Finite Group Databasebeta

← #29575868

Subgroups — #29575868

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#21454487C211yesmaximal, characteristic
3C2×#16839508C211yesmaximal, characteristic, complemented
4#21444207C211yesmaximal, characteristic
5#21443715C211yesmaximal, characteristic, complemented
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1548C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840054C412yes—
10#16840049C412yes—
11#16840044—21no—
12#16840039—21no—
13#16839822—22no—
14#16839818—21no—
15#16839814—21no—
16#16839802—21no—
17#16839786C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839761—21no—
21#16839730—21no—
22#16839720—21no—
23#16839508—21no—
24#16839508—21no—
25#16839494—21no—
26#16839491—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×#333—22no—
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C4×Dic122C2×C411yescharacteristic
36C4×Dic122D411yescharacteristic
37C4×D244C2×C411yescharacteristic
38C4×D244D411yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41#14519736D411yescharacteristic
42#14519734—21no—
43C42×D61—21no—
44#14519710—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C412yes—
51C4⋊#92418D411yescharacteristic
52C4⋊#92418D411yescharacteristic
53#14519700—22no—
54#14519697—22no—
55#14519689—22no—
56#14519689—22no—
57#14519687—22no—
58C8×Dic61—22no—
59C22×Q8×C61—21no—
60C2×M16×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×C61D412yes—
71C22⋊C8×C61—21no—
72C4×C8×C61—21no—
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
91M16×C61—41no—
92M16×C61—41no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C22⋊Dic61—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61C22⋊C411yescharacteristic
107C4⋊Dic61C22⋊C411yescharacteristic
108#11758196—21no—
109#11758196—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113#11758194—41no—
114#11758194—41no—
115C2×#92418—22no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—81no—
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—42no—
157C8×C61—81no—
158#92418—42no—
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—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#1548D6111yescharacteristic, complemented
187C2×#332—611no—
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—1221no—
206#431C2×D6111yescharacteristic
207#428—1221no—
208#423—611no—
209#423C2×D6111yescharacteristic
210C2×C4⋊C8—611no—
211C2×C4⋊C8—611no—
212#417—1221no—
213#408—1221no—
214#405—1221no—
215#333—22no—
216#332—1221no—
217#332—1221no—
218Q8⋊C8—1221no—
219D4⋊C8—1221no—
220C61#916811yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C22×Q8—21no—
223C2×M16—21no—
224C2×M16—1221no—
225C22×C8—1221no—
226C22×C8—1221no—
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—612no—
248C4⋊C8—611no—
249C4⋊C8—611no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254C4⋊C8C22⋊D6112yes—
255#103—1222no—
256#102—1222no—
257C22⋊C8—21no—
258C22⋊C8—1222no—
259C22⋊C8—1222no—
260#97—1222no—
261C4×C8—21no—
262C4×C8—1222no—
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—41no—
282M16—41no—
283M16—2441no—
284M16—2441no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—1222no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—4881no—
291C2×C8—2441no—
292C2×C8—2441no—
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—42no—
347C8—81no—
348C8—4881no—
349C8—2442no—
350C8—2441no—
351C8—2441no—
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#1684002411yescharacteristic
372C4#1684003111yescharacteristic
373C2—21no—
374C2—21no—
375C2—4881no—
376C2#2144612811yescharacteristic
377C2#2144628911yescharacteristic
378C2#2144632411yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1548C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1548D61
hypocenterC61#9168
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. C2×#16839508C2semidirect
5. #21443715C2semidirect
6. #21443693C2semidirect
7. C61×#1548C2semidirect
186. #1548D61semidirect
220. C61#9168semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214544872
C2×#168395082
#214442072
#214437152
#214436932
C61×#15482
#916861