Finite Group Databasebeta

← #30544404

Subgroups — #30544404

Order 15616.

1810 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic
2#21454759C211yesmaximal, characteristic, complemented
3#21454757C212yesmaximal, complemented
4#21454755C218yesmaximal, complemented
5#21454754C211yesmaximal, characteristic, complemented
6#21454752C212yesmaximal, complemented
7#21454750C218yesmaximal, complemented
8#21454749C211yesmaximal, characteristic, complemented
9#21454381C211yesmaximal, characteristic
10#21454380C212yesmaximal
11C2×#16839719C211yesmaximal, characteristic
12#405×D61C212yesmaximal
13C61×#2961C211yesmaximal, characteristic, complemented
14C22×#11758189C2211yescharacteristic
15C2×M16×D61C2212yes—
16C22×C8×D61C2211yescharacteristic
17#16840392C414yes—
18#16840391C414yes—
19#16840389C414yes—
20#16840387C414yes—
21#16840319C2211yescharacteristic
22#16840316C2218yes—
23#16840315C2212yes—
24C2×#14519734C2211yescharacteristic
25#117×D61C2212yes—
26#16839893C2214yescomplemented
27#16839892C2218yescomplemented
28#16839891C2218yescomplemented
29#16839890C2218yescomplemented
30#16839890C2218yescomplemented
31#16839889C2214yescomplemented
32Q8×#92418C2214yescomplemented
33#16839886C2214yescomplemented
34#16839886C2218yescomplemented
35#16839790C2212yes—
36#16839789C2212yes—
37#16839788C2212yes—
38#16839787C2218yes—
39#16839787C2218yes—
40#16839786C2211yescharacteristic
41#16839785C2212yes—
42#16839784C2218yes—
43#16839720C2212yes—
44#16839719C2214yes—
45#16839719C2214yes—
46#16839719C2214yes—
47#16839718C2212yes—
48#16839717C2212yes—
49#16839716C2214yes—
50C2×#14519687C2211yescharacteristic
51#97×D61C2214yes—
52C2×C4×#92418C2211yescharacteristic
53C2×C8×Dic61C2211yescharacteristic
54C4×C8×D61C2214yes—
55C61×#533C2211yescharacteristic
56C61×#446C2218yescomplemented
57C61×#424C2212yes—
58C61×#423C2211yescharacteristic
59C61×#405C2212yes—
60C2×#97×C61C2211yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C2×#11758194C2312yes—
63C2×#11758189—24no—
64C2×#11758189C2314yes—
65C2×#11758189C2314yes—
66M16×D61—28no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C2×C8×D61Q818yescomplemented
70C2×C8×D61C2314yes—
71C2×C8×D61C2312yes—
72C2×C8×D61C2312yes—
73#14519777C2×C412yes—
74#14519776C2×C414yes—
75#14519776C2×C418yes—
76#14519775C2×C418yes—
77#14519769C2×C412yes—
78#14519768C2×C414yes—
79#14519767C2×C418yes—
80#14519767C2×C418yes—
81#14519757C2×C418yes—
82#14519756C2×C414yes—
83#14519755C2×C418yes—
84#14519755C2×C418yes—
85#14519754C2×C418yes—
86#14519753C2×C418yes—
87C4×Dic122C2318yes—
88C4×Dic122C2314yes—
89#14519736C2312yes—
90#14519735C2×C414yes—
91#14519734C2×C412yes—
92#14519734C2×C412yes—
93#14519734C2314yes—
94#14519734C2314yes—
95#14519733C2×C414yes—
96C2×#11758196C2×C412yes—
97C4⋊C4×D61C2×C414yes—
98C2×#11758198C2×C412yes—
99C22⋊C4×D61C2×C414yes—
100C2×C4×Dic61C2311yescharacteristic
101C42×D61C2314yes—
102C4⋊#92418C2318yes—
103C4⋊#92418C2314yes—
104#14519706C2318yes—
105#14519706C2318yes—
106#14519706C2318yes—
107#14519688C2314yes—
108#14519687C2314yes—
109#14519687C2314yes—
110#14519687C2314yes—
111C4×#92418C2314yes—
112C4×#92418C2312yes—
113C4×#92418C2312yes—
114C8×Dic61C2314yes—
115C8×Dic61C2314yes—
116C8×Dic61C2312yes—
117C8×Dic61C2312yes—
118C2×M16×C61C2312yes—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C4⋊Q8×C61C2×C412yes—
122#125×C61C2×C412yes—
123C22⋊Q8×C61C2×C414yes—
124C4×Q8×C61C2314yes—
125#117×C61C2312yes—
126C2×C42×C61C2311yescharacteristic
127C4⋊C8×C61C2318yes—
128C4⋊C8×C61C2314yes—
129#97×C61C2314yes—
130#97×C61C2314yes—
131C4×C8×C61C2314yes—
132C23×D61C22×C411yescharacteristic
133C2×Q8×C61C22×C414yes—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C2411yescharacteristic
136C22×Dic61C22×C412yes—
137C22×Dic61C22×C411yescharacteristic
138C2×C4×D61C22×C418yes—
139C2×C4×D61C22×C412yes—
140C2×C4×D61C2×Q814yes—
141C2×C4×D61#4114yes—
142C2×C4×D61C2412yes—
143C2×Dic122C22×C418yes—
144C2×Dic122C22×C414yes—
145M16×C61—24no—
146C2×C8×C61—22no—
147C2×C8×C61C2×Q814yes—
148C2×C8×C61C2414yes—
149C2×C8×C61C2412yes—
150C2×C8×C61C2412yes—
151C4⋊C4×C61C22×C414yes—
152C4⋊C4×C61C22×C418yes—
153C4⋊C4×C61C22×C414yes—
154C22⋊C4×C61C22×C414yes—
155C42×C61C22×C411yescharacteristic
156C42×C61C22×C411yescharacteristic
157C42×C61C2414yes—
158C42×C61C2412yes—
159C22⋊Dic61C22×C414yes—
160#11758198C22×C418yes—
161#11758198C22×C414yes—
162#11758198C22×C414yes—
163C4⋊Dic61C22×C414yes—
164C4⋊Dic61C22×C418yes—
165C4⋊Dic61C22×C414yes—
166#11758196C22×C418yes—
167#11758196C22×C414yes—
168#11758196C22×C414yes—
169#11758196C22×C418yes—
170#11758196C22×C418yes—
171#11758196C22×C418yes—
172C4×Dic61C22×C418yes—
173C4×Dic61C22×C412yes—
174C4×Dic61C2414yes—
175C4×Dic61C2412yes—
176#11758194—24no—
177C2×#92418—22no—
178C2×#92418C2×Q814yes—
179C2×#92418C2414yes—
180C2×#92418C2412yes—
181C2×#92418C2411yescharacteristic
182C2×#92418C2411yescharacteristic
183#11758189—28no—
184#11758189—28no—
185C8×D61—28no—
186C8×D61C2×Q818yes—
187C8×D61C2×Q818yes—
188C23×C61C23×C411yescharacteristic
189C22×D61—42no—
190C22×D61C4×Q814yes—
191C22×D61C23×C412yes—
192Q8×C61—44no—
193C2×C4×C61—42no—
194C2×C4×C61C23×C418yes—
195C2×C4×C61C23×C412yes—
196C2×C4×C61C23×C412yes—
197C2×C4×C61C23×C411yescharacteristic
198C2×C4×C61C22×Q812yes—
199C2×C4×C61C2×#4112yes—
200C2×C4×C61C2511yescharacteristic
201C2×Dic61—42no—
202C2×Dic61C4×Q814yes—
203C2×Dic61C23×C414yes—
204C2×Dic61C23×C418yes—
205C2×Dic61C23×C412yes—
206C4×D61—48no—
207C4×D61C4×Q818yes—
208C4×D61C22×Q814yes—
209C4×D61C2×#4114yes—
210Dic122—44no—
211Dic122—48no—
212C8×C61—24no—
213C8×C61—22no—
214C8×C61C22×Q814yes—
215#92418—24no—
216#92418—22no—
217#92418C22×Q812yes—
218#92418C22×Q812yes—
219#60191—611nomaximal, Sylow
220C22×C61—22no—
221C22×C61C2×C4×Q812yes—
222C22×C61C24×C411yescharacteristic
223C2×D61—24no—
224C2×D61—44no—
225C2×D61C2×C4×Q814yes—
226C4×C61—22no—
227C4×C61—28no—
228C4×C61—22no—
229C4×C61C2×C4×Q812yes—
230C4×C61C23×Q811yescharacteristic
231C4×C61C22×#4111yescharacteristic
232Dic61—28no—
233Dic61—24no—
234Dic61C2×C4×Q814yes—
235#3458—611no—
236#2961—618no—
237#2961—612no—
238#2961—611no—
239#2961D6111yescharacteristic, complemented
240#2960—618no—
241#2960—612no—
242#2960—611no—
243#2960—611no—
244#2905—612no—
245#2905—611no—
246C2×#405—612no—
247C2×#405—611no—
248C2×C61—22no—
249C2×C61C22×C4×Q811yescharacteristic
250C2×C61#357312yes—
251D61—24no—
252C22×M16—612no—
253C22×M16—611no—
254C23×C8—611no—
255#544—614no—
256#544—614no—
257#544—614no—
258#543—614no—
259#533—618no—
260#533—612no—
261#533—611no—
262#533C2×D6111yescharacteristic
263C2×#117—612no—
264C2×#117—611no—
265#446—614no—
266#446—614no—
267#446—618no—
268#446—618no—
269#446—618no—
270#446—618no—
271#446C2×D6118yescomplemented
272C8×Q8—614no—
273C8×Q8—618no—
274C8×Q8—614no—
275#424—612no—
276#424—612no—
277#424—612no—
278#424—618no—
279#424—618no—
280#424C2×D6112yes—
281#423—612no—
282#423—611no—
283#423—618no—
284#423C2×D6111yescharacteristic
285#405—612no—
286#405—612no—
287#405—612no—
288#405—614no—
289#405—614no—
290#405—614no—
291#405—614no—
292#405C2×D6112yes—
293C2×#97—611no—
294C2×#97—614no—
295C2×#97C2×D6111yescharacteristic
296C2×C4×C8—611no—
297C2×C4×C8—611no—
298C2×C4×C8—614no—
299C61#6019111yescharacteristic, complemented, Sylow
300C23×C4—611no—
301C2×M16—612no—
302C2×M16—614no—
303C2×M16—614no—
304C2×M16—1224no—
305C2×M16—1228no—
306C2×M16C22×D6112yes—
307C22×C8—611no—
308C22×C8—618no—
309C22×C8—612no—
310C22×C8—612no—
311C22×C8—611no—
312C22×C8—614no—
313C22×C8C22×D6111yescharacteristic
314C22×C8C22×D6111yescharacteristic
315C4⋊Q8—618no—
316C4⋊Q8—618no—
317C4⋊Q8—614no—
318C4⋊Q8—612no—
319C4⋊Q8C4×D6112yes—
320#125—618no—
321#125—618no—
322#125—614no—
323#125—612no—
324#125C4×D6112yes—
325C22⋊Q8—618no—
326C22⋊Q8—614no—
327C22⋊Q8—618no—
328C22⋊Q8—618no—
329C22⋊Q8—618no—
330C22⋊Q8—618no—
331C22⋊Q8C4×D6114yes—
332C4×Q8—614no—
333C4×Q8—618no—
334C4×Q8C22×D6114yes—
335#117—612no—
336#117—614no—
337#117—614no—
338#117—612no—
339#117—612no—
340#117—614no—
341#117—614no—
342#117C22×D6112yes—
343C2×C4⋊C4—612no—
344C2×C4⋊C4—614no—
345C2×C22⋊C4—612no—
346C2×C22⋊C4—614no—
347C2×C42—611no—
348C2×C42—614no—
349C2×C42C22×D6111yescharacteristic
350C4⋊C8—618no—
351C4⋊C8—618no—
352C4⋊C8—618no—
353C4⋊C8—614no—
354C4⋊C8—618no—
355C4⋊C8C22×D6118yes—
356C4⋊C8C22×D6114yes—
357#97—614no—
358#97—614no—
359#97—614no—
360#97—614no—
361#97C22×D6114yes—
362#97C22×D6114yes—
363C4×C8—612no—
364C4×C8—614no—
365C4×C8—612no—
366C4×C8—614no—
367C4×C8—612no—
368C4×C8—614no—
369C4×C8—612no—
370C4×C8C22×D6114yes—
371C24—611no—
372C2×Q8—618no—
373C2×Q8—614no—
374C2×Q8C2×C4×D6114yes—
375C22×C4—611no—
376C22×C4—612no—
377C22×C4—614no—
378C22×C4—614no—
379C22×C4—612no—
380C22×C4—612no—
381C22×C4—618no—
382C22×C4C2×C4×D6112yes—
383C22×C4C23×D6111yescharacteristic
384M16—24no—
385M16—1228no—
386M16—1228no—
387M16—1224no—
388C2×C8—22no—
389C2×C8—614no—
390C2×C8—611no—
391C2×C8—611no—
392C2×C8—618no—
393C2×C8—618no—
394C2×C8—614no—
395C2×C8—612no—
396C2×C8—1228no—
397C2×C8—1222no—
398C2×C8Q8×D6114yes—
399C2×C8C23×D6112yes—
400C2×C8C23×D6114yes—
401C2×C8C23×D6112yes—
402C4⋊C4—618no—
403C4⋊C4—614no—
404C4⋊C4—614no—
405C4⋊C4—614no—
406C4⋊C4—618no—
407C4⋊C4—618no—
408C4⋊C4—618no—
409C4⋊C4—618no—
410C4⋊C4—614no—
411C4⋊C4C2×C4×D6114yes—
412C4⋊C4C2×C4×D6114yes—
413C4⋊C4C2×C4×D6118yes—
414C22⋊C4—614no—
415C22⋊C4—618no—
416C22⋊C4—614no—
417C22⋊C4—614no—
418C22⋊C4C2×C4×D6114yes—
419C42—618no—
420C42—612no—
421C42—612no—
422C42—614no—
423C42C2×C4×D6111yescharacteristic
424C42C2×C4×D6111yescharacteristic
425C42C23×D6112yes—
426C42C23×D6114yes—
427C23—612no—
428C23—614no—
429C23—2442no—
430C23C22×C4×D6111yescharacteristic
431Q8—44no—
432Q8—2444no—
433Q8—2448no—
434C2×C4—42no—
435C2×C4—614no—
436C2×C4—612no—
437C2×C4—618no—
438C2×C4—614no—
439C2×C4—614no—
440C2×C4—614no—
441C2×C4—618no—
442C2×C4—2448no—
443C2×C4—2442no—
444C2×C4C22×C4×D6118yes—
445C2×C4C22×C4×D6112yes—
446C2×C4C22×C4×D6112yes—
447C2×C4C22×C4×D6111yescharacteristic
448C2×C4C2×Q8×D6112yes—
449C2×C4#41×D6112yes—
450C2×C4C24×D6111yescharacteristic
451C8—22no—
452C8—24no—
453C8—612no—
454C8—612no—
455C8—1224no—
456C8—1222no—
457C8C2×Q8×D6114yes—
458C22—22no—
459C22—614no—
460C22—1224no—
461C22—2444no—
462C22C4×Q8×D6112yes—
463C22C23×C4×D6111yescharacteristic
464C4—22no—
465C4—22no—
466C4—28no—
467C4—614no—
468C4—1228no—
469C4—1224no—
470C4C4×Q8×D6112yes—
471C4C22×Q8×D6111yescharacteristic
472C4C2×#41×D6111yescharacteristic
473C2—22no—
474C2—1224no—
475C2C2×C4×Q8×D6111yescharacteristic
476C2#2146053212yes—
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2961C2
prime radicalC23×D61C22×C4
cosocleC2×C4×C61C25
hypercenter#2961D61
hypocenterC61#60191
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #21454759C2semidirect
3. #21454757C2semidirect
4. #21454755C2semidirect
5. #21454754C2semidirect
6. #21454752C2semidirect
7. #21454750C2semidirect
8. #21454749C2semidirect
13. C61×#2961C2semidirect
26. #16839893C22semidirect
27. #16839892C22semidirect
28. #16839891C22semidirect
29. #16839890C22semidirect
30. #16839890C22semidirect
31. #16839889C22semidirect
32. Q8×#92418C22semidirect
33. #16839886C22semidirect
34. #16839886C22semidirect
56. C61×#446C22semidirect
69. C2×C8×D61Q8semidirect
239. #2961D61semidirect
271. #446C2×D61semidirect
299. C61#60191semidirect

Maximal subgroups

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

subgroupindex
#214592222
#214547592
#214547572
#214547552
#214547542
#214547522
#214547502
#214547492
#214543812
#214543802
C2×#168397192
#405×D612
C61×#29612
#6019161