Finite Group Databasebeta

← #29575099

Subgroups — #29575099

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#21449089C211yesmaximal, characteristic
3#21444248C211yesmaximal, characteristic, complemented
4#21444131C211yesmaximal, characteristic
5#21443721C211yesmaximal, characteristic, complemented
6#21443720C211yesmaximal, characteristic, complemented
7C61×#1487C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519734C2211yescharacteristic
10#16839815C2211yescharacteristic
11#16839787—22no—
12#16839787—22no—
13#16839786C2211yescharacteristic
14#16839785—21no—
15#16839700C411yescharacteristic
16#16839697C411yescharacteristic
17#16839695—21no—
18#16839684—21no—
19#16839681C411yescharacteristic
20#16839673C411yescharacteristic
21C4×#11758196—21no—
22C4×C4⋊Dic61C2211yescharacteristic
23C4×#11758198—21no—
24Q8⋊#92418—22no—
25#16839487—21no—
26#16839485—21no—
27C2×C4×Q8×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758189—22no—
34M16×D61—42no—
35M16×D61—42no—
36C2×C8×D61—22no—
37#14519734—21no—
38#14519734—21no—
39#14519734—21no—
40#14519734—21no—
41C2×C4⋊Dic61—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196C2×C411yescharacteristic
45C2×#11758196D411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198C2×C411yescharacteristic
49C2×#11758198D411yescharacteristic
50C2×C4×Dic61—21no—
51C2×C4×Dic61D411yescharacteristic
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418D412yes—
55#14519706—24no—
56C22⋊#92418—21no—
57C4×#92418—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C22×Q8×C61C2×C411yescharacteristic
65C2×M16×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C42×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C4⋊C8×C61D412yes—
77C22⋊C8×C61—21no—
78C4×C8×C61—21no—
79C23×D61C22⋊C411yescharacteristic
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—42no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61SD1612yes—
98C2×C4×D61Q1612yes—
99M16×C61—41no—
100M16×C61—41no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113#11758198—21no—
114#11758198—21no—
115#11758198—21no—
116#11758198—21no—
117#11758198—42no—
118#11758198—42no—
119C4⋊Dic61—42no—
120#11758196—21no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124#11758196—42no—
125#11758196—42no—
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—
142Q8×C61—22no—
143Q8×C61—22no—
144Q8×C61—41no—
145Q8×C61—41no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×C4×C61C2×SD1611yescharacteristic
161C2×C4×C61C2×Q1611yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61#13711yescharacteristic
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—22no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61#10312yes—
177C4×D61—22no—
178C4×D61—22no—
179C4×D61—22no—
180C4×D61—22no—
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—42no—
208Dic61—41no—
209Dic61—41no—
210Dic61—81no—
211#2905—611no—
212#2396—611no—
213#1487—611no—
214#1487D6111yescharacteristic, complemented
215#1458—611no—
216#1303—611no—
217#1303—611no—
218C2×C61—21no—
219C2×C61—21no—
220C2×C61#187211yescharacteristic
221C2×C61#188411yescharacteristic
222C2×C61#189111yescharacteristic
223D61—42no—
224C22×M16—1221no—
225C2×C4×Q8C2×D6111yescharacteristic
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—611no—
241C4×C4⋊C4—1221no—
242C4×C22⋊C4—1221no—
243Q8⋊C8—22no—
244Q8⋊C8—1222no—
245#324—1221no—
246#323—1221no—
247C61#903311yescharacteristic, complemented, Sylow
248C22×Q8C4×D6111yescharacteristic
249C23×C4—611no—
250C2×M16—21no—
251C2×M16—1222no—
252C2×M16—1221no—
253C2×M16—2442no—
254C2×M16—2442no—
255C22×C8—1222no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
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—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4C4×D6111yescharacteristic
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⋊C8C22⋊D6112yes—
286C22⋊C8—21no—
287C22⋊C8—1221no—
288C4×C8—21no—
289C4×C8—1221no—
290#95—611no—
291#95—611no—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296C24—611no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—42no—
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—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—2442no—
335C4⋊C4—2442no—
336C4⋊C4—2442no—
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—
349C42#1175822211yescharacteristic
350C42D4×D6111yescharacteristic
351C42#1175822411yescharacteristic
352C42C2×C22⋊D6111yescharacteristic
353C23—612no—
354C23—1221no—
355C23—1221no—
356C23—2441no—
357C23—2441no—
358C23C22⋊C4×D6111yescharacteristic
359Q8—22no—
360Q8—22no—
361Q8—41no—
362Q8—41no—
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#1451973711yescharacteristic
389C2×C4C4×C22⋊D6111yescharacteristic
390C2×C4#1451974511yescharacteristic
391C2×C4#1451974811yescharacteristic
392C2×C4#1451975011yescharacteristic
393C2×C4#1451975911yescharacteristic
394C2×C4SD16×D6111yescharacteristic
395C2×C4Q16×D6111yescharacteristic
396C2×C4#1451980411yescharacteristic
397C2×C4#1451980911yescharacteristic
398C8—42no—
399C8—81no—
400C8—4881no—
401C8—2442no—
402C22—21no—
403C22—21no—
404C22—1222no—
405C22—4881no—
406C22—2442no—
407C22—2441no—
408C22—2441no—
409C22#1683963811yescharacteristic
410C22#103×D6111yescharacteristic
411C22#1683976211yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—1222no—
419C4—4881no—
420C4—2442no—
421C4—2441no—
422C4—2441no—
423C4#1683991111yescharacteristic
424C4#1683991611yescharacteristic
425C4#1684009111yescharacteristic
426C4#1684009611yescharacteristic
427C2—21no—
428C2—21no—
429C2—2442no—
430C2#2144612311yescharacteristic
431C2#2144619911yescharacteristic
432C2#2144623411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1487C2
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1487D61
hypocenterC61#9033
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
3. #21444248C2semidirect
5. #21443721C2semidirect
6. #21443720C2semidirect
7. C61×#1487C2semidirect
214. #1487D61semidirect
247. C61#9033semidirect

Maximal subgroups

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

subgroupindex
#214543812
#214490892
#214442482
#214441312
#214437212
#214437202
C61×#14872
#903361