Finite Group Databasebeta

← #29574889

Subgroups — #29574889

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455601C211yesmaximal, characteristic
2#21454384C211yesmaximal, characteristic
3#21444274C211yesmaximal, characteristic, complemented
4#21444199C211yesmaximal, characteristic
5#21443715C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1481C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9C4×#11758222C2211yescharacteristic
10#16840066—21no—
11#16840059—21no—
12#16840054C411yescharacteristic
13#16840049C411yescharacteristic
14#16840044C411yescharacteristic
15#16840039C411yescharacteristic
16#16839798—21no—
17#16839788—21no—
18#16839787—22no—
19#16839786C2211yescharacteristic
20#16839784—21no—
21C2×C4⋊#92418C2211yescharacteristic
22C4⋊C8×D61—21no—
23#16839756—21no—
24C2×C4×#92418C2211yescharacteristic
25Q8⋊#92418—22no—
26#16839492—21no—
27#16839489—21no—
28C61×#533C2211yescharacteristic
29C61×#431C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C61×Q8⋊C8—21no—
32C61×Q8⋊C8—21no—
33C2×#11758222D411yescharacteristic
34#14519783—42no—
35#14519783—42no—
36C2×#11758194—21no—
37C2×#11758189—22no—
38C22×#92418—21no—
39C22×#92418—21no—
40C2×C8×D61—22no—
41C4×Dic122C2×C411yescharacteristic
42C4×Dic122D411yescharacteristic
43C4×D244C2×C411yescharacteristic
44C4×D244D411yescharacteristic
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47#14519736D411yescharacteristic
48#14519734—21no—
49C42×D61—21no—
50#14519710—21no—
51#14519710—21no—
52#14519708—21no—
53#14519708—21no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56C4⋊#92418C2×C411yescharacteristic
57C4⋊#92418C2×C411yescharacteristic
58C4⋊#92418D412yes—
59#14519706—22no—
60#14519706—22no—
61#14519700—21no—
62#14519700—21no—
63#14519697—21no—
64#14519697—21no—
65C4×#92418—21no—
66C4×#92418—21no—
67C22×C8×C61—21no—
68C4⋊Q8×C61C2×C411yescharacteristic
69C4⋊Q8×C61C2×C411yescharacteristic
70#125×C61—21no—
71C22⋊Q8×C61—21no—
72C22⋊Q8×C61—21no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75#117×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61D411yescharacteristic
80C4⋊C8×C61D411yescharacteristic
81C22⋊C8×C61—21no—
82C4×C8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C2×C22⋊D61—21no—
89#11758222—21no—
90#11758222—21no—
91#11758222SD1612yes—
92#11758222Q1612yes—
93C2×D244C22⋊C411yescharacteristic
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×Dic122C22⋊C411yescharacteristic
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C42×C61—41no—
111C42×C61C22×C411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C22⋊Dic61—21no—
116#11758198—21no—
117#11758198—21no—
118C4⋊Dic61C22⋊C411yescharacteristic
119C4⋊Dic61C22⋊C411yescharacteristic
120#11758196—21no—
121#11758196—21no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125#11758194—41no—
126#11758194—41no—
127C2×#92418—22no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—22no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135#11758189—44no—
136C8×D61—44no—
137C23×C61#12311yescharacteristic
138C22×D61—21no—
139Q8×C61—42no—
140Q8×C61—41no—
141Q8×C61—41no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61C2×SD1611yescharacteristic
154C2×C4×C61C2×Q1611yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61#13711yescharacteristic
157C22⋊D61—22no—
158C22⋊D61—22no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162D244—21no—
163D244#10312yes—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—81no—
169Dic122—21no—
170Dic122#10312yes—
171C8×C61—41no—
172C8×C61—41no—
173C8×C61—81no—
174#92418—42no—
175#92418—41no—
176#92418—41no—
177#92418—42no—
178#8993—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61#38611yescharacteristic
182C22×C61#48311yescharacteristic
183C22×C61#48411yescharacteristic
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—81no—
191C4×C61—81no—
192C4×C61C2×#10311yescharacteristic
193C4×C61#41711yescharacteristic
194C4×C61#44311yescharacteristic
195C4×C61#44411yescharacteristic
196C4×C61#45011yescharacteristic
197C4×C61#45111yescharacteristic
198Dic61—22no—
199Dic61—41no—
200Dic61—41no—
201#3076—611no—
202#2906—611no—
203#1493—611no—
204#1481D6111yescharacteristic, complemented
205#1476—611no—
206#1301—611no—
207#1277—611no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61#187211yescharacteristic
211C2×C61#187611yescharacteristic
212C2×C61#188111yescharacteristic
213D61—42no—
214C2×#131—1221no—
215#533C2×D6111yescharacteristic
216C4×#41—611no—
217#479—1221no—
218#478—1221no—
219#477—611no—
220#476—611no—
221#475—611no—
222#474—611no—
223#431C2×D6111yescharacteristic
224#427—1221no—
225#424—1222no—
226#424—1221no—
227#423—611no—
228#423—1221no—
229C2×C4⋊C8—611no—
230C2×C4⋊C8—1221no—
231C2×C4⋊C8C2×D6111yescharacteristic
232#416—1221no—
233C2×C4×C8—611no—
234Q8⋊C8—21no—
235Q8⋊C8—21no—
236Q8⋊C8—1221no—
237Q8⋊C8—1222no—
238D4⋊C8—1221no—
239C61#899311yescharacteristic, complemented, Sylow
240C2×#41—611no—
241#131—2442no—
242#131—2442no—
243C2×M16—1222no—
244C2×M16—1221no—
245C22×C8—21no—
246C22×C8—1222no—
247C22×C8—1221no—
248C22×C8—1221no—
249C4⋊Q8C4×D6111yescharacteristic
250C4⋊Q8C4×D6111yescharacteristic
251#125—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—611no—
257C4×Q8—611no—
258C4×D4—611no—
259C4×D4—611no—
260C4×D4—1221no—
261C4×D4—1221no—
262#117—21no—
263#117—611no—
264#117—1221no—
265C2×C42—1221no—
266C2×C42C22×D6111yescharacteristic
267#107—1221no—
268#107—1221no—
269#106—1221no—
270#106—1221no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—611no—
274C4⋊C8—611no—
275C4⋊C8—612no—
276C4⋊C8—1222no—
277C4⋊C8—1222no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8C22⋊D6111yescharacteristic
281C4⋊C8C22⋊D6111yescharacteristic
282#103—1221no—
283#103—1221no—
284#102—1221no—
285#102—1221no—
286C22⋊C8—21no—
287C4×C8—21no—
288C4×C8—1221no—
289C4×C8—1221no—
290#41—612no—
291#41—612no—
292#41—1221no—
293#41—1221no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—611no—
297C2×D4—611no—
298C2×D4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4#1175822211yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C22×C4#1175822411yescharacteristic
305M16—2444no—
306M16—2441no—
307M16—2441no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1222no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—1222no—
317C2×C8—2444no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—611no—
329C4⋊C4—611no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C22⋊C4—41no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C42—41no—
337C42—1221no—
338C42—1221no—
339C42—1221no—
340C42C2×C4×D6111yescharacteristic
341C42D4×D6111yescharacteristic
342C42D4×D6111yescharacteristic
343C42C2×C22⋊D6111yescharacteristic
344C23—1221no—
345C23#1451975911yescharacteristic
346Q8—42no—
347Q8—41no—
348Q8—41no—
349Q8—612no—
350Q8—1221no—
351D4—612no—
352D4—1222no—
353D4—1222no—
354D4—1221no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—1221no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—4881no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4C22⋊C4×D6111yescharacteristic
369C2×C4#1451973711yescharacteristic
370C2×C4C4×C22⋊D6111yescharacteristic
371C2×C4#1451974511yescharacteristic
372C2×C4#1451974811yescharacteristic
373C2×C4#1451975011yescharacteristic
374C2×C4SD16×D6111yescharacteristic
375C2×C4Q16×D6111yescharacteristic
376C2×C4#1451980411yescharacteristic
377C2×C4#1451980911yescharacteristic
378C8—41no—
379C8—41no—
380C8—81no—
381C8—2442no—
382C8—2441no—
383C8—2441no—
384C8—2442no—
385C22—21no—
386C22—21no—
387C22—1222no—
388C22—2441no—
389C22—2441no—
390C22#1683963811yescharacteristic
391C22#1684009111yescharacteristic
392C22#1684009611yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—1222no—
399C4—2441no—
400C4—2441no—
401C4#103×D6111yescharacteristic
402C4#1683976211yescharacteristic
403C4#1683987711yescharacteristic
404C4#1683988211yescharacteristic
405C4#1683991111yescharacteristic
406C4#1683991611yescharacteristic
407C2—21no—
408C2—21no—
409C2—2442no—
410C2#2144612311yescharacteristic
411C2#2144614911yescharacteristic
412C2#2144617811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1481C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1481D61
hypocenterC61#8993
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #21444274C2semidirect
5. #21443715C2semidirect
6. #21443653C2semidirect
7. C61×#1481C2semidirect
204. #1481D61semidirect
239. C61#8993semidirect

Maximal subgroups

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

subgroupindex
#214556012
#214543842
#214442742
#214441992
#214437152
#214436532
C61×#14812
#899361