Finite Group Databasebeta

← #29590595

Subgroups — #29590595

Order 15616.

768 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 87 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#21449175C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic, complemented
3#21443821C214yesmaximal, complemented
4C4×#100×C61C211yesmaximal, characteristic, complemented
5C23×D244C411yescharacteristic
6C2×#14519751—21no—
7C2×#14519745—21no—
8#16839726—21no—
9#16839679C2212yes—
10#16839671C412yes—
11#16839664—21no—
12#16839622C411yescharacteristic
13#16839617—21no—
14#16839488C2212yescomplemented
15#16839486—21no—
16C2×C4×D4×C61C2211yescharacteristic
17C2×#100×C61—21no—
18C4×M16×C61—21no—
19C61×#343C2212yescomplemented
20C24×D61—21no—
21C22×D244—21no—
22C22×D244—44no—
23C22×D244—41no—
24C22×D244—41no—
25C22×D244C2×C412yes—
26C22×C22⋊D61—22no—
27C2×#11758194—41no—
28#14519751—44no—
29#14519745—44no—
30C2×C4⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C22⋊#92418—22no—
36C22⋊#92418—41no—
37#14519684C2×C412yes—
38C22×D4×C61D411yescharacteristic
39C23×C4×C61C2×C411yescharacteristic
40C23×C4×C61D411yescharacteristic
41C2×M16×C61—22no—
42C4×D4×C61—41no—
43C4×D4×C61—41no—
44C2×C4⋊C4×C61C2311yescharacteristic
45C2×C22⋊C4×C61C2×C411yescharacteristic
46C2×C22⋊C4×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48#100×C61—24no—
49#97×C61—41no—
50C4×C8×C61—41no—
51C24×C61C22⋊C411yescharacteristic
52C24×C61C22⋊C411yescharacteristic
53C23×D61—22no—
54C23×D61—44no—
55C23×D61—42no—
56C23×D61—42no—
57C23×D61—42no—
58C23×D61—82no—
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×C22⋊D61—44no—
74C2×C22⋊D61—44no—
75C2×C22⋊D61—82no—
76C22×Dic61—22no—
77C2×D244—24no—
78C2×D244—42no—
79C2×D244—42no—
80C2×D244—48no—
81C2×D244—44no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—44no—
85C2×D244—44no—
86M16×C61—24no—
87M16×C61—42no—
88C2×C8×C61—42no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C42×C61—21no—
93C42×C61—21no—
94C22⋊Dic61—42no—
95#11758198—44no—
96#11758198—44no—
97#11758198—82no—
98C4⋊Dic61—42no—
99#11758194—82no—
100C2×#92418—42no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61#10412yes—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—24no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—48no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—88no—
121C22×D61—88no—
122C22×D61—84no—
123C22×D61—84no—
124D4×C61—44no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—81no—
138C2×C4×C61#9911yescharacteristic
139C2×C4×C61#9911yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)12yes—
141C22⋊D61—88no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145D244—44no—
146D244—44no—
147D244—44no—
148D244—44no—
149C8×C61—44no—
150#92418—82no—
151#11779—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—22no—
155C22×C61—42no—
156C22×C61—42no—
157C22×C61—42no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61C2×#9911yescharacteristic
165C22×C61#41811yescharacteristic
166C22×C61C2×#10411yescharacteristic
167C2×D61—44no—
168C2×D61—44no—
169C2×D61—44no—
170C2×D61—82no—
171C2×D61—82no—
172C2×D61—816no—
173C2×D61—82no—
174C2×D61—82no—
175C4×C61—21no—
176C4×C61—22no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61AΣL(1,𝔽16)12yes—
181Dic61—82no—
182#2408—611no—
183C4×#100D6111yescharacteristic, complemented
184#1465—611no—
185#1345—614no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—42no—
189C2×C61—81no—
190C2×C61#150711yescharacteristic
191C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
192C2×C61#213411yescharacteristic
193D61—84no—
194C23×D4—611no—
195C2×#121—1221no—
196C2×#120—1221no—
197C2×C4×D4C2×D6111yescharacteristic
198C2×#100—21no—
199#407—1221no—
200C4×M16—21no—
201#394—612no—
202#392—612no—
203#390—1221no—
204#380—611no—
205#379—1221no—
206#343C2×D6112yescomplemented
207#324—612no—
208#323—1221no—
209C61#1177911yescharacteristic, complemented, Sylow
210C25—1221no—
211C22×D4—612no—
212C22×D4—1222no—
213C22×D4—1221no—
214C22×D4—2441no—
215C22×D4—2441no—
216C22×D4—2444no—
217C22×D4C22⋊D6111yescharacteristic
218C23×C4C4×D6111yescharacteristic
219C23×C4D24411yescharacteristic
220C2×M16—22no—
221C2×M16—2441no—
222#121—2444no—
223#120—2444no—
224C4×D4—41no—
225C4×D4—41no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4C22×D6111yescharacteristic
228C2×C22⋊C4—1222no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1222no—
231C2×C22⋊C4—1222no—
232C2×C22⋊C4C4×D6111yescharacteristic
233C2×C22⋊C4D24411yescharacteristic
234C2×C42C22⋊D6111yescharacteristic
235#100—24no—
236C22⋊C8—1222no—
237C22⋊C8—2441no—
238#97—41no—
239C4×C8—41no—
240#95—612no—
241C24—1222no—
242C24—4882no—
243C24—2442no—
244C24—2442no—
245C24—2444no—
246C24—2442no—
247C24#1175819811yescharacteristic
248C24#1175819811yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C2×D4—1224no—
253C2×D4—4882no—
254C2×D4—2442no—
255C2×D4—2442no—
256C2×D4—2448no—
257C2×D4—2444no—
258C2×D4—2444no—
259C2×D4—2444no—
260C2×D4—2444no—
261C2×D4—2444no—
262C2×D4—2441no—
263C2×D4—2441no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—1222no—
271C22×C4#1175819811yescharacteristic
272C22×C4#1175819811yescharacteristic
273C22×C4C2×C4×D6111yescharacteristic
274C22×C4C2×D24411yescharacteristic
275C22×C4C2×C22⋊D6111yescharacteristic
276M16—24no—
277M16—42no—
278M16—4882no—
279C2×C8—42no—
280C2×C8—2442no—
281C4⋊C4—41no—
282C4⋊C4—2442no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—4882no—
286C22⋊C4—2444no—
287C22⋊C4—2442no—
288C22⋊C4—2444no—
289C42—21no—
290C42—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—1224no—
301C23—4884no—
302C23—4884no—
303C23—4888no—
304C23—4888no—
305C23—2442no—
306C23—2442no—
307C23—2442no—
308C23—2448no—
309C23—2442no—
310C23—2442no—
311C23—2442no—
312C23#1451970512yes—
313C23C2×#1175819811yescharacteristic
314D4—44no—
315D4—4888no—
316D4—2444no—
317D4—2444no—
318D4—2444no—
319D4—2444no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4#1451969111yescharacteristic
337C2×C4#1451969111yescharacteristic
338C2×C4#1451980212yes—
339C8—44no—
340C8—4882no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—81no—
353C22—4882no—
354C22—4882no—
355C22—48816no—
356C22—4882no—
357C22—4882no—
358C22—2444no—
359C22—2444no—
360C22—2444no—
361C22C2×#1451969111yescharacteristic
362C22#1683976611yescharacteristic
363C22C2×#1451970511yescharacteristic
364C4—21no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—4882no—
370C4#1683955012yes—
371C2—21no—
372C2—21no—
373C2—42no—
374C2—81no—
375C2—4884no—
376C2#2144433411yescharacteristic
377C2C2×#1683955011yescharacteristic
378C2#2144751011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC4×#100×C61C2
socleC22×C61C2×#99
prime radical#21449175C2
cosocleC2×C4⋊C4×C61C23
hypercenterC4×#100D61
hypocenterC61#11779
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #21444157C2semidirect
3. #21443821C2semidirect
4. C4×#100×C61C2semidirect
14. #16839488C22semidirect
19. C61×#343C22semidirect
183. C4×#100D61semidirect
206. #343C2×D61semidirect
209. C61#11779semidirect

Maximal subgroups

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

subgroupindex
#214491752
#214441572
#214438212
C4×#100×C612
#1177961