Finite Group Databasebeta

← #29592782

Subgroups — #29592782

Order 15616.

464 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 63 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#21444826C211yesmaximal, characteristic, complemented
3#21444758C211yesmaximal, characteristic, complemented
4#21443825C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic, complemented
6#21443751C211yesmaximal, characteristic, complemented
7C61×#2699C211yesmaximal, characteristic
8#16840393C2211yescharacteristic
9#16840092—21no—
10#16839913—21no—
11#16839767—21no—
12#16839531C2211yescharacteristic
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C2×#121×C61—21no—
19C61×#398C2211yescharacteristic
20C61×#394—21no—
21C61×#394C2211yescharacteristic
22C61×#392—21no—
23C61×#390C2211yescharacteristic
24C61×#388—21no—
25C61×#386—21no—
26C61×#381—21no—
27C2×#11758200—41no—
28C2×#11758194—21no—
29#14519776—41no—
30#14519768—41no—
31#14519756—21no—
32#14519756—21no—
33#14519736—21no—
34#14519708—41no—
35#14519700—41no—
36#14519698—41no—
37#14519698—41no—
38#14519698—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22×D4×C61—21no—
42C22×D4×C61—21no—
43C22×D4×C61D411yescharacteristic
44C22×D4×C61D411yescharacteristic
45C23×C4×C61—21no—
46#121×C61—42no—
47#121×C61—42no—
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×C22⋊C4×C61—21no—
58C2×C42×C61D411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61D411yescharacteristic
63#95×C61D411yescharacteristic
64C24×C61—21no—
65C24×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—42no—
71C2×D4×C61—42no—
72C2×D4×C61—42no—
73C2×D4×C61—81no—
74C2×D4×C61—81no—
75C2×D4×C61—81no—
76C2×D4×C61—81no—
77C2×D4×C61SD1612yescomplemented
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—42no—
83C22×C4×C61—42no—
84C22×C4×C61—81no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C2×Dic122—21no—
89C2×Dic122—21no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—81no—
99C22⋊C4×C61—81no—
100C22⋊C4×C61—81no—
101C22⋊C4×C61—81no—
102C42×C61—41no—
103C22⋊Dic61—41no—
104#11758200—82no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109#11758196—41no—
110#11758196—41no—
111C4×Dic61—41no—
112#11758194—41no—
113#11758194—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C23×C61—22no—
118C23×C61—41no—
119C23×C61—41no—
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#12011yescharacteristic
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—81no—
135D4×C61—84no—
136D4×C61—81no—
137D4×C61—84no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
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—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—84no—
157C2×C4×C61C2×SD1611yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×Dic61—41no—
160C2×Dic61—41no—
161Dic122—81no—
162Dic122—81no—
163#92418—81no—
164#92418—81no—
165#92418—81no—
166#12211—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61#45011yescharacteristic
184C22×C61#45511yescharacteristic
185C22×C61B(4,𝔽2)11yescharacteristic
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—42no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—81no—
192C4×C61—81no—
193C4×C61—81no—
194Dic61—81no—
195Dic61—81no—
196#2699D6111yescharacteristic
197#2027—611no—
198#1611—611no—
199#1599—611no—
200#1346—611no—
201#1345—611no—
202#1318—611no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—82no—
206C2×C61—161no—
207C2×C61#160111yescharacteristic
208C2×C61#220011yescharacteristic
209C2×C61#220411yescharacteristic
210#544—611no—
211C2×#121—21no—
212#483—1221no—
213#450—1221no—
214#418—1221no—
215#398C2×D6111yescharacteristic
216#394—21no—
217#394C2×D6111yescharacteristic
218#392—21no—
219#390C2×D6111yescharacteristic
220#388—21no—
221#386—21no—
222#381—21no—
223#343—611no—
224#339—1221no—
225#328—1221no—
226#328—1221no—
227#324—611no—
228#324—611no—
229C61#1221111yescharacteristic, complemented, Sylow
230C22×D4—21no—
231C22×D4—21no—
232C22×D4C22⋊D6111yescharacteristic
233C22×D4C22⋊D6111yescharacteristic
234C23×C4—21no—
235C2×SD16—2441no—
236C2×M16—1221no—
237C4⋊Q8—2441no—
238#125—2441no—
239C22⋊Q8—1221no—
240C22⋊Q8—1221no—
241#121—42no—
242#121—42no—
243#117—1221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C22⋊D6111yescharacteristic
246C2×C4⋊C4C22×D6111yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C42C22⋊D6111yescharacteristic
255#106—2441no—
256#103—2441no—
257#102—2441no—
258#102—2441no—
259#102—2441no—
260C22⋊C8—1221no—
261C22⋊C8—1221no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95C22⋊D6111yescharacteristic
266#95C22⋊D6111yescharacteristic
267C24—21no—
268C24—21no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—81no—
279C2×D4—81no—
280C2×D4—81no—
281C2×D4—81no—
282C2×D4#1175820012yescomplemented
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—81no—
290C22×C4C2×C22⋊D6111yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292C22×C4C2×C22⋊D6111yescharacteristic
293SD16—4882no—
294M16—2441no—
295M16—2441no—
296C2×C8—2441no—
297C2×C8—2441no—
298C2×C8—2441no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—81no—
314C22⋊C4—81no—
315C22⋊C4—81no—
316C22⋊C4—81no—
317C22⋊C4—2441no—
318C42—41no—
319C42—2441no—
320C23—22no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23#1451974611yescharacteristic
335Q8—4881no—
336Q8—4881no—
337D4—42no—
338D4—42no—
339D4—81no—
340D4—84no—
341D4—81no—
342D4—84no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—84no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4C2×#1175820011yescharacteristic
365C2×C4#1451980311yescharacteristic
366C8—4881no—
367C8—4881no—
368C8—4881no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#1683991311yescharacteristic
386C22#1683994011yescharacteristic
387C22#1683994911yescharacteristic
388C4—21no—
389C4—21no—
390C4—42no—
391C4—41no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—4881no—
397C4—4881no—
398C2—21no—
399C2—21no—
400C2—82no—
401C2—161no—
402C2#2144477111yescharacteristic
403C2#2144782611yescharacteristic
404C2#2144784511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
Fitting, prime radicalC61×#2699C2
socleC22×C61B(4,𝔽2)
hypercenter#2699D61
hypocenterC61#12211
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2699

Complements

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

NH ≅ G/Ntype
1. #21446975C2semidirect
2. #21444826C2semidirect
3. #21444758C2semidirect
4. #21443825C2semidirect
5. #21443822C2semidirect
6. #21443751C2semidirect
77. C2×D4×C61SD16semidirect
229. C61#12211semidirect
282. C2×D4#11758200semidirect

Maximal subgroups

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

subgroupindex
#214469752
#214448262
#214447582
#214438252
#214438222
#214437512
C61×#26992
#1221161