect
12. #20295065C2semidirect
13. #20295019C2semidirect
14. #102×D109C2semidirect
15. #469×C109C2semidirect
25. C2×#13182012C22semidirect
26. C22×#11724784C22semidirect
28. C2×C8×D109C22semidirect
31. #16812679C22semidirect
32. #16812678C22semidirect
40. #16812670C22semidirect
45. #16812633C22semidirect
46. #16812632C22semidirect
47. #16812630C22semidirect
48. #16812624C22semidirect
49. #16812622C22semidirect
52. #16812620C22semidirect
55. C2×M16×C109C22semidirect
57. #121×C109C22semidirect
58. #106×C109C22semidirect
60. #102×C109C22semidirect
88. #13182012D4semidirect
210. C109#3062semidirect
216. #469D109semidirect
237. C2×M16C2×D109semidirect
254. #121C2×D109semidirect
262. #106C2×D109semidirect
270. #102C2×D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127232
C2×#168127072
#202956052
#202955922
#202952782
#202952722
#202952712
#202952602
#202952592
#202952562
#202952532
#202950652
#202950192
#102×D1092
#469×C1092
#3062109