Finite Group Databasebeta

← #29571785

Subgroups — #29571785

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840477C211yesmaximal, characteristic
2#21445808C211yesmaximal, characteristic, complemented
3#21444505C211yesmaximal, characteristic, complemented
4#21444503C211yesmaximal, characteristic, complemented
5#21444244C211yesmaximal, characteristic, complemented
6#21444139C211yesmaximal, characteristic, complemented
7C61×#1486C211yesmaximal, characteristic, complemented
8#16840477—22no—
9#16840477—22no—
10#16840477—22no—
11#16840477—22no—
12C2×#14519777C2211yescharacteristic
13C2×#14519763—22no—
14C2×#14519751—21no—
15C2×#14519748C412yes—
16C2×C4×D244C2211yescharacteristic
17C2×#14519736—21no—
18C2×#14519735C412yes—
19#16839815C2211yescharacteristic
20#16839786C2211yescharacteristic
21C2×#14519693—21no—
22#16839530—21no—
23#16839509—22no—
24#16839507—22no—
25D4⋊#92418—22no—
26#16839485—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×Dic122—21no—
32C22×D244D411yescharacteristic
33C22×C22⋊D61—22no—
34C22×C4×D61C2×C412yes—
35C2×#11758194—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777D412yes—
39#14519777D412yes—
40#14519763—28no—
41#14519763—28no—
42#14519751—24no—
43#14519751—24no—
44#14519748—24no—
45#14519748—24no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244—21no—
49C4×D244—21no—
50#14519736—24no—
51#14519736—24no—
52#14519735—24no—
53#14519735—24no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61C2×C412yes—
56C2×C4⋊Dic61D411yescharacteristic
57C2×C22⋊Dic61—22no—
58C2×#11758198—22no—
59C2×#11758198D412yes—
60C2×C4×Dic61—22no—
61C4⋊#92418—21no—
62C4⋊#92418—21no—
63C4⋊#92418—21no—
64#14519693—42no—
65C22⋊#92418—21no—
66C4×#92418—21no—
67C22×D4×C61C2×C411yescharacteristic
68C23×C4×C61—21no—
69C2×M16×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61D412yes—
73C4×D4×C61D412yes—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C4×C8×C61—21no—
82C24×C61—21no—
83C23×D61C22⋊C412yes—
84C2×D4×C61—21no—
85C2×D4×C61—42no—
86C2×D4×C61C22⋊C412yes—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61C22×C411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C2×C22⋊D61—28no—
98C2×C22⋊D61—84no—
99C22×Dic61—22no—
100C22×Dic61C22⋊C412yes—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244—21no—
104C2×D244—21no—
105C2×D244—21no—
106C2×D244—21no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—44no—
110C2×Dic122—22no—
111C2×Dic122—22no—
112C2×Dic122—82no—
113M16×C61—41no—
114M16×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61C22⋊C412yes—
119C22⋊C4×C61—22no—
120C22⋊C4×C61—22no—
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C22⋊Dic61—28no—
126#11758198—28no—
127#11758198—22no—
128#11758198—22no—
129C4⋊Dic61—22no—
130C4⋊Dic61—22no—
131C4⋊Dic61—22no—
132C4⋊Dic61—21no—
133C4⋊Dic61—21no—
134C4⋊Dic61C22⋊C414yes—
135C4×Dic61—28no—
136#11758194—41no—
137#11758194—41no—
138C2×#92418—41no—
139C2×#92418—41no—
140C23×C61—22no—
141C23×C61—42no—
142C23×C61—42no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61C2×C22⋊C411yescharacteristic
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—42no—
150C22×D61—42no—
151D4×C61—24no—
152D4×C61—42no—
153C2×C4×C61—22no—
154C2×C4×C61—22no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61C2×C22⋊C411yescharacteristic
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12011yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61#13711yescharacteristic
172C22⋊D61—88no—
173C2×Dic61—22no—
174C2×Dic61—24no—
175C2×Dic61—44no—
176C2×Dic61—42no—
177D244—41no—
178D244—41no—
179D244—41no—
180D244—41no—
181C4×D61—44no—
182C4×D61—44no—
183Dic122—82no—
184Dic122—82no—
185C8×C61—81no—
186C8×C61—81no—
187#92418—81no—
188#92418—81no—
189#8397—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—42no—
193C22×C61—42no—
194C22×C61—42no—
195C22×C61—82no—
196C22×C61—82no—
197C22×C61#37911yescharacteristic
198C22×C61#41611yescharacteristic
199C22×C61#41711yescharacteristic
200C2×D61—42no—
201C2×D61—42no—
202C2×D61—42no—
203C2×D61—82no—
204C2×D61—82no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—42no—
209C4×C61#41312yes—
210C4×C61#44911yescharacteristic
211C4×C61#44911yescharacteristic
212C4×C61#45211yescharacteristic
213C4×C61#45211yescharacteristic
214Dic61—44no—
215Dic61—42no—
216C2×#555—611no—
217#1800—611no—
218#1549—611no—
219#1549—611no—
220#1486—611no—
221#1486D6111yescharacteristic, complemented
222#1460—611no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—82no—
226C2×C61#178511yescharacteristic
227C2×C61#178811yescharacteristic
228C2×C61#179511yescharacteristic
229D61—82no—
230#555—1222no—
231#555—1222no—
232#555—1222no—
233#555—1222no—
234C2×C4⋊Q8—611no—
235C2×#124—1222no—
236C2×#121—612no—
237C2×#121—1221no—
238C2×C4×D4—611no—
239C2×C4×D4C2×D6111yescharacteristic
240C2×#117—612no—
241C2×#117—1221no—
242#431—611no—
243#431C2×D6111yescharacteristic
244#423—611no—
245#423C2×D6111yescharacteristic
246C2×#100—1221no—
247#343—1221no—
248#332—1222no—
249#332—1222no—
250D4⋊C8—22no—
251D4⋊C8—1222no—
252#323—1222no—
253C61#839711yescharacteristic, complemented, Sylow
254C22×Q8—1221no—
255C22×D4—611no—
256C22×D4—1222no—
257C22×D4C4×D6111yescharacteristic
258C23×C4—21no—
259C23×C4—612no—
260C2×M16—21no—
261C2×M16—1221no—
262C4⋊Q8—612no—
263C4⋊Q8—612no—
264C4⋊Q8—1221no—
265C4⋊Q8—1221no—
266#124—1228no—
267#124—1228no—
268#121—1224no—
269#121—1224no—
270#121—1224no—
271#121—1224no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—1221no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4—1221no—
278C4×D4D24412yes—
279C4×D4C22⋊D6112yes—
280#117—1224no—
281#117—1224no—
282#117—1224no—
283#117—1224no—
284C2×C4⋊C4—612no—
285C2×C4⋊C4—611no—
286C2×C4⋊C4—1221no—
287C2×C4⋊C4C4×D6111yescharacteristic
288C2×C22⋊C4—21no—
289C2×C22⋊C4—612no—
290C2×C22⋊C4—1222no—
291C2×C22⋊C4—1222no—
292C2×C42—1222no—
293C2×C42C22×D6111yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—1221no—
298C4⋊C8—1221no—
299C4⋊C8—1221no—
300#100—2442no—
301C22⋊C8—21no—
302C22⋊C8—1221no—
303C4×C8—21no—
304C4×C8—1221no—
305C24—21no—
306C24—612no—
307C2×Q8—1222no—
308C2×Q8—1222no—
309C2×Q8—4882no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—1228no—
313C2×D4—1221no—
314C2×D4—1221no—
315C2×D4—1221no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—4884no—
320C2×D4#1175819812yes—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—612no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—1222no—
332C22×C4—2444no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336M16—41no—
337M16—41no—
338M16—2441no—
339M16—2441no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—2441no—
343C2×C8—2441no—
344C4⋊C4—21no—
345C4⋊C4—614no—
346C4⋊C4—1222no—
347C4⋊C4—1221no—
348C4⋊C4—1222no—
349C4⋊C4—1221no—
350C4⋊C4—1222no—
351C4⋊C4#1175819812yes—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—1228no—
355C22⋊C4—1228no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C42—1228no—
359C42C2×D24411yescharacteristic
360C42D4×D6111yescharacteristic
361C42D4×D6111yescharacteristic
362C42C2×C22⋊D6111yescharacteristic
363C23—22no—
364C23—42no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—1222no—
369C23—1222no—
370C23—1222no—
371C23—2442no—
372C23—2442no—
373C23C22⋊C4×D6111yescharacteristic
374Q8—4882no—
375Q8—4882no—
376D4—24no—
377D4—42no—
378D4—4888no—
379D4—2441no—
380D4—2441no—
381D4—2441no—
382D4—2441no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—1222no—
393C2×C4—1224no—
394C2×C4—2444no—
395C2×C4—2444no—
396C2×C4—2444no—
397C2×C4—2442no—
398C2×C4C22⋊C4×D6111yescharacteristic
399C2×C4C2×#1175819811yescharacteristic
400C2×C4#1451974511yescharacteristic
401C2×C4#1451974511yescharacteristic
402C2×C4#1451974711yescharacteristic
403C2×C4#1451974711yescharacteristic
404C2×C4#1451979611yescharacteristic
405C2×C4#1451979811yescharacteristic
406C2×C4#1451980111yescharacteristic
407C2×C4#1451980611yescharacteristic
408C8—81no—
409C8—81no—
410C8—4881no—
411C8—4881no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22—42no—
417C22—82no—
418C22—82no—
419C22—4882no—
420C22—4882no—
421C22—2442no—
422C22—2442no—
423C22—2442no—
424C22#1683961711yescharacteristic
425C22#1683975511yescharacteristic
426C22#1683976011yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—2442no—
432C4—2444no—
433C4#1683974412yes—
434C4#1683990411yescharacteristic
435C4#1683990811yescharacteristic
436C4#1683992111yescharacteristic
437C4#1683992511yescharacteristic
438C2—21no—
439C2—21no—
440C2—82no—
441C2—4882no—
442C2#2144574511yescharacteristic
443C2#2144575611yescharacteristic
444C2#2144578811yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1486C2
socleC22×C61#379
prime radicalC2×#16840477C2
cosocleC2×C42×C61C23
hypercenter#1486D61
hypocenterC61#8397
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #21445808C2semidirect
3. #21444505C2semidirect
4. #21444503C2semidirect
5. #21444244C2semidirect
6. #21444139C2semidirect
7. C61×#1486C2semidirect
221. #1486D61semidirect
253. C61#8397semidirect

Maximal subgroups

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

subgroupindex
C2×#168404772
#214458082
#214445052
#214445032
#214442442
#214441392
C61×#14862
#839761