Finite Group Databasebeta

← #29596073

Subgroups — #29596073

Order 15616.

422 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454590C211yesmaximal, characteristic
2C2×#16839580C211yesmaximal, characteristic, complemented
3C2×#16839570C211yesmaximal, characteristic
4C2×#16839568C211yesmaximal, characteristic
5#21445989C211yesmaximal, characteristic, complemented
6#21443914C211yesmaximal, characteristic, complemented
7C61×#1382C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9#16840230—21no—
10C22×#11758185C2211yescharacteristic
11#16839856C411yescharacteristic
12#16839856C411yescharacteristic
13#16839849—21no—
14#16839849—21no—
15#16839844C411yescharacteristic
16#16839844C411yescharacteristic
17C2×#14519713C2211yescharacteristic
18C2×#14519712—21no—
19#16839785—21no—
20#16839756—21no—
21C2×C8×Dic61C2211yescharacteristic
22#16839580—21no—
23#16839580—21no—
24#16839570—22no—
25#16839568—22no—
26C22×C16×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C61×#427C2211yescharacteristic
29C2×#11758222—21no—
30#14519799—21no—
31#14519799—21no—
32#14519799D412yes—
33#14519799Q812yes—
34C2×Dic244C2×C411yescharacteristic
35C2×#11758190—21no—
36C2×D488C2×C411yescharacteristic
37C2×#11758194—21no—
38C22×#92418D411yescharacteristic
39#14519742—21no—
40#14519742—21no—
41#14519739—21no—
42#14519739—21no—
43#14519737—41no—
44#14519737—41no—
45#14519734—41no—
46C2×C4×Dic61D411yescharacteristic
47C42×D61—41no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50C2×#11758185—21no—
51#14519713—21no—
52#14519713—21no—
53#14519712—42no—
54#14519706—41no—
55#14519706—41no—
56#14519700—21no—
57#14519700—21no—
58#14519697—21no—
59#14519697—21no—
60C8×Dic61C2×C411yescharacteristic
61C8×Dic61C2×C411yescharacteristic
62C8×Dic61D411yescharacteristic
63C8×Dic61D411yescharacteristic
64C2×M16×C61—21no—
65C22×C8×C61C2311yescharacteristic
66#117×C61—21no—
67C2×C16×C61—21no—
68C2×C16×C61—21no—
69C2×C16×C61—21no—
70#108×C61—21no—
71#108×C61—21no—
72#107×C61C2×C411yescharacteristic
73#107×C61C2×C411yescharacteristic
74#106×C61—21no—
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—41no—
77C22×Dic61SD1611yescharacteristic
78C22×Dic61SD1611yescharacteristic
79#11758222—22no—
80#11758222—22no—
81#11758222—41no—
82#11758222—41no—
83C2×D244—21no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×Dic122—21no—
88M16×C61—41no—
89M16×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61C22×C411yescharacteristic
92C2×C8×C61C2×D411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×Q811yescharacteristic
95C2×C8×C61#4111yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C22⋊C4×C61—41no—
100C42×C61—41no—
101#11758198—41no—
102#11758198—41no—
103#11758196—41no—
104#11758196—41no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61D811yescharacteristic
110C4×Dic61D811yescharacteristic
111#11758194—41no—
112#11758194—41no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—41no—
116C2×#92418C22⋊C411yescharacteristic
117C2×#92418C22⋊C411yescharacteristic
118Dic244—21no—
119Dic244C4⋊C412yes—
120D488—21no—
121D488C4⋊C412yes—
122#11758190—22no—
123#11758190—22no—
124C16×C61—41no—
125#11758185—41no—
126C23×C61C2×SD1611yescharacteristic
127C22×D61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61C2×D811yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—22no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#10211yescharacteristic
142C2×Dic61#10211yescharacteristic
143C2×Dic61#10211yescharacteristic
144C2×Dic61#10211yescharacteristic
145D244—22no—
146D244—41no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—82no—
150C4×D61—82no—
151Dic122—22no—
152Dic122—41no—
153C8×C61—81no—
154C8×C61C2×C4⋊C411yescharacteristic
155C8×C61#11711yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61C22⋊Q811yescharacteristic
158#92418—21no—
159#92418—21no—
160#92418—81no—
161#12815—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61C2×#10211yescharacteristic
165C22×C61#46111yescharacteristic
166C22×C61#47611yescharacteristic
167C2×D61—42no—
168C2×D61—81no—
169C2×D61—81no—
170C4×C61—81no—
171C4×C61—81no—
172C4×C61#38011yescharacteristic
173C4×C61#41711yescharacteristic
174C4×C61#45911yescharacteristic
175C4×C61#47411yescharacteristic
176Dic61—21no—
177Dic61—21no—
178Dic61—21no—
179Dic61—42no—
180Dic61#35912yescomplemented
181C4×#135—611no—
182C2×C4⋊C16—611no—
183C2×#359—611no—
184C2×#359—611no—
185#1848—611no—
186#1382—611no—
187#1382D6111yescharacteristic, complemented
188C2×C61—21no—
189C2×C61—21no—
190C2×C61#180211yescharacteristic
191C2×C61C2×#35911yescharacteristic
192C2×C61#214311yescharacteristic
193D61—82no—
194C2×#135—611no—
195C4×#41—1221no—
196C22×C16—611no—
197C22×C16C2×D6111yescharacteristic
198C4×Q16—611no—
199C4×Q16—611no—
200C4×SD16—1221no—
201C4×SD16—1221no—
202C4×D8—611no—
203C4×D8—611no—
204C2×#108—611no—
205C2×#108—1221no—
206C2×#108C2×D6111yescharacteristic
207#427C2×D6111yescharacteristic
208#423—1221no—
209#416—1221no—
210C2×C4×C8—611no—
211C4⋊C16—1221no—
212C4⋊C16—1221no—
213#359—1222no—
214#359—1222no—
215C61#1281511yescharacteristic, complemented, Sylow
216C2×#41—1221no—
217#135—612no—
218#135—612no—
219#135—1221no—
220#135—1221no—
221C2×Q16—611no—
222C2×SD16—1221no—
223C2×D8—611no—
224C2×M16—21no—
225C2×M16—1221no—
226C22×C8—611no—
227C22×C8C22×D6111yescharacteristic
228C4×Q8—1221no—
229C4×Q8—1221no—
230C4×D4—1221no—
231C4×D4—1221no—
232C4×D4—2441no—
233C4×D4—2441no—
234#117—21no—
235#117—2441no—
236C2×C42—611no—
237C2×C42—2441no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—1221no—
242C2×C16—1221no—
243C2×C16—1221no—
244#108—21no—
245#108—21no—
246#108—1221no—
247#108—1221no—
248#108—2442no—
249#107C4×D6111yescharacteristic
250#107C4×D6111yescharacteristic
251#106—21no—
252C4⋊C8—2441no—
253C4⋊C8—2441no—
254#103—1221no—
255#103—1221no—
256#102—1221no—
257#102—1221no—
258C4×C8—611no—
259C4×C8—611no—
260C4×C8—611no—
261C4×C8—611no—
262#41—1222no—
263#41—1222no—
264#41—2441no—
265#41—2441no—
266C2×Q8—1221no—
267C2×D4—1221no—
268C2×D4—2441no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4D4×D6111yescharacteristic
275Q16—612no—
276Q16—1221no—
277SD16—1222no—
278SD16—1222no—
279D8—612no—
280D8—1221no—
281M16—41no—
282M16—41no—
283M16—2441no—
284M16—2441no—
285C2×C8—41no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—2441no—
291C2×C8C2×C4×D6111yescharacteristic
292C2×C8#1175822211yescharacteristic
293C2×C8#1175822211yescharacteristic
294C2×C8D4×D6111yescharacteristic
295C2×C8D4×D6111yescharacteristic
296C2×C8Q8×D6111yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—41no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—41no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—2441no—
310C42—2441no—
311C16—41no—
312C16—2441no—
313C23—2441no—
314C23SD16×D6111yescharacteristic
315Q8—1222no—
316Q8—2441no—
317D4—1222no—
318D4—2442no—
319D4—2442no—
320D4—2441no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—1222no—
328C2×C4—4882no—
329C2×C4—4882no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4C22⋊C4×D6111yescharacteristic
335C2×C4#1451975011yescharacteristic
336C2×C4#1451975511yescharacteristic
337C2×C4D8×D6111yescharacteristic
338C2×C4#1451980411yescharacteristic
339C2×C4#1451980911yescharacteristic
340C8—81no—
341C8—1221no—
342C8—1221no—
343C8—4881no—
344C8C4⋊C4×D6111yescharacteristic
345C8#1451973411yescharacteristic
346C8#1451975011yescharacteristic
347C8#1451975511yescharacteristic
348C22—21no—
349C22—21no—
350C22—4881no—
351C22—4881no—
352C22—2442no—
353C22#102×D6111yescharacteristic
354C22#1683996611yescharacteristic
355C22#1684005111yescharacteristic
356C4—81no—
357C4—81no—
358C4—612no—
359C4—1221no—
360C4—1221no—
361C4—1221no—
362C4—2442no—
363C4#1683962111yescharacteristic
364C4#1683976211yescharacteristic
365C4#1683995611yescharacteristic
366C4#1684004111yescharacteristic
367C2—21no—
368C2—21no—
369C2—4882no—
370C2#2144581811yescharacteristic
371C2#359×D6111yescharacteristic
372C2#2144754511yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1382C2
socleC22×C61C2×#102
prime radicalC2×#14519799C22
cosocleC22×C8×C61C23
hypercenter#1382D61
hypocenterC61#12815
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
2. C2×#16839580C2semidirect
5. #21445989C2semidirect
6. #21443914C2semidirect
7. C61×#1382C2semidirect
180. Dic61#359semidirect
187. #1382D61semidirect
215. C61#12815semidirect

Maximal subgroups

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

subgroupindex
#214545902
C2×#168395802
C2×#168395702
C2×#168395682
#214459892
#214439142
C61×#13822
#1281561