Finite Group Databasebeta

← #29579225

Subgroups — #29579225

Order 15616.

414 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519713C211yesmaximal, characteristic, complemented
2#21444414C211yesmaximal, characteristic, complemented
3#21444411C211yesmaximal, characteristic
4#21444240C211yesmaximal, characteristic, complemented
5#21444236C211yesmaximal, characteristic
6#21444108C211yesmaximal, characteristic, complemented
7C61×#3167C211yesmaximal, characteristic
8#16839815C2211yescharacteristic
9C2×#14519713—21no—
10C4×#11758194C2211yescharacteristic
11C4×#11758194C2211yescharacteristic
12C4×#11758194C2211yescharacteristic
13#16839527—21no—
14#16839504—22no—
15#16839502—22no—
16Q8⋊#92418—22no—
17D4⋊#92418—22no—
18#16839484—21no—
19#16839483—21no—
20C61×#533C2211yescharacteristic
21C61×#532C2211yescharacteristic
22C61×#498C411yescharacteristic
23C61×#492C411yescharacteristic
24C61×#487C411yescharacteristic
25C61×#486C411yescharacteristic
26C61×#465—21no—
27C61×#465—21no—
28C4×SD16×C61—21no—
29C4×SD16×C61—21no—
30C2×C4×C8×C61C2211yescharacteristic
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34#14519713—24no—
35C4⋊#92418D412yes—
36C22⋊#92418—21no—
37#14519688—21no—
38#14519688—21no—
39#14519688D412yes—
40C4×#92418—21no—
41C4×#92418—21no—
42C4×#92418—21no—
43C4×#92418—21no—
44C2×#41×C61—21no—
45C2×SD16×C61—21no—
46C2×SD16×C61—21no—
47C22×C8×C61D411yescharacteristic
48C22×C8×C61D411yescharacteristic
49C4⋊Q8×C61C2×C411yescharacteristic
50C4⋊Q8×C61C2×C411yescharacteristic
51C4⋊Q8×C61C2×C411yescharacteristic
52#127×C61C2×C411yescharacteristic
53#125×C61—21no—
54#124×C61—21no—
55C22⋊Q8×C61—21no—
56C22⋊Q8×C61—21no—
57#121×C61—21no—
58#121×C61—21no—
59C4×Q8×C61—21no—
60C4×Q8×C61—21no—
61C4×D4×C61—21no—
62C4×D4×C61—21no—
63#117×C61—21no—
64C2×C42×C61C2311yescharacteristic
65#106×C61—21no—
66#106×C61—21no—
67#103×C61—21no—
68#103×C61—21no—
69#102×C61—21no—
70#102×C61—21no—
71C4×C8×C61C2×C411yescharacteristic
72C4×C8×C61C2×C411yescharacteristic
73C4×C8×C61D411yescharacteristic
74C4×C8×C61D411yescharacteristic
75#41×C61—82no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C22×C4×C61#4111yescharacteristic
87SD16×C61—42no—
88SD16×C61—42no—
89C2×C8×C61—22no—
90C2×C8×C61—41no—
91C2×C8×C61C22⋊C411yescharacteristic
92C2×C8×C61C22⋊C411yescharacteristic
93C2×C8×C61C22⋊C411yescharacteristic
94C2×C8×C61C22⋊C411yescharacteristic
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C42×C61—41no—
107C42×C61C22×C411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111#11758194—22no—
112#11758194—22no—
113#11758194—42no—
114#11758194—41no—
115#11758194—41no—
116C2×#92418—22no—
117C2×#92418—22no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61—41no—
121C23×C61#12411yescharacteristic
122Q8×C61—41no—
123Q8×C61—41no—
124Q8×C61—42no—
125Q8×C61—81no—
126D4×C61—41no—
127D4×C61—41no—
128D4×C61—42no—
129D4×C61—81no—
130D4×C61—82no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—82no—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12711yescharacteristic
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—21no—
148C8×C61#10412yes—
149#92418—42no—
150#92418—42no—
151#92418—42no—
152#92418—42no—
153#9728—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61#39011yescharacteristic
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61—81no—
167C4×C61C2×#10411yescharacteristic
168C4×C61#42111yescharacteristic
169C4×C61#44412yes—
170C4×C61#47112yes—
171#3167D6111yescharacteristic
172C4×#108—611no—
173#1526—611no—
174#1525—611no—
175#1485—611no—
176#1484—611no—
177#1451—611no—
178C2×C61—41no—
179C2×C61—161no—
180C2×C61#197511yescharacteristic
181C2×C61#197711yescharacteristic
182C2×C61#198011yescharacteristic
183#533C2×D6111yescharacteristic
184#532C2×D6111yescharacteristic
185#498Dic6111yescharacteristic
186#492Dic6111yescharacteristic
187#487Dic6111yescharacteristic
188#486Dic6111yescharacteristic
189#465—21no—
190#465—21no—
191C4×SD16—21no—
192C4×SD16—21no—
193#431—611no—
194C2×#108—1221no—
195C4×M16—611no—
196C4×M16—611no—
197C4×M16—611no—
198C2×C4×C8C2×D6111yescharacteristic
199#341—1221no—
200#330—1222no—
201#329—1222no—
202Q8⋊C8—1222no—
203D4⋊C8—1222no—
204#322—1221no—
205#322—1221no—
206C61#972811yescharacteristic, complemented, Sylow
207C2×#41—21no—
208C2×SD16—21no—
209C2×SD16—21no—
210C2×M16—1221no—
211C2×M16—1221no—
212C2×M16—1221no—
213C22×C8C22⋊D6111yescharacteristic
214C22×C8C22⋊D6111yescharacteristic
215C4⋊Q8C2×Dic6111yescharacteristic
216C4⋊Q8C2×Dic6111yescharacteristic
217C4⋊Q8C2×Dic6111yescharacteristic
218#127C2×Dic6111yescharacteristic
219#125—21no—
220#124—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223#121—21no—
224#121—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×D4—21no—
228C4×D4—21no—
229#117—21no—
230C2×C42C22×D6111yescharacteristic
231#108—1224no—
232#106—21no—
233#106—21no—
234C4⋊C8—612no—
235#103—21no—
236#103—21no—
237#102—21no—
238#102—21no—
239C22⋊C8—1221no—
240#97—612no—
241#97—1221no—
242#97—1221no—
243C4×C8—1221no—
244C4×C8—1221no—
245C4×C8—1221no—
246C4×C8—1221no—
247C4×C8C2×Dic6111yescharacteristic
248C4×C8C2×Dic6111yescharacteristic
249C4×C8C22⋊D6111yescharacteristic
250C4×C8C22⋊D6111yescharacteristic
251#41—82no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—41no—
260C22×C4#1175822411yescharacteristic
261C22×C4#1175822411yescharacteristic
262C22×C4C2×C22⋊D6111yescharacteristic
263SD16—42no—
264SD16—42no—
265M16—1222no—
266M16—1222no—
267M16—2442no—
268M16—2441no—
269M16—2441no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—1222no—
273C2×C8—1222no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8C22⋊Dic6111yescharacteristic
277C2×C8C22⋊Dic6111yescharacteristic
278C2×C8C22⋊Dic6111yescharacteristic
279C2×C8C22⋊Dic6111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—41no—
292C42D4×D6111yescharacteristic
293C42D4×D6111yescharacteristic
294C42C22×Dic6111yescharacteristic
295C42C2×C22⋊D6111yescharacteristic
296C23—41no—
297C23#1451976411yescharacteristic
298Q8—41no—
299Q8—41no—
300Q8—42no—
301Q8—81no—
302D4—41no—
303D4—41no—
304D4—42no—
305D4—81no—
306D4—82no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—82no—
315C2×C4C2×C22⋊Dic6111yescharacteristic
316C2×C4D4×Dic6111yescharacteristic
317C2×C4D4×Dic6111yescharacteristic
318C2×C4#1451974811yescharacteristic
319C2×C4#1451974811yescharacteristic
320C2×C4#1451977311yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—2442no—
325C8—2442no—
326C8—2442no—
327C8—2442no—
328C8#1451970412yes—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1683966511yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4C2×#1451970411yescharacteristic
343C4#1683977911yescharacteristic
344C4#1683988412yes—
345C4#1684002212yes—
346C2—41no—
347C2—161no—
348C2#2144671311yescharacteristic
349C2#2144672411yescharacteristic
350C2#2144673911yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3167C2
socleC22×C61#390
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#3167D61
hypocenterC61#9728
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. C4×#14519713C2semidirect
2. #21444414C2semidirect
4. #21444240C2semidirect
6. #21444108C2semidirect
206. C61#9728semidirect

Maximal subgroups

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

subgroupindex
C4×#145197132
#214444142
#214444112
#214442402
#214442362
#214441082
C61×#31672
#972861