Finite Group Databasebeta

← #29589586

Subgroups — #29589586

Order 15616.

440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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#21450310C211yesmaximal, characteristic
2#21444147C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443762C211yesmaximal, characteristic, complemented
5#21443762C211yesmaximal, characteristic, complemented
6#21443751C211yesmaximal, characteristic, complemented
7C61×#1318C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839724—21no—
11C22⋊C8×D61—21no—
12#16839690—21no—
13#16839690—21no—
14#16839665C411yescharacteristic
15#16839638—21no—
16#16839638—21no—
17#16839628C411yescharacteristic
18#16839627C2211yescharacteristic
19C4×#11758198C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#390C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32C2×C8×D61—41no—
33#14519748—41no—
34#14519748—41no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×#11758196D411yescharacteristic
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519689—41no—
49#14519689—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C22×D4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C42×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C24×C61—21no—
63C23×D61C22⋊C411yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—41no—
90C2×C4×D61—81no—
91C2×C4×D61—81no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—81no—
96C22⋊C4×C61—81no—
97C42×C61—41no—
98C22⋊Dic61—42no—
99C22⋊Dic61—81no—
100C22⋊Dic61—81no—
101#11758198—42no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C2×#92418—41no—
109C2×#92418—41no—
110#11758189—82no—
111C8×D61—82no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—22no—
123C22×D61—41no—
124C22×D61#9911yescharacteristic
125C22×D61#9911yescharacteristic
126D4×C61—81no—
127D4×C61—81no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#13111yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C22⋊D61—82no—
140C22⋊D61—82no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—41no—
157C4×D61—41no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—81no—
161C4×D61—81no—
162C8×C61—81no—
163C8×C61—81no—
164#92418—81no—
165#92418—81no—
166#11553—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61#40811yescharacteristic
177C22×C61C2×#9911yescharacteristic
178C22×C61#41311yescharacteristic
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61#35512yes—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—81no—
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195Dic61—81no—
196Dic61—81no—
197#2504—611no—
198#1463—611no—
199C2×#324—611no—
200#1324—611no—
201#1324—611no—
202#1318—611no—
203#1318D6111yescharacteristic, complemented
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—161no—
207C2×C61#146811yescharacteristic
208C2×C61#212711yescharacteristic
209C2×C61C2×#35511yescharacteristic
210D61—22no—
211D61—41no—
212C2×#121—611no—
213C22×C4⋊C4—611no—
214#407—1221no—
215C2×C22⋊C8—1221no—
216#397—1221no—
217#397—1221no—
218#390—611no—
219#390C2×D6111yescharacteristic
220#386—1221no—
221#386—1221no—
222#382—611no—
223#382—611no—
224C4×C22⋊C4—611no—
225#324—611no—
226#324—611no—
227#324—1221no—
228#324—1221no—
229#324C2×D6111yescharacteristic
230#324C2×D6111yescharacteristic
231C61#1155311yescharacteristic, complemented, Sylow
232C22×D4—1221no—
233C22×D4C4×D6111yescharacteristic
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—611no—
237C2×M16—2441no—
238C22×C8—2441no—
239#121—2441no—
240#121—2441no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—2441no—
246C2×C4⋊C4—2441no—
247C2×C4⋊C4C22×D6111yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42—611no—
255C2×C42C4×D6111yescharacteristic
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—1221no—
259C22⋊C8—1221no—
260C22⋊C8—2441no—
261C22⋊C8—2441no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266#95—1221no—
267C24—21no—
268C24—611no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—2441no—
274C2×D4—2441no—
275C2×D4—2442no—
276C2×D4—2442no—
277C22×C4—21no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—4881no—
292C22×C4—4881no—
293C22×C4—2441no—
294C22×C4C2×C4×D6111yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4D4×D6111yescharacteristic
297M16—4882no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—4882no—
301C2×C8—2441no—
302C2×C8—2441no—
303C4⋊C4—41no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—4881no—
311C22⋊C4—4881no—
312C22⋊C4—2442no—
313C22⋊C4—2442no—
314C42—41no—
315C42—1221no—
316C42—1221no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—611no—
325C23—611no—
326C23—1222no—
327C23—1221no—
328C23—1221no—
329C23—2441no—
330C23C22⋊C4×D6111yescharacteristic
331D4—81no—
332D4—81no—
333D4—4882no—
334D4—4882no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4#1451978311yescharacteristic
366C2×C4#1451978511yescharacteristic
367C8—81no—
368C8—81no—
369C8—4881no—
370C8—4881no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—612no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—1221no—
385C22—1221no—
386C22—2442no—
387C22—2442no—
388C22#1683972711yescharacteristic
389C22#99×D6111yescharacteristic
390C22#1683974311yescharacteristic
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—81no—
396C4—4881no—
397C4—4881no—
398C4—2441no—
399C4—2441no—
400C4—2441no—
401C2—21no—
402C2—21no—
403C2—161no—
404C2—1222no—
405C2—2441no—
406C2#2144416411yescharacteristic
407C2#2144748511yescharacteristic
408C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1318C2
socleC22×C61C2×#99
prime radicalC2×#14519748C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1318D61
hypocenterC61#11553
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #21444147C2semidirect
3. #324×D61C2semidirect
4. #21443762C2semidirect
5. #21443762C2semidirect
6. #21443751C2semidirect
7. C61×#1318C2semidirect
203. #1318D61semidirect
231. C61#11553semidirect

Maximal subgroups

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

subgroupindex
#214503102
#214441472
#324×D612
#214437622
#214437512
C61×#13182
#1155361