Finite Group Databasebeta

← #29663412

Subgroups — #29663412

Order 15616.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457156C212yesmaximal
2#21456405C211yesmaximal, characteristic, complemented
3#21445373C212yesmaximal, complemented
4#21445366C212yesmaximal, complemented
5#21445213C211yesmaximal, characteristic, complemented
6#21445208C211yesmaximal, characteristic, complemented
7#21445189C211yesmaximal, characteristic, complemented
8#21445184C211yesmaximal, characteristic, complemented
9C2×#16839515C211yesmaximal, characteristic, complemented
10#21444520C212yesmaximal, complemented
11C61×#2966C211yesmaximal, characteristic
12#16840319C2212yes—
13#16840167C2211yescharacteristic
14#16840142C2211yescharacteristic
15#16840113C2212yes—
16#16840066—22no—
17#16840047C2212yes—
18#16840042C2212yes—
19#16840003—21no—
20#16840003—21no—
21#16840001—22no—
22#16839989—22no—
23#16839981—22no—
24#16839972C2212yes—
25#16839967C2212yes—
26C4×Dic244—21no—
27C4×Dic244—21no—
28C2×C4⋊#92418C2212yes—
29#16839515C2211yescharacteristic
30#16839515C2211yescharacteristic
31#16839515C2212yes—
32#16839509C2212yes—
33#16839509C2212yes—
34#16839507C2212yes—
35#16839507C2212yes—
36C61×#529C2211yescharacteristic
37C61×#446C2211yescharacteristic
38C8×Q8×C61C2211yescharacteristic
39C61×#436C2211yescharacteristic
40C61×#435—21no—
41C8×D4×C61—21no—
42C8×D4×C61C2211yescharacteristic
43C61×#433—21no—
44C61×#432C2211yescharacteristic
45C61×#405—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×Dic244—21no—
48C2×Dic244—21no—
49C2×#11758202—22no—
50C2×#11758200—22no—
51C22×#92418—22no—
52#14519777C2312yes—
53#14519777C2312yes—
54#14519769—22no—
55#14519756—22no—
56#14519756—22no—
57C4×Dic122—22no—
58C4×Dic122—22no—
59#14519736—22no—
60#14519711—21no—
61#14519711—21no—
62#14519710—22no—
63#14519708—22no—
64C4⋊#92418—22no—
65C4⋊#92418C2312yes—
66C4⋊#92418C2312yes—
67#14519702—22no—
68#14519702—22no—
69#14519701—22no—
70#14519700—22no—
71#14519700—22no—
72#14519698—22no—
73C2×M16×C61—21no—
74C22×C8×C61—21no—
75C22×C8×C61D411yescharacteristic
76C22×C8×C61D411yescharacteristic
77#126×C61—21no—
78#125×C61D411yescharacteristic
79#124×C61D411yescharacteristic
80#123×C61—21no—
81C22⋊Q8×C61D411yescharacteristic
82#121×C61D411yescharacteristic
83C4×Q8×C61C2311yescharacteristic
84C4×D4×C61—21no—
85C4×D4×C61C2311yescharacteristic
86#117×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
102C2×Q8×C61C2×D411yescharacteristic
103C2×D4×C61—21no—
104C2×D4×C61C2×D411yescharacteristic
105C22×C4×C61—21no—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C2×Dic122—22no—
110C2×Dic122—22no—
111M16×C61—42no—
112C2×C8×C61—22no—
113C2×C8×C61—21no—
114C2×C8×C61—21no—
115C2×C8×C61—41no—
116C2×C8×C61—42no—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61C2×D411yescharacteristic
126C4⋊C4×C61C2×D411yescharacteristic
127C22⋊C4×C61—21no—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—21no—
130C22⋊C4×C61—21no—
131C22⋊C4×C61—21no—
132C42×C61—21no—
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C42×C61C2411yescharacteristic
137C22⋊Dic61—42no—
138#11758202—82no—
139#11758200—82no—
140C4⋊Dic61—22no—
141C4⋊Dic61—22no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144#11758196—42no—
145#11758196—42no—
146C4×Dic61—42no—
147C2×#92418—22no—
148C2×#92418—22no—
149C2×#92418—82no—
150Dic244—42no—
151Dic244—42no—
152C23×C61—21no—
153C23×C61#12111yescharacteristic
154Q8×C61—21no—
155Q8×C61—21no—
156D4×C61—21no—
157D4×C61—21no—
158D4×C61—42no—
159C2×C4×C61—22no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61C22×D411yescharacteristic
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C2×#4111yescharacteristic
175C2×Dic61—42no—
176C2×Dic61—42no—
177Dic122—42no—
178Dic122—42no—
179Dic122—42no—
180Dic122—42no—
181C8×C61—21no—
182C8×C61—21no—
183C8×C61—21no—
184C8×C61—41no—
185C8×C61—41no—
186C8×C61#13512yes—
187#92418—42no—
188#92418—42no—
189#19223—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61#47312yes—
196C22×C61C2×#12111yescharacteristic
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—41no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61C2×#13511yescharacteristic
205C4×C61#57511yescharacteristic
206C4×C61#57611yescharacteristic
207C4×C61#57811yescharacteristic
208Dic61—82no—
209Dic61—82no—
210#3248—612no—
211#3170—611no—
212#2966D6111yescharacteristic
213#1700—612no—
214#1699—612no—
215#1674—611no—
216#1673—611no—
217#1670—611no—
218#1669—611no—
219C2×#335—611no—
220#1552—612no—
221C2×C61—22no—
222C2×C61—81no—
223C2×C61#303511yescharacteristic
224C2×C61#306111yescharacteristic
225C2×C61C2×#47311yescharacteristic
226#533—612no—
227#529C2×D6111yescharacteristic
228#500—611no—
229#494—611no—
230#487—612no—
231#479—1222no—
232#475—612no—
233#474—612no—
234#467—1221no—
235#467—1221no—
236#467—1222no—
237#465—1222no—
238#464—1222no—
239#462—612no—
240#461—612no—
241#446C2×D6111yescharacteristic
242C8×Q8C2×D6111yescharacteristic
243C4×Q16—1221no—
244C4×Q16—1221no—
245#436C2×D6111yescharacteristic
246#435—21no—
247C8×D4—21no—
248C8×D4C2×D6111yescharacteristic
249#433—21no—
250#432C2×D6111yescharacteristic
251C2×C4⋊C8—612no—
252#405—21no—
253C2×C4×C8C2×D6111yescharacteristic
254#335—611no—
255#335—611no—
256#335—612no—
257#332—612no—
258#332—612no—
259#332—612no—
260#332—612no—
261C61#1922311yescharacteristic, complemented, Sylow
262C2×Q16—1222no—
263C2×Q16—1221no—
264C2×Q16—1221no—
265C2×SD16—1222no—
266C2×M16—21no—
267C22×C8—21no—
268C22×C8—1222no—
269C22×C8C22⋊D6111yescharacteristic
270C22×C8C22⋊D6111yescharacteristic
271C4⋊Q8—612no—
272C4⋊Q8—612no—
273#126—21no—
274#125—1222no—
275#125D24411yescharacteristic
276#124D24411yescharacteristic
277#123—21no—
278C22⋊Q8—1222no—
279C22⋊Q8—1222no—
280C22⋊Q8D24411yescharacteristic
281#121D24411yescharacteristic
282C4×Q8—1222no—
283C4×Q8—1222no—
284C4×Q8C22×D6111yescharacteristic
285C4×D4—21no—
286C4×D4C22×D6111yescharacteristic
287#117—21no—
288#117—1222no—
289C2×C42C22×D6111yescharacteristic
290#107—1221no—
291#107—1221no—
292#107—1222no—
293#106—1222no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—612no—
297C4⋊C8—612no—
298C4⋊C8—1222no—
299C4⋊C8C22×D6111yescharacteristic
300C4⋊C8C22×D6111yescharacteristic
301#103—1222no—
302#103—1222no—
303#103—1222no—
304#103—1222no—
305#103—1222no—
306#102—1222no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310#97—21no—
311#97—21no—
312C4×C8—21no—
313C4×C8C22⋊D6111yescharacteristic
314C4×C8C22⋊D6111yescharacteristic
315C4×C8C22×D6111yescharacteristic
316C4×C8C22×D6111yescharacteristic
317C2×Q8—1222no—
318C2×Q8—1222no—
319C2×Q8C2×D24411yescharacteristic
320C2×D4—21no—
321C2×D4C2×D24411yescharacteristic
322C22×C4—21no—
323C22×C4C2×D24411yescharacteristic
324C22×C4#1175822211yescharacteristic
325C22×C4C2×C22⋊D6111yescharacteristic
326Q16—4882no—
327Q16—2442no—
328Q16—2442no—
329SD16—4882no—
330M16—42no—
331C2×C8—22no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—41no—
335C2×C8—42no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—4882no—
339C2×C8C2×C22⋊D6111yescharacteristic
340C2×C8C2×C22⋊D6111yescharacteristic
341C2×C8C2×C22⋊D6111yescharacteristic
342C2×C8C2×C22⋊D6111yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—1222no—
350C4⋊C4—1222no—
351C4⋊C4—2442no—
352C4⋊C4—2442no—
353C4⋊C4C2×D24411yescharacteristic
354C4⋊C4C2×D24411yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—2442no—
361C42—21no—
362C42—2442no—
363C42C2×D24411yescharacteristic
364C42#1175822211yescharacteristic
365C42C2×C22⋊D6111yescharacteristic
366C42C23×D6111yescharacteristic
367C23—21no—
368C23#1451975111yescharacteristic
369Q8—21no—
370Q8—21no—
371Q8—2442no—
372Q8—2442no—
373Q8—2442no—
374Q8—2442no—
375D4—21no—
376D4—21no—
377D4—42no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4#1451975111yescharacteristic
391C2×C4#1451975111yescharacteristic
392C2×C4#1451975111yescharacteristic
393C2×C4C22×C22⋊D6111yescharacteristic
394C2×C4C22×D24411yescharacteristic
395C2×C4C2×#1175822211yescharacteristic
396C8—21no—
397C8—21no—
398C8—21no—
399C8—41no—
400C8—41no—
401C8—2442no—
402C8—2442no—
403C8#1451979712yes—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22#1684003712yes—
410C22C2×#1451975111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—4882no—
419C4—4882no—
420C4C2×#1451979711yescharacteristic
421C4#1684056011yescharacteristic
422C4#1684056711yescharacteristic
423C4#1684057911yescharacteristic
424C2—22no—
425C2—81no—
426C2#2145527411yescharacteristic
427C2#2145548911yescharacteristic
428C2C2×#1684003711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2966C2
socleC22×C61C2×#121
prime radical#121×C61D4
hypercenter#2966D61
hypocenterC61#19223
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #21456405C2semidirect
3. #21445373C2semidirect
4. #21445366C2semidirect
5. #21445213C2semidirect
6. #21445208C2semidirect
7. #21445189C2semidirect
8. #21445184C2semidirect
9. C2×#16839515C2semidirect
10. #21444520C2semidirect
261. C61#19223semidirect

Maximal subgroups

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

subgroupindex
#214571562
#214564052
#214453732
#214453662
#214452132
#214452082
#214451892
#214451842
C2×#168395152
#214445202
C61×#29662
#1922361