Finite Group Databasebeta

← #29597085

Subgroups — #29597085

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519722C211yesmaximal, characteristic
2C2×#16839844C211yesmaximal, characteristic
3C2×#16839565C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic
5#21446678C211yesmaximal, characteristic, complemented
6#21443896C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×D488C2211yescharacteristic
10C2×#14519739—21no—
11C2×#14519722—22no—
12C2×#14519722—22no—
13C2×#14519722C414yescomplemented
14C22×#11758185C2211yescharacteristic
15#16839844—22no—
16#16839844—22no—
17C2×#14519700—21no—
18C2×#14519697—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839667—21no—
21#16839565—22no—
22#16839562—22no—
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C22×Dic122—21no—
27C22×D244—21no—
28C22×C4×D61—41no—
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×Dic244—21no—
32C2×Dic244—21no—
33C2×Dic244—21no—
34C2×Dic244C2×C412yescomplemented
35C2×D488—21no—
36C2×D488—21no—
37C2×D488—21no—
38C2×D488C2×C412yes—
39C2×D488D412yes—
40C2×D488D412yes—
41C22×#92418D411yescharacteristic
42#14519739—24no—
43#14519739—42no—
44C2×#11758198—41no—
45C2×C4×Dic61D411yescharacteristic
46#14519722—28no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50#14519700—42no—
51#14519697—24no—
52C8×Dic61—21no—
53C8×Dic61—21no—
54#14519684—41no—
55#14519684—41no—
56C22×C8×C61C2311yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61C2×C412yescomplemented
62#107×C61—21no—
63#107×C61—21no—
64#107×C61—21no—
65#107×C61D412yes—
66C23×D61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—41no—
71C22×Dic61D811yescharacteristic
72C22×Dic61D811yescharacteristic
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×C4×D61—44no—
80C2×C4×D61—82no—
81C2×C4×D61—82no—
82C2×Dic122—22no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87C2×Dic122—41no—
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C4⋊C4×C61—22no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98#11758198—44no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C2×#92418—21no—
102C2×#92418—21no—
103C2×#92418—21no—
104Dic244—22no—
105Dic244—22no—
106Dic244—41no—
107Dic244—41no—
108D488—22no—
109D488—22no—
110D488—22no—
111D488C22⋊C414yes—
112C16×C61—22no—
113#11758185—41no—
114C23×C61C2×D811yescharacteristic
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—81no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61—81no—
122C2×C4×C61—42no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61#12111yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61SD3212yescomplemented
143D244—24no—
144D244—42no—
145D244—42no—
146D244—42no—
147C4×D61—88no—
148Dic122—42no—
149Dic122—42no—
150Dic122—81no—
151Dic122—81no—
152C8×C61C2×C22⋊C411yescharacteristic
153C8×C61C4×D411yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12311yescharacteristic
156#92418—41no—
157#13014—611nomaximal, Sylow
158C22×C61C4×D811yescharacteristic
159C22×C61#44711yescharacteristic
160C22×C61#45911yescharacteristic
161C22×C61C2×SD3211yescharacteristic
162C22×C61#50811yescharacteristic
163C22×C61#50911yescharacteristic
164C22×C61#51011yescharacteristic
165C2×D61—44no—
166C2×D61—82no—
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—82no—
170C2×D61—82no—
171C2×D61—82no—
172C4×C61—82no—
173C4×C61—161no—
174C4×C61#38611yescharacteristic
175C4×C61#44211yescharacteristic
176C4×C61#44911yescharacteristic
177C4×C61#46311yescharacteristic
178Dic61—22no—
179Dic61—41no—
180Dic61—82no—
181C22×SD32—611no—
182C2×C4×D8—611no—
183C2×#358—611no—
184C2×#357—611no—
185#1969—611no—
186#1380D6111yescharacteristic, complemented
187#1374—611no—
188C2×C61#187911yescharacteristic
189C2×C61C4×SD3211yescharacteristic
190C2×C61#217511yescharacteristic
191C2×C61#218711yescharacteristic
192C2×C61#218911yescharacteristic
193C2×C61#220811yescharacteristic
194C2×C61#221011yescharacteristic
195D61—84no—
196C22×Q16—611no—
197C22×D8—611no—
198C2×C4×D4—1221no—
199C2×SD32—614no—
200C2×SD32—1222no—
201C2×SD32—1222no—
202C22×C16—611no—
203C22×C16C2×D6111yescharacteristic
204C4×D8—1222no—
205C4×D8—1222no—
206C2×#107C2×D6111yescharacteristic
207C2×#107C2×D6111yescharacteristic
208C2×#103—1221no—
209C2×#102—1221no—
210C2×C4×C8—611no—
211#391—1221no—
212#358—1222no—
213#357—1222no—
214C61#1301411yescharacteristic, complemented, Sylow
215C22×Q8—1221no—
216C22×D4—1221no—
217C23×C4—2441no—
218C2×Q16—612no—
219C2×Q16—1221no—
220C2×Q16—1221no—
221C2×Q16—1221no—
222C2×Q16—1221no—
223C2×Q16—1221no—
224C2×D8—612no—
225C2×D8—612no—
226C2×D8—612no—
227C2×D8—1221no—
228C2×D8—1221no—
229C2×D8—1221no—
230C22×C8—611no—
231C22×C8C22×D6111yescharacteristic
232C4×D4—1224no—
233C4×D4—2442no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C22⋊C4—2441no—
237C2×C42—611no—
238SD32—1228no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—1221no—
242C2×C16—1221no—
243C2×C16—1221no—
244C2×C16C4×D6112yescomplemented
245#107—21no—
246#107—21no—
247#107—21no—
248#107D24412yes—
249#103—2442no—
250#102—1224no—
251C4×C8—1221no—
252C4×C8—1221no—
253#95—2441no—
254#95—2441no—
255C24—2441no—
256C2×Q8—1222no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×Q8—2441no—
262C2×D4—1222no—
263C2×D4—1222no—
264C2×D4—1222no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2441no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—4882no—
273C22×C4—4882no—
274C22×C4—2444no—
275C22×C4—2441no—
276C22×C4D4×D6111yescharacteristic
277Q16—1222no—
278Q16—1222no—
279Q16—2441no—
280Q16—2441no—
281D8—614no—
282D8—1222no—
283D8—1222no—
284D8—1222no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8C2×C4×D6111yescharacteristic
289C2×C8C2×D24411yescharacteristic
290C2×C8#1175822211yescharacteristic
291C2×C8D4×D6111yescharacteristic
292C2×C8D4×D6111yescharacteristic
293C2×C8#1175822611yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—2444no—
299C42—1221no—
300C42—1221no—
301C16—22no—
302C16—2441no—
303C23—4881no—
304C23—4881no—
305C23—4881no—
306C23—4881no—
307C23—2442no—
308C23—2442no—
309C23—2442no—
310C23D8×D6111yescharacteristic
311Q8—4881no—
312Q8—4881no—
313Q8—2442no—
314Q8—2442no—
315D4—1224no—
316D4—2442no—
317D4—2442no—
318D4—2442no—
319C2×C4—42no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—612no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4888no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—2442no—
335C2×C4#1451973911yescharacteristic
336C2×C4#1451974711yescharacteristic
337C2×C4#1451975011yescharacteristic
338C2×C4#1451980011yescharacteristic
339C2×C4#1451980411yescharacteristic
340C2×C4#1451980411yescharacteristic
341C8—2441no—
342C8C22⋊C4×D6111yescharacteristic
343C8C4×D24411yescharacteristic
344C8#1451975211yescharacteristic
345C8#1451976211yescharacteristic
346C22—4882no—
347C22—4882no—
348C22—4882no—
349C22—4882no—
350C22—4882no—
351C22—4882no—
352C22—2444no—
353C22#1683984411yescharacteristic
354C22#1683989711yescharacteristic
355C22#1683995611yescharacteristic
356C22SD32×D6111yescharacteristic
357C22#1684019311yescharacteristic
358C22#1684019611yescharacteristic
359C22#1684020411yescharacteristic
360C4—82no—
361C4—161no—
362C4—1222no—
363C4—4882no—
364C4—2441no—
365C4#1683964011yescharacteristic
366C4#1683987311yescharacteristic
367C4#1683991011yescharacteristic
368C4#1683998011yescharacteristic
369C2—4884no—
370C2#2144616811yescharacteristic
371C2#2144767011yescharacteristic
372C2#2144768211yescharacteristic
373C2#2144774911yescharacteristic
374C2#2144776211yescharacteristic
375C2#2144786311yescharacteristic
376C2#2144787311yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1380C2
socleC23×C61C2×D8
prime radicalC22×D488C22
cosocleC22×C8×C61C23
hypercenter#1380D61
hypocenterC61#13014
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#16839565C2semidirect
5. #21446678C2semidirect
6. #21443896C2semidirect
7. C61×#1380C2semidirect
13. C2×#14519722C4semidirect
34. C2×Dic244C2×C4semidirect
61. C2×C16×C61C2×C4semidirect
142. C2×Dic61SD32semidirect
186. #1380D61semidirect
214. C61#13014semidirect
244. C2×C16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×#168398442
C2×#168395652
C2×#168395622
#214466782
#214438962
C61×#13802
#1301461