Finite Group Databasebeta

← #29590532

Subgroups — #29590532

Order 15616.

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

normal subgroups only

This group has 488 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#21451299C211yesmaximal, characteristic
2#21444149C211yesmaximal, characteristic, complemented
3#21443845C212yesmaximal, complemented
4#21443821C212yesmaximal, complemented
5C2×C61×#343C211yesmaximal, characteristic, complemented
6C2×#14519751C411yescharacteristic
7#16839726—21no—
8#16839701C411yescharacteristic
9#16839701C2211yescharacteristic
10#16839679C411yescharacteristic
11#16839679C2211yescharacteristic
12#16839652—21no—
13#16839652—21no—
14#16839641—21no—
15#16839641—21no—
16C4×C22⋊Dic61C411yescharacteristic
17#16839488—21no—
18#16839488C2212yes—
19C22×M16×C61—21no—
20C22×C4⋊C4×C61C2211yescharacteristic
21C61×#343—21no—
22C61×#343C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C2×#11758194—41no—
26#14519751—41no—
27#14519751—41no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C22⋊Dic61—21no—
30C2×#11758198—21no—
31C2×#11758198—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×C4×Dic61—21no—
36C22⋊#92418—22no—
37C22⋊#92418—41no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C23×C4×C61C2×C411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C2×M16×C61—24no—
48C2×M16×C61—22no—
49C2×M16×C61—41no—
50C2×M16×C61—42no—
51C22×C8×C61—41no—
52C2×C4⋊C4×C61—41no—
53C2×C4⋊C4×C61—41no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C23×D61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—22no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—81no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C2×D244—41no—
85C2×D244—81no—
86M16×C61—24no—
87M16×C61—44no—
88M16×C61—42no—
89C2×C8×C61—44no—
90C2×C8×C61—42no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊Dic61—42no—
96#11758198—42no—
97#11758198—42no—
98#11758198—41no—
99#11758198—41no—
100#11758198—81no—
101#11758198—81no—
102C4⋊Dic61—41no—
103C4×Dic61—81no—
104#11758194—82no—
105C2×#92418—42no—
106C23×C61—22no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61#9911yescharacteristic
111C23×C61#9911yescharacteristic
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—22no—
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—42no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61#10412yes—
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C22⋊D61—82no—
144C22⋊D61—82no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—82no—
155C8×C61—44no—
156#92418—82no—
157#11766—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61#35512yes—
168C22×C61C2×#9911yescharacteristic
169C22×C61#41711yescharacteristic
170C22×C61C2×#10411yescharacteristic
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—22no—
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—41no—
185Dic61—81no—
186Dic61—81no—
187Dic61—81no—
188#2591—611no—
189C2×#343D6111yescharacteristic, complemented
190#1463—611no—
191#1353—612no—
192#1345—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—22no—
196C2×C61—41no—
197C2×C61#150411yescharacteristic
198C2×C61#212111yescharacteristic
199C2×C61C2×#35511yescharacteristic
200D61—161no—
201C22×M16—21no—
202C2×#121—611no—
203C22×C4⋊C4C2×D6111yescharacteristic
204#407—1221no—
205#400—611no—
206#400—611no—
207#394—611no—
208#394—611no—
209#388—1221no—
210#388—1221no—
211#386—1221no—
212#386—1221no—
213C4×C22⋊C4—611no—
214#343—21no—
215#343C2×D6112yes—
216#324—612no—
217#324—1221no—
218C61#1176611yescharacteristic, complemented, Sylow
219C22×D4—611no—
220C22×D4—1221no—
221C23×C4C4×D6111yescharacteristic
222C23×C4D24411yescharacteristic
223C23×C4C22⋊D6111yescharacteristic
224C2×M16—24no—
225C2×M16—22no—
226C2×M16—41no—
227C2×M16—42no—
228C2×M16—2441no—
229C22×C8—41no—
230#121—2441no—
231#121—2441no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4C4×D6111yescharacteristic
236C2×C4⋊C4D24411yescharacteristic
237C2×C4⋊C4C22⋊D6111yescharacteristic
238C2×C4⋊C4C22×D6111yescharacteristic
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42—1221no—
246C22⋊C8—1222no—
247C22⋊C8—2441no—
248#95—611no—
249#95—611no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254C24—1221no—
255C24#1175819811yescharacteristic
256C2×D4—4881no—
257C2×D4—2441no—
258C2×D4—2442no—
259C2×D4—2442no—
260C2×D4—2441no—
261C2×D4—2441no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4#1175819811yescharacteristic
277C22×C4#1175819811yescharacteristic
278C22×C4#1175819811yescharacteristic
279C22×C4C2×C4×D6111yescharacteristic
280C22×C4C2×D24411yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282M16—24no—
283M16—44no—
284M16—42no—
285M16—4882no—
286C2×C8—44no—
287C2×C8—42no—
288C2×C8—2442no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—2441no—
294C22⋊C4—4881no—
295C22⋊C4—4881no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C22⋊C4—2441no—
299C22⋊C4—2442no—
300C22⋊C4—2441no—
301C42—4881no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—41no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23#1451969111yescharacteristic
314C23#1451969111yescharacteristic
315C23C2×#1175819811yescharacteristic
316D4—4882no—
317D4—4882no—
318D4—4882no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4#1451970512yes—
349C2×C4#1451980311yescharacteristic
350C2×C4#1451980811yescharacteristic
351C8—44no—
352C8—4882no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22#1683955812yes—
370C22C2×#1451969111yescharacteristic
371C22#1683976111yescharacteristic
372C22C2×#1451970511yescharacteristic
373C4—21no—
374C4—21no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4881no—
381C4—4881no—
382C4—4881no—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2—9761no—
388C2#2144432111yescharacteristic
389C2#2144746611yescharacteristic
390C2C2×#1683955811yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#343C2
socleC22×C61C2×#99
prime radicalC2×#14519751C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#343D61
hypocenterC61#11766
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. #21444149C2semidirect
3. #21443845C2semidirect
4. #21443821C2semidirect
5. C2×C61×#343C2semidirect
189. C2×#343D61semidirect
218. C61#11766semidirect

Maximal subgroups

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

subgroupindex
#214512992
#214441492
#214438452
#214438212
C2×C61×#3432
#1176661