Finite Group Databasebeta

← #29596313

Subgroups — #29596313

Order 15616.

404 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D61C211yesmaximal, characteristic
2C2×#16839541C211yesmaximal, characteristic
3#21445854C211yesmaximal, characteristic
4#21443916C211yesmaximal, characteristic, complemented
5#21443915C211yesmaximal, characteristic, complemented
6#21443914C211yesmaximal, characteristic, complemented
7C61×#1382C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9#117×D61—21no—
10C22×#11758185C2211yescharacteristic
11C2×#14519713C2211yescharacteristic
12#16839800C2211yescharacteristic
13#16839799C411yescharacteristic
14#16839799C411yescharacteristic
15#16839798—21no—
16#16839797—21no—
17#107×D61C411yescharacteristic
18#107×D61C411yescharacteristic
19#106×D61—21no—
20#16839725—21no—
21#16839541—21no—
22#16839541—21no—
23#16839526—21no—
24C22×C16×C61C2211yescharacteristic
25C2×#108×C61C2211yescharacteristic
26C61×#427C2211yescharacteristic
27C22×C4×D61D411yescharacteristic
28C2×#11758194—21no—
29C22×#92418D411yescharacteristic
30C2×C8×D61—21no—
31C2×C8×D61—21no—
32C2×C8×D61—21no—
33C2×C8×D61—21no—
34C2×C8×D61C2×C411yescharacteristic
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38#14519736—21no—
39#14519735—21no—
40#14519735—21no—
41#14519734—41no—
42#14519733—41no—
43C4⋊C4×D61—21no—
44C4⋊C4×D61—21no—
45C22⋊C4×D61—41no—
46C42×D61—41no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50#14519713—21no—
51#14519713—21no—
52#14519711C2×C411yescharacteristic
53#14519711C2×C411yescharacteristic
54#14519710—21no—
55#14519710—21no—
56#14519709—21no—
57#14519708—21no—
58#14519708—21no—
59#14519689—41no—
60#14519689—41no—
61C2×M16×C61—21no—
62C22×C8×C61C2311yescharacteristic
63#117×C61—21no—
64C2×C16×C61—21no—
65C2×C16×C61—21no—
66C2×C16×C61—21no—
67#108×C61—21no—
68#108×C61—21no—
69#107×C61C2×C411yescharacteristic
70#107×C61C2×C411yescharacteristic
71#106×C61—21no—
72C23×D61SD1611yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61SD1611yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61C22⋊C411yescharacteristic
82C2×C4×D61C22⋊C411yescharacteristic
83C2×C4×D61D811yescharacteristic
84C2×C4×D61D811yescharacteristic
85M16×C61—41no—
86M16×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C22⋊C4×C61—41no—
97C42×C61—41no—
98C22⋊Dic61—41no—
99#11758198—41no—
100#11758198—41no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103#11758196—41no—
104#11758196—41no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—41no—
113C2×#92418C22⋊C411yescharacteristic
114C2×#92418C22⋊C411yescharacteristic
115C8×D61—21no—
116C8×D61—21no—
117C8×D61—21no—
118C8×D61—21no—
119C8×D61—21no—
120C8×D61—21no—
121C8×D61—21no—
122C8×D61—21no—
123C16×C61—41no—
124#11758185—41no—
125C23×C61C2×SD1611yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—22no—
129C22×D61—41no—
130C22×D61#10211yescharacteristic
131C22×D61#10211yescharacteristic
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×C4×C61C2×D811yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#10211yescharacteristic
145C2×Dic61#10211yescharacteristic
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—82no—
155C4×D61—82no—
156C8×C61—81no—
157C8×C61#11711yescharacteristic
158C8×C61#11711yescharacteristic
159C8×C61#12311yescharacteristic
160C8×C61#12311yescharacteristic
161#92418—21no—
162#92418—21no—
163#92418—81no—
164#12869—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61C2×#10211yescharacteristic
168C22×C61#48311yescharacteristic
169C22×C61#48311yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61#35912yes—
178C4×C61—81no—
179C4×C61—81no—
180C4×C61#38111yescharacteristic
181C4×C61#41911yescharacteristic
182C4×C61#48011yescharacteristic
183C4×C61#48011yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—81no—
187Dic61—81no—
188C2×#427—611no—
189C2×C22⋊C16—611no—
190#1810—611no—
191#1382—611no—
192#1382—611no—
193#1382—611no—
194#1382D6111yescharacteristic, complemented
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#182311yescharacteristic
198C2×C61C2×#35911yescharacteristic
199C2×C61#214311yescharacteristic
200D61—22no—
201D61—41no—
202C23×C8—611no—
203C2×#117—1221no—
204C22×C16—611no—
205C22×C16C2×D6111yescharacteristic
206C2×#108—611no—
207C2×#108C2×D6111yescharacteristic
208#427—611no—
209#427—611no—
210#427—611no—
211#427—1221no—
212#427—1221no—
213#427C2×D6111yescharacteristic
214C2×#107—611no—
215C2×#107—611no—
216C2×#106—1221no—
217#407—1221no—
218C22⋊C16—1221no—
219C22⋊C16—1221no—
220#341—1221no—
221C61#1286911yescharacteristic, complemented, Sylow
222C23×C4—611no—
223C2×M16—21no—
224C2×M16—1221no—
225C22×C8—611no—
226C22×C8—611no—
227C22×C8—611no—
228C22×C8—611no—
229C22×C8—611no—
230C22×C8—1221no—
231C22×C8—1221no—
232C22×C8—1221no—
233C22×C8—1221no—
234C22×C8C22×D6111yescharacteristic
235#117—21no—
236#117—1221no—
237#117—1221no—
238#117—1221no—
239#117—2441no—
240#117—2441no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C22⋊C4—2441no—
244C2×C42—2441no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—1221no—
249C2×C16—1221no—
250C2×C16—1221no—
251#108—21no—
252#108—21no—
253#108—1221no—
254#108—1221no—
255#107—611no—
256#107—611no—
257#107—1221no—
258#107—1221no—
259#107C4×D6111yescharacteristic
260#107C4×D6111yescharacteristic
261#106—21no—
262#106—1221no—
263#106—1221no—
264#106—1221no—
265C22⋊C8—2441no—
266C22⋊C8—2441no—
267C24—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4D4×D6111yescharacteristic
280M16—41no—
281M16—41no—
282M16—2441no—
283M16—2441no—
284C2×C8—41no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—1221no—
293C2×C8—1221no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—2441no—
298C2×C8C2×C4×D6111yescharacteristic
299C2×C8#1175822211yescharacteristic
300C2×C8#1175822211yescharacteristic
301C2×C8D4×D6111yescharacteristic
302C2×C8#1175822411yescharacteristic
303C2×C8#1175822611yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C22⋊C4—41no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C42—41no—
315C42—2441no—
316C42—2441no—
317C42—2441no—
318C16—41no—
319C16—2441no—
320C23—611no—
321C23—611no—
322C23—1222no—
323C23—1221no—
324C23—1221no—
325C23—2441no—
326C23SD16×D6111yescharacteristic
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4C22⋊C4×D6111yescharacteristic
346C2×C4#1451975911yescharacteristic
347C2×C4#1451976211yescharacteristic
348C2×C4D8×D6111yescharacteristic
349C2×C4#1451980611yescharacteristic
350C2×C4#1451980911yescharacteristic
351C8—81no—
352C8—1221no—
353C8—1221no—
354C8—4881no—
355C8#1451973411yescharacteristic
356C8#1451973511yescharacteristic
357C8#1451975911yescharacteristic
358C8#1451976211yescharacteristic
359C22—21no—
360C22—21no—
361C22—612no—
362C22—1221no—
363C22—1221no—
364C22—1221no—
365C22—1221no—
366C22—1221no—
367C22—2442no—
368C22—2442no—
369C22#102×D6111yescharacteristic
370C22#1684009111yescharacteristic
371C22#1684009411yescharacteristic
372C4—81no—
373C4—81no—
374C4—1221no—
375C4—1221no—
376C4—4881no—
377C4—4881no—
378C4#1683962411yescharacteristic
379C4#1683976911yescharacteristic
380C4#1684007411yescharacteristic
381C4#1684007711yescharacteristic
382C2—21no—
383C2—21no—
384C2—1222no—
385C2—2441no—
386C2#2144590411yescharacteristic
387C2#359×D6111yescharacteristic
388C2#2144754511yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1382C2
socleC22×C61C2×#102
prime radicalC23×D61SD16
cosocleC22×C8×C61C23
hypercenter#1382D61
hypocenterC61#12869
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
4. #21443916C2semidirect
5. #21443915C2semidirect
6. #21443914C2semidirect
7. C61×#1382C2semidirect
194. #1382D61semidirect
221. C61#12869semidirect

Maximal subgroups

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

subgroupindex
#427×D612
C2×#168395412
#214458542
#214439162
#214439152
#214439142
C61×#13822
#1286961