Finite Group Databasebeta

← #29836884

Subgroups — #29836884

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458164C211yesmaximal, characteristic
2Q16×C22⋊D61C211yesmaximal, characteristic, complemented
3#21448045C211yesmaximal, characteristic, complemented
4#21448016C211yesmaximal, characteristic, complemented
5#21448015C211yesmaximal, characteristic, complemented
6#21447959C211yesmaximal, characteristic, complemented
7#21447918C211yesmaximal, characteristic, complemented
8#21447915C211yesmaximal, characteristic, complemented
9#21447863C211yesmaximal, characteristic, complemented
10#21447737C211yesmaximal, characteristic, complemented
11#21447736C211yesmaximal, characteristic, complemented
12#21447668C211yesmaximal, characteristic, complemented
13C16×C22⋊D61C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C2×C61×#358C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17Q8×C22⋊D61—21no—
18#16840413—21no—
19C2×#14519722C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21C2×#14519720C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840077—21no—
26#16840075—21no—
27#16840041—21no—
28#16840003C2211yescharacteristic
29#16840000C2211yescharacteristic
30#16839999C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839970—21no—
33#16839918—21no—
34#16839916—21no—
35Q16×Dic61C2211yescharacteristic
36#16839844C2211yescharacteristic
37C8×C22⋊D61C2211yescharacteristic
38#107×D61C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839589C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839564C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C22×Q16×C61C2211yescharacteristic
53C22×C16×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C61×#358C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×#11758222—41no—
60C2×Q8×D61—21no—
61C2×Dic244C2311yescharacteristic
62C2×#11758202—21no—
63C2×#11758202—21no—
64Q16×D61—22no—
65Q16×D61—41no—
66C2×D488C2311yescharacteristic
67C2×C8×D61C2311yescharacteristic
68#14519776—21no—
69#14519775—21no—
70#14519775—41no—
71#14519762—41no—
72#14519760—41no—
73#14519756—21no—
74#14519756—41no—
75#14519755—41no—
76#14519753—21no—
77#14519753—41no—
78#14519752—21no—
79#14519751—21no—
80Q8×Dic61—21no—
81#14519739—21no—
82C4×C22⋊D61—41no—
83C4×C22⋊D61D411yescharacteristic
84C4⋊C4×D61—21no—
85#14519722—41no—
86#14519720—22no—
87#14519720—41no—
88C2×#11758185C2311yescharacteristic
89C2×#11758185C2311yescharacteristic
90C16×D61—41no—
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519706D411yescharacteristic
96#14519702—21no—
97#14519701—21no—
98#14519701—21no—
99#14519699—21no—
100#14519697—21no—
101#14519697—21no—
102C22⋊#92418D411yescharacteristic
103#14519689D411yescharacteristic
104C8×Dic61C2311yescharacteristic
105C22×Q8×C61—21no—
106C2×Q16×C61—22no—
107C2×Q16×C61—21no—
108C2×Q16×C61—41no—
109C2×Q16×C61C2311yescharacteristic
110C2×Q16×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C4⋊C4×C61—21no—
113C2×C16×C61—41no—
114C2×C16×C61C2311yescharacteristic
115C2×C16×C61C2311yescharacteristic
116#107×C61—21no—
117#107×C61C2311yescharacteristic
118#107×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61—42no—
122C2×Q8×C61—41no—
123C2×Q8×C61—81no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—41no—
128C2×C22⋊D61D811yescharacteristic
129Q8×D61—42no—
130Q8×D61—81no—
131#11758222—84no—
132C2×D244—21no—
133C2×D244—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61C2×D411yescharacteristic
138C2×Dic122—21no—
139C2×Dic122—41no—
140C2×Dic122—41no—
141Q16×C61—21no—
142Q16×C61—21no—
143Q16×C61—21no—
144Q16×C61—42no—
145Q16×C61#4112yescomplemented
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61C2×D411yescharacteristic
149C2×C8×C61C2411yescharacteristic
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—41no—
153C22⋊Dic61—41no—
154C22⋊Dic61D811yescharacteristic
155#11758202—42no—
156#11758202—81no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198D811yescharacteristic
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61—41no—
165#11758196—41no—
166#11758196—41no—
167#11758196—41no—
168#11758196—41no—
169#11758196—41no—
170#11758196—41no—
171#11758196D811yescharacteristic
172C4×Dic61—41no—
173C4×Dic61C2×D411yescharacteristic
174C2×#92418C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176Dic244—21no—
177Dic244—21no—
178D488—21no—
179D488—21no—
180C8×D61—21no—
181C8×D61—21no—
182C16×C61—21no—
183C16×C61—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61C2×D811yescharacteristic
187C22×D61—41no—
188C22×D61C2×D811yescharacteristic
189Q8×C61—22no—
190Q8×C61—41no—
191Q8×C61—41no—
192Q8×C61—41no—
193Q8×C61—82no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—82no—
201C2×C4×C61—82no—
202C2×C4×C61C2×D811yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C22⋊D61—82no—
205C22⋊D61SD3214yescomplemented
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61C2×D811yescharacteristic
210C2×Dic61C2×D811yescharacteristic
211C2×Dic61C2×D811yescharacteristic
212D244—41no—
213D244—41no—
214D244—82no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—82no—
218C4×D61—82no—
219C4×D61—82no—
220Dic122—41no—
221Dic122—41no—
222Dic122—82no—
223Dic122—82no—
224C8×C61—21no—
225C8×C61C2×#4111yescharacteristic
226C8×C61H(5,𝔽2)11yescharacteristic
227#92418—21no—
228#92418—21no—
229#33865—611nomaximal, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61C2×SD3212yes—
233C22×C61C22×D811yescharacteristic
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—81no—
239C2×D61C2×SD3212yes—
240C4×C61—21no—
241C4×C61—42no—
242C4×C61—81no—
243C4×C61—81no—
244C4×C61—81no—
245C4×C61#54611yescharacteristic
246C4×C61#57711yescharacteristic
247Dic61—21no—
248Dic61—21no—
249Dic61—81no—
250Dic61—81no—
251Dic61—81no—
252Dic61C2×SD3212yes—
253#3334—611no—
254D4×Q16—611no—
255#2241—611no—
256#2235—611no—
257#2235—611no—
258#2225—611no—
259#2217—611no—
260#2217—611no—
261#2208—611no—
262#2185—611no—
263#2185—611no—
264C4×SD32—611no—
265D4×C16—611no—
266C2×#358—611no—
267C2×#358D6111yescharacteristic, complemented
268C2×C61—22no—
269C2×C61#329411yescharacteristic
270C2×C61C22×SD3211yescharacteristic
271C2×C61#341711yescharacteristic
272D61—22no—
273D61—161no—
274C22×Q16—611no—
275C22×Q16C2×D6111yescharacteristic
276D4×Q8—1221no—
277#547—1221no—
278C2×SD32—611no—
279C2×SD32—611no—
280C2×SD32—611no—
281C22×C16—611no—
282C22×C16C2×D6111yescharacteristic
283#500—611no—
284#494—611no—
285#480—1221no—
286#480—1221no—
287#474—1221no—
288#467—611no—
289#467—611no—
290#466—611no—
291#466—611no—
292#462—1221no—
293#451—1221no—
294#451—1221no—
295C4×Q16—611no—
296C4×D8—611no—
297C8×D4—611no—
298C2×#107—611no—
299C2×#107C2×D6111yescharacteristic
300#367—611no—
301#367—611no—
302#367—611no—
303C4⋊C16—611no—
304#358—611no—
305#358—611no—
306#358—611no—
307#358—611no—
308#358—611no—
309#358C2×D6111yescharacteristic
310#358C2×D6111yescharacteristic
311#358C2×D6111yescharacteristic
312#358C2×D6111yescharacteristic
313#357—611no—
314C22⋊C16—611no—
315C22⋊C16—611no—
316C4×C16—611no—
317C61#3386511yescharacteristic, complemented, Sylow
318C2×#41—2441no—
319C22×Q8—21no—
320C22×Q8—1221no—
321C2×Q16—22no—
322C2×Q16—21no—
323C2×Q16—41no—
324C2×Q16—611no—
325C2×Q16—1221no—
326C2×Q16—1221no—
327C2×Q16—1222no—
328C2×Q16—2441no—
329C2×Q16C22×D6111yescharacteristic
330C2×Q16C22×D6111yescharacteristic
331C2×D8—611no—
332C22×C8—611no—
333C22×C8C22×D6111yescharacteristic
334C4⋊Q8—1221no—
335C4⋊Q8—1221no—
336C4⋊Q8—2441no—
337#123—2441no—
338#123—2441no—
339C22⋊Q8—1221no—
340C22⋊Q8—1221no—
341C22⋊Q8—2441no—
342C22⋊Q8—2441no—
343C22⋊Q8—2441no—
344#121—1221no—
345#121—1221no—
346C4×Q8—1221no—
347C4×D4—611no—
348C4×D4—1221no—
349C4×D4—2441no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—1221no—
352SD32—1222no—
353SD32—2441no—
354SD32—2441no—
355C2×C16—41no—
356C2×C16—611no—
357C2×C16—611no—
358C2×C16—2441no—
359C2×C16C22×D6111yescharacteristic
360C2×C16C22×D6111yescharacteristic
361#107—21no—
362#107—611no—
363#107—611no—
364#107—1221no—
365#107—1221no—
366#107C22×D6111yescharacteristic
367#107C22×D6111yescharacteristic
368C4⋊C8—611no—
369#103—1221no—
370#103—1221no—
371#103—1221no—
372#102—1221no—
373#102—1221no—
374#102—1221no—
375C22⋊C8—611no—
376C22⋊C8—611no—
377C4×C8—611no—
378#41—4884no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—42no—
382C2×Q8—41no—
383C2×Q8—81no—
384C2×Q8—1221no—
385C2×Q8—4881no—
386C2×Q8—2441no—
387C2×Q8—2441no—
388C2×Q8—2442no—
389C2×D4—611no—
390C2×D4—1221no—
391C2×D4—2441no—
392C2×D4—2441no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—611no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4D4×D6111yescharacteristic
400Q16—21no—
401Q16—21no—
402Q16—21no—
403Q16—42no—
404Q16—1221no—
405Q16—1221no—
406Q16—4881no—
407Q16—2442no—
408Q16#1175822212yescomplemented
409D8—1221no—
410D8—1221no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—611no—
414C2×C8—611no—
415C2×C8—1221no—
416C2×C8—1221no—
417C2×C8D4×D6111yescharacteristic
418C2×C8C23×D6111yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—611no—
423C4⋊C4—1221no—
424C4⋊C4—1221no—
425C4⋊C4—2441no—
426C4⋊C4—2441no—
427C4⋊C4—2441no—
428C4⋊C4—2441no—
429C4⋊C4—2441no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C22⋊C4—611no—
433C22⋊C4—611no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C42—611no—
440C42—2441no—
441C16—21no—
442C16—21no—
443C16—1221no—
444C16—1221no—
445C23—611no—
446C23—2441no—
447C23D8×D6111yescharacteristic
448Q8—22no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452Q8—82no—
453Q8—4882no—
454Q8—4882no—
455Q8—2441no—
456Q8—2441no—
457D4—614no—
458D4—4882no—
459D4—4882no—
460D4—2441no—
461D4—2441no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—611no—
471C2×C4—611no—
472C2×C4—611no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—4882no—
476C2×C4—4882no—
477C2×C4—4882no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4D8×D6111yescharacteristic
482C2×C4C2×D4×D6111yescharacteristic
483C8—21no—
484C8—1221no—
485C8—1221no—
486C8C2×#1175822211yescharacteristic
487C8#1451982211yescharacteristic
488C22—21no—
489C22—21no—
490C22—612no—
491C22—1221no—
492C22—1221no—
493C22—4881no—
494C22—4881no—
495C22—4881no—
496C22SD32×D6112yes—
497C22C2×D8×D6111yescharacteristic
498C4—21no—
499C4—42no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—612no—
504C4—1221no—
505C4—1221no—
506C4—4881no—
507C4—4881no—
508C4—4881no—
509C4#1684040211yescharacteristic
510C4#1684056811yescharacteristic
511C2—22no—
512C2—1222no—
513C2—9761no—
514C2#2145762811yescharacteristic
515C2C2×SD32×D6111yescharacteristic
516C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#358C2
socleC22×C61C22×D8
prime radical#21458164C2
hypercenterC2×#358D61
hypocenterC61#33865
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. Q16×C22⋊D61C2semidirect
3. #21448045C2semidirect
4. #21448016C2semidirect
5. #21448015C2semidirect
6. #21447959C2semidirect
7. #21447918C2semidirect
8. #21447915C2semidirect
9. #21447863C2semidirect
10. #21447737C2semidirect
11. #21447736C2semidirect
12. #21447668C2semidirect
13. C16×C22⋊D61C2semidirect
14. #358×D61C2semidirect
15. C2×C61×#358C2semidirect
145. Q16×C61#41semidirect
205. C22⋊D61SD32semidirect
267. C2×#358D61semidirect
317. C61#33865semidirect
408. Q16#11758222semidirect

Maximal subgroups

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

subgroupindex
#214581642
Q16×C22⋊D612
#214480452
#214480162
#214480152
#214479592
#214479182
#214479152
#214478632
#214477372
#214477362
#214476682
C16×C22⋊D612
#358×D612
C2×C61×#3582
#3386561