Finite Group Databasebeta

← #29575872

Subgroups — #29575872

Order 15616.

432 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455635C211yesmaximal, characteristic
2#21454487C211yesmaximal, characteristic
3#21444501C211yesmaximal, characteristic, complemented
4C2×#16839509C211yesmaximal, characteristic, complemented
5#21444204C211yesmaximal, characteristic
6#21443714C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C4×#11758222C2211yescharacteristic
10#16840058C412yes—
11#16840053C412yes—
12#16840048—21no—
13#16840043—21no—
14#16839822—22no—
15#16839818—21no—
16#16839815C2211yescharacteristic
17#16839814—21no—
18#16839804—21no—
19C2×C4⋊#92418C2211yescharacteristic
20#16839764—21no—
21#16839730—21no—
22#16839720—21no—
23#16839510—22no—
24#16839509—21no—
25#16839509—21no—
26#16839492—21no—
27#16839489—21no—
28C61×#423C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C22×Dic122—21no—
33C22×#92418—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777C2×C412yes—
38C4×Dic122C2×C411yescharacteristic
39C4×Dic122D411yescharacteristic
40C4×D244C2×C411yescharacteristic
41C4×D244D411yescharacteristic
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44#14519736D411yescharacteristic
45#14519734—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C42×D61—21no—
49#14519711—22no—
50#14519709—22no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418D411yescharacteristic
54C4⋊#92418D411yescharacteristic
55#14519702—22no—
56#14519699—22no—
57C22⋊#92418—21no—
58#14519689—22no—
59#14519689—22no—
60#14519687—22no—
61C4×#92418—21no—
62C8×Dic61—22no—
63C2×M16×C61—21no—
64C2×M16×C61—21no—
65C22×C8×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61C2×C412yes—
72C4⋊C8×C61D412yes—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61#4111yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C2×C22⋊D61—21no—
77C22×Dic61—41no—
78#11758222—21no—
79#11758222—21no—
80#11758222—21no—
81#11758222—21no—
82C2×D244C22⋊C411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×Dic122—22no—
87C2×Dic122—41no—
88C2×Dic122—81no—
89C2×Dic122—81no—
90C2×Dic122C22⋊C411yescharacteristic
91M16×C61—41no—
92M16×C61—41no—
93M16×C61—41no—
94M16×C61—41no—
95C2×C8×C61—22no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C2×C8×C61—81no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C22⋊Dic61—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61—22no—
107C4⋊Dic61—22no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61C22⋊C411yescharacteristic
111C4⋊Dic61C22⋊C411yescharacteristic
112#11758196—21no—
113#11758196—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61#12311yescharacteristic
123C22×D61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61C2×C22⋊C411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C22⋊D61—41no—
138C22⋊D61—41no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—42no—
143C2×Dic61—82no—
144D244—21no—
145D244—21no—
146C4×D61—41no—
147C4×D61—41no—
148C4×D61—41no—
149C4×D61—41no—
150C4×D61—81no—
151Dic122—21no—
152Dic122—21no—
153Dic122—81no—
154Dic122—81no—
155Dic122—82no—
156C8×C61—42no—
157C8×C61—42no—
158C8×C61—81no—
159#92418—41no—
160#92418—41no—
161#92418—81no—
162#9168—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38611yescharacteristic
166C22×C61#48511yescharacteristic
167C22×C61#48511yescharacteristic
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61#41611yescharacteristic
175C4×C61#41911yescharacteristic
176C4×C61#45211yescharacteristic
177C4×C61#45211yescharacteristic
178C4×C61#47111yescharacteristic
179C4×C61#47211yescharacteristic
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183Dic61—82no—
184#3079—611no—
185#2925—611no—
186#1548—611no—
187C2×#332—611no—
188#1477—611no—
189#1301—611no—
190#1292D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#187311yescharacteristic
194C2×C61#190211yescharacteristic
195C2×C61#190711yescharacteristic
196D61—81no—
197C2×C4⋊Q8—611no—
198C4×#41—611no—
199#477—612no—
200#476—612no—
201#475—1221no—
202#474—1221no—
203#433—1222no—
204#432—1221no—
205#431—611no—
206#431—1221no—
207#428—1221no—
208#423C2×D6111yescharacteristic
209#423C2×D6111yescharacteristic
210C2×C4⋊C8—611no—
211C2×C4⋊C8C2×D6111yescharacteristic
212#417—1221no—
213#408—1221no—
214#405—1221no—
215#333—1222no—
216#332—1221no—
217#332—1221no—
218Q8⋊C8—1221no—
219D4⋊C8—1221no—
220C61#916811yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C22×Q8—1221no—
223C2×M16—21no—
224C2×M16—21no—
225C22×C8—21no—
226C22×C8—1221no—
227C4⋊Q8—612no—
228C4⋊Q8—1221no—
229C4⋊Q8—1221no—
230C4⋊Q8—1221no—
231C4×Q8—611no—
232C4×Q8—611no—
233C4×D4—611no—
234C4×D4—611no—
235C4×D4—1221no—
236C4×D4—1221no—
237#117—611no—
238#117—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C42—1221no—
242C2×C42C22×D6111yescharacteristic
243#107—1222no—
244#106—1222no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—611no—
250C4⋊C8—611no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8C4×D6112yes—
254C4⋊C8D24412yes—
255#103—1222no—
256#102—1222no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259C22⋊C8—1221no—
260#97—1222no—
261C4×C8—1222no—
262C4×C8—1221no—
263#41—1221no—
264#41—1221no—
265#41—1221no—
266#41—1221no—
267C2×Q8—611no—
268C2×Q8—1222no—
269C2×Q8—4881no—
270C2×Q8—4881no—
271C2×Q8—2441no—
272C2×D4—611no—
273C2×D4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—2441no—
278C22×C4#1175822211yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4#1175822611yescharacteristic
281M16—41no—
282M16—41no—
283M16—41no—
284M16—41no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—81no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2441no—
294C4⋊C4—611no—
295C4⋊C4—611no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1222no—
299C4⋊C4—1222no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C42C2×C4×D6111yescharacteristic
309C42C2×D24411yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C23—1221no—
313C23#1451976211yescharacteristic
314Q8—1221no—
315Q8—1221no—
316Q8—4882no—
317Q8—4881no—
318Q8—4881no—
319D4—1221no—
320D4—1221no—
321D4—2441no—
322D4—2441no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—4881no—
330C2×C4—4882no—
331C2×C4—2442no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4C22⋊C4×D6111yescharacteristic
337C2×C4#1451973911yescharacteristic
338C2×C4C4×D24411yescharacteristic
339C2×C4#1451974711yescharacteristic
340C2×C4#1451975011yescharacteristic
341C2×C4#1451975211yescharacteristic
342C2×C4#1451979611yescharacteristic
343C2×C4#1451979811yescharacteristic
344C2×C4#1451980611yescharacteristic
345C2×C4#1451980911yescharacteristic
346C8—42no—
347C8—42no—
348C8—81no—
349C8—4881no—
350C8—2441no—
351C8—2441no—
352C22—21no—
353C22—21no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22#1683964011yescharacteristic
358C22#1684010511yescharacteristic
359C22#1684010611yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—4882no—
364C4—2441no—
365C4—2441no—
366C4—2441no—
367C4#1683975511yescharacteristic
368C4#1683976911yescharacteristic
369C4#1683992511yescharacteristic
370C4#1683992711yescharacteristic
371C4#1684002811yescharacteristic
372C4#1684003111yescharacteristic
373C2—21no—
374C2—21no—
375C2—4881no—
376C2#2144613011yescharacteristic
377C2#2144629311yescharacteristic
378C2#2144632811yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1292C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1292D61
hypocenterC61#9168
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #21444501C2semidirect
4. C2×#16839509C2semidirect
6. #21443714C2semidirect
7. C61×#1292C2semidirect
190. #1292D61semidirect
220. C61#9168semidirect

Maximal subgroups

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

subgroupindex
#214556352
#214544872
#214445012
C2×#168395092
#214442042
#214437142
C61×#12922
#916861