Finite Group Databasebeta

← #29582067

Subgroups — #29582067

Order 15616.

496 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 105 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#21456970C211yesmaximal, characteristic, complemented
2#21455616C211yesmaximal, characteristic
3#21444500C211yesmaximal, characteristic, complemented
4#21444221C211yesmaximal, characteristic, complemented
5#21444140C211yesmaximal, characteristic
6#21443716C211yesmaximal, characteristic, complemented
7C2×C61×#474C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840165—21no—
10#16840114—21no—
11#16840097—22no—
12#16840062—22no—
13#16840054—22no—
14#16840052—21no—
15#16840042—21no—
16#16839815C2211yescharacteristic
17#16839815C2211yescharacteristic
18#16839802—21no—
19#16839786C2211yescharacteristic
20#16839767—21no—
21#16839511—22no—
22#16839492—22no—
23#16839486—22no—
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×C4×D4×C61C2211yescharacteristic
26C61×#474—22no—
27C61×#474—22no—
28C2×#107×C61—21no—
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#102×C61—21no—
31C2×#11758194—21no—
32#14519777D411yescharacteristic
33#14519777D411yescharacteristic
34#14519769—21no—
35#14519756—21no—
36#14519756—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39#14519736—21no—
40#14519710—22no—
41#14519710—24no—
42#14519708—22no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418D412yes—
47#14519700—24no—
48#14519698—22no—
49#14519698—22no—
50C22⋊#92418—21no—
51C22⋊#92418D412yes—
52C4×#92418—21no—
53C4×#92418—21no—
54C22×Q8×C61—21no—
55C22×D4×C61D411yescharacteristic
56C23×C4×C61—21no—
57C22×C8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61D412yes—
62C4×D4×C61—21no—
63C4×D4×C61—21no—
64C4×D4×C61—21no—
65C4×D4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C22⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71#107×C61—24no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61D412yes—
74#102×C61—24no—
75C24×C61—21no—
76C2×Q8×C61—22no—
77C2×Q8×C61—41no—
78C2×Q8×C61—82no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61Q1612yes—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—82no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C2×Dic122—21no—
94C2×Dic122—21no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C22⋊Dic61—41no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115#11758196—41no—
116#11758196—41no—
117C4×Dic61—41no—
118#11758194—41no—
119#11758194—41no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—41no—
123C23×C61—22no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—81no—
127C23×C61—81no—
128C23×C61#12111yescharacteristic
129Q8×C61—82no—
130Q8×C61—82no—
131D4×C61—22no—
132D4×C61—22no—
133D4×C61—41no—
134D4×C61—41no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—82no—
140C2×C4×C61—82no—
141C2×C4×C61—82no—
142C2×C4×C61—81no—
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12711yescharacteristic
149C2×C4×C61C2×Q1611yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61#13711yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—41no—
154C2×Dic61—41no—
155Dic122—42no—
156Dic122—42no—
157C8×C61—42no—
158#92418—42no—
159#92418—42no—
160#92418—81no—
161#10190—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—42no—
165C22×C61—82no—
166C22×C61—82no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61#39211yescharacteristic
170C22×C61#46711yescharacteristic
171C22×C61#47011yescharacteristic
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—81no—
176C4×C61—82no—
177C4×C61#45111yescharacteristic
178C4×C61#45111yescharacteristic
179C4×C61#45211yescharacteristic
180C4×C61#45211yescharacteristic
181C4×C61#47212yes—
182Dic61—81no—
183Dic61—81no—
184#3230—611no—
185#3077—611no—
186C2×#474D6111yescharacteristic
187#1548—611no—
188#1481—611no—
189#1460—611no—
190#1301—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—82no—
194C2×C61#200111yescharacteristic
195C2×C61#200911yescharacteristic
196C2×C61#201811yescharacteristic
197#533—611no—
198C2×C4⋊Q8C2×D6111yescharacteristic
199C2×C4×D4C2×D6111yescharacteristic
200#500—1221no—
201#487—1221no—
202#484—1222no—
203#478—1222no—
204#477—1222no—
205#476—1221no—
206#474—22no—
207#474—22no—
208#474—1221no—
209#431—611no—
210#431—611no—
211#428—1221no—
212C2×#107—21no—
213#423—611no—
214C2×C4⋊C8C2×D6111yescharacteristic
215#418—1221no—
216C2×#102—21no—
217#333—1222no—
218Q8⋊C8—1222no—
219#323—1222no—
220C61#1019011yescharacteristic, complemented, Sylow
221C22×Q8—21no—
222C22×D4C22⋊D6111yescharacteristic
223C23×C4—21no—
224C2×M16—1221no—
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—611no—
230C4⋊Q8—611no—
231C4⋊Q8C22⋊D6112yes—
232#125—1221no—
233C22⋊Q8—1221no—
234C22⋊Q8—1221no—
235C4×Q8—1221no—
236C4×Q8—1221no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241#117—1221no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C22⋊D6111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C22×D6111yescharacteristic
247#107—24no—
248#107—1222no—
249#107—1224no—
250#106—1222no—
251C4⋊C8—21no—
252C4⋊C8—612no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255C4⋊C8—1221no—
256C4⋊C8C22⋊D6112yes—
257#103—1224no—
258#102—24no—
259#102—1222no—
260#102—1222no—
261C22⋊C8—612no—
262C22⋊C8—1221no—
263C4×C8—1221no—
264C4×C8—1221no—
265C24—21no—
266C2×Q8—22no—
267C2×Q8—41no—
268C2×Q8—82no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4#1175820212yes—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—82no—
282C22×C4D4×D6111yescharacteristic
283C22×C4#1175822411yescharacteristic
284C22×C4C2×C22⋊D6111yescharacteristic
285M16—2441no—
286M16—2441no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—1222no—
291C2×C8—1222no—
292C2×C8—2441no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—2441no—
308C42—2441no—
309C42D4×D6111yescharacteristic
310C42D4×D6111yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C42C2×C22⋊D6111yescharacteristic
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23#1451974911yescharacteristic
319Q8—82no—
320Q8—82no—
321Q8—2442no—
322Q8—2442no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4#1451974511yescharacteristic
338C2×C4#1451974511yescharacteristic
339C2×C4#1451974611yescharacteristic
340C2×C4#1451974811yescharacteristic
341C2×C4#1451974911yescharacteristic
342C2×C4#1451977311yescharacteristic
343C2×C4C2×#1175820211yescharacteristic
344C2×C4#1451979711yescharacteristic
345C2×C4#1451980711yescharacteristic
346C2×C4#1451980811yescharacteristic
347C8—42no—
348C8—4881no—
349C8—2442no—
350C8—2442no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22#1683967011yescharacteristic
359C22#1684000111yescharacteristic
360C22#1684001811yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—82no—
366C4—4881no—
367C4—4881no—
368C4#1683991711yescharacteristic
369C4#1683991811yescharacteristic
370C4#1683992211yescharacteristic
371C4#1683992411yescharacteristic
372C4#1684002912yes—
373C2—21no—
374C2—21no—
375C2—82no—
376C2#2144682711yescharacteristic
377C2#2144687711yescharacteristic
378C2#2144692611yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#474C2
socleC22×C61#392
prime radicalC22×D4×C61D4
hypercenterC2×#474D61
hypocenterC61#10190
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #21456970C2semidirect
3. #21444500C2semidirect
4. #21444221C2semidirect
6. #21443716C2semidirect
220. C61#10190semidirect

Maximal subgroups

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

subgroupindex
#214569702
#214556162
#214445002
#214442212
#214441402
#214437162
C2×C61×#4742
#1019061