Finite Group Databasebeta

← #29596955

Subgroups — #29596955

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839999C211yesmaximal, characteristic
2C2×#16839799C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519752—21no—
11C2×#14519735—21no—
12C22×#11758185C2211yescharacteristic
13#16839999—22no—
14#16839999C414yescomplemented
15#16839799—22no—
16#16839799—22no—
17C2×#14519711C2211yescharacteristic
18C2×#14519708—21no—
19C2×#14519697—21no—
20#16839564—22no—
21#16839562—22no—
22#16839541—22no—
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C22×D244—21no—
27C22×D244—41no—
28C22×C4×D61D411yescharacteristic
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488C2×C412yes—
35C22×#92418D411yescharacteristic
36C2×C8×D61—21no—
37C2×C8×D61—21no—
38C2×C8×D61—21no—
39C2×C8×D61—21no—
40C2×C8×D61C2×C412yes—
41C2×C8×D61D412yes—
42#14519752—24no—
43#14519752—42no—
44#14519735—24no—
45#14519735—42no—
46C2×C4⋊Dic61—21no—
47C2×#11758198—41no—
48C2×#11758198—41no—
49C2×C4×Dic61—41no—
50C2×#11758185—21no—
51C2×#11758185—21no—
52C2×#11758185—21no—
53#14519711—21no—
54#14519711D412yescomplemented
55#14519708—24no—
56#14519697—24no—
57C22×C8×C61C2311yescharacteristic
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63#107×C61—21no—
64#107×C61—21no—
65#107×C61C2×C412yes—
66#107×C61D412yescomplemented
67C23×D61—41no—
68C23×D61D811yescharacteristic
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—41no—
73C22×Dic61D811yescharacteristic
74C2×D244—22no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—44no—
80C2×D244—41no—
81C2×D244—82no—
82C2×D244—82no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61C22⋊C412yes—
88C2×C4×D61SD1612yes—
89C2×C8×C61C22×C411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61C2×D411yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C2×C8×C61#4111yescharacteristic
95C4⋊C4×C61—22no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99#11758198—44no—
100#11758198—44no—
101C4⋊Dic61—22no—
102C4⋊Dic61—41no—
103C4×Dic61—44no—
104C2×#92418—21no—
105C2×#92418—21no—
106C2×#92418C22⋊C412yes—
107D488—22no—
108D488—22no—
109D488—41no—
110D488—41no—
111C8×D61—22no—
112C8×D61—22no—
113C8×D61—22no—
114C8×D61—22no—
115C16×C61—41no—
116#11758185—41no—
117C23×C61C2×D811yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—42no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61#10212yes—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61C2×SD1611yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—42no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61#10212yes—
150D244—42no—
151D244—42no—
152D244—88no—
153D244—81no—
154D244—81no—
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159C8×C61C4×D411yescharacteristic
160C8×C61C4×D411yescharacteristic
161C8×C61#12111yescharacteristic
162C8×C61#12111yescharacteristic
163#92418—22no—
164#12992—611nomaximal, Sylow
165C22×C61C2×#10211yescharacteristic
166C22×C61#44711yescharacteristic
167C22×C61#48011yescharacteristic
168C22×C61#50811yescharacteristic
169C22×C61#50811yescharacteristic
170C22×C61#50911yescharacteristic
171C22×C61#50911yescharacteristic
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—22no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—82no—
182C2×D61—161no—
183C2×D61—161no—
184C2×D61—161no—
185C2×D61—161no—
186C4×C61—82no—
187C4×C61—82no—
188C4×C61#38611yescharacteristic
189C4×C61#41711yescharacteristic
190C4×C61#44811yescharacteristic
191C4×C61#48111yescharacteristic
192Dic61—22no—
193Dic61—82no—
194C2×#466—611no—
195C2×#427—611no—
196C2×#357—611no—
197C2×#357—611no—
198C2×C22⋊C16—611no—
199#1380—611no—
200#1380D6111yescharacteristic, complemented
201C2×C61#187411yescharacteristic
202C2×C61#213811yescharacteristic
203C2×C61#214011yescharacteristic
204C2×C61#218611yescharacteristic
205C2×C61#218611yescharacteristic
206C2×C61#223411yescharacteristic
207C2×C61#223411yescharacteristic
208D61—42no—
209D61—162no—
210C22×D8—611no—
211C23×C8—611no—
212C2×#121—1221no—
213C2×#117—1221no—
214C22×C16—611no—
215C22×C16C2×D6111yescharacteristic
216#466—614no—
217#466—1222no—
218#427—1222no—
219#427—1222no—
220C2×#107—611no—
221C2×#107C2×D6111yescharacteristic
222C2×#107C2×D6111yescharacteristic
223C2×#106—1221no—
224C2×#102—1221no—
225#357—1222no—
226#357—1222no—
227C22⋊C16—1222no—
228C61#1299211yescharacteristic, complemented, Sylow
229C22×D4—1221no—
230C22×D4—2441no—
231C23×C4—611no—
232C2×D8—612no—
233C2×D8—1221no—
234C2×D8—1221no—
235C2×D8—1221no—
236C2×D8—1221no—
237C2×D8—1221no—
238C22×C8—611no—
239C22×C8—612no—
240C22×C8—612no—
241C22×C8—1221no—
242C22×C8—1221no—
243C22×C8—1221no—
244C22×C8—1221no—
245C22×C8C22×D6111yescharacteristic
246#121—1224no—
247#121—2442no—
248#117—1224no—
249#117—2442no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—1221no—
253C2×C22⋊C4—2441no—
254C2×C22⋊C4—2441no—
255C2×C42—2441no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16—1221no—
260C2×C16—1221no—
261C2×C16—1221no—
262#107—21no—
263#107—21no—
264#107—612no—
265#107—1221no—
266#107C4×D6112yes—
267#107D24412yescomplemented
268#106—1224no—
269#102—1224no—
270C24—611no—
271C24—2441no—
272C2×D4—1222no—
273C2×D4—4882no—
274C2×D4—4882no—
275C2×D4—2444no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—611no—
284C22×C4—612no—
285C22×C4—612no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4D4×D6111yescharacteristic
292D8—1222no—
293D8—1222no—
294D8—2441no—
295D8—2441no—
296C2×C8—612no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1222no—
300C2×C8—1222no—
301C2×C8—1222no—
302C2×C8—1222no—
303C2×C8C2×C4×D6111yescharacteristic
304C2×C8C2×D24411yescharacteristic
305C2×C8#1175822211yescharacteristic
306C2×C8D4×D6111yescharacteristic
307C2×C8D4×D6111yescharacteristic
308C2×C8#1175822611yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—1222no—
314C4⋊C4—2441no—
315C22⋊C4—2444no—
316C22⋊C4—2444no—
317C42—2444no—
318C16—41no—
319C16—2441no—
320C23—612no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—4881no—
328C23—4881no—
329C23—4881no—
330C23—4881no—
331C23—4881no—
332C23—4881no—
333C23—2442no—
334C23D8×D6111yescharacteristic
335D4—4888no—
336D4—4881no—
337D4—4881no—
338D4—2442no—
339D4—2442no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—612no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4—2442no—
356C2×C4C22⋊C4×D6111yescharacteristic
357C2×C4#1451974711yescharacteristic
358C2×C4#1451976211yescharacteristic
359C2×C4SD16×D6111yescharacteristic
360C2×C4#1451980411yescharacteristic
361C2×C4#1451980911yescharacteristic
362C8—1222no—
363C8#1451973911yescharacteristic
364C8C4×D24411yescharacteristic
365C8#1451975011yescharacteristic
366C8#1451975211yescharacteristic
367C22—1222no—
368C22—1222no—
369C22—1222no—
370C22—9761no—
371C22—9761no—
372C22—9761no—
373C22—9761no—
374C22—4882no—
375C22—4882no—
376C22—4882no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22#102×D6111yescharacteristic
382C22#1683989711yescharacteristic
383C22#1684007711yescharacteristic
384C22#1684019311yescharacteristic
385C22#1684019511yescharacteristic
386C22#1684019611yescharacteristic
387C22#1684019911yescharacteristic
388C4—82no—
389C4—82no—
390C4—1222no—
391C4—4882no—
392C4#1683964011yescharacteristic
393C4#1683976211yescharacteristic
394C4#1683990211yescharacteristic
395C4#1684008211yescharacteristic
396C2—9762no—
397C2—2442no—
398C2#2144613511yescharacteristic
399C2#2144752511yescharacteristic
400C2#2144753311yescharacteristic
401C2#2144774311yescharacteristic
402C2#2144774511yescharacteristic
403C2#2144801211yescharacteristic
404C2#2144801311yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1380C2
socleC23×C61C2×D8
prime radicalC2×#16839999C2
cosocleC22×C8×C61C23
hypercenter#1380D61
hypocenterC61#12992
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#16839799C2semidirect
3. C2×#16839564C2semidirect
4. C2×#16839562C2semidirect
5. C2×#16839541C2semidirect
6. #21443910C2semidirect
7. C61×#1380C2semidirect
14. #16839999C4semidirect
54. #14519711D4semidirect
66. #107×C61D4semidirect
200. #1380D61semidirect
228. C61#12992semidirect
267. #107D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168399992
C2×#168397992
C2×#168395642
C2×#168395622
C2×#168395412
#214439102
C61×#13802
#1299261