Finite Group Databasebeta

← #30606619

Subgroups — #30606619

Order 15616.

428 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462146C211yesmaximal, characteristic
2#21462139C211yesmaximal, characteristic
3C4×#14519852C211yesmaximal, characteristic, complemented
4#21461621C211yesmaximal, characteristic, complemented
5#21460899C211yesmaximal, characteristic, complemented
6#21460896C211yesmaximal, characteristic, complemented
7#443×D61C211yesmaximal, characteristic
8C2×#14519852C2211yescharacteristic
9C2×#14519852C2211yescharacteristic
10D61⋊#108C2211yescharacteristic
11#16840772C2211yescharacteristic
12#16840725—21no—
13#16840681C412yescomplemented
14#16840680C412yescomplemented
15#16840679C412yescomplemented
16#16840678C412yescomplemented
17#16840651—21no—
18C4×#11758187—21no—
19#16840633—21no—
20#135×D61C2211yescharacteristic
21#131×D61—21no—
22#16839880C411yescharacteristic, complemented
23#16839879C411yescharacteristic, complemented
24#16839878C411yescharacteristic, complemented
25#16839877—21no—
26#16839876—21no—
27#108×D61C2211yescharacteristic
28#104×D61—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#443C411yescharacteristic, complemented
31D61⋊M16—21no—
32#14519856—21no—
33#14519852—21no—
34#14519852—21no—
35#14519852C2×C412yes—
36#14519852C2×C412yes—
37C2×#11758187—21no—
38C2×#11758187—21no—
39#14519848—21no—
40#14519847C2×C412yes—
41#14519846—21no—
42#14519845C2×C412yes—
43#14519831—41no—
44C8×#6923—41no—
45#41×D61—21no—
46#14519800C2×C411yescharacteristic
47#14519799C2×C411yescharacteristic
48#14519798—21no—
49#14519797—21no—
50#14519796C2×C411yescharacteristic
51Q16×D61C2×C411yescharacteristic
52SD16×D61—21no—
53D8×D61C2×C411yescharacteristic
54#14519785—21no—
55#14519785—41no—
56#14519784—21no—
57#14519783—21no—
58#14519783—41no—
59M16×D61—21no—
60M16×D61—41no—
61C2×C8×D61—41no—
62C2×C8×D61D411yescharacteristic
63C2×C8×D61C2311yescharacteristic
64C42×D61D411yescharacteristic
65#14519713C2×C411yescharacteristic
66#14519712—21no—
67#14519705—21no—
68#14519704—21no—
69#14519703—21no—
70C4×#92418D411yescharacteristic
71C8×Dic61C2×C411yescharacteristic
72C8×Dic61D411yescharacteristic
73#135×C61C2×C411yescharacteristic
74#131×C61—21no—
75#108×C61C2×C411yescharacteristic
76#104×C61—21no—
77C4×C8×C61C2×C411yescharacteristic
78#41×C61—21no—
79#11758226—21no—
80Q8×D61—21no—
81#11758224—21no—
82#11758224—41no—
83D4×D61—21no—
84D4×D61—41no—
85#11758222—21no—
86#11758222—41no—
87C2×C4×D61—21no—
88C2×C4×D61—41no—
89C2×C4×D61C2×D411yescharacteristic
90C22⋊#6923—41no—
91#11758217—41no—
92C4⋊#6923—22no—
93C4×#6923—41no—
94#11758213—22no—
95D61⋊C8—41no—
96Q16×C61C4211yescharacteristic
97SD16×C61—21no—
98D8×C61C4211yescharacteristic
99M16×C61—21no—
100M16×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61C22⋊C411yescharacteristic
103C2×C8×C61C22×C411yescharacteristic
104C42×C61C22⋊C411yescharacteristic
105#11758202—21no—
106#11758201—21no—
107#11758200—21no—
108#11758199—21no—
109C4×Dic61—21no—
110C4×Dic61C22⋊C411yescharacteristic
111#11758194—21no—
112#11758194—41no—
113C2×#92418—41no—
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C2×D411yescharacteristic
116Dic244C4211yescharacteristic
117D488C4211yescharacteristic
118#11758190—21no—
119#11758189—41no—
120#11758189—41no—
121#11758189—41no—
122C8×D61—41no—
123C8×D61—41no—
124C8×D61—41no—
125C8×D61D811yescharacteristic
126C8×D61D811yescharacteristic
127C8×D61SD1611yescharacteristic
128C8×D61SD1611yescharacteristic
129C8×D61C22×C411yescharacteristic
130C8×D61C22×C411yescharacteristic
131C8×D61#4111yescharacteristic
132C8×D61#4111yescharacteristic
133#11758187—22no—
134#11758187—22no—
135C22×D61—41no—
136C22×D61#13511yescharacteristic
137C2×#6923—42no—
138Q8×C61—21no—
139D4×C61—21no—
140D4×C61—41no—
141C2×C4×C61—21no—
142C2×C4×C61—41no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C22⋊D61—41no—
145C22⋊D61—41no—
146C22⋊D61—41no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61#13511yescharacteristic
150D244—21no—
151D244—41no—
152C4×D61—42no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61C4×D411yescharacteristic
157C4×D61C4×D411yescharacteristic
158C4×D61C2×D811yescharacteristic
159C4×D61C2×SD1611yescharacteristic
160Dic122—21no—
161Dic122—41no—
162#92420—42no—
163C8×C61—41no—
164C8×C61#10211yescharacteristic
165C8×C61#10211yescharacteristic
166C8×C61C2×C4211yescharacteristic
167C8×C61#11711yescharacteristic
168#92418—41no—
169#92418#10211yescharacteristic
170#92418#10211yescharacteristic
171#92418C4×D411yescharacteristic
172#92418C4×D411yescharacteristic
173#12646—611nomaximal, Sylow
174C22×C61—41no—
175C22×C61#41611yescharacteristic
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—82no—
179C2×D61C4×D811yescharacteristic
180C2×D61C4×SD1611yescharacteristic
181#6923—82no—
182C4×C61—22no—
183C4×C61—41no—
184C4×C61C4×C22⋊C411yescharacteristic
185C4×C61C2×#10211yescharacteristic
186Dic61—41no—
187Dic61—41no—
188Dic61C4×D811yescharacteristic
189Dic61C4×SD1611yescharacteristic
190C2×#443—611no—
191#2148—611no—
192#2145—611no—
193C4×M32—611no—
194#1772—611no—
195#1389—611no—
196#1388—611no—
197C2×C61—21no—
198C2×C61—81no—
199C2×C61C4×#10211yescharacteristic
200D61—21no—
201D61—21no—
202D61—81no—
203C2×#135—611no—
204C2×#131—1221no—
205C2×M32—611no—
206C2×M32—611no—
207#443—611no—
208#443—611no—
209#443—611no—
210#443—1221no—
211#443—1221no—
212#443#692311yescharacteristic, complemented
213C2×#108—611no—
214C2×#108—611no—
215#427—611no—
216C2×#104—1221no—
217#405—1221no—
218C2×C4×C8—611no—
219#362—612no—
220#361—612no—
221#360—612no—
222#360—612no—
223#346—1221no—
224C4×C16—1221no—
225#339—1221no—
226C61#1264611yescharacteristic, complemented, Sylow
227C2×#41—1221no—
228#135—611no—
229#135—611no—
230#135—611no—
231#135—1221no—
232#135—1221no—
233#135C2×#692311yescharacteristic
234C2×Q16—611no—
235C2×SD16—1221no—
236C2×D8—611no—
237#131—21no—
238#131—1221no—
239#131—1221no—
240#131—1221no—
241#131—2441no—
242#131—2441no—
243C2×M16—1221no—
244C2×M16—1221no—
245C2×M16—2441no—
246C22×C8—611no—
247C22×C8—611no—
248C22×C8—2441no—
249#117—1221no—
250C2×C42—611no—
251M32—612no—
252M32—612no—
253M32—1221no—
254M32—1221no—
255C2×C16—1221no—
256C2×C16—1221no—
257#108—612no—
258#108—611no—
259#108—1221no—
260#108—1221no—
261#108C2×#692311yescharacteristic
262#107—1221no—
263#106—612no—
264#104—21no—
265#104—1221no—
266#104—1221no—
267#104—1221no—
268#97—2441no—
269C4×C8—611no—
270C4×C8—611no—
271C4×C8—611no—
272C4×C8—2441no—
273C4×C8C2×#692311yescharacteristic
274#41—21no—
275#41—1221no—
276#41—1221no—
277#41—1221no—
278#41—2441no—
279#41—2441no—
280C2×Q8—1221no—
281C2×D4—1221no—
282C2×D4—2441no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—2441no—
286Q16—611no—
287Q16—1221no—
288Q16C4×#692311yescharacteristic
289SD16—21no—
290SD16—1221no—
291SD16—1221no—
292SD16—1221no—
293D8—611no—
294D8—1221no—
295D8C4×#692311yescharacteristic
296M16—21no—
297M16—41no—
298M16—1222no—
299M16—1221no—
300M16—2441no—
301M16—2441no—
302M16—2441no—
303M16—2441no—
304M16—2441no—
305C2×C8—41no—
306C2×C8—611no—
307C2×C8—611no—
308C2×C8—611no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—611no—
312C2×C8—611no—
313C2×C8—611no—
314C2×C8—611no—
315C2×C8—611no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8C22⋊#692311yescharacteristic
322C2×C8C22×#692311yescharacteristic
323C4⋊C4—1222no—
324C22⋊C4—2441no—
325C42—611no—
326C42—1221no—
327C42—2441no—
328C42C22⋊#692311yescharacteristic
329C16—1222no—
330C16—1222no—
331C23—611no—
332C23—2441no—
333Q8—21no—
334Q8—1221no—
335Q8—2441no—
336D4—21no—
337D4—41no—
338D4—1221no—
339D4—2441no—
340D4—2441no—
341D4—2441no—
342D4—2441no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1221no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4C2×C22⋊#692311yescharacteristic
358C8—41no—
359C8—611no—
360C8—611no—
361C8—611no—
362C8—611no—
363C8—2442no—
364C8—2441no—
365C8#1451983911yescharacteristic
366C8#1451983911yescharacteristic
367C8C2×C4×#692311yescharacteristic
368C8#1451985611yescharacteristic
369C22—41no—
370C22—611no—
371C22—611no—
372C22—4882no—
373C22—2441no—
374C22—2441no—
375C22#1684075211yescharacteristic
376C4—22no—
377C4—41no—
378C4—611no—
379C4—611no—
380C4—4882no—
381C4—2441no—
382C4—2441no—
383C4C4×C22⋊#692311yescharacteristic
384C4C2×#1451983911yescharacteristic
385C2—21no—
386C2—81no—
387C2—1221no—
388C2—1221no—
389C2—4881no—
390C2C4×#1451983911yescharacteristic
subgroupG/H
centerC4C2×#14519839
commutatorC8×C61C2×C42
FrattiniC2×C8C22×#6923
FittingC61×#443C4
socleC2×C61C4×#102
prime radical#135×D61C22
cosocleC2×C8×D61C23
hypercenter#443#6923
hypocenterC61#12646
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
3. C4×#14519852C2semidirect
4. #21461621C2semidirect
5. #21460899C2semidirect
6. #21460896C2semidirect
13. #16840681C4semidirect
14. #16840680C4semidirect
15. #16840679C4semidirect
16. #16840678C4semidirect
22. #16839880C4semidirect
23. #16839879C4semidirect
24. #16839878C4semidirect
30. C61×#443C4semidirect
212. #443#6923semidirect
226. C61#12646semidirect

Maximal subgroups

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

subgroupindex
#214621462
#214621392
C4×#145198522
#214616212
#214608992
#214608962
#443×D612
#1264661