Finite Group Databasebeta

← #29575874

Subgroups — #29575874

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#21455628C211yesmaximal, characteristic
2#21454484C211yesmaximal, characteristic
3#21444500C211yesmaximal, characteristic, complemented
4#21444204C211yesmaximal, characteristic
5#21443716C211yesmaximal, characteristic, complemented
6#21443694C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840054C412yes—
10#16840049C412yes—
11#16840044—21no—
12#16840039—21no—
13#16839822—22no—
14#16839818—21no—
15#16839815C2211yescharacteristic
16#16839814—21no—
17#16839802—21no—
18#16839786C2211yescharacteristic
19#16839786C2211yescharacteristic
20#16839761—21no—
21#16839728—21no—
22#16839717—21no—
23#16839511—22no—
24#16839492—21no—
25#16839489—21no—
26C2×C4⋊Q8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C61×#332—21no—
30C61×#332—21no—
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
34C4×Dic122C2×C411yescharacteristic
35C4×Dic122D411yescharacteristic
36C4×D244C2×C411yescharacteristic
37C4×D244D411yescharacteristic
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40#14519736D411yescharacteristic
41#14519734—21no—
42C42×D61—21no—
43#14519710—22no—
44#14519708—22no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418C2×C412yes—
49C4⋊#92418D412yes—
50#14519700—22no—
51#14519697—22no—
52C22⋊#92418—21no—
53#14519689—22no—
54#14519689—22no—
55#14519687—22no—
56C4×#92418—21no—
57C8×Dic61—22no—
58C22×Q8×C61—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61C2×C412yes—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61D411yescharacteristic
72C4⋊C8×C61D411yescharacteristic
73C2×Q8×C61—22no—
74C2×Q8×C61—41no—
75C2×Q8×C61—81no—
76C2×Q8×C61—81no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×C22⋊D61—21no—
82#11758222—21no—
83#11758222—21no—
84#11758222—21no—
85#11758222—21no—
86C2×D244C22⋊C411yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×Dic122C22⋊C411yescharacteristic
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—81no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C22⋊Dic61—21no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61C22⋊C411yescharacteristic
109C4⋊Dic61C22⋊C411yescharacteristic
110#11758196—21no—
111#11758196—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115#11758194—41no—
116#11758194—41no—
117#11758194—41no—
118#11758194—41no—
119C2×#92418—22no—
120C2×#92418—22no—
121C2×#92418—41no—
122C23×C61#12311yescharacteristic
123C22×D61—21no—
124Q8×C61—82no—
125Q8×C61—81no—
126Q8×C61—81no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—82no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C22⋊D61—41no—
143C22⋊D61—41no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147D244—21no—
148D244—21no—
149C4×D61—41no—
150C4×D61—41no—
151C4×D61—41no—
152C4×D61—41no—
153C4×D61—81no—
154Dic122—21no—
155Dic122—21no—
156C8×C61—41no—
157C8×C61—41no—
158C8×C61—81no—
159#92418—42no—
160#92418—42no—
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—82no—
175C4×C61#41611yescharacteristic
176C4×C61#41911yescharacteristic
177C4×C61#45211yescharacteristic
178C4×C61#45211yescharacteristic
179C4×C61#47111yescharacteristic
180C4×C61#47211yescharacteristic
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184#3079—611no—
185#2925—611no—
186#1548—611no—
187C2×#332D6111yescharacteristic, complemented
188#1477—611no—
189#1301—611no—
190#1292—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#187311yescharacteristic
194C2×C61#190211yescharacteristic
195C2×C61#190711yescharacteristic
196D61—81no—
197C2×C4⋊Q8C2×D6111yescharacteristic
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#423—611no—
209#423—611no—
210C2×C4⋊C8C2×D6111yescharacteristic
211C2×C4⋊C8C2×D6111yescharacteristic
212#417—1221no—
213#408—1221no—
214#405—1221no—
215#333—1222no—
216#332—21no—
217#332—21no—
218Q8⋊C8—1221no—
219D4⋊C8—1221no—
220C61#916811yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C22×Q8—21no—
223C2×M16—1221no—
224C2×M16—1221no—
225C22×C8—21no—
226C22×C8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8C4×D6112yes—
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—21no—
240C2×C4⋊C4—21no—
241C2×C42—1221no—
242C2×C42C22×D6111yescharacteristic
243#107—1222no—
244#106—1222no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—612no—
249C4⋊C8—612no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8C22⋊D6111yescharacteristic
254C4⋊C8C22⋊D6111yescharacteristic
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—22no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×Q8—81no—
271C2×Q8—611no—
272C2×D4—611no—
273C2×D4—1221no—
274C22×C4—41no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4#1175822211yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4#1175822411yescharacteristic
281M16—2441no—
282M16—2441no—
283M16—2441no—
284M16—2441no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—81no—
291C2×C8—1222no—
292C2×C8—1222no—
293C2×C8—2441no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—611no—
299C4⋊C4—611no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C42C2×C4×D6111yescharacteristic
309C42D4×D6111yescharacteristic
310C42D4×D6111yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—1221no—
313C23#1451975911yescharacteristic
314Q8—82no—
315Q8—81no—
316Q8—81no—
317Q8—1221no—
318Q8—1221no—
319D4—1221no—
320D4—1221no—
321D4—2441no—
322D4—2441no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4881no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4C22⋊C4×D6111yescharacteristic
337C2×C4#1451973711yescharacteristic
338C2×C4C4×C22⋊D6111yescharacteristic
339C2×C4#1451974511yescharacteristic
340C2×C4#1451974811yescharacteristic
341C2×C4#1451975011yescharacteristic
342C2×C4#1451979811yescharacteristic
343C2×C4#1451980011yescharacteristic
344C2×C4#1451980611yescharacteristic
345C2×C4#1451980911yescharacteristic
346C8—41no—
347C8—41no—
348C8—81no—
349C8—4881no—
350C8—2442no—
351C8—2442no—
352C22—21no—
353C22—21no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22#1683963811yescharacteristic
358C22#1684010111yescharacteristic
359C22#1684010211yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—82no—
364C4—2441no—
365C4—2441no—
366C4—2441no—
367C4#1683975711yescharacteristic
368C4#1683976911yescharacteristic
369C4#1683992111yescharacteristic
370C4#1683992311yescharacteristic
371C4#1684002211yescharacteristic
372C4#1684002911yescharacteristic
373C2—21no—
374C2—21no—
375C2—4881no—
376C2#2144612811yescharacteristic
377C2#2144629511yescharacteristic
378C2#2144633011yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenterC2×#332D61
hypocenterC61#9168
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #21444500C2semidirect
5. #21443716C2semidirect
6. #21443694C2semidirect
7. C2×C61×#332C2semidirect
187. C2×#332D61semidirect
220. C61#9168semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214544842
#214445002
#214442042
#214437162
#214436942
C2×C61×#3322
#916861