Finite Group Databasebeta

← #30607395

Subgroups — #30607395

Order 15616.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840772C211yesmaximal, characteristic
2C2×#16840689C211yesmaximal, characteristic, complemented
3C2×#16840688C211yesmaximal, characteristic, complemented
4#21461696C211yesmaximal, characteristic
5#21460877C211yesmaximal, characteristic, complemented
6#21460877C211yesmaximal, characteristic, complemented
7C22⋊C16×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840772—22no—
10#16840772—22no—
11C2×#14519846C2211yescharacteristic
12C2×#14519846C2211yescharacteristic
13C2×#14519846C2211yescharacteristic
14C2×#14519846C2211yescharacteristic
15C2×#14519845—21no—
16#16840704—21no—
17#16840689—22no—
18#16840688—22no—
19#16840636—21no—
20C22×C8×D61C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic
23C22⋊#11758185C411yescharacteristic, complemented
24#16839541C411yescharacteristic, complemented
25#16839541C411yescharacteristic, complemented
26C61×C22⋊C16C411yescharacteristic, complemented
27#14519856—24no—
28#14519856—42no—
29C2×C4⋊#6923—21no—
30C2×C4⋊#6923—21no—
31C2×C4⋊#6923—21no—
32C2×C4⋊#6923—21no—
33C2×C22⋊#6923—41no—
34C2×C22⋊#6923—41no—
35C2×C4×#6923—41no—
36#14519846—21no—
37#14519846—21no—
38#14519846—21no—
39#14519846—21no—
40#14519846—21no—
41#14519846—21no—
42#14519846D412yes—
43#14519846D412yes—
44#14519845—24no—
45(C2×#6923)⋊C4—41no—
46C22×C4×D61D411yescharacteristic
47C22×#92418Q811yescharacteristic
48C2×C8×D61—21no—
49C2×C8×D61—21no—
50C2×C8×D61—21no—
51C2×C8×D61—21no—
52C2×C8×D61C2×C411yescharacteristic
53C2×C8×D61D411yescharacteristic
54C2×C8×D61Q811yescharacteristic
55C2×C8×D61C2311yescharacteristic
56C2×#11758185C2×C411yescharacteristic
57C2×#11758185C2×C411yescharacteristic
58C16×D61—21no—
59C16×D61—21no—
60C16×D61—21no—
61C16×D61—21no—
62C22×C8×C61C2×C411yescharacteristic
63C2×C16×C61C2×C411yescharacteristic
64C2×C16×C61C2×C411yescharacteristic
65C23×D61D811yescharacteristic
66C22×#6923—41no—
67C22×#6923—41no—
68C22×#6923—41no—
69C22×#6923—41no—
70C22×C4×C61C4⋊C411yescharacteristic
71C22×Dic61Q1611yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61C4⋊C411yescharacteristic
77C2×C4×D61D811yescharacteristic
78C2×C4×D61Q1611yescharacteristic
79C2×C4×D61C2×D411yescharacteristic
80C22⋊#6923—44no—
81C22⋊#6923—82no—
82C4⋊#6923—22no—
83C4⋊#6923—22no—
84C4⋊#6923—41no—
85C4⋊#6923—41no—
86C4⋊#6923—41no—
87C4⋊#6923—41no—
88C4⋊#6923—41no—
89C4⋊#6923—41no—
90C4×#6923—44no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61C4⋊C411yescharacteristic
94C2×C8×C61C22×C411yescharacteristic
95C2×#92418—21no—
96C2×#92418—21no—
97C2×#92418C4⋊C411yescharacteristic
98C2×#92418C2×Q811yescharacteristic
99C8×D61—21no—
100C8×D61—21no—
101C8×D61—21no—
102C8×D61—21no—
103C8×D61—21no—
104C8×D61—21no—
105C8×D61C2×D411yescharacteristic
106C8×D61C2×D411yescharacteristic
107C8×D61#4111yescharacteristic
108C8×D61#4111yescharacteristic
109C16×C61—21no—
110C16×C61—21no—
111#11758185—21no—
112#11758185—21no—
113C23×C61#10711yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61#10711yescharacteristic
121C22×D61C2×D811yescharacteristic
122C2×#6923—42no—
123C2×#6923—42no—
124C2×#6923—81no—
125C2×#6923—81no—
126C2×#6923—81no—
127C2×#6923—81no—
128C2×#6923—81no—
129C2×#6923—81no—
130C2×#6923—81no—
131C2×#6923—81no—
132C2×#6923—81no—
133C2×#6923—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61#10711yescharacteristic
137C2×C4×C61C2×C4⋊C411yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61#10711yescharacteristic
141C2×Dic61C2×Q1611yescharacteristic
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61#12011yescharacteristic
149C4×D61#12311yescharacteristic
150C4×D61AGL(1,ℤ/8)11yescharacteristic
151C4×D61#13711yescharacteristic
152C8×C61—21no—
153C8×C61C4×D411yescharacteristic
154C8×C61C4×D411yescharacteristic
155#92418—21no—
156#92418C22⋊Q811yescharacteristic
157#92418C22⋊Q811yescharacteristic
158#12921—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61C2×#10711yescharacteristic
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61#44711yescharacteristic
171C2×D61#48011yescharacteristic
172C2×D61#50811yescharacteristic
173C2×D61#50811yescharacteristic
174C2×D61#50911yescharacteristic
175C2×D61#51011yescharacteristic
176#6923—82no—
177#6923—82no—
178#6923—161no—
179#6923—161no—
180C4×C61—21no—
181C4×C61#38511yescharacteristic
182C4×C61#42811yescharacteristic
183Dic61—21no—
184Dic61#45111yescharacteristic
185Dic61#48411yescharacteristic
186C2×#427—611no—
187C2×#367—611no—
188C2×#366—611no—
189C2×C22⋊C16—611no—
190#1808—611no—
191#1380—611no—
192#1380—611no—
193C2×C61—41no—
194C2×C61#185211yescharacteristic
195C2×C61#215811yescharacteristic
196C2×C61#215911yescharacteristic
197D61—41no—
198D61#218611yescharacteristic
199D61#218911yescharacteristic
200D61#223411yescharacteristic
201D61#223711yescharacteristic
202C23×C8—611no—
203C2×#117—1221no—
204C22×C16—611no—
205C22×C16—611no—
206#427—1222no—
207#427—1222no—
208C2×#107—611no—
209C2×#107—611no—
210C2×#107—611no—
211C2×#107—611no—
212C2×#106—1221no—
213#380—1221no—
214#367—1222no—
215#366—1222no—
216C22⋊C16—611no—
217C22⋊C16—611no—
218C22⋊C16—611no—
219C22⋊C16#692311yescharacteristic, complemented
220#340—1221no—
221C61#1292111yescharacteristic, complemented, Sylow
222C23×C4—611no—
223C22×C8—611no—
224C22×C8—611no—
225C22×C8—611no—
226C22×C8—611no—
227C22×C8—611no—
228C22×C8—1221no—
229C22×C8—1221no—
230C22×C8—1221no—
231C22×C8—1221no—
232C22×C8C2×#692311yescharacteristic
233#117—1224no—
234#117—2442no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C22⋊C4—2441no—
240C2×C22⋊C4—2441no—
241C2×C42—2441no—
242C2×C16—611no—
243C2×C16—611no—
244C2×C16—1221no—
245C2×C16—1221no—
246C2×C16—1221no—
247C2×C16—1221no—
248C2×C16C2×#692311yescharacteristic
249C2×C16C2×#692311yescharacteristic
250#107—612no—
251#107—612no—
252#107—1221no—
253#107—1221no—
254#107—1221no—
255#107—1221no—
256#107—1221no—
257#107—1221no—
258#106—1224no—
259#95—2441no—
260C24—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4C4⋊#692311yescharacteristic
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8C4⋊#692311yescharacteristic
292C2×C8C22×#692311yescharacteristic
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—4882no—
302C22⋊C4—2444no—
303C42—2444no—
304C16—21no—
305C16—21no—
306C16—1221no—
307C16—1221no—
308C23—611no—
309C23—611no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23#1451984611yescharacteristic
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4#1451984611yescharacteristic
346C2×C4C2×C4⋊#692311yescharacteristic
347C8—21no—
348C8—611no—
349C8—611no—
350C8—1221no—
351C8D4×#692311yescharacteristic
352C8D4×#692311yescharacteristic
353C22—21no—
354C22—21no—
355C22—21no—
356C22—611no—
357C22—611no—
358C22—611no—
359C22—611no—
360C22—611no—
361C22—611no—
362C22—1221no—
363C22—1221no—
364C22—1221no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22C2×#1451984611yescharacteristic
370C4—21no—
371C4—611no—
372C4—611no—
373C4—1221no—
374C4—9761no—
375C4—9761no—
376C4—4882no—
377C4—4882no—
378C4#1684070911yescharacteristic
379C4#1684077311yescharacteristic
380C2—41no—
381C2—611no—
382C2—611no—
383C2—611no—
384C2—611no—
385C2—2441no—
386C2#2146176811yescharacteristic
387C2#2146217011yescharacteristic
388C2#2146217111yescharacteristic
subgroupG/H
centerC22C2×#14519846
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×C22⋊C16C4
socleC22×C61C2×#107
prime radicalC23×D61D8
cosocleC2×C8×D61C23
hypercenterC22⋊C16#6923
hypocenterC61#12921
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#16840689C2semidirect
3. C2×#16840688C2semidirect
5. #21460877C2semidirect
6. #21460877C2semidirect
23. C22⋊#11758185C4semidirect
24. #16839541C4semidirect
25. #16839541C4semidirect
26. C61×C22⋊C16C4semidirect
219. C22⋊C16#6923semidirect
221. C61#12921semidirect

Maximal subgroups

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

subgroupindex
C2×#168407722
C2×#168406892
C2×#168406882
#214616962
#214608772
C22⋊C16×D612
#1292161