Finite Group Databasebeta

← D61×#2236 #29834801

Subgroups — D61×#2236 #29834801

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#467×D61C211yesmaximal, characteristic
2C2×#107×D61C211yesmaximal, characteristic
3#21448023C212yesmaximal, complemented
4#21448022C211yesmaximal, characteristic, complemented
5#21448021C211yesmaximal, characteristic, complemented
6#21448020C212yesmaximal, complemented
7#21448019C211yesmaximal, characteristic, complemented
8#366×D61C212yesmaximal, complemented
9#358×D61C212yesmaximal, complemented
10C22⋊C16×D61C211yesmaximal, characteristic
11C61×#2236C211yesmaximal, characteristic, complemented
12C2×Q16×D61C2211yescharacteristic
13C22×C8×D61C2211yescharacteristic
14C22⋊Q8×D61—21no—
15C2×C4⋊C4×D61—21no—
16C2×C16×D61C2212yes—
17#16840004C2211yescharacteristic
18#16840003C2211yescharacteristic
19#16840002—21no—
20#16840001—21no—
21#16840000C2211yescharacteristic
22C2×#14519711C2211yescharacteristic
23C2×#14519710—21no—
24#107×D61—21no—
25#107×D61—21no—
26#107×D61C2211yescharacteristic
27#107×D61C2212yes—
28#107×D61C2212yes—
29#103×D61—21no—
30#16839588C2212yescomplemented
31#16839587C2212yescomplemented
32#16839587C2212yescomplemented
33#16839567C2212yescomplemented
34#16839566C2212yescomplemented
35#16839565C2212yescomplemented
36C22⋊#11758185C2211yescharacteristic
37#16839541C2212yes—
38C61×#467C2211yescharacteristic
39C2×#107×C61C2211yescharacteristic
40C61×#366C2212yescomplemented
41C61×#358C2212yescomplemented
42C61×C22⋊C16C2211yescharacteristic
43C2×Q8×D61—21no—
44C22×C4×D61—41no—
45C22×C4×D61D411yescharacteristic
46C2×Dic244C2311yescharacteristic
47C2×#11758202—21no—
48Q16×D61—24no—
49C22×#92418D411yescharacteristic
50C2×C8×D61—24no—
51C2×C8×D61D411yescharacteristic
52C2×C8×D61D411yescharacteristic
53C2×C8×D61C2311yescharacteristic
54C2×C8×D61C2311yescharacteristic
55#14519757—21no—
56#14519756—21no—
57#14519755—41no—
58#14519754—41no—
59#14519753—21no—
60C2×C4⋊Dic61—21no—
61C2×#11758196—41no—
62C4⋊C4×D61—22no—
63C4⋊C4×D61—22no—
64C4⋊C4×D61—21no—
65C4⋊C4×D61—41no—
66C4⋊C4×D61—41no—
67C4⋊C4×D61—41no—
68C22⋊C4×D61—41no—
69C2×#11758185C2312yes—
70C16×D61—24no—
71#14519711—21no—
72#14519711C2311yescharacteristic
73#14519711C2312yes—
74#14519710—21no—
75#14519710—22no—
76#14519710—22no—
77#14519702—21no—
78#14519701—21no—
79#14519700—21no—
80C2×Q16×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C22⋊Q8×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C16×C61C2312yes—
85#107×C61—21no—
86#107×C61C2311yescharacteristic
87#107×C61C2312yes—
88#103×C61—21no—
89C23×D61D811yescharacteristic
90C2×Q8×C61—21no—
91C22×C4×C61—41no—
92C22×C4×C61C2×D411yescharacteristic
93C22×Dic61—41no—
94C22×Dic61D811yescharacteristic
95Q8×D61—42no—
96Q8×D61—42no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—84no—
104C2×C4×D61D811yescharacteristic
105C2×C4×D61D811yescharacteristic
106C2×C4×D61C2×D411yescharacteristic
107C2×C4×D61C2×D411yescharacteristic
108C2×Dic122—21no—
109C2×Dic122—41no—
110Q16×C61—22no—
111C2×C8×C61—22no—
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2411yescharacteristic
114C4⋊C4×C61—21no—
115C4⋊C4×C61—22no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊Dic61—41no—
120#11758202—42no—
121#11758198—41no—
122#11758198—41no—
123C4⋊Dic61—21no—
124C4⋊Dic61—22no—
125C4⋊Dic61—41no—
126C4⋊Dic61—41no—
127#11758196—41no—
128#11758196—42no—
129#11758196—42no—
130#11758196—41no—
131#11758196—41no—
132C2×#92418—22no—
133C2×#92418C2×D411yescharacteristic
134C2×#92418C2×D411yescharacteristic
135Dic244—22no—
136C8×D61—22no—
137C8×D61—22no—
138C8×D61—22no—
139C8×D61#4114yes—
140C16×C61—22no—
141#11758185—22no—
142C23×C61C2×D811yescharacteristic
143C22×D61—22no—
144C22×D61—22no—
145C22×D61Q3214yes—
146C22×D61C2×D811yescharacteristic
147C22×D61C2×D811yescharacteristic
148Q8×C61—41no—
149Q8×C61—41no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—42no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—82no—
156C2×C4×C61C2×D811yescharacteristic
157C2×C4×C61C22×D411yescharacteristic
158C2×Dic61—22no—
159C2×Dic61—41no—
160C2×Dic61—42no—
161C2×Dic61—41no—
162C2×Dic61—82no—
163C2×Dic61C2×D811yescharacteristic
164C2×Dic61C2×D811yescharacteristic
165C4×D61—22no—
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—22no—
169C4×D61—84no—
170C4×D61—82no—
171C4×D61—82no—
172C4×D61—84no—
173C4×D61#12312yes—
174C4×D61#13712yes—
175Dic122—41no—
176Dic122—41no—
177Dic122—82no—
178C8×C61—21no—
179C8×C61C2×#4112yes—
180#92418—21no—
181#92418#12312yes—
182C2×#2236—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61C2×Q3212yes—
186C22×C61C22×D811yescharacteristic
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—28no—
190C2×D61#48012yes—
191C2×D61C2×Q3212yes—
192C2×D61C2×Q3212yes—
193C2×D61#50912yes—
194C4×C61—21no—
195C4×C61—81no—
196C4×C61—82no—
197C4×C61—81no—
198C4×C61C2×#12311yescharacteristic
199C4×C61C2×#13711yescharacteristic
200Dic61—21no—
201Dic61—81no—
202Dic61—82no—
203Dic61—81no—
204Dic61#48012yes—
205C2×#467—611no—
206C22×#107—611no—
207#2236—611no—
208#2236—611no—
209#2236—612no—
210#2236—612no—
211#2236—611no—
212#2236D6111yescharacteristic, direct product factor
213C2×#366—612no—
214C2×#358—612no—
215C2×C22⋊C16—611no—
216C2×C61—22no—
217C2×C61C2×#48011yescharacteristic
218C2×C61C22×Q3211yescharacteristic
219C2×C61C2×#50911yescharacteristic
220D61—22no—
221D61#223614yesdirect product factor
222C22×Q16—611no—
223C23×C8—611no—
224C2×C22⋊Q8—1221no—
225C22×C4⋊C4—1221no—
226C22×C16—612no—
227#467—611no—
228#467—611no—
229#467—611no—
230#467—1221no—
231#467—1221no—
232#467C2×D6111yescharacteristic
233C2×#107—611no—
234C2×#107—612no—
235C2×#107—612no—
236C2×#107—611no—
237C2×#107—1221no—
238C2×#107—1221no—
239C2×#107—1221no—
240C2×#107C2×D6111yescharacteristic
241C2×#103—1221no—
242#366—612no—
243#366—612no—
244#366—612no—
245#366C2×D6112yescomplemented
246#358—612no—
247#358—612no—
248#358—612no—
249#358C2×D6112yescomplemented
250C22⋊C16—611no—
251C22⋊C16—612no—
252C22⋊C16C2×D6111yescharacteristic
253C61C2×#223611yescharacteristic, complemented, Sylow
254C22×Q8—1221no—
255C23×C4—611no—
256C23×C4—2441no—
257C2×Q16—611no—
258C2×Q16—1224no—
259C2×Q16—1221no—
260C2×Q16C22×D6111yescharacteristic
261C22×C8—611no—
262C22×C8—611no—
263C22×C8—611no—
264C22×C8—611no—
265C22×C8—611no—
266C22×C8—1224no—
267C22×C8C22×D6111yescharacteristic
268C22⋊Q8—21no—
269C22⋊Q8—1221no—
270C22⋊Q8—1221no—
271C22⋊Q8—1221no—
272C22⋊Q8—2441no—
273C22⋊Q8—2441no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—1222no—
276C2×C4⋊C4—1222no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—2441no—
280C2×C4⋊C4—2441no—
281C2×C4⋊C4—2441no—
282C2×C4⋊C4—2441no—
283C2×C22⋊C4—2441no—
284C2×C16—612no—
285C2×C16—1224no—
286C2×C16C22×D6112yes—
287#107—21no—
288#107—612no—
289#107—611no—
290#107—1222no—
291#107—1222no—
292#107—1221no—
293#107—1221no—
294#107C22×D6112yes—
295#107C22×D6111yescharacteristic
296#103—21no—
297#103—1221no—
298#103—1221no—
299#103—1221no—
300C24—611no—
301C2×Q8—21no—
302C2×Q8—1221no—
303C2×Q8—2441no—
304C2×Q8—2442no—
305C2×Q8—2442no—
306C22×C4—41no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—1222no—
313C22×C4—1222no—
314C22×C4—4884no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2442no—
318C22×C4—2442no—
319C22×C4—2441no—
320C22×C4D4×D6111yescharacteristic
321Q16—22no—
322Q16—1222no—
323Q16—2442no—
324C2×C8—22no—
325C2×C8—611no—
326C2×C8—614no—
327C2×C8—611no—
328C2×C8—1222no—
329C2×C8—1222no—
330C2×C8—1222no—
331C2×C8—1222no—
332C2×C8D4×D6111yescharacteristic
333C2×C8C23×D6111yescharacteristic
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—1221no—
339C4⋊C4—1222no—
340C4⋊C4—2442no—
341C4⋊C4—2442no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C22⋊C4—41no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C16—22no—
352C16—1222no—
353C23—611no—
354C23—611no—
355C23—614no—
356C23—1222no—
357C23—1222no—
358C23D8×D6111yescharacteristic
359Q8—41no—
360Q8—41no—
361Q8—4882no—
362Q8—2441no—
363Q8—2441no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—82no—
370C2×C4—611no—
371C2×C4—612no—
372C2×C4—612no—
373C2×C4—611no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—1222no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—4884no—
380C2×C4—4882no—
381C2×C4—4882no—
382C2×C4—4884no—
383C2×C4—4882no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2442no—
387C2×C4D8×D6111yescharacteristic
388C2×C4C2×D4×D6111yescharacteristic
389C8—21no—
390C8—612no—
391C8—1221no—
392C8#41×D6112yes—
393C22—21no—
394C22—21no—
395C22—612no—
396C22—612no—
397C22—612no—
398C22—612no—
399C22—1228no—
400C22—1221no—
401C22—1221no—
402C22Q32×D6112yes—
403C22C2×D8×D6111yescharacteristic
404C4—21no—
405C4—81no—
406C4—82no—
407C4—81no—
408C4—612no—
409C4—1221no—
410C4—4881no—
411C4—4882no—
412C4—4881no—
413C4#123×D6111yescharacteristic
414C4#137×D6111yescharacteristic
415C2—22no—
416C2—614no—
417C2—1222no—
418C2#480×D6111yescharacteristic
419C2C2×Q32×D6111yescharacteristic
420C2#509×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2236C2
socleC22×C61C22×D8
prime radicalC23×D61D8
hypercenter#2236D61
hypocenterC61C2×#2236
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
3. #21448023C2semidirect
4. #21448022C2semidirect
5. #21448021C2semidirect
6. #21448020C2semidirect
7. #21448019C2semidirect
8. #366×D61C2semidirect
9. #358×D61C2semidirect
11. C61×#2236C2semidirect
30. #16839588C22semidirect
31. #16839587C22semidirect
32. #16839587C22semidirect
33. #16839567C22semidirect
34. #16839566C22semidirect
35. #16839565C22semidirect
40. C61×#366C22semidirect
41. C61×#358C22semidirect
212. #2236D61direct (N × H)
221. D61#2236direct (N × H)
245. #366C2×D61semidirect
249. #358C2×D61semidirect
253. C61C2×#2236semidirect

Maximal subgroups

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

subgroupindex
#467×D612
C2×#107×D612
#214480232
#214480222
#214480212
#214480202
#214480192
#366×D612
#358×D612
C22⋊C16×D612
C61×#22362
C2×#223661