Finite Group Databasebeta

← #29836897

Subgroups — #29836897

Order 15616.

548 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458209C211yesmaximal, characteristic
2#21457568C211yesmaximal, characteristic
3#21448045C211yesmaximal, characteristic, complemented
4#21448023C211yesmaximal, characteristic, complemented
5#21447970C211yesmaximal, characteristic, complemented
6#21447911C211yesmaximal, characteristic, complemented
7#21447908C211yesmaximal, characteristic, complemented
8#21447868C211yesmaximal, characteristic, complemented
9#21447755C211yesmaximal, characteristic, complemented
10#21447754C211yesmaximal, characteristic, complemented
11#21447677C211yesmaximal, characteristic, complemented
12#21447636C211yesmaximal, characteristic
13C2×#16839565C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C61×#2236C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18#16840467—21no—
19#16840425—21no—
20C2×Dic488C2211yescharacteristic
21C2×Dic488C2211yescharacteristic
22C2×#14519723C2211yescharacteristic
23C22×#11758185C2211yescharacteristic
24C2×C16×D61C2211yescharacteristic
25#16840166C2211yescharacteristic
26#16840140C2211yescharacteristic
27#16840099—21no—
28#16840097—21no—
29#16840056—21no—
30#16840004C2211yescharacteristic
31#16840004C2211yescharacteristic
32#16840003C2211yescharacteristic
33#16839971—21no—
34#16839919—21no—
35#16839917—21no—
36#16839856C2211yescharacteristic
37#16839856C2211yescharacteristic
38C8×C22⋊D61C2211yescharacteristic
39#107×D61C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839565C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#366C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C22×Dic122—21no—
60C2×Q8×D61—21no—
61C2×Dic244—22no—
62C2×Dic244—21no—
63C2×Dic244—41no—
64C2×Dic244C2311yescharacteristic
65C2×Dic244C2311yescharacteristic
66C2×Dic244C2311yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69Q16×D61—22no—
70Q16×D61—41no—
71C2×C8×D61C2311yescharacteristic
72#14519776—21no—
73#14519776—41no—
74#14519775—21no—
75#14519767—41no—
76#14519757—21no—
77#14519757—21no—
78#14519756—21no—
79#14519756—41no—
80#14519755—41no—
81#14519755—41no—
82#14519754—41no—
83#14519742—21no—
84#14519742—21no—
85C4×C22⋊D61—41no—
86C4×C22⋊D61D411yescharacteristic
87#14519737—41no—
88C4⋊C4×D61—21no—
89Dic488—22no—
90Dic488—41no—
91#14519723—41no—
92C2×#11758185—41no—
93C2×#11758185C2311yescharacteristic
94C2×#11758185C2311yescharacteristic
95C16×D61—41no—
96#14519711C2311yescharacteristic
97#14519710—21no—
98#14519710—21no—
99#14519706D411yescharacteristic
100#14519702—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105C22⋊#92418D411yescharacteristic
106#14519689D411yescharacteristic
107C8×Dic61C2311yescharacteristic
108C2×Q16×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22⋊Q8×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114#107×C61—21no—
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#103×C61—21no—
119C2×Q8×C61—21no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61D811yescharacteristic
123C22×Dic61—41no—
124Q8×D61—42no—
125Q8×D61—81no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×C4×D61C2×D411yescharacteristic
129C2×Dic122—21no—
130C2×Dic122—21no—
131C2×Dic122—21no—
132C2×Dic122—42no—
133C2×Dic122—41no—
134C2×Dic122—41no—
135C2×Dic122—41no—
136C2×Dic122—81no—
137Q16×C61—21no—
138Q16×C61—21no—
139C2×C8×C61—21no—
140C2×C8×C61—21no—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C22⋊Dic61—41no—
150C22⋊Dic61D811yescharacteristic
151#11758202—42no—
152#11758202—81no—
153#11758198—41no—
154#11758198—41no—
155#11758198D811yescharacteristic
156C4⋊Dic61—21no—
157C4⋊Dic61—41no—
158C4⋊Dic61—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162#11758196—41no—
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
166#11758196D811yescharacteristic
167C4×Dic61—41no—
168C4×Dic61—41no—
169C4×Dic61C2×D411yescharacteristic
170C2×#92418C2×D411yescharacteristic
171C2×#92418C2×D411yescharacteristic
172Dic244—21no—
173Dic244—21no—
174Dic244—21no—
175Dic244—21no—
176Dic244—21no—
177Dic244—42no—
178Dic244#4112yes—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61C2×D811yescharacteristic
186C22×D61C2×D811yescharacteristic
187Q8×C61—41no—
188Q8×C61—41no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—161no—
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C22⋊D61Q3214yescomplemented
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—82no—
204C2×Dic61C2×D811yescharacteristic
205C2×Dic61C2×D811yescharacteristic
206C2×Dic61C2×D811yescharacteristic
207C4×D61—21no—
208C4×D61—21no—
209C4×D61—82no—
210C4×D61—161no—
211Dic122—22no—
212Dic122—41no—
213Dic122—41no—
214Dic122—41no—
215Dic122—41no—
216Dic122—41no—
217Dic122—82no—
218Dic122—82no—
219Dic122—161no—
220C8×C61—21no—
221C8×C61C2×#4111yescharacteristic
222C8×C61H(5,𝔽2)11yescharacteristic
223#92418—21no—
224#92418—21no—
225#33866—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61C2×Q3212yes—
229C22×C61C22×D811yescharacteristic
230C2×D61—21no—
231C2×D61—21no—
232C2×D61C2×Q3212yes—
233C4×C61—21no—
234C4×C61—81no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61—81no—
238C4×C61#54611yescharacteristic
239C4×C61#57711yescharacteristic
240Dic61—21no—
241Dic61—21no—
242Dic61—42no—
243Dic61—81no—
244Dic61—81no—
245Dic61—81no—
246Dic61C2×Q3212yes—
247#3338—611no—
248D4×Q16—611no—
249#2241—611no—
250#2236—611no—
251#2236D6111yescharacteristic, complemented
252#2227—611no—
253#2216—611no—
254#2216—611no—
255#2209—611no—
256#2188—611no—
257#2188—611no—
258C4×Q32—611no—
259D4×C16—611no—
260C2×#358—611no—
261C2×#358—611no—
262C2×C61—22no—
263C2×C61#329411yescharacteristic
264C2×C61C22×Q3211yescharacteristic
265C2×C61#341611yescharacteristic
266D61—22no—
267C22×Q16—611no—
268C22×Q16—611no—
269#554—1221no—
270D4×Q8—1221no—
271C2×Q32—611no—
272C2×Q32—611no—
273C2×Q32—611no—
274C22×C16—611no—
275C22×C16—611no—
276#500—611no—
277#494—611no—
278#484—1221no—
279#484—1221no—
280#477—1221no—
281#467—611no—
282#467—611no—
283#467—611no—
284#467C2×D6111yescharacteristic
285#462—1221no—
286#451—1221no—
287#451—1221no—
288C4×Q16—611no—
289C4×Q16—611no—
290C8×D4—611no—
291C2×#107—611no—
292C2×#107C2×D6111yescharacteristic
293#366—611no—
294#366C2×D6111yescharacteristic
295#366C2×D6111yescharacteristic
296C4⋊C16—611no—
297#358—611no—
298#358—611no—
299#358—611no—
300#358—611no—
301#358—611no—
302#358—611no—
303#358—611no—
304#358—611no—
305#358C2×D6111yescharacteristic
306#358C2×D6111yescharacteristic
307C22⋊C16—611no—
308C22⋊C16C2×D6111yescharacteristic
309C4×C16—611no—
310C61#3386611yescharacteristic, complemented, Sylow
311C22×Q8—1221no—
312C22×Q8—1221no—
313C2×Q16—611no—
314C2×Q16—611no—
315C2×Q16—611no—
316C2×Q16—1222no—
317C2×Q16—1221no—
318C2×Q16—1221no—
319C2×Q16—1222no—
320C2×Q16—1221no—
321C2×Q16—2441no—
322C2×Q16—2441no—
323C2×Q16C22×D6111yescharacteristic
324C22×C8—611no—
325C22×C8C22×D6111yescharacteristic
326C4⋊Q8—1221no—
327C4⋊Q8—1221no—
328C4⋊Q8—2441no—
329#125—2441no—
330C22⋊Q8—21no—
331C22⋊Q8—1221no—
332C22⋊Q8—1221no—
333C22⋊Q8—1221no—
334C22⋊Q8—2441no—
335C22⋊Q8—2441no—
336C22⋊Q8—2441no—
337C22⋊Q8—2441no—
338C4×Q8—1221no—
339C4×Q8—1221no—
340C4×D4—611no—
341C4×D4—2441no—
342C4×D4—2441no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—1221no—
345Q32—1222no—
346Q32—2441no—
347Q32—2441no—
348C2×C16—611no—
349C2×C16—611no—
350C2×C16—2441no—
351C2×C16—2441no—
352C2×C16C22×D6111yescharacteristic
353C2×C16C22×D6111yescharacteristic
354#107—21no—
355#107—611no—
356#107—1221no—
357#107—1221no—
358#107C22×D6111yescharacteristic
359#107C22×D6111yescharacteristic
360#107C22×D6111yescharacteristic
361C4⋊C8—611no—
362#103—21no—
363#103—1221no—
364#103—1221no—
365#103—1221no—
366#103—1221no—
367#103—1221no—
368C22⋊C8—611no—
369C22⋊C8—611no—
370C4×C8—611no—
371C2×Q8—21no—
372C2×Q8—1221no—
373C2×Q8—1221no—
374C2×Q8—1221no—
375C2×Q8—4881no—
376C2×Q8—4881no—
377C2×Q8—2442no—
378C2×Q8—2441no—
379C2×Q8—2441no—
380C2×Q8—2442no—
381C2×Q8—2441no—
382C2×D4—611no—
383C22×C4—41no—
384C22×C4—611no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4D4×D6111yescharacteristic
389Q16—21no—
390Q16—21no—
391Q16—612no—
392Q16—1221no—
393Q16—1221no—
394Q16—1221no—
395Q16—1221no—
396Q16—1221no—
397Q16—4881no—
398Q16—2442no—
399Q16—2442no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—611no—
403C2×C8—611no—
404C2×C8—1221no—
405C2×C8—1221no—
406C2×C8D4×D6111yescharacteristic
407C2×C8C23×D6111yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—611no—
414C4⋊C4—1221no—
415C4⋊C4—2441no—
416C4⋊C4—2441no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C4⋊C4—2441no—
420C4⋊C4—2441no—
421C4⋊C4—2441no—
422C4⋊C4—2441no—
423C4⋊C4—2441no—
424C22⋊C4—41no—
425C22⋊C4—611no—
426C22⋊C4—611no—
427C22⋊C4—2441no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C42—611no—
431C42—2441no—
432C42—2441no—
433C16—21no—
434C16—21no—
435C16—1221no—
436C16—1221no—
437C23—611no—
438C23D8×D6111yescharacteristic
439Q8—41no—
440Q8—41no—
441Q8—1222no—
442Q8—9761no—
443Q8—4882no—
444Q8—4882no—
445Q8—2441no—
446Q8—2441no—
447Q8—2441no—
448Q8—2441no—
449Q8—2441no—
450D4—614no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—161no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—611no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—9761no—
464C2×C4—4882no—
465C2×C4—4882no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4D8×D6111yescharacteristic
471C2×C4C2×D4×D6111yescharacteristic
472C8—21no—
473C8—1221no—
474C8—1221no—
475C8#41×D6111yescharacteristic
476C8#1451982311yescharacteristic
477C22—21no—
478C22—21no—
479C22—612no—
480C22—1221no—
481C22—1221no—
482C22Q32×D6112yes—
483C22C2×D8×D6111yescharacteristic
484C4—21no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—612no—
490C4—1221no—
491C4—1221no—
492C4—4881no—
493C4—4881no—
494C4—4881no—
495C4—2442no—
496C4#1684040411yescharacteristic
497C4#1684057111yescharacteristic
498C2—22no—
499C2—1222no—
500C2#2145763011yescharacteristic
501C2C2×Q32×D6111yescharacteristic
502C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2236C2
socleC22×C61C22×D8
prime radicalC2×C22⋊D61D8
hypercenter#2236D61
hypocenterC61#33866
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
3. #21448045C2semidirect
4. #21448023C2semidirect
5. #21447970C2semidirect
6. #21447911C2semidirect
7. #21447908C2semidirect
8. #21447868C2semidirect
9. #21447755C2semidirect
10. #21447754C2semidirect
11. #21447677C2semidirect
13. C2×#16839565C2semidirect
14. #358×D61C2semidirect
15. C61×#2236C2semidirect
198. C22⋊D61Q32semidirect
251. #2236D61semidirect
310. C61#33866semidirect

Maximal subgroups

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

subgroupindex
#214582092
#214575682
#214480452
#214480232
#214479702
#214479112
#214479082
#214478682
#214477552
#214477542
#214476772
#214476362
C2×#168395652
#358×D612
C61×#22362
#3386661