Finite Group Databasebeta

← #29597414

Subgroups — #29597414

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×#16839999C211yesmaximal, characteristic
3C2×#16839576C211yesmaximal, characteristic, complemented
4C2×#16839574C211yesmaximal, characteristic, complemented
5#21445854C211yesmaximal, characteristic, complemented
6#21443927C211yesmaximal, characteristic, complemented
7C61×#1387C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519752—21no—
11C2×#14519717C2211yescharacteristic
12C2×#14519716—21no—
13M32×D61—22no—
14M32×D61—22no—
15C2×C16×D61—21no—
16#16839999—21no—
17#16839999—21no—
18#16839999C412yes—
19#16839999C412yes—
20C2×#14519713C2211yescharacteristic
21C2×#14519697—21no—
22#16839725—21no—
23#16839576—22no—
24#16839574—22no—
25#16839526—21no—
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C22×D244—21no—
30C22×D244—41no—
31C22×C4×D61D411yescharacteristic
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488C2×C412yes—
38C2×#11758194—21no—
39C22×#92418D411yescharacteristic
40C2×C8×D61—21no—
41C2×C8×D61—21no—
42C2×C8×D61—21no—
43C2×C8×D61—21no—
44C2×C8×D61C2×C411yescharacteristic
45C2×C8×D61C2×C411yescharacteristic
46C2×C8×D61D411yescharacteristic
47C2×C8×D61D411yescharacteristic
48#14519752—22no—
49#14519752—22no—
50#14519752—41no—
51#14519752—41no—
52C2×#11758198—41no—
53#14519717—21no—
54#14519717D412yescomplemented
55#14519716—24no—
56C2×#11758185—21no—
57C16×D61—24no—
58#14519713—21no—
59#14519713—21no—
60#14519697—22no—
61#14519697—22no—
62#14519689—41no—
63#14519689—41no—
64C2×M16×C61—21no—
65C22×C8×C61C2311yescharacteristic
66C2×C4⋊C4×C61—21no—
67M32×C61—21no—
68M32×C61D412yescomplemented
69C2×C16×C61—21no—
70#108×C61—21no—
71#108×C61—21no—
72#107×C61—21no—
73#107×C61C2×C412yes—
74C23×D61—41no—
75C23×D61SD1611yescharacteristic
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61SD1611yescharacteristic
79C2×D244—22no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—42no—
85C2×D244—42no—
86C2×D244—41no—
87C2×D244—84no—
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
96M16×C61—41no—
97M16×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61C22×C411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61#4111yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C4⋊C4×C61—22no—
106C4⋊C4×C61—41no—
107#11758198—42no—
108#11758198—42no—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—41no—
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116D488—22no—
117D488—22no—
118D488—41no—
119D488—41no—
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×C61C2×SD1611yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—42no—
136C22×D61—82no—
137C22×D61—82no—
138C22×D61—81no—
139C22×D61—81no—
140C22×D61#10211yescharacteristic
141C22×D61#10211yescharacteristic
142C2×C4×C61—42no—
143C2×C4×C61—82no—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61#10211yescharacteristic
153C2×Dic61#10211yescharacteristic
154D244—42no—
155D244—42no—
156D244—84no—
157D244—84no—
158D244—81no—
159D244—81no—
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×C61C2×#10211yescharacteristic
180C22×C61#46511yescharacteristic
181C22×C61#46511yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—42no—
188C2×D61—42no—
189C2×D61—82no—
190C2×D61—82no—
191C2×D61—82no—
192C2×D61—162no—
193C2×D61—162no—
194C2×D61#36112yescomplemented
195C4×C61—82no—
196C4×C61#38611yescharacteristic
197C4×C61#41611yescharacteristic
198C4×C61#46611yescharacteristic
199C4×C61#46611yescharacteristic
200Dic61—21no—
201Dic61—21no—
202C22×M32—611no—
203C2×#466—611no—
204C2×#361—611no—
205C2×#361—611no—
206#1810—611no—
207#1387—611no—
208#1387D6111yescharacteristic, complemented
209C2×C61—21no—
210C2×C61—21no—
211C2×C61#189311yescharacteristic
212C2×C61C2×#36111yescharacteristic
213C2×C61#214811yescharacteristic
214D61—22no—
215D61—41no—
216D61—162no—
217C22×D8—611no—
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×#107C2×D6111yescharacteristic
233C2×#102—1221no—
234#407—1221no—
235#361—1222no—
236#361—1222no—
237#341—1221no—
238C61#1306711yescharacteristic, complemented, Sylow
239C22×D4—1221no—
240C22×D4—2441no—
241C23×C4—611no—
242C2×D8—612no—
243C2×D8—1221no—
244C2×D8—1221no—
245C2×D8—1221no—
246C2×D8—1221no—
247C2×D8—1221no—
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—21no—
265C2×C22⋊C4—2441no—
266M32—21no—
267M32—612no—
268M32—1224no—
269M32—1221no—
270M32D24412yescomplemented
271C2×C16—21no—
272C2×C16—1224no—
273C2×C16—1221no—
274#108—21no—
275#108—21no—
276#108—1221no—
277#108—1221no—
278#107—21no—
279#107C4×D6112yes—
280#102—1222no—
281#102—1222no—
282C22⋊C8—2441no—
283C22⋊C8—2441no—
284C24—611no—
285C24—2441no—
286C2×D4—1222no—
287C2×D4—4884no—
288C2×D4—2442no—
289C2×D4—2442no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C22×C4—41no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4D4×D6111yescharacteristic
306D8—1222no—
307D8—1222no—
308D8—2441no—
309D8—2441no—
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×C8C2×D24411yescharacteristic
330C2×C8#1175822211yescharacteristic
331C2×C8D4×D6111yescharacteristic
332C2×C8D4×D6111yescharacteristic
333C2×C8#1175822611yescharacteristic
334C4⋊C4—22no—
335C4⋊C4—41no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C16—22no—
339C16—1222no—
340C23—611no—
341C23—611no—
342C23—1222no—
343C23—1221no—
344C23—1221no—
345C23—4882no—
346C23—4882no—
347C23—4881no—
348C23—4881no—
349C23—2441no—
350C23—2442no—
351C23SD16×D6111yescharacteristic
352D4—4884no—
353D4—4884no—
354D4—4881no—
355D4—4881no—
356D4—2442no—
357D4—2442no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—611no—
361C2×C4—611no—
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—1221no—
371C2×C4—1221no—
372C2×C4C22⋊C4×D6111yescharacteristic
373C2×C4#1451975011yescharacteristic
374C2×C4#1451975211yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4#1451979811yescharacteristic
377C2×C4#1451980011yescharacteristic
378C8—81no—
379C8—1221no—
380C8—1221no—
381C8—4881no—
382C8#1451973911yescharacteristic
383C8C4×D24411yescharacteristic
384C8#1451974711yescharacteristic
385C8#1451976211yescharacteristic
386C22—21no—
387C22—21no—
388C22—612no—
389C22—1221no—
390C22—1221no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—9762no—
395C22—9762no—
396C22—4882no—
397C22—4882no—
398C22—4882no—
399C22—2442no—
400C22—2442no—
401C22#102×D6111yescharacteristic
402C22#1683999211yescharacteristic
403C22#1683999411yescharacteristic
404C4—82no—
405C4—1221no—
406C4—1221no—
407C4#1683964011yescharacteristic
408C4#1683975711yescharacteristic
409C4#1683999711yescharacteristic
410C4#1683999911yescharacteristic
411C2—21no—
412C2—21no—
413C2—1222no—
414C2—9762no—
415C2—2441no—
416C2#2144624611yescharacteristic
417C2#361×D6111yescharacteristic
418C2#2144756711yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1387C2
socleC22×C61C2×#102
prime radicalC2×#16839999C2
cosocleC22×C8×C61C23
hypercenter#1387D61
hypocenterC61#13067
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
1. C2×M32×D61C2semidirect
3. C2×#16839576C2semidirect
4. C2×#16839574C2semidirect
5. #21445854C2semidirect
6. #21443927C2semidirect
7. C61×#1387C2semidirect
54. #14519717D4semidirect
68. M32×C61D4semidirect
194. C2×D61#361semidirect
208. #1387D61semidirect
238. C61#13067semidirect
270. M32D244semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D612
C2×#168399992
C2×#168395762
C2×#168395742
#214458542
#214439272
C61×#13872
#1306761