Finite Group Databasebeta

← #29576304

Subgroups — #29576304

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455819C211yesmaximal, characteristic
2#21448284C211yesmaximal, characteristic, complemented
3#21446646C211yesmaximal, characteristic, complemented
4#21444315C211yesmaximal, characteristic, complemented
5#21443720C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1486C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×#14519736—21no—
10#16840075—21no—
11#16840042C412yescomplemented
12#16839957C412yescomplemented
13#16839896—21no—
14C4×#11758199—22no—
15#16839815C2211yescharacteristic
16C2×#14519703—21no—
17C2×#14519703—21no—
18#16839665—21no—
19#16839661—21no—
20#16839655—22no—
21C4×C4⋊Dic61C2211yescharacteristic
22C4×C22⋊Dic61—21no—
23C42×Dic61C2211yescharacteristic
24#16839497—22no—
25C2×C4×D4×C61C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C61×D4⋊C8—22no—
29C2×#11758222—21no—
30C2×#11758199—22no—
31#14519777C2×C411yescharacteristic
32#14519774C2×C411yescharacteristic
33#14519765—21no—
34#14519751—21no—
35#14519751—21no—
36C4×D244—21no—
37C4×D244—21no—
38#14519736—42no—
39#14519736—42no—
40C2×C4⋊Dic61—22no—
41C2×C4⋊Dic61—21no—
42C2×C22⋊Dic61—22no—
43C2×C22⋊Dic61—22no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519710—22no—
50C4⋊#92418C2×C412yes—
51#14519703—42no—
52#14519703—42no—
53#14519698—22no—
54#14519697—22no—
55C22⋊#92418—21no—
56C4×#92418—21no—
57#14519684—22no—
58#14519684D412yes—
59C22×D4×C61D411yescharacteristic
60C23×C4×C61—21no—
61C2×M16×C61—21no—
62C4×D4×C61—21no—
63C4×D4×C61—21no—
64C4×D4×C61C2×C412yes—
65C4×D4×C61D412yes—
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C22⋊C4×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74C24×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—42no—
77C2×D4×C61C22⋊C412yes—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C2×C22⋊D61—41no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—22no—
92#11758222—41no—
93#11758222—41no—
94#11758222—41no—
95#11758222—41no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—21no—
99C2×C4×D61—41no—
100C2×Dic122—21no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61C22⋊C412yes—
107C22⋊C4×C61—22no—
108C22⋊C4×C61—22no—
109C42×C61C22×C411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113C22⋊Dic61—44no—
114C22⋊Dic61—44no—
115#11758199—44no—
116#11758198—41no—
117#11758198—41no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—44no—
121C4⋊Dic61—42no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—42no—
126C4×Dic61—42no—
127C4×Dic61—41no—
128C4×Dic61—41no—
129C4×Dic61D812yescomplemented
130C2×#92418—22no—
131C23×C61—22no—
132C23×C61—42no—
133C23×C61—42no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61#12011yescharacteristic
137C22×D61—41no—
138D4×C61—22no—
139D4×C61—22no—
140D4×C61—42no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×C4×C61C2×D811yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C22⋊D61—81no—
161C22⋊D61—81no—
162C2×Dic61—22no—
163C2×Dic61—22no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172D244—42no—
173D244—41no—
174D244—41no—
175D244—81no—
176C4×D61—81no—
177C4×D61—81no—
178Dic122—41no—
179Dic122—41no—
180C8×C61—81no—
181C8×C61—81no—
182#92418—42no—
183#9237—611nomaximal, Sylow
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—42no—
187C22×C61—42no—
188C22×C61—42no—
189C22×C61—82no—
190C22×C61—82no—
191C22×C61#38611yescharacteristic
192C22×C61#44711yescharacteristic
193C22×C61#44911yescharacteristic
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—42no—
201C4×C61#42112yes—
202C4×C61C4×D811yescharacteristic
203C4×C61#44211yescharacteristic
204C4×C61#45911yescharacteristic
205C4×C61#46311yescharacteristic
206Dic61—42no—
207Dic61—42no—
208Dic61—82no—
209Dic61—81no—
210#3100—611no—
211#2293—611no—
212#1962—611no—
213#1502—611no—
214#1486D6111yescharacteristic, complemented
215#1303—611no—
216#1276—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—82no—
220C2×C61#187911yescharacteristic
221C2×C61#189711yescharacteristic
222C2×C61#190611yescharacteristic
223D61—161no—
224#532—611no—
225C2×C4×D4C2×D6111yescharacteristic
226C2×#117—1221no—
227#480—1221no—
228#474—612no—
229#459—612no—
230#447—1221no—
231C4×D8—1222no—
232#431—611no—
233#431C2×D6111yescharacteristic
234#423C2×D6111yescharacteristic
235C2×#104—1221no—
236C2×#104—1221no—
237#390—1221no—
238#389—1221no—
239#388—1222no—
240C4×C4⋊C4—611no—
241C4×C22⋊C4—1221no—
242C43—611no—
243#327—1222no—
244D4⋊C8—22no—
245C61#923711yescharacteristic, complemented, Sylow
246C2×#41—1221no—
247C22×D4D24411yescharacteristic
248C23×C4—21no—
249C2×D8—1222no—
250C2×M16—21no—
251C4⋊Q8—611no—
252#127—611no—
253#124—1221no—
254#121—1221no—
255#121—1221no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—1221no—
259C4×D4—1221no—
260C4×D4C4×D6112yes—
261C4×D4C22⋊D6112yes—
262#117—2442no—
263#117—2442no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4D24411yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—1222no—
269C2×C22⋊C4—1222no—
270C2×C42—611no—
271C2×C42—611no—
272C2×C42—1221no—
273C2×C42—1221no—
274C2×C42—1221no—
275C2×C42C22×D6111yescharacteristic
276#107—1222no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—612no—
281#104—2442no—
282#104—2442no—
283#102—1222no—
284#102—1222no—
285C22⋊C8—21no—
286C22⋊C8—1221no—
287C4×C8—21no—
288C4×C8—1221no—
289#95—612no—
290#95—1222no—
291C24—21no—
292#41—2441no—
293#41—2441no—
294#41—2441no—
295#41—2441no—
296C2×Q8—1221no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—2441no—
303C2×D4#1175819812yes—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1222no—
314C22×C4—2441no—
315C22×C4C2×D24411yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318D8—2444no—
319M16—41no—
320M16—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—1222no—
324C4⋊C4—21no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—2442no—
328C4⋊C4—2444no—
329C4⋊C4#1175819812yes—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—2444no—
333C22⋊C4—2444no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—612no—
337C42—1221no—
338C42—1221no—
339C42—1221no—
340C42—2442no—
341C42—2442no—
342C42—2441no—
343C42—2441no—
344C42C2×C4×D6111yescharacteristic
345C42#1175822411yescharacteristic
346C42#1175822411yescharacteristic
347C42C2×C22⋊D6111yescharacteristic
348C23—22no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—2441no—
354C23#1451974711yescharacteristic
355Q8—2441no—
356Q8—2441no—
357D4—22no—
358D4—22no—
359D4—42no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—2442no—
364D4—2441no—
365D4—2441no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—1222no—
376C2×C4—1222no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2441no—
382C2×C4—2442no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4C2×#1175819811yescharacteristic
388C2×C4#1451973711yescharacteristic
389C2×C4#1451973711yescharacteristic
390C2×C4#1451974911yescharacteristic
391C2×C4#1451974911yescharacteristic
392C2×C4#1451976111yescharacteristic
393C2×C4D8×D6111yescharacteristic
394C2×C4#1451979811yescharacteristic
395C2×C4#1451980111yescharacteristic
396C2×C4#1451980411yescharacteristic
397C8—81no—
398C8—81no—
399C8—2442no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22—82no—
407C22—4881no—
408C22—4881no—
409C22—4881no—
410C22#1683963911yescharacteristic
411C22#1683989711yescharacteristic
412C22#1683990811yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—4882no—
418C4—4881no—
419C4—2442no—
420C4—2442no—
421C4#1683977812yes—
422C4#1683984211yescharacteristic
423C4#1683987111yescharacteristic
424C4#1683995511yescharacteristic
425C4#1683997911yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—9761no—
430C2#2144616511yescharacteristic
431C2#2144626511yescharacteristic
432C2#2144631811yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1486C2
socleC22×C61#386
prime radical#21455819C2
cosocleC2×C42×C61C23
hypercenter#1486D61
hypocenterC61#9237
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #21448284C2semidirect
3. #21446646C2semidirect
4. #21444315C2semidirect
5. #21443720C2semidirect
6. #21443651C2semidirect
7. C61×#1486C2semidirect
11. #16840042C4semidirect
12. #16839957C4semidirect
129. C4×Dic61D8semidirect
214. #1486D61semidirect
245. C61#9237semidirect

Maximal subgroups

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

subgroupindex
#214558192
#214482842
#214466462
#214443152
#214437202
#214436512
C61×#14862
#923761