Finite Group Databasebeta

← #29571765

Subgroups — #29571765

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840416C211yesmaximal, characteristic
2#21445808C211yesmaximal, characteristic, complemented
3#21444501C211yesmaximal, characteristic, complemented
4#21444499C211yesmaximal, characteristic, complemented
5#21444244C211yesmaximal, characteristic, complemented
6#21444139C211yesmaximal, characteristic, complemented
7C61×#1486C211yesmaximal, characteristic, complemented
8C22×#11758224C412yes—
9#16840416—22no—
10#16840416—22no—
11#16840416—22no—
12#16840416—22no—
13C2×#14519777C2211yescharacteristic
14C2×#14519761—22no—
15C2×#14519757C412yes—
16C2×#14519751—21no—
17C2×C4×D244C2211yescharacteristic
18C22×C4⋊Dic61—21no—
19#16839815C2211yescharacteristic
20#16839786C2211yescharacteristic
21C2×#14519693—21no—
22#16839530—21no—
23#16839510—22no—
24#16839510—22no—
25D4⋊#92418—22no—
26#16839485—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×D4⋊C8—22no—
31C2×#11758224—24no—
32C2×#11758224—24no—
33C2×#11758224—48no—
34C22×Dic122C2×C412yes—
35C22×D244D411yescharacteristic
36C22×C22⋊D61—22no—
37C23×Dic61—22no—
38C22×C4×D61C2×C412yes—
39C2×#11758194—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777D412yes—
43#14519777D412yes—
44#14519761—28no—
45#14519761—28no—
46#14519757—24no—
47#14519757—24no—
48#14519751—24no—
49#14519751—24no—
50C4×D244—21no—
51C4×D244—21no—
52C4×D244—21no—
53C4×D244—21no—
54C2×C4⋊Dic61—24no—
55C2×C4⋊Dic61—24no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61D411yescharacteristic
60C2×#11758198—22no—
61C2×#11758198D412yes—
62C4⋊#92418—21no—
63C4⋊#92418—21no—
64C4⋊#92418—21no—
65#14519693—42no—
66C22⋊#92418—21no—
67C4×#92418—21no—
68C22×D4×C61C2×C411yescharacteristic
69C23×C4×C61—21no—
70C2×M16×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61D412yes—
74C4×D4×C61D412yes—
75C2×C4⋊C4×C61C2×C411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C4⋊C8×C61—21no—
81C22⋊C8×C61—21no—
82C4×C8×C61—21no—
83C24×C61—21no—
84C23×D61C22⋊C412yes—
85C2×D4×C61—24no—
86C2×D4×C61—21no—
87C2×D4×C61C22⋊C412yes—
88C22×C4×C61—21no—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—28no—
99C2×C22⋊D61—48no—
100C22×Dic61—28no—
101C22×Dic61—22no—
102C22×Dic61—48no—
103C22×Dic61C22⋊C412yes—
104#11758224—48no—
105#11758224—416no—
106#11758224—48no—
107C2×D244—21no—
108C2×D244—21no—
109C2×D244—21no—
110C2×D244—21no—
111C2×D244—21no—
112C2×D244—21no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—44no—
116C2×Dic122—22no—
117C2×Dic122—44no—
118C2×Dic122C22⋊C414yes—
119M16×C61—41no—
120M16×C61—41no—
121C2×C8×C61—41no—
122C2×C8×C61—41no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61C22⋊C412yes—
125C22⋊C4×C61—22no—
126C22⋊C4×C61—22no—
127C42×C61C2×D411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131#11758198—28no—
132#11758198—22no—
133#11758198—22no—
134C4⋊Dic61—28no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61—22no—
138C4⋊Dic61—22no—
139C4⋊Dic61—22no—
140C4⋊Dic61—22no—
141#11758194—41no—
142#11758194—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C23×C61—24no—
146C23×C61—22no—
147C23×C61—42no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61C2×C22⋊C411yescharacteristic
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—42no—
155C22×D61—42no—
156D4×C61—24no—
157D4×C61—22no—
158D4×C61#10014yescomplemented
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C2×C22⋊C411yescharacteristic
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#13511yescharacteristic
175C2×C4×C61#13511yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C61#13711yescharacteristic
178C22⋊D61—416no—
179C2×Dic61—24no—
180C2×Dic61—22no—
181C2×Dic61—44no—
182C2×Dic61—416no—
183C2×Dic61—42no—
184D244—41no—
185D244—41no—
186D244—41no—
187D244—41no—
188C4×D61—44no—
189C4×D61—44no—
190Dic122—44no—
191Dic122—44no—
192C8×C61—81no—
193C8×C61—81no—
194#92418—81no—
195#92418—81no—
196#8393—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—24no—
200C22×C61—44no—
201C22×C61—44no—
202C22×C61—42no—
203C22×C61—42no—
204C22×C61#37911yescharacteristic
205C22×C61#41611yescharacteristic
206C22×C61#41711yescharacteristic
207C2×D61—42no—
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—82no—
211C2×D61—82no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—42no—
216C4×C61C2×#10012yes—
217C4×C61#44911yescharacteristic
218C4×C61#44911yescharacteristic
219C4×C61#45211yescharacteristic
220C4×C61#45211yescharacteristic
221Dic61—44no—
222Dic61—42no—
223C2×#547—611no—
224#1800—611no—
225#1548—611no—
226#1548—611no—
227#1486—611no—
228#1486D6111yescharacteristic, complemented
229#1460—611no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—44no—
233C2×C61#178311yescharacteristic
234C2×C61#178811yescharacteristic
235C2×C61#179611yescharacteristic
236D61—82no—
237C22×#41—612no—
238#547—1222no—
239#547—1222no—
240#547—1222no—
241#547—1222no—
242C2×C4⋊Q8—611no—
243C2×#123—1222no—
244C2×C22⋊Q8—612no—
245C2×#121—1221no—
246C2×C4×D4—611no—
247C2×C4×D4C2×D6111yescharacteristic
248C22×C4⋊C4—1221no—
249#431—611no—
250#431C2×D6111yescharacteristic
251#423—611no—
252#423C2×D6111yescharacteristic
253C2×#100—1221no—
254#343—1221no—
255#333—1222no—
256#333—1222no—
257D4⋊C8—22no—
258D4⋊C8—1222no—
259#323—1222no—
260C61#839311yescharacteristic, complemented, Sylow
261C2×#41—1224no—
262C2×#41—1224no—
263C2×#41—2448no—
264C22×Q8—612no—
265C22×D4—611no—
266C22×D4—1222no—
267C22×D4C4×D6111yescharacteristic
268C23×C4—21no—
269C23×C4—612no—
270C23×C4—1222no—
271C2×M16—21no—
272C2×M16—1221no—
273C4⋊Q8—612no—
274C4⋊Q8—612no—
275C4⋊Q8—1221no—
276C4⋊Q8—1221no—
277#123—1228no—
278#123—1228no—
279C22⋊Q8—1224no—
280C22⋊Q8—1224no—
281#121—1224no—
282#121—1224no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—1221no—
286C4×D4—1221no—
287C4×D4—1221no—
288C4×D4—1221no—
289C4×D4D24412yes—
290C4×D4C22⋊D6112yes—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—1222no—
293C2×C4⋊C4—1224no—
294C2×C4⋊C4—1224no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4C4×D6111yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4—612no—
300C2×C22⋊C4—1222no—
301C2×C42C22×D6111yescharacteristic
302C4⋊C8—21no—
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8—1221no—
306C4⋊C8—1221no—
307C4⋊C8—1221no—
308#100—2442no—
309C22⋊C8—21no—
310C22⋊C8—1221no—
311C4×C8—21no—
312C4×C8—1221no—
313C24—21no—
314C24—612no—
315#41—24416no—
316#41—2448no—
317#41—2448no—
318C2×Q8—614no—
319C2×Q8—1222no—
320C2×Q8—2444no—
321C2×D4—24no—
322C2×D4—21no—
323C2×D4—1228no—
324C2×D4—1221no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—2448no—
331C2×D4#1175819812yes—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—612no—
340C22×C4—1228no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—2444no—
345C22×C4—2448no—
346C22×C4C2×C4×D6111yescharacteristic
347C22×C4D4×D6111yescharacteristic
348C22×C4D4×D6111yescharacteristic
349M16—41no—
350M16—41no—
351M16—2441no—
352M16—2441no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—2441no—
356C2×C8—2441no—
357C4⋊C4—21no—
358C4⋊C4—1228no—
359C4⋊C4—1221no—
360C4⋊C4—1222no—
361C4⋊C4—1222no—
362C4⋊C4—1221no—
363C4⋊C4—1222no—
364C4⋊C4—1222no—
365C4⋊C4#1175819812yes—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—1228no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C42C2×D24411yescharacteristic
372C42D4×D6111yescharacteristic
373C42D4×D6111yescharacteristic
374C42C2×C22⋊D6111yescharacteristic
375C23—24no—
376C23—22no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—1222no—
381C23—1222no—
382C23—1222no—
383C23—2442no—
384C23—2442no—
385C23C22⋊C4×D6111yescharacteristic
386Q8—2444no—
387Q8—2444no—
388D4—24no—
389D4—22no—
390D4—24416no—
391D4—2441no—
392D4—2441no—
393D4—2441no—
394D4—2441no—
395D4#1451969314yescomplemented
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—1222no—
406C2×C4—1224no—
407C2×C4—2444no—
408C2×C4—2444no—
409C2×C4—24416no—
410C2×C4—2444no—
411C2×C4—2442no—
412C2×C4C22⋊C4×D6111yescharacteristic
413C2×C4C2×#1175819811yescharacteristic
414C2×C4#1451974511yescharacteristic
415C2×C4#1451974511yescharacteristic
416C2×C4#1451974711yescharacteristic
417C2×C4#1451974711yescharacteristic
418C2×C4#1451979611yescharacteristic
419C2×C4#1451979811yescharacteristic
420C2×C4#1451980111yescharacteristic
421C2×C4#1451980611yescharacteristic
422C8—81no—
423C8—81no—
424C8—4881no—
425C8—4881no—
426C22—21no—
427C22—21no—
428C22—24no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—42no—
433C22—4882no—
434C22—4882no—
435C22—2442no—
436C22—2442no—
437C22—2442no—
438C22#1683961711yescharacteristic
439C22#1683975511yescharacteristic
440C22#1683976011yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—42no—
445C4—2442no—
446C4—2444no—
447C4C2×#1451969312yes—
448C4#1683990411yescharacteristic
449C4#1683990811yescharacteristic
450C4#1683992111yescharacteristic
451C4#1683992511yescharacteristic
452C2—21no—
453C2—21no—
454C2—44no—
455C2—4882no—
456C2#2144573911yescharacteristic
457C2#2144575611yescharacteristic
458C2#2144579311yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1486C2
socleC22×C61#379
prime radicalC2×#16840416C2
cosocleC2×C42×C61C23
hypercenter#1486D61
hypocenterC61#8393
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. #21444501C2semidirect
4. #21444499C2semidirect
5. #21444244C2semidirect
6. #21444139C2semidirect
7. C61×#1486C2semidirect
158. D4×C61#100semidirect
228. #1486D61semidirect
260. C61#8393semidirect
395. D4#14519693semidirect

Maximal subgroups

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

subgroupindex
C2×#168404162
#214458082
#214445012
#214444992
#214442442
#214441392
C61×#14862
#839361