Finite Group Databasebeta

← #29597412

Subgroups — #29597412

Order 15616.

536 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D61C211yesmaximal, characteristic, complemented
2C2×#16839995C211yesmaximal, characteristic
3C2×#16839575C211yesmaximal, characteristic, complemented
4#21445854C211yesmaximal, characteristic, complemented
5#21443929C211yesmaximal, characteristic, complemented
6#21443928C211yesmaximal, characteristic, complemented
7C2×C61×#361C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9C2×#14519748—21no—
10C2×#14519717C2211yescharacteristic
11C2×#14519716—21no—
12M32×D61—22no—
13M32×D61—22no—
14C2×C16×D61—21no—
15#16839995—21no—
16#16839995—21no—
17#16839995C412yes—
18#16839995C412yes—
19C2×#14519713C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519698—21no—
22#16839725—21no—
23#16839575—22no—
24#16839526—21no—
25C22×D8×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C61×#361—22no—
29C22×C22⋊D61—41no—
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C22×#92418D411yescharacteristic
33C2×C8×D61—21no—
34C2×C8×D61—21no—
35C2×C8×D61—21no—
36C2×C8×D61—21no—
37C2×C8×D61C2×C411yescharacteristic
38C2×C8×D61C2×C411yescharacteristic
39C2×C8×D61D411yescharacteristic
40C2×C8×D61D411yescharacteristic
41#14519748—22no—
42#14519748—22no—
43#14519748—41no—
44#14519748—41no—
45C2×C4⋊Dic61—21no—
46C2×C22⋊Dic61—41no—
47#14519717—21no—
48#14519717D412yescomplemented
49#14519716—24no—
50C2×#11758185—21no—
51C16×D61—24no—
52#14519713—21no—
53#14519713—21no—
54#14519711—21no—
55#14519711C2×C412yes—
56#14519698—22no—
57#14519698—22no—
58#14519689—41no—
59#14519689—41no—
60C22×D4×C61—21no—
61C2×D8×C61—21no—
62C2×D8×C61—21no—
63C2×D8×C61—21no—
64C2×D8×C61—21no—
65C2×D8×C61—21no—
66C2×D8×C61C2×C412yes—
67C2×M16×C61—21no—
68C22×C8×C61C2311yescharacteristic
69M32×C61—21no—
70M32×C61D412yescomplemented
71C2×C16×C61—21no—
72#108×C61—21no—
73#108×C61—21no—
74C24×C61—41no—
75C23×D61SD1611yescharacteristic
76C2×D4×C61—22no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C22×C4×C61C2×D411yescharacteristic
83C2×C22⋊D61—42no—
84C2×C22⋊D61—42no—
85C2×C22⋊D61—84no—
86C22×Dic61—41no—
87C22×Dic61SD1611yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61C22⋊C411yescharacteristic
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61D811yescharacteristic
95C2×C4×D61D811yescharacteristic
96D8×C61—22no—
97D8×C61—22no—
98D8×C61—41no—
99D8×C61—41no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61C22×C411yescharacteristic
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61#4111yescharacteristic
108C2×C8×C61#4111yescharacteristic
109C22⋊Dic61—42no—
110C22⋊Dic61—42no—
111C4⋊Dic61—22no—
112C4⋊Dic61—41no—
113#11758194—41no—
114#11758194—41no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—41no—
118C2×#92418C22⋊C411yescharacteristic
119C2×#92418C22⋊C411yescharacteristic
120C8×D61—21no—
121C8×D61—21no—
122C8×D61—21no—
123C8×D61—21no—
124C8×D61—21no—
125C8×D61—21no—
126C8×D61—21no—
127C8×D61—21no—
128C16×C61—22no—
129#11758185—22no—
130C23×C61—42no—
131C23×C61—82no—
132C23×C61—82no—
133C23×C61—81no—
134C23×C61—81no—
135C23×C61C2×SD1611yescharacteristic
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—22no—
139C22×D61—41no—
140C22×D61#10211yescharacteristic
141C22×D61#10211yescharacteristic
142D4×C61—42no—
143D4×C61—42no—
144D4×C61—81no—
145D4×C61—81no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C22⋊D61—84no—
153C22⋊D61—84no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—42no—
157C2×Dic61—82no—
158C2×Dic61#10211yescharacteristic
159C2×Dic61#10211yescharacteristic
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—21no—
168C8×C61—81no—
169C8×C61C4×D411yescharacteristic
170C8×C61C4×D411yescharacteristic
171C8×C61#12011yescharacteristic
172C8×C61#12311yescharacteristic
173#92418—21no—
174#92418—21no—
175#92418—81no—
176#13067—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—82no—
180C22×C61—82no—
181C22×C61—82no—
182C22×C61—162no—
183C22×C61—162no—
184C22×C61C2×#10211yescharacteristic
185C22×C61#46511yescharacteristic
186C22×C61#46511yescharacteristic
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—21no—
192C2×D61—42no—
193C2×D61—42no—
194C2×D61#36112yescomplemented
195C4×C61#38611yescharacteristic
196C4×C61#41611yescharacteristic
197C4×C61#46611yescharacteristic
198C4×C61#46611yescharacteristic
199Dic61—21no—
200Dic61—21no—
201Dic61—82no—
202C22×M32—611no—
203C2×#466—611no—
204C2×#361—611no—
205C2×#361D6111yescharacteristic, complemented
206#1810—611no—
207#1387—611no—
208#1387—611no—
209C2×C61—21no—
210C2×C61—21no—
211C2×C61—162no—
212C2×C61#189311yescharacteristic
213C2×C61C2×#36111yescharacteristic
214C2×C61#214811yescharacteristic
215D61—22no—
216D61—41no—
217C22×D8C2×D6111yescharacteristic
218C23×C8—611no—
219C2×#121—1221no—
220C2×M32—611no—
221C2×M32—1221no—
222C2×M32—1222no—
223C2×M32—1222no—
224C2×M32C2×D6111yescharacteristic
225C22×C16—1221no—
226#466—612no—
227#466—612no—
228#466—1221no—
229#466—1221no—
230C2×#108—611no—
231C2×#108C2×D6111yescharacteristic
232C2×#107—611no—
233C2×#102—1221no—
234#407—1221no—
235#361—22no—
236#361—1222no—
237#341—1221no—
238C61#1306711yescharacteristic, complemented, Sylow
239C22×D4—21no—
240C22×D4—2441no—
241C23×C4—611no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8C4×D6112yes—
248C2×M16—21no—
249C2×M16—1221no—
250C22×C8—611no—
251C22×C8—611no—
252C22×C8—611no—
253C22×C8—611no—
254C22×C8—611no—
255C22×C8—1221no—
256C22×C8—1221no—
257C22×C8—1221no—
258C22×C8—1221no—
259C22×C8C22×D6111yescharacteristic
260#121—1222no—
261#121—1222no—
262#121—2441no—
263#121—2441no—
264C2×C4⋊C4—1221no—
265C2×C22⋊C4—2441no—
266M32—21no—
267M32—612no—
268M32—1224no—
269M32—1221no—
270M32C22⋊D6112yescomplemented
271C2×C16—21no—
272C2×C16—1224no—
273C2×C16—1221no—
274#108—21no—
275#108—21no—
276#108—1221no—
277#108—1221no—
278#107—612no—
279#107—1221no—
280#102—1222no—
281#102—1222no—
282C22⋊C8—2441no—
283C22⋊C8—2441no—
284C24—41no—
285C24—611no—
286C2×D4—22no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—4884no—
293C2×D4—2442no—
294C2×D4—2442no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—2441no—
305C22×C4D4×D6111yescharacteristic
306D8—22no—
307D8—22no—
308D8—41no—
309D8—41no—
310M16—41no—
311M16—41no—
312M16—2441no—
313M16—2441no—
314C2×C8—41no—
315C2×C8—611no—
316C2×C8—611no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—1221no—
323C2×C8—1221no—
324C2×C8—1221no—
325C2×C8—1221no—
326C2×C8—1221no—
327C2×C8—2441no—
328C2×C8C2×C4×D6111yescharacteristic
329C2×C8#1175822211yescharacteristic
330C2×C8D4×D6111yescharacteristic
331C2×C8D4×D6111yescharacteristic
332C2×C8#1175822411yescharacteristic
333C2×C8C2×C22⋊D6111yescharacteristic
334C4⋊C4—1222no—
335C4⋊C4—2441no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C16—22no—
339C16—1222no—
340C23—42no—
341C23—82no—
342C23—82no—
343C23—81no—
344C23—81no—
345C23—611no—
346C23—611no—
347C23—1222no—
348C23—1221no—
349C23—1221no—
350C23—2441no—
351C23SD16×D6111yescharacteristic
352D4—42no—
353D4—42no—
354D4—81no—
355D4—81no—
356D4—4884no—
357D4—4884no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—4882no—
371C2×C4—2442no—
372C2×C4C22⋊C4×D6111yescharacteristic
373C2×C4#1451974811yescharacteristic
374C2×C4#1451975011yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4#1451979611yescharacteristic
377C2×C4#1451979811yescharacteristic
378C8—81no—
379C8—1221no—
380C8—1221no—
381C8—4881no—
382C8#1451973711yescharacteristic
383C8C4×C22⋊D6111yescharacteristic
384C8#1451974511yescharacteristic
385C8#1451975911yescharacteristic
386C22—21no—
387C22—21no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22—162no—
392C22—162no—
393C22—612no—
394C22—1221no—
395C22—1221no—
396C22—1221no—
397C22—1221no—
398C22—1221no—
399C22—2442no—
400C22—2442no—
401C22#102×D6111yescharacteristic
402C22#1683998811yescharacteristic
403C22#1683999011yescharacteristic
404C4—1221no—
405C4—1221no—
406C4—4882no—
407C4#1683963811yescharacteristic
408C4#1683975511yescharacteristic
409C4#1683999511yescharacteristic
410C4#1683999711yescharacteristic
411C2—21no—
412C2—21no—
413C2—162no—
414C2—1222no—
415C2—2441no—
416C2#2144624411yescharacteristic
417C2#361×D6111yescharacteristic
418C2#2144756511yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#361C2
socleC22×C61C2×#102
prime radicalC2×#16839995C2
cosocleC22×C8×C61C23
hypercenterC2×#361D61
hypocenterC61#13067
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
1. C2×M32×D61C2semidirect
3. C2×#16839575C2semidirect
4. #21445854C2semidirect
5. #21443929C2semidirect
6. #21443928C2semidirect
7. C2×C61×#361C2semidirect
48. #14519717D4semidirect
70. M32×C61D4semidirect
194. C2×D61#361semidirect
205. C2×#361D61semidirect
238. C61#13067semidirect
270. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D612
C2×#168399952
C2×#168395752
#214458542
#214439292
#214439282
C2×C61×#3612
#1306761