Finite Group Databasebeta

← #29581572

Subgroups — #29581572

Order 15616.

454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457210C211yesmaximal, characteristic
2#21456361C211yesmaximal, characteristic
3#21446809C211yesmaximal, characteristic
4#21444414C211yesmaximal, characteristic
5#21444239C211yesmaximal, characteristic
6#21443710C211yesmaximal, characteristic
7C61×#3229C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840168—22no—
10#16840165—21no—
11#16840158—21no—
12#16840047—21no—
13#16840044—21no—
14#16840018—22no—
15#16839972—21no—
16#16839969—21no—
17#16839802—22no—
18#16839786C2211yescharacteristic
19C4×#11758194C2211yescharacteristic
20C4×#11758194C2211yescharacteristic
21#16839531—22no—
22#16839504—22no—
23#16839492—22no—
24C61×#533C2211yescharacteristic
25C2×C4⋊Q8×C61C2211yescharacteristic
26C61×#498—21no—
27C61×#487—21no—
28C61×#483—22no—
29C61×#475—22no—
30C61×#431C2211yescharacteristic
31C2×#11758202—22no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758194D412yes—
35#14519777D411yescharacteristic
36#14519777D411yescharacteristic
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43#14519710—24no—
44#14519708—22no—
45#14519708—24no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519701—22no—
49#14519700—22no—
50#14519688—21no—
51#14519688D412yes—
52C4×#92418—21no—
53C4×#92418—21no—
54C22×Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61D411yescharacteristic
60C4⋊Q8×C61D411yescharacteristic
61#125×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C4×Q8×C61—21no—
65C4×Q8×C61—21no—
66#117×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D412yes—
69C2×C42×C61C2311yescharacteristic
70#106×C61—24no—
71C4⋊C8×C61D412yes—
72#103×C61—24no—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C2×Q8×C61—82no—
80C22×C4×C61—22no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C2×Dic122—21no—
85C2×Dic122—21no—
86C2×C8×C61—22no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C42×C61—41no—
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C22⋊Dic61—41no—
104#11758202—82no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109#11758196—41no—
110#11758196—41no—
111C4×Dic61—41no—
112#11758194—24no—
113#11758194—22no—
114#11758194—41no—
115#11758194—42no—
116C2×#92418—22no—
117C2×#92418—22no—
118C2×#92418—41no—
119C23×C61#12111yescharacteristic
120Q8×C61—41no—
121Q8×C61—42no—
122Q8×C61—41no—
123Q8×C61—82no—
124Q8×C61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—21no—
128C2×C4×C61—22no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—82no—
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12711yescharacteristic
139C2×Dic61—41no—
140C2×Dic61—41no—
141Dic122—41no—
142Dic122—41no—
143Dic122—42no—
144C8×C61—42no—
145#92418—24no—
146#92418—42no—
147#92418—42no—
148#10119—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61#39211yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—81no—
157C4×C61—81no—
158C4×C61—82no—
159C4×C61#45511yescharacteristic
160C4×C61#45611yescharacteristic
161C4×C61#45612yes—
162C4×C61#47112yes—
163Dic61—81no—
164Dic61—81no—
165#3255—611no—
166#3229D6111yescharacteristic
167#3165—611no—
168#1997—611no—
169#1526—611no—
170#1485—611no—
171#1299—611no—
172C2×C61—41no—
173C2×C61#200511yescharacteristic
174C2×C61#200711yescharacteristic
175C2×C61#201911yescharacteristic
176#533—611no—
177#533C2×D6111yescharacteristic
178C2×C4⋊Q8C2×D6111yescharacteristic
179#501—1222no—
180#500—1221no—
181#498—21no—
182#498—1221no—
183#487—21no—
184#483—22no—
185#475—22no—
186#475—1221no—
187#475—1221no—
188#470—1222no—
189#462—1221no—
190#462—1221no—
191#431C2×D6111yescharacteristic
192#428—1222no—
193#423—611no—
194C4×M16—611no—
195C4×M16—611no—
196#343—1222no—
197#330—1222no—
198Q8⋊C8—1222no—
199C61#1011911yescharacteristic, complemented, Sylow
200C22×Q8—21no—
201C2×Q16—1222no—
202C2×M16—612no—
203C2×M16—1221no—
204C2×M16—1221no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—611no—
210C4⋊Q8—611no—
211C4⋊Q8C22⋊D6111yescharacteristic
212C4⋊Q8C22⋊D6111yescharacteristic
213#125—21no—
214#125—1221no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—1221no—
218C22⋊Q8—1221no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—1221no—
222C4×Q8—1221no—
223#117—21no—
224#117—1221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D6112yes—
227C2×C42C22×D6111yescharacteristic
228#107—1224no—
229#106—24no—
230#106—1224no—
231#106—1222no—
232C4⋊C8—1221no—
233C4⋊C8—1221no—
234C4⋊C8C22⋊D6112yes—
235#103—24no—
236#103—1222no—
237#103—1222no—
238C22⋊C8—21no—
239#97—612no—
240#97—1221no—
241C4×C8—21no—
242C4×C8—1221no—
243C4×C8—1221no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—82no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C22×C4—22no—
252C22×C4D4×D6111yescharacteristic
253C22×C4#1175822411yescharacteristic
254C22×C4C2×C22⋊D6111yescharacteristic
255Q16—4882no—
256M16—1224no—
257M16—1222no—
258M16—2441no—
259M16—2442no—
260C2×C8—22no—
261C2×C8—1222no—
262C2×C8—1222no—
263C2×C8—2441no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—41no—
281C22⋊C4—2441no—
282C42—41no—
283C42—2441no—
284C42D4×D6111yescharacteristic
285C42D4×D6111yescharacteristic
286C42C2×C22⋊D6111yescharacteristic
287C42C2×C22⋊D6111yescharacteristic
288C23#1451974911yescharacteristic
289Q8—41no—
290Q8—41no—
291Q8—42no—
292Q8—82no—
293Q8—82no—
294Q8—2441no—
295Q8—2441no—
296Q8—2442no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4#1451974511yescharacteristic
308C2×C4#1451974511yescharacteristic
309C2×C4#1451974611yescharacteristic
310C2×C4#1451974811yescharacteristic
311C2×C4#1451974911yescharacteristic
312C2×C4#1451977311yescharacteristic
313C8—42no—
314C8—1224no—
315C8—2442no—
316C8—2442no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#1683967011yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—82no—
325C4—81no—
326C4—81no—
327C4—4881no—
328C4—4881no—
329C4#1683993811yescharacteristic
330C4#1683994311yescharacteristic
331C4#1683994512yes—
332C4#1684002212yes—
333C2—41no—
334C2#2144685311yescharacteristic
335C2#2144686411yescharacteristic
336C2#2144693111yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3229C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#3229D61
hypocenterC61#10119
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
199. C61#10119semidirect

Maximal subgroups

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

subgroupindex
#214572102
#214563612
#214468092
#214444142
#214442392
#214437102
C61×#32292
#1011961