Finite Group Databasebeta

← #29590701

Subgroups — #29590701

Order 15616.

472 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 69 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#21449058C211yesmaximal, characteristic
2#21445901C211yesmaximal, characteristic, complemented
3#21444152C211yesmaximal, characteristic, complemented
4#21443826C211yesmaximal, characteristic, complemented
5#21443824C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C2×D4×Dic61C411yescharacteristic
9C2×#14519737—21no—
10C2×#14519735C2211yescharacteristic
11#16839816—21no—
12#16839725—21no—
13#16839692C2211yescharacteristic
14#16839689C411yescharacteristic
15#16839685—21no—
16#16839677—21no—
17#16839670C411yescharacteristic
18#16839613C411yescharacteristic
19C22⋊C4×Dic61—21no—
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C22⋊D61—21no—
28C23×Dic61—21no—
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31D4×Dic61—41no—
32D4×Dic61—41no—
33#14519737—42no—
34#14519737—42no—
35#14519735—41no—
36#14519735—41no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50C22⋊#92418—21no—
51#14519689—41no—
52#14519689—41no—
53#14519687—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×D4×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C22⋊C8×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C2×D4×C61—41no—
67C2×D4×C61—42no—
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—42no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—41no—
89M16×C61—41no—
90M16×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—42no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—42no—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—42no—
112#11758194—41no—
113#11758194—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61—22no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—41no—
128C22×D61—41no—
129D4×C61—42no—
130D4×C61—42no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C22⋊D61—48no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—82no—
156C2×Dic61—82no—
157C2×Dic61#9911yescharacteristic
158C2×Dic61#9911yescharacteristic
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C8×C61—81no—
164C8×C61—81no—
165#92418—81no—
166#92418—81no—
167#11804—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—42no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61C2×#9911yescharacteristic
178C22×C61#41811yescharacteristic
179C22×C61#42111yescharacteristic
180C2×D61—42no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—81no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61—81no—
190Dic61—21no—
191Dic61—21no—
192Dic61—42no—
193Dic61—41no—
194Dic61—41no—
195Dic61—81no—
196#2392—611no—
197#1822—611no—
198#1464—611no—
199#1346—611no—
200#1346—611no—
201#1345—611no—
202#1345D6111yescharacteristic, complemented
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—82no—
206C2×C61#151011yescharacteristic
207C2×C61#212011yescharacteristic
208C2×C61#213211yescharacteristic
209D61—81no—
210C2×C4×D4—611no—
211C2×C4×D4—1221no—
212C2×#117—611no—
213#432—1221no—
214#407—1221no—
215#398—611no—
216#397—611no—
217#396—1221no—
218#394—1221no—
219#394C2×D6111yescharacteristic
220#392—611no—
221C4×C4⋊C4—611no—
222C4×C22⋊C4—1221no—
223#343—611no—
224#343—1221no—
225#343C2×D6111yescharacteristic
226#324—611no—
227#324C2×D6111yescharacteristic
228#323—1221no—
229C61#1180411yescharacteristic, complemented, Sylow
230C22×D4—1221no—
231C22×D4C4×D6111yescharacteristic
232C23×C4—611no—
233C23×C4—1221no—
234C2×M16—21no—
235C2×M16—1221no—
236C4×D4—2441no—
237C4×D4—2441no—
238C4×D4—2442no—
239C4×D4—2442no—
240#117—2441no—
241#117—2441no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4C22×D6111yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—611no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—1221no—
257C4⋊C8—2441no—
258C22⋊C8—21no—
259C22⋊C8—1221no—
260C22⋊C8—2441no—
261C22⋊C8—2441no—
262#97—2441no—
263#95—611no—
264#95—1221no—
265#95—1221no—
266#95C4×D6111yescharacteristic
267C24—21no—
268C24—611no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—2442no—
272C2×D4—2442no—
273C2×D4—2442no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2442no—
288C22×C4—2442no—
289C22×C4C2×C4×D6111yescharacteristic
290C22×C4D4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292M16—41no—
293M16—41no—
294M16—2441no—
295M16—2441no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—2441no—
299C2×C8—2441no—
300C4⋊C4—41no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2442no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C22⋊C4—2442no—
314C42—1221no—
315C42—1221no—
316C42—1221no—
317C42—1221no—
318C42—2442no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23C22⋊C4×D6111yescharacteristic
332D4—42no—
333D4—42no—
334D4—2448no—
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—611no—
345C2×C4—611no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1222no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4#1451980111yescharacteristic
365C2×C4#1451980411yescharacteristic
366C8—81no—
367C8—81no—
368C8—4881no—
369C8—4881no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—4881no—
380C22—2442no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22#99×D6111yescharacteristic
385C22#1683976511yescharacteristic
386C22#1683977711yescharacteristic
387C4—21no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—81no—
392C4—1221no—
393C4—1221no—
394C4—4881no—
395C4—2442no—
396C4—2441no—
397C4—2441no—
398C2—21no—
399C2—21no—
400C2—82no—
401C2—4881no—
402C2#2144434611yescharacteristic
403C2#2144745711yescharacteristic
404C2#2144750111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radical#16839670C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11804
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445901C2semidirect
3. #21444152C2semidirect
4. #21443826C2semidirect
5. #21443824C2semidirect
6. #21443822C2semidirect
7. C61×#1345C2semidirect
202. #1345D61semidirect
229. C61#11804semidirect

Maximal subgroups

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

subgroupindex
#214490582
#214459012
#214441522
#214438262
#214438242
#214438222
C61×#13452
#1180461