Finite Group Databasebeta

← #29576700

Subgroups — #29576700

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454537C211yesmaximal, characteristic, complemented
2#21446644C211yesmaximal, characteristic, complemented
3#21444487C211yesmaximal, characteristic, complemented
4#21444379C211yesmaximal, characteristic, complemented
5#21443678C211yesmaximal, characteristic, complemented
6#21443649C211yesmaximal, characteristic, complemented
7C61×#3205C211yesmaximal, characteristic
8C2×#14519784—21no—
9#16839834—22no—
10#16839834—22no—
11#16839815C2211yescharacteristic
12#16839786C2211yescharacteristic
13C2×#14519698—21no—
14C2×#14519698—21no—
15#16839729—21no—
16C2×#14519688C2211yescharacteristic
17#16839628C2211yescharacteristic
18#16839506—22no—
19#16839496—22no—
20C61×#532C2211yescharacteristic
21C2×#127×C61C2211yescharacteristic
22C61×#493C412yescomplemented
23C61×#486C412yescomplemented
24C61×#459—22no—
25C61×#447—22no—
26C61×#431C2211yescharacteristic
27#14519784—42no—
28#14519784—42no—
29C2×#11758194—22no—
30C2×#11758194—21no—
31C22×#92418—22no—
32C22×#92418D411yescharacteristic
33C22×#92418D411yescharacteristic
34C2×C4⋊Dic61—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418D412yes—
38#14519698—42no—
39#14519698—42no—
40C22⋊#92418—24no—
41C22⋊#92418—21no—
42#14519688—21no—
43#14519688—21no—
44C4×#92418—21no—
45#14519684—21no—
46#14519684—21no—
47C2×#41×C61—21no—
48C22×D4×C61—21no—
49C22×D4×C61—21no—
50C22×D4×C61—21no—
51C2×D8×C61—24no—
52C4⋊Q8×C61C2×C411yescharacteristic
53#127×C61—21no—
54#127×C61—21no—
55#127×C61—21no—
56#127×C61C2×C412yes—
57#127×C61C2×C411yescharacteristic
58#124×C61—21no—
59#121×C61—21no—
60#121×C61D412yes—
61C4×D4×C61—21no—
62C4×D4×C61D412yes—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65#102×C61—24no—
66C22⋊C8×C61—21no—
67C4×C8×C61C2×C412yes—
68C24×C61—41no—
69#41×C61—41no—
70#41×C61—41no—
71#41×C61—41no—
72#41×C61—41no—
73C2×Q8×C61—21no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61—21no—
77C2×D4×C61—22no—
78C2×D4×C61—21no—
79C2×D4×C61—22no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—82no—
88C2×D4×C61—82no—
89C2×D4×C61C22⋊C412yes—
90C22×C4×C61—22no—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×Dic61—41no—
95D8×C61—84no—
96C2×C8×C61—22no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61C22⋊C412yes—
99C22⋊C4×C61—22no—
100C22⋊C4×C61—22no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758194—44no—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—22no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—44no—
117C2×#92418—41no—
118C2×#92418D812yescomplemented
119C23×C61—22no—
120C23×C61—42no—
121C23×C61—82no—
122C23×C61—82no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61#12111yescharacteristic
126Q8×C61—41no—
127Q8×C61—41no—
128D4×C61—42no—
129D4×C61—44no—
130D4×C61—42no—
131D4×C61—42no—
132D4×C61—41no—
133D4×C61—42no—
134D4×C61—41no—
135D4×C61—42no—
136D4×C61—81no—
137D4×C61—82no—
138D4×C61—82no—
139D4×C61—82no—
140D4×C61—81no—
141D4×C61—81no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12311yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×Dic61—81no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160C8×C61—42no—
161#92418—22no—
162#92418—42no—
163#92418—41no—
164#92418—81no—
165#9293—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—82no—
172C22×C61—82no—
173C22×C61—82no—
174C22×C61—162no—
175C22×C61—162no—
176C22×C61#38611yescharacteristic
177C22×C61#45911yescharacteristic
178C22×C61#46311yescharacteristic
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—42no—
184C4×C61C4×D811yescharacteristic
185C4×C61#44211yescharacteristic
186C4×C61#44711yescharacteristic
187C4×C61#44911yescharacteristic
188Dic61—161no—
189#3205D6111yescharacteristic
190#2932—611no—
191#1961—611no—
192#1545—611no—
193#1517—611no—
194#1286—611no—
195#1275—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—82no—
199C2×C61—162no—
200C2×C61#187911yescharacteristic
201C2×C61#190311yescharacteristic
202C2×C61#191011yescharacteristic
203C2×#131—1221no—
204#532C2×D6111yescharacteristic
205C2×#127C2×D6111yescharacteristic
206#493Dic6112yescomplemented
207#486Dic6112yescomplemented
208#459—22no—
209#447—22no—
210#435—1222no—
211#435—1222no—
212#431—611no—
213#431C2×D6111yescharacteristic
214#423—611no—
215C2×#102—1221no—
216C2×#102—1221no—
217#408—1221no—
218C2×#97—611no—
219#382—611no—
220#331—1222no—
221#327—1222no—
222C61#929311yescharacteristic, complemented, Sylow
223C2×#41—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C2×D8—24no—
228#131—2442no—
229#131—2442no—
230C2×M16—1222no—
231C2×M16—1221no—
232C22×C8—611no—
233C22×C8—611no—
234C22×C8—1222no—
235C4⋊Q8C2×Dic6111yescharacteristic
236#127—21no—
237#127—21no—
238#127—21no—
239#127C2×Dic6112yes—
240#127C2×Dic6111yescharacteristic
241#124—21no—
242#121—21no—
243#121C22⋊D6112yes—
244C4×D4—21no—
245C4×D4C22⋊D6112yes—
246C2×C4⋊C4—1221no—
247C2×C42C22×D6111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—612no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252#102—24no—
253#102—2442no—
254#102—2442no—
255C22⋊C8—21no—
256C22⋊C8—1224no—
257C22⋊C8—1221no—
258#97—1221no—
259#97—1221no—
260C4×C8—1221no—
261C4×C8C2×Dic6112yes—
262#95—1221no—
263#95—1221no—
264C24—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—82no—
284C2×D4—82no—
285C2×D4C22⋊Dic6112yes—
286C22×C4—22no—
287C22×C4—2441no—
288C22×C4D4×D6111yescharacteristic
289C22×C4#1175822411yescharacteristic
290C22×C4C2×C22⋊D6111yescharacteristic
291D8—84no—
292M16—2444no—
293M16—2441no—
294M16—2441no—
295C2×C8—22no—
296C2×C8—612no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—1222no—
301C2×C8—1221no—
302C2×C8—1221no—
303C2×C8—2444no—
304C2×C8—2441no—
305C4⋊C4—21no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4C22⋊Dic6112yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C42D4×D6111yescharacteristic
312C42#1175822411yescharacteristic
313C42C22×Dic6111yescharacteristic
314C42C2×C22⋊D6111yescharacteristic
315C23—22no—
316C23—42no—
317C23—82no—
318C23—82no—
319C23—81no—
320C23—81no—
321C23#1451974911yescharacteristic
322Q8—41no—
323Q8—41no—
324D4—42no—
325D4—44no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—42no—
330D4—41no—
331D4—42no—
332D4—81no—
333D4—82no—
334D4—82no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4C2×C22⋊Dic6111yescharacteristic
347C2×C4D4×Dic6111yescharacteristic
348C2×C4D4×Dic6111yescharacteristic
349C2×C4#1451974511yescharacteristic
350C2×C4#1451974911yescharacteristic
351C2×C4#1451975811yescharacteristic
352C2×C4D8×D6111yescharacteristic
353C2×C4#1451979611yescharacteristic
354C2×C4#1451980111yescharacteristic
355C2×C4#1451980111yescharacteristic
356C8—42no—
357C8—1222no—
358C8—4881no—
359C8—2442no—
360C8—2441no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—162no—
370C22—162no—
371C22#1683964211yescharacteristic
372C22#1683995511yescharacteristic
373C22#1683997511yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—9761no—
380C4D8×Dic6111yescharacteristic
381C4#1683987411yescharacteristic
382C4#1683989411yescharacteristic
383C4#1683990411yescharacteristic
384C2—21no—
385C2—21no—
386C2—82no—
387C2—162no—
388C2#2144616911yescharacteristic
389C2#2144630111yescharacteristic
390C2#2144634711yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3205C2
socleC22×C61#386
cosocleC2×C42×C61C23
hypercenter#3205D61
hypocenterC61#9293
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #21454537C2semidirect
2. #21446644C2semidirect
3. #21444487C2semidirect
4. #21444379C2semidirect
5. #21443678C2semidirect
6. #21443649C2semidirect
22. C61×#493C4semidirect
23. C61×#486C4semidirect
118. C2×#92418D8semidirect
206. #493Dic61semidirect
207. #486Dic61semidirect
222. C61#9293semidirect

Maximal subgroups

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

subgroupindex
#214545372
#214466442
#214444872
#214443792
#214436782
#214436492
C61×#32052
#929361