Finite Group Databasebeta

← #29662770

Subgroups — #29662770

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456405C211yesmaximal, characteristic, complemented
2#21455890C212yesmaximal
3#21445373C212yesmaximal, complemented
4#21445366C212yesmaximal, complemented
5#21445337C211yesmaximal, characteristic, complemented
6#21445332C211yesmaximal, characteristic, complemented
7#21445313C211yesmaximal, characteristic, complemented
8#21445308C211yesmaximal, characteristic, complemented
9#21444567C211yesmaximal, characteristic, complemented
10#21444483C212yesmaximal, complemented
11C61×#2965C211yesmaximal, characteristic
12#16840319C2212yes—
13#16840167C2211yescharacteristic
14#16840142C2211yescharacteristic
15#16840113C2212yes—
16#16840103—22no—
17#16840047C2212yes—
18#16840042C2212yes—
19#16840003—21no—
20#16840003—21no—
21#16839972C2212yes—
22#16839967C2212yes—
23#16839924—22no—
24C4×Dic244—21no—
25C4×Dic244—21no—
26C4×#11758202—22no—
27C4×#11758200—22no—
28#16839815C2212yes—
29#16839515C2212yes—
30#16839513C2211yescharacteristic
31#16839513C2211yescharacteristic
32#16839509C2212yes—
33#16839509C2212yes—
34#16839507C2212yes—
35#16839507C2212yes—
36C4×#41×C61C2211yescharacteristic
37C61×#446C2211yescharacteristic
38C61×#446C2211yescharacteristic
39C61×#436C2211yescharacteristic
40C61×#436C2211yescharacteristic
41C61×#435—21no—
42C61×#435—21no—
43C61×#431—21no—
44C61×#431C2211yescharacteristic
45C4×M16×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×Dic244—21no—
48C2×Dic244—21no—
49C2×#11758202—22no—
50C2×#11758200—22no—
51#14519777C2312yes—
52#14519777C2312yes—
53#14519769—22no—
54#14519756—22no—
55#14519756—22no—
56C4×Dic122—22no—
57C4×Dic122—22no—
58#14519736—22no—
59#14519711—21no—
60#14519711—21no—
61#14519710—22no—
62#14519708—22no—
63C4⋊#92418C2312yes—
64C4⋊#92418C2312yes—
65#14519702—22no—
66#14519702—22no—
67#14519701—22no—
68#14519700—22no—
69#14519700—22no—
70#14519698—22no—
71C22⋊#92418—22no—
72C4×#92418—22no—
73C2×#41×C61D411yescharacteristic
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C22×C8×C61D411yescharacteristic
77C22×C8×C61D411yescharacteristic
78C4×Q8×C61D411yescharacteristic
79C4×Q8×C61C2311yescharacteristic
80C4×D4×C61—21no—
81C4×D4×C61—21no—
82C4×D4×C61D411yescharacteristic
83C4×D4×C61C2311yescharacteristic
84#117×C61—21no—
85#117×C61D411yescharacteristic
86C2×C42×C61—21no—
87C2×C42×C61C2311yescharacteristic
88C4⋊C8×C61—21no—
89C4⋊C8×C61—21no—
90C4⋊C8×C61C2311yescharacteristic
91C4⋊C8×C61C2311yescharacteristic
92C22⋊C8×C61—21no—
93C22⋊C8×C61—21no—
94C22⋊C8×C61—21no—
95#97×C61—21no—
96#97×C61—21no—
97C4×C8×C61—21no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102#41×C61—42no—
103C2×Q8×C61C2×D411yescharacteristic
104C2×D4×C61—21no—
105C2×D4×C61C2×D411yescharacteristic
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×Dic122—22no—
113C2×Dic122—22no—
114M16×C61—42no—
115M16×C61—42no—
116C2×C8×C61—22no—
117C2×C8×C61—21no—
118C2×C8×C61—21no—
119C2×C8×C61—41no—
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61C2×D411yescharacteristic
127C4⋊C4×C61C2×D411yescharacteristic
128C22⋊C4×C61—21no—
129C22⋊C4×C61—21no—
130C22⋊C4×C61—21no—
131C42×C61—21no—
132C42×C61—21no—
133C42×C61—21no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61#4111yescharacteristic
137C42×C61C2411yescharacteristic
138C22⋊Dic61—42no—
139#11758202—44no—
140#11758200—44no—
141C4⋊Dic61—22no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145#11758196—42no—
146#11758196—42no—
147C4×Dic61—42no—
148C2×#92418—22no—
149C2×#92418—22no—
150Dic244—42no—
151Dic244—42no—
152C23×C61—21no—
153C23×C61#12111yescharacteristic
154Q8×C61—22no—
155D4×C61—22no—
156D4×C61—42no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—42no—
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61C22×D411yescharacteristic
172C2×C4×C61C22×D411yescharacteristic
173C2×C4×C61C2×#4111yescharacteristic
174C2×Dic61—42no—
175C2×Dic61—42no—
176Dic122—42no—
177Dic122—42no—
178Dic122—42no—
179Dic122—42no—
180C8×C61—21no—
181C8×C61—21no—
182C8×C61—21no—
183C8×C61—41no—
184C8×C61—41no—
185C8×C61#13512yes—
186#92418—42no—
187#92418—42no—
188#19161—611nomaximal, Sylow
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61C2×#12111yescharacteristic
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—41no—
202C4×C61#47312yes—
203C4×C61C2×#13511yescharacteristic
204C4×C61#57511yescharacteristic
205C4×C61#57512yes—
206Dic61—82no—
207Dic61—82no—
208#3170—611no—
209#3107—612no—
210#2965D6111yescharacteristic
211#1700—612no—
212#1699—612no—
213#1694—611no—
214#1693—611no—
215#1690—611no—
216#1689—611no—
217#1564—611no—
218#1544—612no—
219C2×C61—41no—
220C2×C61—81no—
221C2×C61#303511yescharacteristic
222C2×C61#305411yescharacteristic
223C2×C61C2×#47311yescharacteristic
224#533—612no—
225C4×#41C2×D6111yescharacteristic
226#500—611no—
227#494—611no—
228#487—612no—
229#485—1222no—
230#475—612no—
231#474—612no—
232#467—1221no—
233#467—1221no—
234#462—612no—
235#461—612no—
236#452—1222no—
237#446C2×D6111yescharacteristic
238#446C2×D6111yescharacteristic
239C4×Q16—1222no—
240C4×Q16—1221no—
241C4×Q16—1221no—
242C4×SD16—1222no—
243#436C2×D6111yescharacteristic
244#436C2×D6111yescharacteristic
245#435—21no—
246#435—21no—
247#431—21no—
248#431—612no—
249#431C2×D6111yescharacteristic
250C4×M16—21no—
251C2×C4×C8C2×D6111yescharacteristic
252#335—612no—
253#334—611no—
254#334—611no—
255#332—612no—
256#332—612no—
257#332—612no—
258#332—612no—
259C61#1916111yescharacteristic, complemented, Sylow
260C2×#41D24411yescharacteristic
261C2×Q16—1222no—
262C2×Q16—1221no—
263C2×Q16—1221no—
264C2×SD16—1222no—
265C2×M16—21no—
266C2×M16—21no—
267C22×C8C22⋊D6111yescharacteristic
268C22×C8C22⋊D6111yescharacteristic
269C4⋊Q8—612no—
270C4⋊Q8—612no—
271#125—1222no—
272C22⋊Q8—1222no—
273C22⋊Q8—1222no—
274C4×Q8—1222no—
275C4×Q8—1222no—
276C4×Q8D24411yescharacteristic
277C4×Q8C22×D6111yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D24411yescharacteristic
281C4×D4C22×D6111yescharacteristic
282#117—21no—
283#117—1222no—
284#117D24411yescharacteristic
285C2×C42—21no—
286C2×C42C22×D6111yescharacteristic
287#107—1221no—
288#107—1221no—
289#107—1222no—
290#106—1222no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—612no—
294C4⋊C8—612no—
295C4⋊C8C22×D6111yescharacteristic
296C4⋊C8C22×D6111yescharacteristic
297#103—1222no—
298#103—1222no—
299#103—1222no—
300#103—1222no—
301#103—1222no—
302#102—1222no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—1222no—
307#97—21no—
308#97—21no—
309C4×C8—21no—
310C4×C8—1222no—
311C4×C8C22⋊D6111yescharacteristic
312C4×C8C22⋊D6111yescharacteristic
313C4×C8C22×D6111yescharacteristic
314C4×C8C22×D6111yescharacteristic
315#41—42no—
316C2×Q8—1222no—
317C2×Q8—1222no—
318C2×Q8C2×D24411yescharacteristic
319C2×D4—21no—
320C2×D4C2×D24411yescharacteristic
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4C2×D24411yescharacteristic
325C22×C4#1175822211yescharacteristic
326C22×C4C2×C22⋊D6111yescharacteristic
327Q16—2442no—
328Q16—2444no—
329Q16—2442no—
330SD16—2444no—
331M16—42no—
332M16—42no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—1222no—
338C2×C8—1222no—
339C2×C8C2×C22⋊D6111yescharacteristic
340C2×C8C2×C22⋊D6111yescharacteristic
341C2×C8C2×C22⋊D6111yescharacteristic
342C2×C8C2×C22⋊D6111yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—1222no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—2442no—
350C4⋊C4—2442no—
351C4⋊C4C2×D24411yescharacteristic
352C4⋊C4C2×D24411yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—2442no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—2442no—
361C42C2×D24411yescharacteristic
362C42#1175822211yescharacteristic
363C42C2×C22⋊D6111yescharacteristic
364C42C23×D6111yescharacteristic
365C23—21no—
366C23#1451975111yescharacteristic
367Q8—22no—
368Q8—2442no—
369Q8—2442no—
370Q8—2442no—
371Q8—2442no—
372D4—22no—
373D4—42no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4#1451975111yescharacteristic
388C2×C4#1451975111yescharacteristic
389C2×C4#1451975111yescharacteristic
390C2×C4C22×C22⋊D6111yescharacteristic
391C2×C4C22×D24411yescharacteristic
392C2×C4C2×#1175822211yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—41no—
397C8—41no—
398C8—2442no—
399C8—2442no—
400C8#1451979712yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22C2×#1451975111yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—4882no—
415C4—4882no—
416C4#1684003712yes—
417C4C2×#1451979711yescharacteristic
418C4#1684056011yescharacteristic
419C4#1684056212yes—
420C2—41no—
421C2—81no—
422C2#2145527411yescharacteristic
423C2#2145542811yescharacteristic
424C2C2×#1684003711yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2965C2
socleC22×C61C2×#121
prime radicalC2×#41×C61D4
hypercenter#2965D61
hypocenterC61#19161
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #21456405C2semidirect
3. #21445373C2semidirect
4. #21445366C2semidirect
5. #21445337C2semidirect
6. #21445332C2semidirect
7. #21445313C2semidirect
8. #21445308C2semidirect
9. #21444567C2semidirect
10. #21444483C2semidirect
259. C61#19161semidirect

Maximal subgroups

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

subgroupindex
#214564052
#214558902
#214453732
#214453662
#214453372
#214453322
#214453132
#214453082
#214445672
#214444832
C61×#29652
#1916161