Finite Group Databasebeta

← #29593159

Subgroups — #29593159

Order 15616.

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

normal subgroups only

This group has 512 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#21446975C211yesmaximal, characteristic, complemented
2#21444792C211yesmaximal, characteristic, complemented
3#21444758C211yesmaximal, characteristic, complemented
4#21443849C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic, complemented
6#21443751C211yesmaximal, characteristic, complemented
7C61×#2555C211yesmaximal, characteristic
8#16840393C2211yescharacteristic
9#16839918—21no—
10#16839913—21no—
11#16839767—21no—
12#16839531C2211yescharacteristic
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C2×#124×C61—21no—
19C2×#121×C61—21no—
20C61×#395C2211yescharacteristic
21C61×#394C2211yescharacteristic
22C61×#392—21no—
23C61×#390C2211yescharacteristic
24C61×#388—21no—
25C61×#386—21no—
26C4×C22⋊C4×C61—21no—
27C2×#11758202—41no—
28C2×#11758200—41no—
29C2×#11758194—21no—
30#14519776—41no—
31#14519768—41no—
32#14519756—21no—
33#14519756—21no—
34#14519736—21no—
35#14519701—41no—
36#14519698—41no—
37#14519698—41no—
38#14519698—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22×Q8×C61D411yescharacteristic
42C22×D4×C61—21no—
43C22×D4×C61—21no—
44C22×D4×C61D411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C23×C4×C61—21no—
47#124×C61—44no—
48#121×C61—44no—
49C2×C4⋊C4×C61—21no—
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×C22⋊C4×C61—21no—
58C2×C42×C61—21no—
59C2×C42×C61D411yescharacteristic
60#95×C61—21no—
61#95×C61—21no—
62#95×C61D411yescharacteristic
63#95×C61D411yescharacteristic
64C24×C61—21no—
65C24×C61—21no—
66C2×Q8×C61—42no—
67C2×Q8×C61—41no—
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—42no—
74C2×D4×C61—42no—
75C2×D4×C61—42no—
76C2×D4×C61—42no—
77C2×D4×C61—42no—
78C2×D4×C61—81no—
79C2×D4×C61—81no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—42no—
85C22×C4×C61—42no—
86C22×C4×C61—81no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C2×Dic122—21no—
91C2×Dic122—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—42no—
94C22⋊C4×C61—24no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C42×C61—42no—
103C42×C61—41no—
104C22⋊Dic61—41no—
105#11758202—82no—
106#11758200—82no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111#11758196—41no—
112#11758196—41no—
113C4×Dic61—41no—
114#11758194—41no—
115#11758194—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C23×C61—22no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61#12011yescharacteristic
134Q8×C61—42no—
135Q8×C61—81no—
136D4×C61—42no—
137D4×C61—42no—
138D4×C61—81no—
139D4×C61—81no—
140D4×C61—84no—
141D4×C61—84no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—84no—
161C2×C4×C61#13511yescharacteristic
162C2×C4×C61#13711yescharacteristic
163C2×Dic61—41no—
164C2×Dic61—41no—
165Dic122—81no—
166Dic122—81no—
167#92418—81no—
168#92418—81no—
169#92418—81no—
170#12270—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61#45211yescharacteristic
188C22×C61#45511yescharacteristic
189C22×C61B(4,𝔽2)11yescharacteristic
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—42no—
193C4×C61—42no—
194C4×C61—41no—
195C4×C61—41no—
196C4×C61—42no—
197C4×C61—81no—
198Dic61—81no—
199Dic61—81no—
200#2555D6111yescharacteristic
201#2027—611no—
202#1605—611no—
203#1599—611no—
204#1354—611no—
205#1345—611no—
206#1318—611no—
207C2×C61—21no—
208C2×C61—21no—
209C2×C61—82no—
210C2×C61—161no—
211C2×C61#160611yescharacteristic
212C2×C61#219611yescharacteristic
213C2×C61#220411yescharacteristic
214#544—611no—
215C2×#124—21no—
216C2×#121—21no—
217#451—1221no—
218#450—1221no—
219#418—1221no—
220#395C2×D6111yescharacteristic
221#394C2×D6111yescharacteristic
222#392—21no—
223#390C2×D6111yescharacteristic
224#388—21no—
225#386—21no—
226C4×C22⋊C4—21no—
227#343—611no—
228#339—1221no—
229#328—1221no—
230#328—1221no—
231#324—611no—
232#324—611no—
233C61#1227011yescharacteristic, complemented, Sylow
234C22×Q8C22⋊D6111yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4C22⋊D6111yescharacteristic
238C22×D4C22⋊D6111yescharacteristic
239C23×C4—21no—
240C2×Q16—2441no—
241C2×SD16—2441no—
242C2×M16—1221no—
243C4⋊Q8—2441no—
244#125—2441no—
245#124—44no—
246C22⋊Q8—1221no—
247C22⋊Q8—1221no—
248#121—44no—
249#117—1221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C22×D6111yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C42—21no—
260C2×C42C22⋊D6111yescharacteristic
261#103—2441no—
262#102—2441no—
263#102—2441no—
264#102—2441no—
265C22⋊C8—1221no—
266C22⋊C8—1221no—
267#95—21no—
268#95—21no—
269#95C22⋊D6111yescharacteristic
270#95C22⋊D6111yescharacteristic
271C24—21no—
272C24—21no—
273C2×Q8—42no—
274C2×Q8—41no—
275C2×Q8—1221no—
276C2×Q8—1221no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—81no—
288C2×D4—81no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—81no—
296C22×C4C2×C22⋊D6111yescharacteristic
297C22×C4C2×C22⋊D6111yescharacteristic
298C22×C4C2×C22⋊D6111yescharacteristic
299Q16—4882no—
300SD16—4882no—
301M16—2441no—
302M16—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C2×C8—2441no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—24no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—2441no—
323C42—41no—
324C42—42no—
325C42—2441no—
326C23—22no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23#1451974611yescharacteristic
341Q8—42no—
342Q8—81no—
343Q8—4881no—
344Q8—4881no—
345D4—42no—
346D4—42no—
347D4—81no—
348D4—81no—
349D4—84no—
350D4—84no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—84no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4#1451979711yescharacteristic
373C2×C4#1451980711yescharacteristic
374C8—4881no—
375C8—4881no—
376C8—4881no—
377C22—21no—
378C22—21no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22#1683992411yescharacteristic
394C22#1683994011yescharacteristic
395C22#1683994911yescharacteristic
396C4—21no—
397C4—21no—
398C4—42no—
399C4—42no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—81no—
404C4—4881no—
405C4—4881no—
406C2—21no—
407C2—21no—
408C2—82no—
409C2—161no—
410C2#2144479911yescharacteristic
411C2#2144780311yescharacteristic
412C2#2144784511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
Fitting, prime radicalC61×#2555C2
socleC22×C61B(4,𝔽2)
hypercenter#2555D61
hypocenterC61#12270
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2555

Complements

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

NH ≅ G/Ntype
1. #21446975C2semidirect
2. #21444792C2semidirect
3. #21444758C2semidirect
4. #21443849C2semidirect
5. #21443822C2semidirect
6. #21443751C2semidirect
233. C61#12270semidirect

Maximal subgroups

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

subgroupindex
#214469752
#214447922
#214447582
#214438492
#214438222
#214437512
C61×#25552
#1227061