Finite Group Databasebeta

← #29592717

Subgroups — #29592717

Order 15616.

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

normal subgroups only

This group has 424 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#21446860C211yesmaximal, characteristic
2#21444821C211yesmaximal, characteristic, complemented
3#21444787C211yesmaximal, characteristic, complemented
4#21443849C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443751C211yesmaximal, characteristic, complemented
7C61×#2830C211yesmaximal, characteristic, complemented
8C2×#14519803—21no—
9#16840343C2211yescharacteristic
10#16840075—21no—
11#16839901—21no—
12C2×#14519705—21no—
13#16839531C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#398C2211yescharacteristic
19C61×#397—21no—
20C61×#397—21no—
21C61×#396—21no—
22C61×#395C2211yescharacteristic
23C61×#394—21no—
24C61×#393—21no—
25C61×#390C2211yescharacteristic
26C61×#387—21no—
27C2×#11758222—21no—
28#14519803—42no—
29#14519803—42no—
30C2×#11758200—41no—
31C2×#11758201—41no—
32C2×#11758199—41no—
33C2×#11758194—21no—
34#14519757—41no—
35#14519752—41no—
36#14519751—21no—
37#14519751—21no—
38#14519710—41no—
39#14519705—42no—
40#14519701—41no—
41#14519697—41no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22×Q8×C61D411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61C2311yescharacteristic
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C42×C61D411yescharacteristic
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C24×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—81no—
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C2×C22⋊D61—41no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×C4×D61—41no—
89C2×Dic122—21no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—81no—
95C4⋊C4×C61—81no—
96C22⋊C4×C61—81no—
97C22⋊C4×C61—81no—
98C22⋊C4×C61—81no—
99C22⋊C4×C61—81no—
100C22⋊C4×C61—81no—
101C22⋊C4×C61—81no—
102C42×C61—41no—
103#11758201—82no—
104#11758200—44no—
105#11758199—44no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758194—22no—
111#11758194—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61#12011yescharacteristic
123C22×D61—41no—
124Q8×C61—42no—
125Q8×C61—81no—
126D4×C61—42no—
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—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C22⋊D61—81no—
152C22⋊D61—81no—
153C2×Dic61—41no—
154D244—41no—
155D244—41no—
156D244—81no—
157D244—81no—
158C4×D61—81no—
159C4×D61—81no—
160Dic122—41no—
161Dic122—41no—
162#92418—42no—
163#92418—81no—
164#92418—81no—
165#12200—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61#44911yescharacteristic
176C22×C61#45311yescharacteristic
177C22×C61B(4,𝔽2)11yescharacteristic
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186C4×C61—81no—
187C4×C61—81no—
188C4×C61—81no—
189C4×C61—81no—
190Dic61—81no—
191#2830D6111yescharacteristic, complemented
192#2006—611no—
193#1610—611no—
194#1604—611no—
195#1354—611no—
196#1346—611no—
197#1318—611no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—161no—
201C2×C61#160011yescharacteristic
202C2×C61#220011yescharacteristic
203C2×C61#220311yescharacteristic
204D61—161no—
205C2×AGL(1,ℤ/8)—1221no—
206#537—611no—
207#480—1221no—
208#448—1221no—
209C2×#104—1221no—
210#398C2×D6111yescharacteristic
211#397—21no—
212#397—21no—
213#396—21no—
214#395C2×D6111yescharacteristic
215#394—21no—
216#393—21no—
217#390C2×D6111yescharacteristic
218#387—21no—
219#343—611no—
220#327—1221no—
221#327—1221no—
222#324—611no—
223#324—611no—
224C61#1220011yescharacteristic, complemented, Sylow
225C2×#41—1221no—
226C22×Q8C22⋊D6111yescharacteristic
227C22×D4C22⋊D6111yescharacteristic
228AGL(1,ℤ/8)—2442no—
229AGL(1,ℤ/8)—2442no—
230C2×SD16—2441no—
231C2×SD16—2441no—
232C2×D8—2441no—
233C2×M16—1221no—
234C22⋊Q8—2441no—
235#121—1221no—
236#121—1221no—
237#121—2441no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C22⋊D6111yescharacteristic
242C2×C4⋊C4C22×D6111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C42C22⋊D6111yescharacteristic
250#107—2441no—
251#104—2442no—
252#103—2441no—
253#102—2441no—
254C22⋊C8—1221no—
255C22⋊C8—1221no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95C22⋊D6111yescharacteristic
262#95C22⋊D6111yescharacteristic
263C24—21no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×Q8—1221no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—2441no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—2441no—
285C22×C4C2×C22⋊D6111yescharacteristic
286C22×C4C2×C22⋊D6111yescharacteristic
287C22×C4C2×C22⋊D6111yescharacteristic
288SD16—4882no—
289SD16—2444no—
290D8—2444no—
291M16—1222no—
292M16—2441no—
293C2×C8—2441no—
294C2×C8—2441no—
295C2×C8—2441no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4—81no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C42—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—2441no—
321C23#1451974611yescharacteristic
322Q8—42no—
323Q8—81no—
324Q8—2441no—
325Q8—2441no—
326D4—42no—
327D4—81no—
328D4—4881no—
329D4—4881no—
330D4—4881no—
331D4—4881no—
332D4—2441no—
333D4—2441no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—2441no—
358C2×C4#1451979711yescharacteristic
359C2×C4#1451980211yescharacteristic
360C8—4881no—
361C8—4881no—
362C8—2442no—
363C22—21no—
364C22—21no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—4881no—
373C22—4881no—
374C22—4881no—
375C22#1683990711yescharacteristic
376C22#1683993011yescharacteristic
377C22#1683994911yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—4881no—
388C2—21no—
389C2—21no—
390C2—161no—
391C2—9761no—
392C2#2144476511yescharacteristic
393C2#2144782611yescharacteristic
394C2#2144784011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2830C2
socleC22×C61B(4,𝔽2)
prime radical#21446860C2
hypercenter#2830D61
hypocenterC61#12200
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2830

Complements

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

NH ≅ G/Ntype
2. #21444821C2semidirect
3. #21444787C2semidirect
4. #21443849C2semidirect
5. #21443825C2semidirect
6. #21443751C2semidirect
7. C61×#2830C2semidirect
191. #2830D61semidirect
224. C61#12200semidirect

Maximal subgroups

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

subgroupindex
#214468602
#214448212
#214447872
#214438492
#214438252
#214437512
C61×#28302
#1220061