Finite Group Databasebeta

← #29596945

Subgroups — #29596945

Order 15616.

518 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
1#21455401C211yesmaximal, characteristic
2C2×#108×D61C211yesmaximal, characteristic, complemented
3C2×#16839570C211yesmaximal, characteristic, complemented
4C2×#16839568C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21443914C211yesmaximal, characteristic, complemented
7C61×#1382C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9C2×M16×D61—21no—
10C22×C8×D61C2211yescharacteristic
11#16840274—21no—
12C22×#11758185C2211yescharacteristic
13#16840004C411yescharacteristic
14#16840004C411yescharacteristic
15#16839999C411yescharacteristic
16#16839999C411yescharacteristic
17#16839992—21no—
18#16839992—21no—
19C2×#14519713C2211yescharacteristic
20C2×#14519712—21no—
21#108×D61—22no—
22#108×D61—22no—
23#16839756—21no—
24#16839570—22no—
25#16839568—22no—
26#16839541—21no—
27#16839541—21no—
28C22×C16×C61C2211yescharacteristic
29C2×#108×C61C2211yescharacteristic
30C61×#427C2211yescharacteristic
31C2×#11758222—21no—
32C22×C4×D61D411yescharacteristic
33#14519799—21no—
34#14519799—21no—
35#14519799—21no—
36#14519799—21no—
37C2×Dic244C2×C411yescharacteristic
38C2×#11758190—21no—
39C2×D488C2×C411yescharacteristic
40C2×#11758194—21no—
41C2×#11758189—41no—
42M16×D61—24no—
43M16×D61—42no—
44C22×#92418D411yescharacteristic
45C2×C8×D61—21no—
46C2×C8×D61—21no—
47C2×C8×D61—21no—
48C2×C8×D61—21no—
49C2×C8×D61—41no—
50C2×C8×D61C2×C411yescharacteristic
51C2×C8×D61C2×C411yescharacteristic
52C2×C8×D61D411yescharacteristic
53C2×C8×D61D411yescharacteristic
54#14519761—41no—
55#14519757—21no—
56#14519757—21no—
57#14519752—21no—
58#14519752—21no—
59#14519747—41no—
60C4×D244—41no—
61C4×D244—41no—
62C2×#11758185—21no—
63C2×#11758185—21no—
64C2×#11758185—21no—
65#14519713—21no—
66#14519713D412yescomplemented
67#14519712—24no—
68#14519700—21no—
69#14519700—21no—
70#14519697—21no—
71#14519697—21no—
72C2×M16×C61—21no—
73C22×C8×C61C2311yescharacteristic
74#117×C61—21no—
75C2×C16×C61—21no—
76C2×C16×C61—21no—
77C2×C16×C61—21no—
78#108×C61—21no—
79#108×C61D412yescomplemented
80#107×C61C2×C411yescharacteristic
81#107×C61C2×C411yescharacteristic
82#106×C61—21no—
83C23×D61SD1611yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—41no—
86C22×Dic61SD1611yescharacteristic
87#11758222—41no—
88#11758222—41no—
89#11758222—41no—
90#11758222—41no—
91C2×D244—21no—
92C2×D244—41no—
93C2×D244—41no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—41no—
99C2×C4×D61C22⋊C411yescharacteristic
100C2×C4×D61C22⋊C411yescharacteristic
101C2×C4×D61D811yescharacteristic
102C2×C4×D61D811yescharacteristic
103C2×Dic122—21no—
104M16×C61—22no—
105M16×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61C22×C411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61#4111yescharacteristic
112C2×C8×C61#4111yescharacteristic
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C22⋊C4×C61—41no—
116C42×C61—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198—41no—
120#11758198—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123#11758194—22no—
124#11758194—41no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—41no—
128C2×#92418C22⋊C411yescharacteristic
129C2×#92418C22⋊C411yescharacteristic
130Dic244—21no—
131Dic244—21no—
132D488—21no—
133D488—21no—
134#11758190—41no—
135#11758190—41no—
136#11758189—44no—
137C8×D61—21no—
138C8×D61—21no—
139C8×D61—21no—
140C8×D61—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C8×D61—21no—
145C8×D61—44no—
146C16×C61—41no—
147#11758185—41no—
148C23×C61C2×SD1611yescharacteristic
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—22no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61#10211yescharacteristic
155C22×D61#10211yescharacteristic
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61C2×C22⋊C411yescharacteristic
159C2×C4×C61#12011yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61C2×D811yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61#13711yescharacteristic
164C22⋊D61—81no—
165C22⋊D61—81no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—41no—
169C2×Dic61#10211yescharacteristic
170C2×Dic61#10211yescharacteristic
171D244—41no—
172D244—41no—
173D244—82no—
174D244—82no—
175C4×D61—21no—
176C4×D61—21no—
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—21no—
180C4×D61—21no—
181C4×D61—21no—
182C4×D61—21no—
183C4×D61—81no—
184C4×D61—81no—
185Dic122—41no—
186Dic122—41no—
187C8×C61—42no—
188C8×C61C4×D411yescharacteristic
189C8×C61C4×D411yescharacteristic
190C8×C61#12111yescharacteristic
191C8×C61#12111yescharacteristic
192#92418—21no—
193#92418—21no—
194#92418—42no—
195#12990—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61C2×#10211yescharacteristic
199C22×C61#44811yescharacteristic
200C22×C61#48111yescharacteristic
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—42no—
207C2×D61—42no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—81no—
211C2×D61#35912yescomplemented
212C4×C61—81no—
213C4×C61—81no—
214C4×C61#38611yescharacteristic
215C4×C61#41711yescharacteristic
216C4×C61#44711yescharacteristic
217C4×C61#48011yescharacteristic
218Dic61—21no—
219Dic61—21no—
220Dic61—81no—
221#3050—611no—
222C22×#108—611no—
223C2×#359—611no—
224C2×#359—611no—
225C2×C22⋊C16—611no—
226#1382—611no—
227#1382D6111yescharacteristic, complemented
228C2×C61—21no—
229C2×C61—21no—
230C2×C61#187411yescharacteristic
231C2×C61C2×#35911yescharacteristic
232C2×C61#214311yescharacteristic
233D61—22no—
234D61—41no—
235D61—161no—
236C2×#135—611no—
237C22×M16—1221no—
238C23×C8—611no—
239#525—1221no—
240C22×C16—611no—
241C22×C16C2×D6111yescharacteristic
242#467—611no—
243#467—611no—
244#466—611no—
245#466—611no—
246#465—1221no—
247#465—1221no—
248C2×#108—611no—
249C2×#108—1222no—
250C2×#108—1221no—
251C2×#108—1222no—
252C2×#108C2×D6111yescharacteristic
253#427C2×D6111yescharacteristic
254#416—1221no—
255#359—1222no—
256#359—1222no—
257C22⋊C16—1221no—
258C22⋊C16—1221no—
259C61#1299011yescharacteristic, complemented, Sylow
260C2×#41—1221no—
261C23×C4—611no—
262#135—1221no—
263#135—1221no—
264#135—1221no—
265#135—1221no—
266C2×Q16—611no—
267C2×SD16—1221no—
268C2×D8—611no—
269C2×M16—21no—
270C2×M16—1224no—
271C2×M16—1221no—
272C2×M16—2441no—
273C2×M16—2442no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—611no—
278C22×C8—611no—
279C22×C8—1221no—
280C22×C8—1221no—
281C22×C8—1221no—
282C22×C8—1221no—
283C22×C8—2441no—
284C22×C8C22×D6111yescharacteristic
285#123—2441no—
286C22⋊Q8—1221no—
287C22⋊Q8—1221no—
288#121—1221no—
289#121—1221no—
290#120—2441no—
291C4×D4—2441no—
292C4×D4—2441no—
293#117—21no—
294C2×C16—21no—
295C2×C16—21no—
296C2×C16—21no—
297C2×C16—1221no—
298C2×C16—1221no—
299C2×C16—1221no—
300#108—21no—
301#108—612no—
302#108—1224no—
303#108—1221no—
304#108D24412yescomplemented
305#107C4×D6111yescharacteristic
306#107C4×D6111yescharacteristic
307#106—21no—
308#103—1221no—
309#103—1221no—
310#102—1221no—
311#102—1221no—
312C24—611no—
313#41—2441no—
314#41—2441no—
315#41—2441no—
316#41—2441no—
317C2×Q8—1221no—
318C2×D4—1221no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—2441no—
332C22×C4D4×D6111yescharacteristic
333Q16—1221no—
334Q16—1221no—
335SD16—2441no—
336SD16—2441no—
337D8—1221no—
338D8—1221no—
339M16—22no—
340M16—41no—
341M16—1222no—
342M16—2444no—
343M16—2441no—
344C2×C8—41no—
345C2×C8—611no—
346C2×C8—611no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—2444no—
358C2×C8—2441no—
359C2×C8C2×C4×D6111yescharacteristic
360C2×C8C2×D24411yescharacteristic
361C2×C8#1175822211yescharacteristic
362C2×C8D4×D6111yescharacteristic
363C2×C8D4×D6111yescharacteristic
364C2×C8#1175822611yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C22⋊C4—41no—
370C22⋊C4—2441no—
371C22⋊C4—2441no—
372C22⋊C4—2441no—
373C22⋊C4—2441no—
374C42—41no—
375C16—41no—
376C16—2441no—
377C23—611no—
378C23—611no—
379C23—1222no—
380C23—1221no—
381C23—1221no—
382C23—2441no—
383C23—2441no—
384C23SD16×D6111yescharacteristic
385Q8—2441no—
386Q8—2441no—
387D4—4882no—
388D4—4882no—
389D4—4881no—
390D4—4881no—
391D4—2441no—
392D4—2441no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—611no—
396C2×C4—611no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—2441no—
410C2×C4C22⋊C4×D6111yescharacteristic
411C2×C4#1451974711yescharacteristic
412C2×C4#1451976211yescharacteristic
413C2×C4D8×D6111yescharacteristic
414C2×C4#1451980411yescharacteristic
415C2×C4#1451980911yescharacteristic
416C8—42no—
417C8—1221no—
418C8—1221no—
419C8—2442no—
420C8#1451973911yescharacteristic
421C8C4×D24411yescharacteristic
422C8#1451975011yescharacteristic
423C8#1451975211yescharacteristic
424C22—21no—
425C22—21no—
426C22—612no—
427C22—1221no—
428C22—1221no—
429C22—1221no—
430C22—1221no—
431C22—1221no—
432C22—4881no—
433C22—4881no—
434C22—4881no—
435C22—2442no—
436C22—2442no—
437C22#102×D6111yescharacteristic
438C22#1683990211yescharacteristic
439C22#1684008211yescharacteristic
440C4—81no—
441C4—81no—
442C4—1221no—
443C4—1221no—
444C4—4881no—
445C4#1683964011yescharacteristic
446C4#1683976211yescharacteristic
447C4#1683989711yescharacteristic
448C4#1684007711yescharacteristic
449C2—21no—
450C2—21no—
451C2—1222no—
452C2—9761no—
453C2—2441no—
454C2#2144613511yescharacteristic
455C2#359×D6111yescharacteristic
456C2#2144754511yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1382C2
socleC22×C61C2×#102
prime radical#21455401C2
cosocleC22×C8×C61C23
hypercenter#1382D61
hypocenterC61#12990
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
2. C2×#108×D61C2semidirect
3. C2×#16839570C2semidirect
4. C2×#16839568C2semidirect
5. C2×#16839541C2semidirect
6. #21443914C2semidirect
7. C61×#1382C2semidirect
66. #14519713D4semidirect
79. #108×C61D4semidirect
211. C2×D61#359semidirect
227. #1382D61semidirect
259. C61#12990semidirect
304. #108D244semidirect

Maximal subgroups

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

subgroupindex
#214554012
C2×#108×D612
C2×#168395702
C2×#168395682
C2×#168395412
#214439142
C61×#13822
#1299061