Finite Group Databasebeta

← #29573859

Subgroups — #29573859

Order 15616.

520 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×#16839784C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3C4×#14519689C211yesmaximal, characteristic
4C2×#16839515C211yesmaximal, characteristic, complemented
5C2×#16839514C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×C42×D61C2211yescharacteristic
10#16839784—22no—
11#16839784—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519706—21no—
15C2×#14519689—21no—
16C2×#14519689C411yescharacteristic
17C2×#14519689C411yescharacteristic
18C2×C4×#92418C2211yescharacteristic
19#16839516—21no—
20#16839516C411yescharacteristic
21#16839516C411yescharacteristic
22#16839515—22no—
23#16839514—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4×C8×C61C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61Q811yescharacteristic
30C2×#11758189—24no—
31C2×#11758189—42no—
32C2×#11758189—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35C22×#92418C2×C411yescharacteristic
36C22×#92418C2×C411yescharacteristic
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61Q811yescharacteristic
40C42×D61—21no—
41C42×D61—21no—
42C42×D61—21no—
43C42×D61—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418D412yes—
48#14519706—24no—
49#14519689—22no—
50#14519689—22no—
51#14519689—42no—
52C4×#92418—21no—
53C4×#92418—21no—
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C22×C8×C61C2×C411yescharacteristic
57C22×C8×C61C2×C411yescharacteristic
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61D412yes—
63C4×C8×C61—21no—
64C4×C8×C61—21no—
65C23×D61C4⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×Q811yescharacteristic
69C22×Dic61C4⋊C411yescharacteristic
70C22×Dic61C4⋊C411yescharacteristic
71C22×Dic61C4⋊C411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—22no—
85C2×C4×D61—41no—
86C2×C4×D61D812yes—
87C2×C4×D61Q1612yes—
88C2×C8×C61—21no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—22no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61M1612yescomplemented
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—22no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418M1612yescomplemented
122#11758189—48no—
123C23×C61C2×C4⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61#10712yes—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61C22⋊Q811yescharacteristic
137C2×C4×C61C22⋊Q811yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61#13111yescharacteristic
142C2×C4×C61#13111yescharacteristic
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61C2×Q1611yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61#13711yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61#10712yes—
155C2×Dic61#10812yes—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C8×C61—22no—
167C8×C61—41no—
168C8×C61—42no—
169C8×C61—81no—
170#92418—22no—
171#92418—41no—
172#92418—42no—
173#92418—81no—
174#8832—611nomaximal, Sylow
175C22×C61#38511yescharacteristic
176C22×C61#42311yescharacteristic
177C22×C61#42411yescharacteristic
178C22×C61C2×#10711yescharacteristic
179C22×C61#42811yescharacteristic
180C22×C61C2×#10811yescharacteristic
181C22×C61#43011yescharacteristic
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61#43511yescharacteristic
192C4×C61#43511yescharacteristic
193C4×C61#43611yescharacteristic
194C4×C61#43611yescharacteristic
195C4×C61#44711yescharacteristic
196C4×C61#45111yescharacteristic
197C4×C61#48011yescharacteristic
198C4×C61#48411yescharacteristic
199Dic61—22no—
200Dic61—22no—
201Dic61—41no—
202C2×#423—611no—
203#1797—611no—
204C4×C22⋊C8—611no—
205C2×#335—611no—
206C2×#335—611no—
207#1277—611no—
208#1277D6111yescharacteristic, complemented
209C2×C61#156711yescharacteristic
210C2×C61#156911yescharacteristic
211C2×C61#157111yescharacteristic
212C2×C61#157411yescharacteristic
213C2×C61#185111yescharacteristic
214C2×C61#185211yescharacteristic
215C2×C61#185511yescharacteristic
216D61—42no—
217C22×M16—1221no—
218C22×C42—611no—
219#423—1222no—
220#423—1222no—
221C2×C4⋊C8—611no—
222C2×C4⋊C8—611no—
223C2×C4⋊C8—1221no—
224C2×C4⋊C8C2×D6111yescharacteristic
225C2×C4⋊C8C2×D6111yescharacteristic
226C2×C22⋊C8—611no—
227C2×C22⋊C8—611no—
228C2×C22⋊C8—1221no—
229C2×C4×C8—611no—
230C2×C4×C8C2×D6111yescharacteristic
231#336—611no—
232#336—611no—
233#336—1221no—
234#335—1222no—
235#335—1222no—
236C61#883211yescharacteristic, complemented, Sylow
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—611no—
240C2×M16—1224no—
241C2×M16—2442no—
242C2×M16—2442no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—611no—
246C22×C8—611no—
247C22×C8—1221no—
248C22×C8—1221no—
249C22×C8C4×D6111yescharacteristic
250C22×C8C4×D6111yescharacteristic
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—1221no—
255C2×C42—1221no—
256C2×C42—1221no—
257C2×C42—1221no—
258C2×C42C22×D6111yescharacteristic
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—612no—
263C4⋊C8—1224no—
264C4⋊C8—1221no—
265C4⋊C8—1221no—
266C4⋊C8—1221no—
267C4⋊C8D24412yes—
268C22⋊C8—1222no—
269C22⋊C8—1222no—
270C22⋊C8—2442no—
271C4×C8—21no—
272C4×C8—21no—
273C4×C8—1221no—
274C4×C8—1221no—
275C24—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4—611no—
281C22×C4—1222no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—2441no—
295C22×C4C2×C4×D6111yescharacteristic
296C22×C4D4×D6111yescharacteristic
297C22×C4Q8×D6111yescharacteristic
298M16—2448no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—22no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—612no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—1221no—
314C2×C8—1222no—
315C2×C8—1221no—
316C2×C8—1221no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8#1175818912yescomplemented
323C42—1221no—
324C42—1221no—
325C42—1221no—
326C42—1221no—
327C42—1221no—
328C42—1221no—
329C42C2×D24411yescharacteristic
330C42#1175822211yescharacteristic
331C42D4×D6111yescharacteristic
332C42#1175822411yescharacteristic
333C23—612no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23C4⋊C4×D6111yescharacteristic
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4#1451973711yescharacteristic
363C2×C4C4×D24411yescharacteristic
364C2×C4#1451974711yescharacteristic
365C2×C4#1451975511yescharacteristic
366C2×C4#1451975711yescharacteristic
367C2×C4#1451975911yescharacteristic
368C2×C4M16×D6111yescharacteristic
369C2×C4C2×#1175818911yescharacteristic
370C2×C4#1451978311yescharacteristic
371C2×C4#1451978511yescharacteristic
372C2×C4D8×D6111yescharacteristic
373C2×C4Q16×D6111yescharacteristic
374C2×C4#1451980411yescharacteristic
375C2×C4#1451980611yescharacteristic
376C8—22no—
377C8—41no—
378C8—42no—
379C8—81no—
380C8—1222no—
381C8—4881no—
382C8—2441no—
383C8—2442no—
384C22—1222no—
385C22—1222no—
386C22—1222no—
387C22—2441no—
388C22—2441no—
389C22—2441no—
390C22—2441no—
391C22#1683963611yescharacteristic
392C22#1683978411yescharacteristic
393C22#1683978711yescharacteristic
394C22#107×D6111yescharacteristic
395C22#1683980111yescharacteristic
396C22#108×D6111yescharacteristic
397C22#1683980911yescharacteristic
398C4—21no—
399C4—21no—
400C4—1222no—
401C4—1222no—
402C4—2441no—
403C4#1683983011yescharacteristic
404C4#1683983511yescharacteristic
405C4#1683983711yescharacteristic
406C4#1683984111yescharacteristic
407C4#1683989711yescharacteristic
408C4#1683991911yescharacteristic
409C4#1684007411yescharacteristic
410C4#1684009611yescharacteristic
411C2—2442no—
412C2#2144457611yescharacteristic
413C2#2144458311yescharacteristic
414C2#2144459211yescharacteristic
415C2#2144460611yescharacteristic
416C2#2144600311yescharacteristic
417C2#2144600811yescharacteristic
418C2#2144602511yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61C2×C4⋊C4
prime radicalC23×D61C4⋊C4
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#8832
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
4. C2×#16839515C2semidirect
5. C2×#16839514C2semidirect
6. #21443653C2semidirect
7. C61×#1277C2semidirect
99. C2×C8×C61M16semidirect
121. C2×#92418M16semidirect
208. #1277D61semidirect
236. C61#8832semidirect
322. C2×C8#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×#168397842
#214457962
C4×#145196892
C2×#168395152
C2×#168395142
#214436532
C61×#12772
#883261