Finite Group Databasebeta

← #29835168

Subgroups — #29835168

Order 15616.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456458C211yesmaximal, characteristic
2#21454688C211yesmaximal, characteristic, complemented
3#21448028C211yesmaximal, characteristic, complemented
4#21448011C211yesmaximal, characteristic
5#21447972C211yesmaximal, characteristic, complemented
6#21447962C211yesmaximal, characteristic, complemented
7#21447882C211yesmaximal, characteristic, complemented
8#21447882C211yesmaximal, characteristic, complemented
9#21447755C211yesmaximal, characteristic, complemented
10#21447738C211yesmaximal, characteristic
11#21447691C211yesmaximal, characteristic, complemented
12#21447685C211yesmaximal, characteristic, complemented
13C4×Dic488C211yesmaximal, characteristic, complemented
14C4×#14519722C211yesmaximal, characteristic, complemented
15C61×#2164C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic
17#16840383—21no—
18#16840239—21no—
19C2×Dic488C2211yescharacteristic
20C2×Dic488C2211yescharacteristic
21C2×#14519722C2211yescharacteristic
22C2×#14519722C2211yescharacteristic
23#16840167C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840122—21no—
26#16840008—21no—
27#16840003C2211yescharacteristic
28#16839998C2211yescharacteristic
29#16839870—21no—
30#16839870—21no—
31#16839864—21no—
32C4×Dic244C2211yescharacteristic
33C4×Dic244C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35C4×Dic244C2211yescharacteristic
36C4×Dic244C2211yescharacteristic
37C4×D488C2211yescharacteristic
38#16839800C2211yescharacteristic
39#16839772—21no—
40#16839590C2211yescharacteristic
41#16839590C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839588C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839567C2211yescharacteristic
49#16839567C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C61×#405C2211yescharacteristic
53C61×C4⋊C16C2211yescharacteristic
54C61×C4⋊C16C2211yescharacteristic
55C61×C22⋊C16C2211yescharacteristic
56C61×C22⋊C16C2211yescharacteristic
57C61×#346C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C22×Dic122—21no—
60C2×Dic244—21no—
61C2×Dic244—22no—
62C2×Dic244—22no—
63C2×Dic244C2311yescharacteristic
64C2×Dic244C2311yescharacteristic
65C2×Dic244C2311yescharacteristic
66C2×#11758190—21no—
67C2×D488C2311yescharacteristic
68#14519777—21no—
69#14519772—41no—
70#14519765—21no—
71#14519763—41no—
72#14519759—41no—
73#14519756—21no—
74#14519755—41no—
75#14519751—21no—
76C4×Dic122—21no—
77C4×Dic122—21no—
78C4×Dic122—21no—
79C4×Dic122—21no—
80C4×Dic122—21no—
81#14519742—41no—
82#14519742—41no—
83C4×D244—21no—
84#14519736—21no—
85#14519733—41no—
86#14519733—41no—
87Dic488—22no—
88Dic488—22no—
89#14519722—22no—
90#14519722—22no—
91#14519711—21no—
92#14519711C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519709—21no—
97#14519702—21no—
98#14519702—21no—
99#14519702—21no—
100#14519702—21no—
101#14519702—21no—
102#14519702—21no—
103#14519699—21no—
104#14519699—21no—
105C2×M16×C61D411yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#117×C61D411yescharacteristic
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C22×Dic61—41no—
119C2×D244—21no—
120C2×C4×D61—41no—
121C2×Dic122—24no—
122C2×Dic122—21no—
123C2×Dic122—21no—
124C2×Dic122—21no—
125C2×Dic122—42no—
126C2×Dic122—41no—
127C2×Dic122—41no—
128M16×C61—41no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61D811yescharacteristic
136C4⋊C4×C61D811yescharacteristic
137C22⋊C4×C61D811yescharacteristic
138C22⋊C4×C61D811yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C22⋊Dic61—41no—
142C22⋊Dic61—41no—
143#11758198—41no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61—41no—
162C4×Dic61—41no—
163C4×Dic61—41no—
164Dic244—24no—
165Dic244—21no—
166Dic244—21no—
167Dic244—21no—
168Dic244—21no—
169Dic244#4112yes—
170Dic244#4112yes—
171D488—21no—
172D488—21no—
173#11758190—42no—
174C16×C61—21no—
175C16×C61—21no—
176C16×C61—21no—
177C16×C61—21no—
178C23×C61C2×D811yescharacteristic
179C22×D61—41no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61C2×D811yescharacteristic
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C22⋊D61—161no—
189C2×Dic61—44no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197D244—41no—
198D244—41no—
199C4×D61—161no—
200Dic122—22no—
201Dic122—22no—
202Dic122—44no—
203Dic122—41no—
204Dic122—41no—
205Dic122—41no—
206Dic122—41no—
207Dic122—161no—
208C8×C61—21no—
209C8×C61—21no—
210C8×C61—21no—
211C8×C61C2×#4111yescharacteristic
212C8×C61C2×#4111yescharacteristic
213#33681—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61C22×D811yescharacteristic
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61#52511yescharacteristic
227C4×C61#57511yescharacteristic
228Dic61—42no—
229Dic61—42no—
230Dic61—81no—
231Dic61—81no—
232Dic61—81no—
233Dic61—81no—
234Dic61—81no—
235#3175—611no—
236#2950—611no—
237#2237—611no—
238#2234—611no—
239#2227—611no—
240#2225—611no—
241#2211—611no—
242#2211—611no—
243#2188—611no—
244#2185—611no—
245#2176—611no—
246#2175—611no—
247C4×Q32—611no—
248C4×SD32—611no—
249#2164D6111yescharacteristic, complemented
250C2×C61—41no—
251C2×C61#310011yescharacteristic
252C2×C61#341611yescharacteristic
253C2×C61#341711yescharacteristic
254D61—161no—
255C22×Q16—611no—
256#542—1221no—
257#519—1221no—
258C2×Q32—611no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262#500—611no—
263#495—611no—
264#489—1221no—
265#468—1221no—
266#467—611no—
267#466—611no—
268#441—1221no—
269#441—1221no—
270#440—1221no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×Q16—611no—
274C4×Q16—611no—
275C4×Q16—611no—
276C4×D8—611no—
277#427—611no—
278#419—1221no—
279#405C2×D6111yescharacteristic
280#367—611no—
281#367—611no—
282#366—611no—
283#366—611no—
284C4⋊C16C2×D6111yescharacteristic
285C4⋊C16C2×D6111yescharacteristic
286#358—611no—
287#358—611no—
288#358—611no—
289#358—611no—
290#358—611no—
291#358—611no—
292#357—611no—
293#357—611no—
294C22⋊C16C2×D6111yescharacteristic
295C22⋊C16C2×D6111yescharacteristic
296#346C2×D6111yescharacteristic
297C4×C16C2×D6111yescharacteristic
298C61#3368111yescharacteristic, complemented, Sylow
299C22×Q8—1221no—
300C2×Q16—611no—
301C2×Q16—611no—
302C2×Q16—611no—
303C2×Q16—1222no—
304C2×Q16—1222no—
305C2×Q16—1221no—
306C2×SD16—1221no—
307C2×D8—611no—
308C2×M16D24411yescharacteristic
309C22×C8C22×D6111yescharacteristic
310C4⋊Q8—1221no—
311#126—2441no—
312#124—1221no—
313#124—2441no—
314#123—2441no—
315C22⋊Q8—1221no—
316C22⋊Q8—2441no—
317#121—1221no—
318C4×Q8—1221no—
319C4×Q8—1221no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×Q8—1221no—
323C4×Q8—2441no—
324C4×Q8—2441no—
325C4×D4—1221no—
326#117—1221no—
327#117—2441no—
328#117—2441no—
329#117D24411yescharacteristic
330Q32—1222no—
331Q32—1222no—
332SD32—1222no—
333SD32—1222no—
334C2×C16C22×D6111yescharacteristic
335C2×C16C22×D6111yescharacteristic
336C2×C16C22×D6111yescharacteristic
337C2×C16C22×D6111yescharacteristic
338#107—611no—
339#107—611no—
340#107—611no—
341#107—611no—
342#107—1221no—
343#106—1221no—
344#103—1221no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350#102—1221no—
351#102—1221no—
352#97D24411yescharacteristic
353#97D24411yescharacteristic
354C4×C8C22×D6111yescharacteristic
355C4×C8C22×D6111yescharacteristic
356C2×Q8—1224no—
357C2×Q8—1221no—
358C2×Q8—1221no—
359C2×Q8—1221no—
360C2×Q8—2442no—
361C2×Q8—2441no—
362C2×Q8—2441no—
363C2×D4—1221no—
364C2×D4—2441no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4C2×D24411yescharacteristic
368Q16—612no—
369Q16—612no—
370Q16—1224no—
371Q16—1221no—
372Q16—1221no—
373Q16—1221no—
374Q16—1221no—
375SD16—2442no—
376D8—1221no—
377D8—1221no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×D24411yescharacteristic
382C2×C8C2×D24411yescharacteristic
383C2×C8C2×D24411yescharacteristic
384C2×C8C23×D6111yescharacteristic
385C4⋊C4—1221no—
386C4⋊C4—1221no—
387C4⋊C4—1221no—
388C4⋊C4—1221no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4D48811yescharacteristic
397C4⋊C4D48811yescharacteristic
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C22⋊C4D48811yescharacteristic
405C22⋊C4D48811yescharacteristic
406C42—2441no—
407C42—2441no—
408C42—2441no—
409C42—2441no—
410C42—2441no—
411C42—2441no—
412C42C2×D24411yescharacteristic
413C42C2×D24411yescharacteristic
414C16—21no—
415C16—21no—
416C16—21no—
417C16—21no—
418C23—2441no—
419C23C2×D48811yescharacteristic
420Q8—1222no—
421Q8—1222no—
422Q8—9761no—
423Q8—2444no—
424Q8—2441no—
425Q8—2441no—
426Q8—2441no—
427Q8—2441no—
428D4—9761no—
429D4—2441no—
430D4—2441no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—9761no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2444no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4C2×D48811yescharacteristic
443C2×C4C2×D48811yescharacteristic
444C2×C4C2×D48811yescharacteristic
445C2×C4C2×D48811yescharacteristic
446C2×C4C2×D48811yescharacteristic
447C2×C4C22×D24411yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8#41×D6111yescharacteristic
452C8#41×D6111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—4881no—
457C22—4881no—
458C22—4881no—
459C22C22×D48811yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—4881no—
466C4—4881no—
467C4—4881no—
468C4—4881no—
469C4—4881no—
470C4—2442no—
471C4—2442no—
472C4#1684027411yescharacteristic
473C4#1684056211yescharacteristic
474C2—41no—
475C2—9761no—
476C2#2145582011yescharacteristic
477C2#2145896711yescharacteristic
478C2#2145897211yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2164C2
socleC22×C61C22×D8
prime radical#16839998C22
hypercenter#2164D61
hypocenterC61#33681
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
2. #21454688C2semidirect
3. #21448028C2semidirect
5. #21447972C2semidirect
6. #21447962C2semidirect
7. #21447882C2semidirect
8. #21447882C2semidirect
9. #21447755C2semidirect
11. #21447691C2semidirect
12. #21447685C2semidirect
13. C4×Dic488C2semidirect
14. C4×#14519722C2semidirect
15. C61×#2164C2semidirect
249. #2164D61semidirect
298. C61#33681semidirect

Maximal subgroups

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

subgroupindex
#214564582
#214546882
#214480282
#214480112
#214479722
#214479622
#214478822
#214477552
#214477382
#214476912
#214476852
C4×Dic4882
C4×#145197222
C61×#21642
#3368161