Finite Group Databasebeta

← #29592323

Subgroups — #29592323

Order 15616.

394 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 59 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#21447070C211yesmaximal, characteristic
2#21444838C211yesmaximal, characteristic
3#21444804C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443767C211yesmaximal, characteristic, complemented
7C61×#2834C211yesmaximal, characteristic, complemented
8#16840324C2211yescharacteristic
9#16840080—21no—
10#16840075—21no—
11C2×#14519691—21no—
12#16839641—21no—
13#16839529C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#401—21no—
19C61×#399C2211yescharacteristic
20C61×#398—21no—
21C61×#398—21no—
22C61×#398—21no—
23C61×#397—21no—
24C61×#397C2211yescharacteristic
25C61×#385—21no—
26C61×#385C2211yescharacteristic
27C22×C22⋊D61—21no—
28#14519761—41no—
29#14519751—21no—
30#14519751—21no—
31#14519747—41no—
32C2×C22⋊Dic61—21no—
33C2×#11758198—41no—
34#14519710—41no—
35#14519708—41no—
36#14519697—41no—
37#14519697—41no—
38#14519691—42no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41#14519684—41no—
42C23×C4×C61D411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61D411yescharacteristic
62#95×C61D411yescharacteristic
63C24×C61C2×D411yescharacteristic
64C23×D61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—81no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C22×Dic61—21no—
82C22×Dic61—41no—
83C2×D244—21no—
84C2×D244—21no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—81no—
88C4⋊C4×C61—81no—
89C4⋊C4×C61—81no—
90C4⋊C4×C61—81no—
91C4⋊C4×C61—81no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—81no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—82no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61#12011yescharacteristic
112C23×C61#13511yescharacteristic
113C23×C61AGL(1,ℤ/8)11yescharacteristic
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—81no—
118C22×D61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—81no—
143C22⋊D61—81no—
144C22⋊D61—81no—
145C22⋊D61—81no—
146C22⋊D61—81no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153D244—81no—
154D244—81no—
155#92418—81no—
156#92418—81no—
157#12138—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—81no—
167C22×C61#44911yescharacteristic
168C22×C61#45411yescharacteristic
169C22×C61B(4,𝔽2)11yescharacteristic
170C2×D61—82no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—161no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—81no—
178C4×C61—81no—
179C4×C61—81no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61—81no—
183Dic61—81no—
184Dic61—161no—
185#2834D6111yescharacteristic, complemented
186#2044—611no—
187#1613—611no—
188#1607—611no—
189#1352—611no—
190#1344—611no—
191#1326—611no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61—41no—
195C2×C61—41no—
196C2×C61#159711yescharacteristic
197C2×C61#220011yescharacteristic
198C2×C61#220111yescharacteristic
199D61—161no—
200#534—611no—
201#481—1221no—
202#480—1221no—
203C2×#99—1221no—
204#401—21no—
205#399C2×D6111yescharacteristic
206#398—21no—
207#398—21no—
208#398—21no—
209#397—21no—
210#397C2×D6111yescharacteristic
211#386—1221no—
212#385—21no—
213#385C2×D6111yescharacteristic
214#342—611no—
215#327—1221no—
216#327—1221no—
217#323—611no—
218#323—611no—
219C61#1213811yescharacteristic, complemented, Sylow
220C22×D4—1221no—
221C23×C4C22⋊D6111yescharacteristic
222#123—2441no—
223#121—1221no—
224#121—1221no—
225#120—2441no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C22⋊D6111yescharacteristic
232C2×C4⋊C4C22⋊D6111yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—2441no—
237C2×C22⋊C4C22⋊D6111yescharacteristic
238C2×C22⋊C4C22×D6111yescharacteristic
239#107—2441no—
240#106—2441no—
241#102—2441no—
242#102—2441no—
243#99—2442no—
244C22⋊C8—1221no—
245C22⋊C8—1221no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—2441no—
254#95C22⋊D6111yescharacteristic
255#95C22⋊D6111yescharacteristic
256C24—1221no—
257C24C2×C22⋊D6111yescharacteristic
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—2441no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4—2441no—
264C2×D4—2441no—
265C2×D4—2441no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—81no—
274C22×C4—1221no—
275C22×C4—2441no—
276C22×C4C2×C22⋊D6111yescharacteristic
277C22×C4C2×C22⋊D6111yescharacteristic
278C2×C8—2441no—
279C2×C8—2441no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—81no—
295C22⋊C4—4882no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—4881no—
305C23—4881no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23#1451974611yescharacteristic
310C23#1451979711yescharacteristic
311C23#1451980211yescharacteristic
312D4—4881no—
313D4—4881no—
314D4—4881no—
315D4—4881no—
316D4—4881no—
317D4—4881no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C8—4881no—
349C8—4881no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—9761no—
360C22—4882no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22#1683990711yescharacteristic
365C22#1683993511yescharacteristic
366C22#1683994911yescharacteristic
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—9761no—
376C4—4881no—
377C2—21no—
378C2—21no—
379C2—41no—
380C2—41no—
381C2—9761no—
382C2#2144474811yescharacteristic
383C2#2144782611yescharacteristic
384C2#2144783211yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2834C2
socleC22×C61B(4,𝔽2)
prime radical#16840324C22
hypercenter#2834D61
hypocenterC61#12138
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2834

Complements

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

NH ≅ G/Ntype
4. #21443843C2semidirect
5. #21443819C2semidirect
6. #21443767C2semidirect
7. C61×#2834C2semidirect
185. #2834D61semidirect
219. C61#12138semidirect

Maximal subgroups

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

subgroupindex
#214470702
#214448382
#214448042
#214438432
#214438192
#214437672
C61×#28342
#1213861