Finite Group Databasebeta

← #29575101

Subgroups — #29575101

Order 15616.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454381C211yesmaximal, characteristic
2#21449091C211yesmaximal, characteristic
3#21444249C211yesmaximal, characteristic, complemented
4#21444247C211yesmaximal, characteristic, complemented
5#21444131C211yesmaximal, characteristic
6#21443722C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C4×Dic122C2211yescharacteristic
10C2×#14519734C2211yescharacteristic
11#16839815C2211yescharacteristic
12#16839787—22no—
13#16839787—22no—
14#16839786C2211yescharacteristic
15#16839785—21no—
16#16839702C411yescharacteristic
17#16839699C411yescharacteristic
18#16839692—21no—
19#16839684—21no—
20#16839683C411yescharacteristic
21#16839675C411yescharacteristic
22C4×C4⋊Dic61—21no—
23C4×#11758198—21no—
24#16839494—22no—
25#16839492—22no—
26#16839487—21no—
27#16839485—21no—
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758194—21no—
34C2×#11758189—22no—
35M16×D61—42no—
36M16×D61—42no—
37C2×C8×D61—22no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519734—21no—
43#14519734—21no—
44#14519734—21no—
45#14519734—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196—21no—
50C2×#11758196C2×C411yescharacteristic
51C2×#11758196D411yescharacteristic
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198C2×C411yescharacteristic
55C2×#11758198D411yescharacteristic
56C2×C4×Dic61—21no—
57C2×C4×Dic61D411yescharacteristic
58C4⋊#92418—21no—
59C4⋊#92418—21no—
60C4⋊#92418D412yes—
61#14519706—24no—
62C22⋊#92418—21no—
63C4×#92418—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C2×M16×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C4⋊C8×C61D412yes—
75C22⋊C8×C61—21no—
76C4×C8×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61SD1612yes—
95C2×C4×D61Q1612yes—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—42no—
99M16×C61—41no—
100M16×C61—41no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C4⋊C4×C61—42no—
104C42×C61—41no—
105C42×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114#11758198—42no—
115#11758198—42no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—42no—
119C4⋊Dic61—42no—
120#11758196—21no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124#11758196—41no—
125#11758196—41no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130#11758194—41no—
131#11758194—41no—
132C2×#92418—22no—
133C2×#92418—41no—
134#11758189—44no—
135C8×D61—44no—
136C23×C61C2×C22⋊C411yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61#10312yes—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×C4×C61C2×SD1611yescharacteristic
157C2×C4×C61C2×Q1611yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—22no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61#10312yes—
173C4×D61—22no—
174C4×D61—22no—
175C4×D61—22no—
176C4×D61—22no—
177Dic122—22no—
178Dic122—22no—
179Dic122—41no—
180Dic122—41no—
181C8×C61—42no—
182C8×C61—81no—
183#92418—42no—
184#92418—81no—
185#9033—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61#38611yescharacteristic
189C22×C61C2×#10311yescharacteristic
190C22×C61#41711yescharacteristic
191C2×D61—22no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—42no—
195C2×D61—81no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—42no—
201C4×C61—81no—
202C4×C61#45011yescharacteristic
203C4×C61#45111yescharacteristic
204C4×C61#48311yescharacteristic
205C4×C61#48411yescharacteristic
206Dic61—22no—
207Dic61—41no—
208Dic61—42no—
209Dic61—41no—
210Dic61—81no—
211#2905—611no—
212#2396—611no—
213#1487—611no—
214#1487—611no—
215#1458—611no—
216#1303—611no—
217#1303D6111yescharacteristic, complemented
218C2×C61—21no—
219C2×C61—21no—
220C2×C61#187211yescharacteristic
221C2×C61#188411yescharacteristic
222C2×C61#189111yescharacteristic
223D61—42no—
224C22×M16—1221no—
225C2×C4×Q8—611no—
226C2×#117—611no—
227#431—611no—
228#431C2×D6111yescharacteristic
229#424—1222no—
230#424—1222no—
231#423—611no—
232#423—1221no—
233#423C2×D6111yescharacteristic
234#400—611no—
235#399—611no—
236#398—1221no—
237#396—1221no—
238#395—611no—
239#393—611no—
240C4×C4⋊C4—1221no—
241C4×C4⋊C4C2×D6111yescharacteristic
242C4×C22⋊C4—1221no—
243Q8⋊C8—1222no—
244Q8⋊C8—1222no—
245#324—1221no—
246#323—1221no—
247C61#903311yescharacteristic, complemented, Sylow
248C22×Q8—611no—
249C23×C4—611no—
250C2×M16—21no—
251C2×M16—1222no—
252C2×M16—1221no—
253C2×M16—2442no—
254C2×M16—2442no—
255C22×C8—1222no—
256C4×Q8—1221no—
257C4×Q8—1221no—
258C4×Q8—1221no—
259C4×Q8—1221no—
260#117—1221no—
261#117—1221no—
262#117—1221no—
263#117—1221no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C42—21no—
276C2×C42—611no—
277C2×C42—1221no—
278C2×C42C22×D6111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—612no—
282C4⋊C8—1224no—
283C4⋊C8—1221no—
284C4⋊C8—1221no—
285C4⋊C8D24412yes—
286C22⋊C8—21no—
287C22⋊C8—1221no—
288C4×C8—21no—
289C4×C8—1221no—
290#95—1221no—
291#95—1221no—
292#95—1221no—
293#95—1221no—
294#95C4×D6111yescharacteristic
295#95C4×D6111yescharacteristic
296C24—611no—
297C2×Q8—1221no—
298C2×Q8—1221no—
299C2×Q8—2442no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4C2×C4×D6111yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4D4×D6111yescharacteristic
316M16—41no—
317M16—41no—
318M16—2444no—
319M16—2441no—
320M16—2441no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—1222no—
324C2×C8—2444no—
325C2×C8—2441no—
326C4⋊C4—42no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—2442no—
334C4⋊C4—2442no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—2442no—
342C22⋊C4—2442no—
343C42—41no—
344C42—41no—
345C42—1221no—
346C42—1221no—
347C42—2441no—
348C42—2441no—
349C42C2×D24411yescharacteristic
350C42#1175822211yescharacteristic
351C42D4×D6111yescharacteristic
352C42#1175822611yescharacteristic
353C23—612no—
354C23—1221no—
355C23—1221no—
356C23—2441no—
357C23—2441no—
358C23C22⋊C4×D6111yescharacteristic
359Q8—1222no—
360Q8—1222no—
361Q8—2441no—
362Q8—2441no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—612no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—1222no—
377C2×C4—1222no—
378C2×C4—1222no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4#1451973911yescharacteristic
389C2×C4C4×D24411yescharacteristic
390C2×C4#1451974711yescharacteristic
391C2×C4#1451975011yescharacteristic
392C2×C4#1451975211yescharacteristic
393C2×C4#1451976211yescharacteristic
394C2×C4SD16×D6111yescharacteristic
395C2×C4Q16×D6111yescharacteristic
396C2×C4#1451980111yescharacteristic
397C2×C4#1451980611yescharacteristic
398C8—42no—
399C8—81no—
400C8—4881no—
401C8—2442no—
402C22—21no—
403C22—21no—
404C22—1222no—
405C22—4881no—
406C22—2442no—
407C22—2441no—
408C22—2441no—
409C22#1683964011yescharacteristic
410C22#103×D6111yescharacteristic
411C22#1683976011yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—1222no—
419C4—4881no—
420C4—2441no—
421C4—2441no—
422C4—2442no—
423C4#1683991411yescharacteristic
424C4#1683991911yescharacteristic
425C4#1684009411yescharacteristic
426C4#1684009911yescharacteristic
427C2—21no—
428C2—21no—
429C2—2442no—
430C2#2144612511yescharacteristic
431C2#2144620111yescharacteristic
432C2#2144623611yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9033
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #21444249C2semidirect
4. #21444247C2semidirect
6. #21443722C2semidirect
7. C61×#1303C2semidirect
217. #1303D61semidirect
247. C61#9033semidirect

Maximal subgroups

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

subgroupindex
#214543812
#214490912
#214442492
#214442472
#214441312
#214437222
C61×#13032
#903361