Finite Group Databasebeta

← #30599024

Subgroups — #30599024

Order 15616.

454 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461683C212yesmaximal
2#21461376C211yesmaximal, characteristic, complemented
3#21461373C211yesmaximal, characteristic, complemented
4#21460689C212yesmaximal, complemented
5C2×#16839837C211yesmaximal, characteristic
6#16840765C2212yes—
7#16840765C2212yes—
8C2×#14519837—22no—
9#16840642—22no—
10#16840626—21no—
11#16840625—21no—
12#16840624—21no—
13#16840623—21no—
14C22×#11758194C411yescharacteristic
15C22×#11758189C411yescharacteristic
16C2×C4×C22⋊D61C2211yescharacteristic
17#16839837—21no—
18#16839837—21no—
19#16839837—21no—
20#16839837—21no—
21C2×#14519706C2211yescharacteristic
22C2×#14519689C411yescharacteristic
23C2×C8×Dic61C2211yescharacteristic
24C2×C22⋊C8×C61C411yescharacteristic
25C2×#11758217—22no—
26C2×#11758217—22no—
27#14519844—22no—
28#14519844—22no—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31#14519837—44no—
32C22×C22⋊D61D411yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C2×#11758194—21no—
35C2×#11758194—21no—
36C2×#11758194—42no—
37C2×#11758189—21no—
38C2×#11758189—21no—
39C2×#11758189—42no—
40C22×#92418C2×C411yescharacteristic
41C22×#92418C2×C411yescharacteristic
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46C2×#11758196D411yescharacteristic
47C2×C22⋊Dic61Q811yescharacteristic
48C2×#11758198Q811yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50#14519706—21no—
51#14519706—21no—
52#14519689—21no—
53#14519689—21no—
54C8×Dic61D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C8×Dic61D411yescharacteristic
57C8×Dic61D411yescharacteristic
58C23×C4×C61C2×C411yescharacteristic
59C22×C8×C61C2×C411yescharacteristic
60C22×C8×C61C2×C411yescharacteristic
61C22⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C24×C61C4⋊C411yescharacteristic
64C23×D61C4⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61C4⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61—22no—
75C22×Dic61C4⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×Q811yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82#11758217—42no—
83#11758217—42no—
84#11758217—42no—
85#11758217—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×C8×C61—21no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61C22⋊C411yescharacteristic
92C2×C8×C61C22⋊C411yescharacteristic
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758198—21no—
96#11758198—21no—
97#11758196—21no—
98#11758196—21no—
99C4×Dic61C2×D411yescharacteristic
100C4×Dic61C2×D411yescharacteristic
101C4×Dic61#4111yescharacteristic
102C4×Dic61#4111yescharacteristic
103#11758194—42no—
104#11758194—42no—
105C2×#92418—22no—
106C2×#92418—21no—
107C2×#92418—41no—
108C2×#92418C22⋊C411yescharacteristic
109C2×#92418C22⋊C411yescharacteristic
110#11758189—42no—
111#11758189—42no—
112C23×C61—21no—
113C23×C61—22no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61C2×C4⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—22no—
119C22×D61—41no—
120C22×D61—41no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61#11711yescharacteristic
130C22⋊D61—42no—
131C22⋊D61—41no—
132C22⋊D61—41no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61#12111yescharacteristic
137C2×Dic61#12111yescharacteristic
138C2×Dic61C22⋊Q811yescharacteristic
139C2×Dic61C22⋊Q811yescharacteristic
140C2×Dic61AGL(1,ℤ/8)12yes—
141C2×Dic61#13712yes—
142C4×D61—42no—
143C4×D61—41no—
144C4×D61—41no—
145#92420—82no—
146#92420—82no—
147C8×C61—21no—
148C8×C61—21no—
149C8×C61—41no—
150#92418—21no—
151#92418—41no—
152#92418#10012yescomplemented
153#8618—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—82no—
160C22×C61#38011yescharacteristic
161C22×C61#42812yes—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—82no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61C2×#10011yescharacteristic
169C4×C61#41311yescharacteristic
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61#46812yes—
174Dic61#46911yescharacteristic
175Dic61#47011yescharacteristic
176C2×#436—611no—
177#1800—612no—
178#1567—611no—
179#1566—611no—
180#1292—612no—
181C2×C61—22no—
182C2×C61—81no—
183C2×C61#180011yescharacteristic
184C2×C61#180911yescharacteristic
185C2×C61#181311yescharacteristic
186D61—81no—
187C22×M16—611no—
188C22×M16—611no—
189C2×C4×D4—611no—
190#436—1221no—
191#436—1221no—
192#436—1221no—
193#436—1221no—
194#423—612no—
195#423—612no—
196C2×C4⋊C8—611no—
197C2×#100—1222no—
198C2×C22⋊C8—611no—
199C2×C22⋊C8#692311yescharacteristic
200C2×C4×C8—611no—
201#343—1222no—
202#335—1221no—
203#335—1221no—
204#334—1221no—
205#334—1221no—
206C61#861811yescharacteristic, complemented, Sylow
207C22×D4—611no—
208C23×C4—611no—
209C23×C4C2×#692311yescharacteristic
210C2×M16—1221no—
211C2×M16—1221no—
212C2×M16—1221no—
213C2×M16—1221no—
214C2×M16—1222no—
215C2×M16—1222no—
216C2×M16—2442no—
217C2×M16—2442no—
218C22×C8—611no—
219C22×C8—611no—
220C22×C8C2×#692311yescharacteristic
221C22×C8C2×#692311yescharacteristic
222C4×D4—1221no—
223C4×D4—1221no—
224C4×D4—1221no—
225C4×D4—1221no—
226C2×C4⋊C4—611no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C42—611no—
230C4⋊C8—1221no—
231C4⋊C8—1221no—
232C4⋊C8—1222no—
233C4⋊C8—1222no—
234C4⋊C8—1222no—
235C4⋊C8—1222no—
236#100—2444no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239C22⋊C8—1221no—
240C22⋊C8—1221no—
241C4×C8—611no—
242C4×C8—611no—
243C4×C8—611no—
244C4×C8—611no—
245C24—611no—
246C24C4⋊#692311yescharacteristic
247C2×D4—1222no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1222no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4C4⋊#692311yescharacteristic
263C22×C4C22×#692311yescharacteristic
264M16—2442no—
265M16—2442no—
266M16—2442no—
267M16—2442no—
268M16—2442no—
269M16—2442no—
270M16—2442no—
271M16—2442no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8—1222no—
278C2×C8—1221no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2441no—
282C2×C8C22⋊#692311yescharacteristic
283C2×C8C22⋊#692311yescharacteristic
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C42—611no—
291C42—611no—
292C42—611no—
293C42—611no—
294C23—21no—
295C23—22no—
296C23—41no—
297C23—41no—
298C23—1222no—
299C23—1221no—
300C23—2441no—
301C23—2441no—
302C23C2×C4⋊#692311yescharacteristic
303D4—2442no—
304D4—2441no—
305D4—2441no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—1221no—
320C2×C4—2442no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4C2×C22⋊#692311yescharacteristic
326C2×C4#1451985611yescharacteristic
327C8—21no—
328C8—21no—
329C8—41no—
330C8—612no—
331C8—1221no—
332C8—4882no—
333C8—4882no—
334C8—2441no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—82no—
341C22—4882no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22#1684070411yescharacteristic
346C22#1684077312yes—
347C4—21no—
348C4—41no—
349C4—612no—
350C4—611no—
351C4—611no—
352C4—1221no—
353C4—1221no—
354C4—2441no—
355C4D61⋊#10011yescharacteristic
356C4#1684074911yescharacteristic
357C2—22no—
358C2—81no—
359C2—4881no—
360C2#2146168411yescharacteristic
361C2#2146169711yescharacteristic
362C2#2146170311yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#380
prime radicalC22×C22⋊D61D4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#8618
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #21461376C2semidirect
3. #21461373C2semidirect
4. #21460689C2semidirect
152. #92418#100semidirect
206. C61#8618semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214613762
#214613732
#214606892
C2×#168398372
#861861