Finite Group Databasebeta

← #29580736

Subgroups — #29580736

Order 15616.

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

normal subgroups only

This group has 510 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#21456640C211yesmaximal, characteristic
2C2×#16840092C211yesmaximal, characteristic
3#21445899C211yesmaximal, characteristic
4#21444183C211yesmaximal, characteristic
5#21444182C211yesmaximal, characteristic
6#21443707C211yesmaximal, characteristic
7C2×C61×#484C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840092—22no—
10#16840092—21no—
11#16840092—22no—
12#16840090—21no—
13#16840018—22no—
14#16839918—21no—
15#16839917—21no—
16C2×#14519708—21no—
17C2×#14519700—21no—
18#16839726C2211yescharacteristic
19#16839726C2211yescharacteristic
20C2×C22⋊#92418C2211yescharacteristic
21#16839531—22no—
22#16839488—22no—
23#16839487—22no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C61×#484—22no—
27C61×#484—22no—
28C2×#107×C61—21no—
29C2×#103×C61—21no—
30C2×C22⋊C8×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C2×#11758202—22no—
33C2×#11758194—21no—
34C2×#11758194D412yes—
35C22×#92418—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43#14519708—22no—
44#14519708—24no—
45#14519701—22no—
46#14519700—24no—
47#14519700—22no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418D412yes—
54C22×Q8×C61D411yescharacteristic
55C23×C4×C61—21no—
56C23×C4×C61C2311yescharacteristic
57C22×C8×C61—21no—
58C22⋊Q8×C61—21no—
59C22⋊Q8×C61—21no—
60C22⋊Q8×C61—21no—
61C22⋊Q8×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C4⋊C4×C61D412yes—
70C2×C22⋊C4×C61—21no—
71#107×C61—24no—
72#103×C61—24no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75C24×C61#4111yescharacteristic
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—42no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—42no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—82no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—21no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—42no—
97C2×C8×C61—22no—
98C2×C8×C61—42no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111#11758202—82no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114#11758196—41no—
115#11758196—41no—
116#11758194—42no—
117#11758194—42no—
118C2×#92418—22no—
119C2×#92418—22no—
120C2×#92418—42no—
121C2×#92418—41no—
122C23×C61—22no—
123C23×C61—22no—
124C23×C61—41no—
125C23×C61#12111yescharacteristic
126C23×C61#12111yescharacteristic
127C23×C61#12111yescharacteristic
128Q8×C61—42no—
129Q8×C61—42no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—82no—
141C2×C4×C61—82no—
142C2×C4×C61—82no—
143C2×C4×C61—81no—
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61#12711yescharacteristic
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—42no—
151C2×Dic61—81no—
152Dic122—42no—
153Dic122—42no—
154C8×C61—42no—
155#92418—42no—
156#92418—42no—
157#92418—81no—
158#9995—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—44no—
167C22×C61#39211yescharacteristic
168C22×C61#47112yes—
169C22×C61#47312yes—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—81no—
174C4×C61—82no—
175C4×C61—81no—
176C4×C61#45812yes—
177Dic61—81no—
178Dic61—81no—
179#3195—611no—
180C2×#484D6111yescharacteristic
181C2×#483—611no—
182#1821—611no—
183#1472—611no—
184#1472—611no—
185#1298—611no—
186C2×C61—22no—
187C2×C61—22no—
188C2×C61—41no—
189C2×C61#201911yescharacteristic
190C2×C61#202011yescharacteristic
191C2×C61#202211yescharacteristic
192C2×C22⋊Q8—611no—
193C2×C22⋊Q8C2×D6111yescharacteristic
194C22×C4⋊C4C2×D6111yescharacteristic
195#484—22no—
196#484—22no—
197#483—1222no—
198#483—1221no—
199#483—1222no—
200#483—1221no—
201#470—1222no—
202#451—1221no—
203#451—1221no—
204C2×#107—21no—
205C2×#106—1221no—
206C2×#103—21no—
207C2×#103—1221no—
208#407—611no—
209#407—611no—
210C2×C22⋊C8—611no—
211C2×C22⋊C8C2×D6111yescharacteristic
212#343—1222no—
213#324—1222no—
214#324—1222no—
215C61#999511yescharacteristic, complemented, Sylow
216C22×Q8—611no—
217C22×Q8C22⋊D6111yescharacteristic
218C23×C4—21no—
219C23×C4C22×D6111yescharacteristic
220C2×Q16—1222no—
221C2×M16—612no—
222C2×M16—1221no—
223C22×C8—21no—
224C22×C8—1221no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—1221no—
230C22⋊Q8—1221no—
231C22⋊Q8—1221no—
232C22⋊Q8—1221no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4C22⋊D6112yes—
242C2×C4⋊C4C22⋊D6111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—1221no—
245#107—24no—
246#106—1224no—
247#106—1222no—
248#103—24no—
249#103—1224no—
250#103—1222no—
251#103—1222no—
252C22⋊C8—21no—
253C22⋊C8—612no—
254C22⋊C8—1221no—
255C22⋊C8—1221no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258C22⋊C8—1221no—
259C22⋊C8C22⋊D6112yes—
260C24#1175822411yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—42no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×Q8—2442no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—82no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4D4×D6111yescharacteristic
277C22×C4D4×D6111yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4C2×C22⋊D6111yescharacteristic
280C22×C4C2×C22⋊D6111yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282Q16—4882no—
283M16—2442no—
284M16—2442no—
285C2×C8—22no—
286C2×C8—42no—
287C2×C8—1222no—
288C2×C8—1222no—
289C2×C8—2441no—
290C2×C8—2442no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23#1451974811yescharacteristic
311C23#1451974911yescharacteristic
312C23#1451974911yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—2442no—
316Q8—2442no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4—4881no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4#1451974511yescharacteristic
336C2×C4#1451974511yescharacteristic
337C2×C4#1451974611yescharacteristic
338C2×C4#1451977311yescharacteristic
339C8—42no—
340C8—4881no—
341C8—2442no—
342C8—2442no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1683967011yescharacteristic
352C22#1684002312yes—
353C22#1684003412yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4—4881no—
361C4—4881no—
362C4#1683995112yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#2144693311yescharacteristic
367C2#2144693811yescharacteristic
368C2#2144694711yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#484C2
socleC22×C61#392
prime radicalC24×C61#41
hypercenterC2×#484D61
hypocenterC61#9995
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
215. C61#9995semidirect

Maximal subgroups

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

subgroupindex
#214566402
C2×#168400922
#214458992
#214441832
#214441822
#214437072
C2×C61×#4842
#999561