Finite Group Databasebeta

← #29590917

Subgroups — #29590917

Order 15616.

572 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 83 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#21449154C211yesmaximal, characteristic
2#21445899C211yesmaximal, characteristic, complemented
3#21443850C212yesmaximal, complemented
4#21443823C212yesmaximal, complemented
5C2×C61×#324C211yesmaximal, characteristic, complemented
6C22×#11758222C411yescharacteristic
7C2×#14519760—21no—
8#16839726—21no—
9#16839682C411yescharacteristic
10#16839682C2211yescharacteristic
11#16839679C411yescharacteristic
12#16839679C2211yescharacteristic
13#16839641—21no—
14#16839633—21no—
15#16839633—21no—
16#16839625C411yescharacteristic
17#16839531—21no—
18#16839531C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C2×#11758222—41no—
24C2×#11758222—41no—
25C2×#11758222—44no—
26C22×Dic122C2×C411yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C4×D61—21no—
30C2×#11758194—22no—
31#14519760—44no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C22⋊#92418—41no—
40C22⋊#92418—41no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C22×C8×C61—41no—
50C2×C4⋊C4×C61—41no—
51C2×C4⋊C4×C61—41no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61C2311yescharacteristic
56C22⋊C8×C61—22no—
57C22⋊C8×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C23×D61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—22no—
67C22×C4×C61—41no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—24no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83#11758222—44no—
84#11758222—44no—
85#11758222—44no—
86#11758222—44no—
87C2×D244—41no—
88C2×D244—42no—
89C2×C4×D61—42no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×Dic122—41no—
93C2×Dic122—42no—
94C2×C8×C61—42no—
95C2×C8×C61—82no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C22⋊Dic61—42no—
101#11758198—42no—
102#11758198—42no—
103#11758198—42no—
104#11758198—42no—
105#11758196—42no—
106#11758196—42no—
107#11758194—42no—
108#11758194—42no—
109C2×#92418—42no—
110C23×C61—22no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61#9911yescharacteristic
115C23×C61#9911yescharacteristic
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—22no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—81no—
143C2×C4×C61#13512yes—
144C22⋊D61—44no—
145C22⋊D61—44no—
146C2×Dic61—22no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155D244—42no—
156D244—42no—
157C4×D61—48no—
158Dic122—42no—
159Dic122—42no—
160C8×C61—82no—
161#92418—82no—
162#11848—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61AΣL(1,𝔽16)12yes—
173C22×C61C2×#9911yescharacteristic
174C22×C61#41611yescharacteristic
175C22×C61#42111yescharacteristic
176C2×D61—42no—
177C2×D61—42no—
178C2×D61—42no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C4×C61—22no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189Dic61—42no—
190Dic61—81no—
191Dic61—81no—
192#2406—611no—
193#1821—611no—
194C2×#324D6111yescharacteristic, complemented
195#1354—612no—
196#1345—612no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—22no—
200C2×C61—41no—
201C2×C61#151611yescharacteristic
202C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
203C2×C61#213311yescharacteristic
204D61—82no—
205C22×#41—611no—
206C2×#123—1221no—
207C22×C4⋊C4C2×D6111yescharacteristic
208#407—1221no—
209C2×C22⋊C8—21no—
210#395—611no—
211#395—611no—
212#394—611no—
213#394—611no—
214#386—1221no—
215#385—1221no—
216#385—1221no—
217#381—611no—
218#343—612no—
219#343—1221no—
220#324—21no—
221#324C2×D6112yes—
222C61#1184811yescharacteristic, complemented, Sylow
223C2×#41—2441no—
224C2×#41—2441no—
225C2×#41—2444no—
226C22×Q8—611no—
227C22×D4—611no—
228C22×D4—1221no—
229C23×C4—1221no—
230C23×C4C4×D6111yescharacteristic
231C23×C4D24411yescharacteristic
232C23×C4C22⋊D6111yescharacteristic
233C2×M16—1222no—
234C22×C8—41no—
235#123—2444no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C4×D6111yescharacteristic
241C2×C4⋊C4D24411yescharacteristic
242C2×C4⋊C4C22⋊D6111yescharacteristic
243C2×C4⋊C4C22×D6111yescharacteristic
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C22⋊C8—22no—
250C22⋊C8—41no—
251C22⋊C8—2441no—
252C22⋊C8—2441no—
253#95—611no—
254#95—611no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258C24—1221no—
259C24#1175819811yescharacteristic
260#41—2444no—
261#41—2444no—
262#41—2444no—
263#41—2444no—
264C2×Q8—2441no—
265C2×Q8—2442no—
266C2×D4—1224no—
267C2×D4—2441no—
268C2×D4—2442no—
269C2×D4—2442no—
270C2×D4—2441no—
271C2×D4—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4#1175819811yescharacteristic
289C22×C4#1175819811yescharacteristic
290C22×C4#1175819811yescharacteristic
291C22×C4C2×C4×D6111yescharacteristic
292C22×C4C2×D24411yescharacteristic
293C22×C4C2×C22⋊D6111yescharacteristic
294M16—2442no—
295M16—2442no—
296C2×C8—42no—
297C2×C8—82no—
298C2×C8—2442no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—2442no—
304C4⋊C4—2442no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C23—21no—
311C23—21no—
312C23—22no—
313C23—41no—
314C23—1222no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23#1451969111yescharacteristic
322C23#1451969111yescharacteristic
323C23C2×#1175819811yescharacteristic
324Q8—2442no—
325Q8—2442no—
326D4—2442no—
327D4—2442no—
328D4—2444no—
329D4—2444no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—1222no—
350C2×C4—2448no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4#1451979912yes—
360C8—82no—
361C8—4882no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—4881no—
375C22—2442no—
376C22—2442no—
377C22—2442no—
378C22#1683954812yes—
379C22C2×#1451969111yescharacteristic
380C22#1683975911yescharacteristic
381C22#1683977811yescharacteristic
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—4881no—
389C4—4881no—
390C4—2442no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—41no—
395C2—4882no—
396C2#2144437611yescharacteristic
397C2C2×#1683954811yescharacteristic
398C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#324C2
socleC22×C61C2×#99
prime radicalC22×#11758222C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#324D61
hypocenterC61#11848
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21445899C2semidirect
3. #21443850C2semidirect
4. #21443823C2semidirect
5. C2×C61×#324C2semidirect
194. C2×#324D61semidirect
222. C61#11848semidirect

Maximal subgroups

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

subgroupindex
#214491542
#214458992
#214438502
#214438232
C2×C61×#3242
#1184861