Finite Group Databasebeta

← #29571449

Subgroups — #29571449

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840370C211yesmaximal, characteristic
2#21444215C211yesmaximal, characteristic, complemented
3#21444214C211yesmaximal, characteristic, complemented
4#21444213C211yesmaximal, characteristic, complemented
5#21444131C211yesmaximal, characteristic
6#21444131C211yesmaximal, characteristic
7C61×#1479C211yesmaximal, characteristic, complemented
8#16840370—22no—
9#16840370—22no—
10#16840370—22no—
11#16840370—22no—
12C2×#14519775C411yescharacteristic
13C2×#14519772—21no—
14C2×#14519771—21no—
15C2×#14519769—21no—
16C2×#14519768C411yescharacteristic
17C2×#14519767—21no—
18C2×#14519757C411yescharacteristic
19C2×#14519753C411yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22#16839815C2211yescharacteristic
23#16839815C2211yescharacteristic
24#16839494—22no—
25Q8⋊#92418—22no—
26#16839492—22no—
27#16839487—21no—
28#16839487—21no—
29#16839485—21no—
30#16839485—21no—
31C2×C4×Q8×C61C2211yescharacteristic
32C61×#431C2211yescharacteristic
33C61×#431C2211yescharacteristic
34C61×Q8⋊C8—22no—
35C22×Dic122C2×C411yescharacteristic
36C22×C4×D61C2×C411yescharacteristic
37#14519775—22no—
38#14519775—22no—
39#14519772—24no—
40#14519772—24no—
41#14519771—24no—
42#14519771—24no—
43#14519769—24no—
44#14519769—24no—
45#14519768—22no—
46#14519768—22no—
47#14519767—24no—
48#14519767—24no—
49#14519757—22no—
50#14519757—22no—
51#14519753—22no—
52#14519753—22no—
53C4×Dic122—21no—
54C4×Dic122—21no—
55C4×Dic122D412yes—
56C4×Dic122D412yes—
57#14519734—21no—
58#14519734—21no—
59#14519734—21no—
60#14519734—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×#11758196—21no—
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758196D411yescharacteristic
70C2×#11758196D411yescharacteristic
71C2×#11758198—21no—
72C2×#11758198—21no—
73C2×#11758198D411yescharacteristic
74C2×#11758198D411yescharacteristic
75C2×C4×Dic61—21no—
76C2×C4×Dic61C2×C411yescharacteristic
77C4⋊#92418—21no—
78C4⋊#92418—21no—
79C22⋊#92418—21no—
80C22⋊#92418—21no—
81C4×#92418—21no—
82C4×#92418—21no—
83C22×Q8×C61C2×C411yescharacteristic
84C4×Q8×C61—21no—
85C4×Q8×C61—21no—
86C4×Q8×C61D412yes—
87C4×Q8×C61D412yes—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61C2×C411yescharacteristic
90C2×C42×C61—21no—
91C2×C42×C61C2311yescharacteristic
92C4⋊C8×C61—21no—
93C4⋊C8×C61—21no—
94C22⋊C8×C61—21no—
95C22⋊C8×C61—21no—
96C4×C8×C61—21no—
97C4×C8×C61—21no—
98C23×D61C22⋊C411yescharacteristic
99C2×Q8×C61—21no—
100C2×Q8×C61—22no—
101C2×Q8×C61—22no—
102C2×Q8×C61C22⋊C412yes—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C22⋊C411yescharacteristic
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×Dic122—22no—
118C2×Dic122—22no—
119C2×Dic122—21no—
120C2×Dic122C22⋊C412yes—
121C2×C8×C61—41no—
122C2×C8×C61—41no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61C22⋊C412yes—
127C42×C61—22no—
128C42×C61—22no—
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133#11758198—24no—
134#11758198—24no—
135#11758198—21no—
136#11758198—21no—
137#11758198—21no—
138#11758198—21no—
139C4⋊Dic61—24no—
140C4⋊Dic61—24no—
141C4⋊Dic61—21no—
142C4⋊Dic61C22⋊C412yes—
143#11758196—24no—
144#11758196—24no—
145#11758196—24no—
146#11758196—24no—
147#11758196—22no—
148#11758196—22no—
149#11758196—21no—
150#11758196—21no—
151#11758196—21no—
152#11758196—21no—
153C4×Dic61—21no—
154C4×Dic61—21no—
155C4×Dic61—22no—
156C4×Dic61—22no—
157C2×#92418—41no—
158C2×#92418—41no—
159C23×C61C2×C22⋊C411yescharacteristic
160C22×D61—21no—
161C22×D61—22no—
162C22×D61—41no—
163C22×D61—41no—
164Q8×C61—22no—
165Q8×C61—22no—
166Q8×C61—42no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#13112yes—
180C2×C4×C61#13112yes—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—22no—
184C2×Dic61—22no—
185C2×Dic61—21no—
186C2×Dic61—22no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C4×D61—42no—
192C4×D61—41no—
193C4×D61—41no—
194Dic122—24no—
195Dic122—41no—
196Dic122—41no—
197C8×C61—81no—
198C8×C61—81no—
199#92418—81no—
200#92418—81no—
201#8327—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61#37911yescharacteristic
205C22×C61#40812yes—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—82no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—42no—
215C4×C61—42no—
216C4×C61#40812yes—
217C4×C61#40811yescharacteristic
218C4×C61#40811yescharacteristic
219Dic61—41no—
220Dic61—41no—
221Dic61—42no—
222Dic61—42no—
223Dic61—41no—
224C2×#541—611no—
225#1479—611no—
226#1479—611no—
227#1479—611no—
228#1479D6111yescharacteristic, complemented
229#1458—611no—
230#1458—611no—
231C2×C61—22no—
232C2×C61#178011yescharacteristic
233C2×C61#179611yescharacteristic
234C2×C61#179611yescharacteristic
235D61—81no—
236#541—1222no—
237#541—1222no—
238#541—1222no—
239#541—1222no—
240C2×C4⋊Q8—611no—
241C2×#126—1221no—
242C2×#126—1221no—
243C2×#125—611no—
244C2×#125—1221no—
245C2×#125—1221no—
246C2×C22⋊Q8—611no—
247C2×C22⋊Q8—611no—
248C2×C4×Q8—611no—
249C2×C4×Q8C2×D6111yescharacteristic
250C2×#117—611no—
251#431—611no—
252#431—611no—
253#431C2×D6111yescharacteristic
254#431C2×D6111yescharacteristic
255Q8⋊C8—22no—
256Q8⋊C8—1222no—
257Q8⋊C8—1222no—
258Q8⋊C8—1222no—
259#324—1221no—
260#324—1221no—
261#323—1221no—
262#323—1221no—
263C61#832711yescharacteristic, complemented, Sylow
264C22×Q8—611no—
265C22×Q8C4×D6111yescharacteristic
266C23×C4—611no—
267C4⋊Q8—1222no—
268C4⋊Q8—1222no—
269#126—1224no—
270#126—1224no—
271#126—1224no—
272#126—1224no—
273#125—1224no—
274#125—1224no—
275#125—1222no—
276#125—1224no—
277#125—1224no—
278#125—1222no—
279C22⋊Q8—1222no—
280C22⋊Q8—1222no—
281C22⋊Q8—1222no—
282C22⋊Q8—1222no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—612no—
286C4×Q8—612no—
287C4×Q8—1221no—
288C4×Q8—1221no—
289C4×Q8D24412yes—
290C4×Q8C22⋊D6112yes—
291#117—1221no—
292#117—1221no—
293#117—1221no—
294#117—1221no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—611no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4C4×D6111yescharacteristic
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C42—21no—
312C2×C42—611no—
313C2×C42—1221no—
314C2×C42C22×D6111yescharacteristic
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8—1221no—
318C4⋊C8—1221no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—1221no—
322C22⋊C8—1221no—
323C4×C8—21no—
324C4×C8—21no—
325C4×C8—1221no—
326C4×C8—1221no—
327C24—611no—
328C2×Q8—21no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—612no—
332C2×Q8—1221no—
333C2×Q8—1222no—
334C2×Q8—1222no—
335C2×Q8#1175819812yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4—1221no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4C2×C4×D6111yescharacteristic
348C22×C4D4×D6111yescharacteristic
349C22×C4D4×D6111yescharacteristic
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—2441no—
353C2×C8—2441no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—612no—
358C4⋊C4—1224no—
359C4⋊C4—1224no—
360C4⋊C4—1224no—
361C4⋊C4—1224no—
362C4⋊C4—1224no—
363C4⋊C4—1224no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1222no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C4⋊C4—1222no—
371C4⋊C4#1175819812yes—
372C22⋊C4—1224no—
373C22⋊C4—1224no—
374C22⋊C4—1221no—
375C22⋊C4—1221no—
376C22⋊C4—1221no—
377C22⋊C4—1221no—
378C42—22no—
379C42—22no—
380C42—1221no—
381C42—1221no—
382C42—1222no—
383C42—1222no—
384C42C2×D24411yescharacteristic
385C42D4×D6111yescharacteristic
386C42D4×D6111yescharacteristic
387C42C2×C22⋊D6111yescharacteristic
388C23—1222no—
389C23—1221no—
390C23—2441no—
391C23—2441no—
392C23C22⋊C4×D6111yescharacteristic
393Q8—22no—
394Q8—22no—
395Q8—42no—
396Q8—1224no—
397Q8—2441no—
398Q8—2441no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—1222no—
406C2×C4—1222no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1222no—
410C2×C4—1221no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4C22⋊C4×D6111yescharacteristic
419C2×C4C2×#1175819811yescharacteristic
420C2×C4#1451974511yescharacteristic
421C2×C4#1451974511yescharacteristic
422C2×C4#1451974711yescharacteristic
423C2×C4#1451974711yescharacteristic
424C2×C4#1451978312yes—
425C2×C4#1451978512yes—
426C8—81no—
427C8—81no—
428C8—4881no—
429C8—4881no—
430C22—21no—
431C22—21no—
432C22—4882no—
433C22—2441no—
434C22—2441no—
435C22—2441no—
436C22#1683961711yescharacteristic
437C22#1683972712yes—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—2441no—
445C4—2442no—
446C4—2441no—
447C4—2442no—
448C4—2441no—
449C4#1683972712yes—
450C4#1683972811yescharacteristic
451C4#1683973011yescharacteristic
452C2—22no—
453C2—4881no—
454C2#2144573011yescharacteristic
455C2#2144579111yescharacteristic
456C2#2144579311yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1479C2
socleC22×C61#379
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1479D61
hypocenterC61#8327
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #21444215C2semidirect
3. #21444214C2semidirect
4. #21444213C2semidirect
7. C61×#1479C2semidirect
228. #1479D61semidirect
263. C61#8327semidirect

Maximal subgroups

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

subgroupindex
C2×#168403702
#214442152
#214442142
#214442132
#214441312
C61×#14792
#832761