Finite Group Databasebeta

← #29646075

Subgroups — #29646075

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840370C211yesmaximal, characteristic
2#21454902C211yesmaximal, characteristic, complemented
3#21454899C211yesmaximal, characteristic, complemented
4#21444187C214yesmaximal
5#21444173C214yesmaximal, complemented
6#21444143C211yesmaximal, characteristic, complemented
7#21444131C211yesmaximal, characteristic
8#21444131C211yesmaximal, characteristic
9C61×#1461C211yesmaximal, characteristic, complemented
10#16840370—22no—
11#16840370—22no—
12#16840370—22no—
13#16840370—22no—
14C2×#14519775C411yescharacteristic
15C2×#14519772C2212yes—
16C2×#14519771C412yes—
17C2×#14519769C412yes—
18C2×#14519768C411yescharacteristic
19C2×#14519767C2212yes—
20C2×#14519757C411yescharacteristic
21C2×#14519753C411yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519734C2211yescharacteristic
24#16839892—22no—
25#16839889—22no—
26C8×Dic122—22no—
27#16839886—22no—
28#16839816C2214yes—
29#16839815C2211yescharacteristic
30#16839815C2211yescharacteristic
31#16839812C2214yes—
32#16839488C2214yes—
33#16839487C2212yes—
34#16839487C2212yes—
35#16839485C2212yes—
36#16839485C2212yes—
37C2×C4×Q8×C61C2211yescharacteristic
38C61×#431C2211yescharacteristic
39C61×#431C2211yescharacteristic
40C61×#324C2214yes—
41C22×Dic122C2×C411yescharacteristic
42C22×C4×D61C2×C411yescharacteristic
43#14519775—22no—
44#14519775—22no—
45#14519772—24no—
46#14519772—24no—
47#14519771—24no—
48#14519771—24no—
49#14519769—24no—
50#14519769—24no—
51#14519768—22no—
52#14519768—22no—
53#14519767—24no—
54#14519767—24no—
55#14519757—22no—
56#14519757—22no—
57#14519753—22no—
58#14519753—22no—
59C4×Dic122D412yes—
60C4×Dic122D412yes—
61C4×Dic122D412yes—
62C4×Dic122D412yes—
63#14519734—21no—
64#14519734—21no—
65#14519734—21no—
66#14519734—21no—
67C2×C4⋊Dic61C2×C412yes—
68C2×C4⋊Dic61C2×C412yes—
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2×C412yes—
72C2×#11758196C2×C412yes—
73C2×#11758196C2×C412yes—
74C2×#11758196C2×C412yes—
75C2×#11758196C2×C412yes—
76C2×#11758196C2311yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2×C412yes—
79C2×#11758198C2×C412yes—
80C2×#11758198C2311yescharacteristic
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2312yes—
83C4⋊#92418—21no—
84C4⋊#92418—21no—
85#14519706—24no—
86#14519706—24no—
87C22⋊#92418C2312yes—
88C22⋊#92418C2312yes—
89#14519687—24no—
90C4×#92418—21no—
91C4×#92418—21no—
92C8×Dic61—24no—
93C22×Q8×C61C2×C411yescharacteristic
94C4×Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×Q8×C61—21no—
98C2×C4⋊C4×C61C2×C411yescharacteristic
99C2×C4⋊C4×C61C2312yes—
100C2×C42×C61C2×C412yes—
101C2×C42×C61C2311yescharacteristic
102C4⋊C8×C61—21no—
103C4⋊C8×C61—21no—
104C22⋊C8×C61C2312yes—
105C22⋊C8×C61C2312yes—
106C4×C8×C61—21no—
107C4×C8×C61—21no—
108C23×D61C22×C411yescharacteristic
109C2×Q8×C61—21no—
110C2×Q8×C61—21no—
111C2×Q8×C61—22no—
112C2×Q8×C61—22no—
113C22×C4×C61C22×C412yes—
114C22×C4×C61C22×C412yes—
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C2411yescharacteristic
118C22×Dic61C22×C411yescharacteristic
119C22×Dic61C22×C412yes—
120C22×Dic61C22×C411yescharacteristic
121C22×Dic61C22×C411yescharacteristic
122C22×Dic61C22×C412yes—
123C2×C4×D61—21no—
124C2×C4×D61—21no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×Dic122—22no—
128C2×Dic122—22no—
129C2×Dic122C22⋊C412yes—
130C2×Dic122C22⋊C412yes—
131C2×C8×C61—22no—
132C2×C8×C61—22no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C42×C61—22no—
138C42×C61—22no—
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143#11758198—21no—
144#11758198—21no—
145#11758198—21no—
146#11758198—21no—
147#11758198—24no—
148#11758198—24no—
149C4⋊Dic61—24no—
150C4⋊Dic61—24no—
151C4⋊Dic61C22⋊C412yes—
152C4⋊Dic61C22⋊C412yes—
153#11758196—21no—
154#11758196—21no—
155#11758196—21no—
156#11758196—21no—
157#11758196—24no—
158#11758196—24no—
159#11758196—24no—
160#11758196—24no—
161#11758196C22⋊C414yes—
162#11758196C22⋊C414yes—
163C4×Dic61—21no—
164C4×Dic61—21no—
165C4×Dic61C2×D414yes—
166C4×Dic61C2×D414yes—
167C2×#92418—22no—
168C2×#92418—22no—
169C23×C61C23×C411yescharacteristic
170C22×D61—21no—
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—41no—
174C22×D61—41no—
175Q8×C61—42no—
176Q8×C61—42no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—42no—
184C2×C4×C61C2×C22⋊C411yescharacteristic
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61C2×C22⋊C411yescharacteristic
188C2×C4×C61#13112yes—
189C2×C4×C61#13112yes—
190C2×C4×C61C22×D411yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—42no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61C2×C22⋊C414yes—
203C2×Dic61C2×C22⋊C414yes—
204C4×D61—42no—
205C4×D61—42no—
206Dic122—24no—
207Dic122—24no—
208C8×C61—42no—
209C8×C61—42no—
210#92418—42no—
211#92418—42no—
212#17391—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61C22×C22⋊C411yescharacteristic
216C22×C61C2×#13111yescharacteristic
217C22×C61C2×#13111yescharacteristic
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—42no—
228C4×C61—42no—
229C4×C61#40812yes—
230C4×C61#40812yes—
231Dic61—24no—
232Dic61—24no—
233Dic61—41no—
234Dic61—41no—
235Dic61—41no—
236C2×#541—611no—
237#2983—611no—
238#2982—611no—
239#1473—614no—
240#1470—614no—
241#1461—611no—
242#1461D6111yescharacteristic, complemented
243#1458—611no—
244#1458—611no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61C2×#40811yescharacteristic
248C2×C61#288411yescharacteristic
249C2×C61#288911yescharacteristic
250D61—81no—
251#541—1222no—
252#541—1222no—
253#541—1222no—
254#541—1222no—
255C2×C4⋊Q8—611no—
256C2×#126—612no—
257C2×#126—612no—
258C2×#125—611no—
259C2×#125—612no—
260C2×#125—612no—
261C2×C22⋊Q8—611no—
262C2×C22⋊Q8—611no—
263C2×C4×Q8—611no—
264C2×C4×Q8C2×D6111yescharacteristic
265C2×#117—611no—
266#446—1222no—
267#446—1222no—
268C8×Q8—1222no—
269C8×Q8—1222no—
270#432—614no—
271#431—611no—
272#431—611no—
273#431—614no—
274#431C2×D6111yescharacteristic
275#431C2×D6111yescharacteristic
276#324—614no—
277#324—612no—
278#324—612no—
279#324C2×D6114yes—
280#323—612no—
281#323—612no—
282C61#1739111yescharacteristic, complemented, Sylow
283C22×Q8—611no—
284C22×Q8C4×D6111yescharacteristic
285C23×C4—611no—
286C4⋊Q8—1222no—
287C4⋊Q8—1222no—
288#126—1224no—
289#126—1224no—
290#126—1224no—
291#126—1224no—
292#125—1224no—
293#125—1224no—
294#125—1224no—
295#125—1224no—
296#125—1222no—
297#125—1222no—
298C22⋊Q8—1222no—
299C22⋊Q8—1222no—
300C22⋊Q8—1222no—
301C22⋊Q8—1222no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—612no—
307C4×Q8—612no—
308C4×Q8—612no—
309C4×Q8—612no—
310#117—1221no—
311#117—1221no—
312#117—1221no—
313#117—1221no—
314C2×C4⋊C4—611no—
315C2×C4⋊C4—612no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—612no—
318C2×C4⋊C4—612no—
319C2×C4⋊C4—612no—
320C2×C4⋊C4—612no—
321C2×C4⋊C4—612no—
322C2×C4⋊C4—612no—
323C2×C4⋊C4—611no—
324C2×C4⋊C4C4×D6111yescharacteristic
325C2×C4⋊C4C22×D6112yes—
326C2×C22⋊C4—611no—
327C2×C22⋊C4—612no—
328C2×C22⋊C4—612no—
329C2×C22⋊C4—611no—
330C2×C42—612no—
331C2×C42—611no—
332C2×C42C4×D6112yes—
333C2×C42C22×D6111yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—1224no—
337C4⋊C8—1224no—
338C4⋊C8—1221no—
339C4⋊C8—1221no—
340C22⋊C8—612no—
341C22⋊C8—612no—
342C22⋊C8C22×D6112yes—
343C22⋊C8C22×D6112yes—
344#97—1224no—
345C4×C8—21no—
346C4×C8—21no—
347C4×C8—1224no—
348C4×C8—1221no—
349C4×C8—1221no—
350C24—611no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—612no—
356C2×Q8—612no—
357C2×Q8—1222no—
358C2×Q8—1222no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4C2×C4×D6112yes—
369C22×C4C2×C4×D6112yes—
370C22×C4C2×C4×D6111yescharacteristic
371C22×C4C2×C4×D6111yescharacteristic
372C22×C4C23×D6111yescharacteristic
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—1222no—
376C2×C8—1222no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—614no—
382C4⋊C4—614no—
383C4⋊C4—612no—
384C4⋊C4—612no—
385C4⋊C4—1224no—
386C4⋊C4—1224no—
387C4⋊C4—1224no—
388C4⋊C4—1224no—
389C4⋊C4—1224no—
390C4⋊C4—1224no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—1221no—
394C4⋊C4—1221no—
395C22⋊C4—1224no—
396C22⋊C4—1224no—
397C22⋊C4—1221no—
398C22⋊C4—1221no—
399C22⋊C4—1221no—
400C22⋊C4—1221no—
401C42—22no—
402C42—22no—
403C42—614no—
404C42—614no—
405C42—1221no—
406C42—1221no—
407C42D4×D6111yescharacteristic
408C42D4×D6111yescharacteristic
409C42D4×D6111yescharacteristic
410C42D4×D6111yescharacteristic
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—2441no—
415C23—2441no—
416C23C22×C4×D6111yescharacteristic
417Q8—42no—
418Q8—42no—
419Q8—1224no—
420Q8—1224no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—614no—
429C2×C4—614no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4C22⋊C4×D6111yescharacteristic
443C2×C4C22⋊C4×D6111yescharacteristic
444C2×C4C22⋊C4×D6111yescharacteristic
445C2×C4C22⋊C4×D6111yescharacteristic
446C2×C4#1451978312yes—
447C2×C4#1451978512yes—
448C2×C4C2×D4×D6111yescharacteristic
449C2×C4C2×D4×D6111yescharacteristic
450C8—42no—
451C8—42no—
452C8—2442no—
453C8—2442no—
454C22—21no—
455C22—21no—
456C22—4881no—
457C22—4881no—
458C22—2441no—
459C22—2441no—
460C22—2441no—
461C22C2×C22⋊C4×D6111yescharacteristic
462C22C2×#1451978311yescharacteristic
463C22C2×#1451978511yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—42no—
470C4—1224no—
471C4—1224no—
472C4—2441no—
473C4—2441no—
474C4—2441no—
475C4#1683972712yes—
476C4#1683972712yes—
477C2—21no—
478C2—21no—
479C2—4881no—
480C2C2×#1683972711yescharacteristic
481C2#2145428111yescharacteristic
482C2#2145429911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1461C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1461D61
hypocenterC61#17391
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #21454902C2semidirect
3. #21454899C2semidirect
5. #21444173C2semidirect
6. #21444143C2semidirect
9. C61×#1461C2semidirect
242. #1461D61semidirect
282. C61#17391semidirect

Maximal subgroups

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

subgroupindex
C2×#168403702
#214549022
#214548992
#214441872
#214441732
#214441432
#214441312
C61×#14612
#1739161