Finite Group Databasebeta

← #29599606

Subgroups — #29599606

Order 15616.

482 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
1C22×#14519718C211yesmaximal, characteristic
2C2×#16839580C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic, complemented
4#21446686C211yesmaximal, characteristic, complemented
5#21446683C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#357C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519718—22no—
10C2×#14519718—22no—
11C2×#14519718—22no—
12C22×#11758185C2211yescharacteristic
13C2×#14519711C2211yescharacteristic
14C2×#14519698—21no—
15C2×#14519697—21no—
16C2×C8×Dic61C2211yescharacteristic
17#16839665—21no—
18#16839663—21no—
19#16839580—22no—
20#16839564—22no—
21C22×D8×C61C2211yescharacteristic
22C22×C16×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#357—22no—
25C22×D244—21no—
26C2×D488—21no—
27C2×D488—21no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488D412yes—
32C22×#92418D411yescharacteristic
33C2×C4⋊Dic61—21no—
34C2×C22⋊Dic61—41no—
35C2×C22⋊Dic61—41no—
36C2×#11758198—41no—
37C2×#11758198—41no—
38C2×C4×Dic61D411yescharacteristic
39#14519718—28no—
40C2×#11758185—21no—
41C2×#11758185—21no—
42C2×#11758185D412yes—
43#14519711—21no—
44#14519711—21no—
45#14519698—42no—
46#14519697—42no—
47C8×Dic61—21no—
48C8×Dic61—21no—
49C22×D4×C61—21no—
50C2×D8×C61—21no—
51C2×D8×C61—21no—
52C2×D8×C61—21no—
53C2×D8×C61—21no—
54C2×D8×C61—21no—
55C2×D8×C61D412yes—
56C22×C8×C61C2311yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61#107×C61—21no—
62#107×C61—21no—
63C24×C61—41no—
64C23×D61—41no—
65C2×D4×C61—22no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—41no—
74C22×Dic61D811yescharacteristic
75C22×Dic61D811yescharacteristic
76C2×D244—22no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82D8×C61—22no—
83D8×C61—22no—
84D8×C61—41no—
85D8×C61—41no—
86C2×C8×C61C2×D411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C22⋊Dic61—82no—
95C22⋊Dic61—82no—
96#11758198—82no—
97#11758198—82no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418—21no—
105D488—22no—
106D488—22no—
107D488—41no—
108D488—41no—
109C16×C61—41no—
110#11758185—22no—
111C23×C61—42no—
112C23×C61—81no—
113C23×C61—81no—
114C23×C61—81no—
115C23×C61—81no—
116C23×C61—81no—
117C23×C61—81no—
118C23×C61C2×D811yescharacteristic
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126D4×C61—42no—
127D4×C61—42no—
128D4×C61—81no—
129D4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61D1612yescomplemented
148D244—42no—
149D244—42no—
150D244—81no—
151D244—81no—
152C8×C61#12011yescharacteristic
153C8×C61#12311yescharacteristic
154C8×C61#12311yescharacteristic
155C8×C61#12411yescharacteristic
156#92418—41no—
157#13448—611nomaximal, Sylow
158C22×C61—82no—
159C22×C61—82no—
160C22×C61—82no—
161C22×C61—161no—
162C22×C61—161no—
163C22×C61—161no—
164C22×C61—161no—
165C22×C61#45911yescharacteristic
166C22×C61#45911yescharacteristic
167C22×C61#46611yescharacteristic
168C22×C61C2×D1611yescharacteristic
169C22×C61#50811yescharacteristic
170C22×C61#50911yescharacteristic
171C22×C61#50911yescharacteristic
172C2×D61—82no—
173C2×D61—82no—
174C2×D61—82no—
175C2×D61—161no—
176C2×D61—161no—
177C2×D61—161no—
178C2×D61—161no—
179C4×C61—161no—
180C4×C61#39411yescharacteristic
181C4×C61#46311yescharacteristic
182C4×C61#46311yescharacteristic
183C4×C61#46911yescharacteristic
184Dic61—22no—
185Dic61—41no—
186Dic61—161no—
187C22×D16—611no—
188C2×C4⋊C16—611no—
189C2×#357—611no—
190C2×#357D6111yescharacteristic, complemented
191#1970—611no—
192#1970—611no—
193#1380—611no—
194C2×C61—162no—
195C2×C61#205411yescharacteristic
196C2×C61#220611yescharacteristic
197C2×C61#220611yescharacteristic
198C2×C61#221011yescharacteristic
199C2×C61#221011yescharacteristic
200C2×C61#221511yescharacteristic
201C2×C61#221811yescharacteristic
202D61—162no—
203C22×D8—611no—
204C22×D8C2×D6111yescharacteristic
205C2×D16—1222no—
206C2×D16—1222no—
207C2×D16—1222no—
208C22×C16—611no—
209C22×C16C2×D6111yescharacteristic
210C2×#107—611no—
211C2×#107C2×D6111yescharacteristic
212C2×#102—1221no—
213C2×#102—1221no—
214C2×C4×C8—611no—
215#390—1221no—
216#390—1221no—
217C4⋊C16—1222no—
218#357—22no—
219#357—1222no—
220C61#1344811yescharacteristic, complemented, Sylow
221C22×D4—21no—
222C22×D4—1221no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—612no—
229C2×D8—1221no—
230C2×D8—1221no—
231C2×D8—1221no—
232C2×D8—1221no—
233C2×D8—1221no—
234C2×D8C22⋊D6112yes—
235C22×C8—611no—
236C22×C8C22×D6111yescharacteristic
237C2×C4⋊C4—21no—
238C2×C4⋊C4—1221no—
239C2×C22⋊C4—2441no—
240C2×C22⋊C4—2441no—
241C2×C22⋊C4—2441no—
242C2×C22⋊C4—2441no—
243C2×C42—611no—
244D16—1228no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—612no—
249C2×C16—1221no—
250C2×C16—1221no—
251#107—21no—
252#107—21no—
253#107—1221no—
254#107—1221no—
255#102—2442no—
256#102—2442no—
257C4×C8—1221no—
258C4×C8—1221no—
259C24—41no—
260C24—2441no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—1222no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2441no—
273C22×C4—41no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—2441no—
277C22×C4D4×D6111yescharacteristic
278D8—22no—
279D8—22no—
280D8—41no—
281D8—41no—
282D8—1222no—
283D8—1222no—
284D8—2441no—
285D8—2441no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8#1175822211yescharacteristic
290C2×C8#1175822211yescharacteristic
291C2×C8D4×D6111yescharacteristic
292C2×C8D4×D6111yescharacteristic
293C2×C8#1175822411yescharacteristic
294C2×C8C2×C22⋊D6111yescharacteristic
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C22⋊C4—4882no—
300C22⋊C4—4882no—
301C22⋊C4—4882no—
302C22⋊C4—4882no—
303C42—1221no—
304C42—1221no—
305C16—41no—
306C16—1222no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—4881no—
315C23—4881no—
316C23—4881no—
317C23—4881no—
318C23—4881no—
319C23—4881no—
320C23—2442no—
321C23D8×D6111yescharacteristic
322D4—42no—
323D4—42no—
324D4—81no—
325D4—81no—
326D4—4881no—
327D4—4881no—
328D4—2442no—
329D4—2442no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—612no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4#1451974911yescharacteristic
343C2×C4#1451975011yescharacteristic
344C2×C4#1451975011yescharacteristic
345C2×C4#1451979811yescharacteristic
346C2×C4#1451980111yescharacteristic
347C2×C4#1451980411yescharacteristic
348C8—2441no—
349C8#1451974511yescharacteristic
350C8#1451975911yescharacteristic
351C8#1451976011yescharacteristic
352C8#1451976311yescharacteristic
353C22—82no—
354C22—82no—
355C22—82no—
356C22—161no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—9761no—
361C22—9761no—
362C22—9761no—
363C22—9761no—
364C22—4882no—
365C22—4882no—
366C22—4882no—
367C22#1683995511yescharacteristic
368C22#1683995611yescharacteristic
369C22#1683999711yescharacteristic
370C22D16×D6111yescharacteristic
371C22#1684019311yescharacteristic
372C22#1684019611yescharacteristic
373C22#1684019911yescharacteristic
374C4—161no—
375C4—1222no—
376C4—9761no—
377C4—2441no—
378C4#1683967711yescharacteristic
379C4#1683997611yescharacteristic
380C4#1683997911yescharacteristic
381C4#1684001411yescharacteristic
382C2—162no—
383C2—9762no—
384C2#2144712811yescharacteristic
385C2#2144785211yescharacteristic
386C2#2144785311yescharacteristic
387C2#2144787311yescharacteristic
388C2#2144787611yescharacteristic
389C2#2144790411yescharacteristic
390C2#2144792111yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#357C2
socleC23×C61C2×D8
prime radicalC22×#14519718C2
hypercenterC2×#357D61
hypocenterC61#13448
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#16839580C2semidirect
3. C2×#16839564C2semidirect
4. #21446686C2semidirect
5. #21446683C2semidirect
6. #21443910C2semidirect
7. C2×C61×#357C2semidirect
147. C2×Dic61D16semidirect
190. C2×#357D61semidirect
220. C61#13448semidirect

Maximal subgroups

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

subgroupindex
C22×#145197182
C2×#168395802
C2×#168395642
#214466862
#214466832
#214439102
C2×C61×#3572
#1344861