Finite Group Databasebeta

← #29729815

Subgroups — #29729815

Order 15616.

732 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456194C211yesmaximal, characteristic
2#21455624C211yesmaximal, characteristic, complemented
3C2×#16839962C211yesmaximal, characteristic
4#21454766C211yesmaximal, characteristic, complemented
5#21447180C212yesmaximal, complemented
6#21447078C212yesmaximal, complemented
7#21446723C212yesmaximal, complemented
8#21446659C211yesmaximal, characteristic
9#21446594C211yesmaximal, characteristic, complemented
10#21446479C212yesmaximal, complemented
11C4×#101×C61C211yesmaximal, characteristic, complemented
12C22×#11758201C2212yes—
13#16840319C2211yescharacteristic
14C2×#14519774C2211yescharacteristic
15#16840127—22no—
16#16840109—21no—
17#16840109—21no—
18#16840069—22no—
19#16840057—21no—
20#16840047—21no—
21#16839962—21no—
22#16839962—22no—
23#16839962—21no—
24#16839892—21no—
25#16839890—22no—
26C8×Dic122—21no—
27C2×#14519712C2212yes—
28#16839802C2212yes—
29#16839790C2212yes—
30#16839786C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32#16839771C2212yes—
33#16839768C2212yes—
34#16839768C2212yes—
35C2×#14519697C2212yes—
36C2×#14519693C2212yes—
37C2×#14519693C2212yes—
38#16839720C2212yes—
39#16839526C2212yes—
40C2×C4×Q8×C61C2211yescharacteristic
41C2×#101×C61C2211yescharacteristic
42C2×#101×C61C2211yescharacteristic
43C4×M16×C61C2211yescharacteristic
44C4×M16×C61C2211yescharacteristic
45C61×#343C2211yescharacteristic
46C61×#343C2211yescharacteristic
47C22×D244—21no—
48C22×D244—21no—
49C22×D244C2312yes—
50C2×#11758201—24no—
51C2×#11758201—22no—
52C2×#11758201—22no—
53C2×#11758201—42no—
54C2×#11758194C2312yes—
55C22×#92418C2312yes—
56#14519777D411yescharacteristic
57#14519777D411yescharacteristic
58#14519774—21no—
59#14519774—21no—
60#14519774—21no—
61#14519774—21no—
62#14519769D412yes—
63#14519756—21no—
64#14519756—21no—
65C4×Dic122—21no—
66C4×Dic122—21no—
67#14519736C2312yes—
68#14519712—42no—
69#14519710—22no—
70#14519708—22no—
71C4⋊#92418—21no—
72C4⋊#92418—21no—
73C4⋊#92418D411yescharacteristic
74C4⋊#92418D412yes—
75C4⋊#92418D411yescharacteristic
76#14519706—22no—
77#14519706—22no—
78#14519701—22no—
79#14519701—22no—
80#14519699—22no—
81#14519699—22no—
82#14519699—22no—
83#14519699—22no—
84#14519697—22no—
85#14519697—22no—
86#14519693—24no—
87#14519693—42no—
88#14519687—22no—
89C8×Dic61—22no—
90C22×Q8×C61C2311yescharacteristic
91C2×M16×C61C2311yescharacteristic
92C2×M16×C61C2311yescharacteristic
93C2×M16×C61C2311yescharacteristic
94C2×M16×C61C2311yescharacteristic
95C4×Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×Q8×C61—21no—
98C4×Q8×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C42×C61—21no—
102C2×C42×C61C2311yescharacteristic
103#101×C61—22no—
104#101×C61—22no—
105#97×C61—21no—
106#97×C61—21no—
107C4×C8×C61—21no—
108C4×C8×C61—21no—
109C23×D61—22no—
110C2×Q8×C61—21no—
111C2×Q8×C61—21no—
112C2×Q8×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61#4112yes—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61C2411yescharacteristic
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—41no—
128C2×D244—41no—
129C2×D244—41no—
130C2×D244—41no—
131C2×D244—82no—
132C2×D244—82no—
133C2×Dic122—21no—
134C2×Dic122—21no—
135M16×C61—21no—
136M16×C61—21no—
137M16×C61—21no—
138M16×C61—21no—
139M16×C61—21no—
140M16×C61—21no—
141M16×C61—21no—
142M16×C61#4112yes—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—41no—
150C4⋊C4×C61—41no—
151C42×C61—41no—
152C42×C61—41no—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C22⋊Dic61—22no—
158#11758201—44no—
159#11758201—44no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162C4⋊Dic61C2×D412yes—
163C4⋊Dic61C2×D412yes—
164#11758196—22no—
165#11758196—22no—
166C4×Dic61—22no—
167#11758194—22no—
168#11758194—22no—
169C2×#92418—22no—
170C2×#92418—22no—
171C2×#92418—22no—
172C2×#92418C2×D412yes—
173C2×#92418C2×D412yes—
174C23×C61C2×#4111yescharacteristic
175C22×D61—42no—
176C22×D61—42no—
177C22×D61—42no—
178C22×D61—82no—
179C22×D61—82no—
180Q8×C61—22no—
181Q8×C61—22no—
182Q8×C61—41no—
183Q8×C61—41no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—81no—
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12111yescharacteristic
193C2×C4×C61#12111yescharacteristic
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C2×C4×C61C2×#4111yescharacteristic
198C2×C4×C61C2×#4111yescharacteristic
199C2×C4×C61H(5,𝔽2)11yescharacteristic
200C2×C4×C612−1+411yescharacteristic
201C2×Dic61—22no—
202C2×Dic61—22no—
203D244—42no—
204D244—42no—
205D244—42no—
206D244—42no—
207D244—82no—
208D244—82no—
209D244—82no—
210D244—82no—
211Dic122—42no—
212Dic122—81no—
213C8×C61—22no—
214C8×C61—41no—
215C8×C61—41no—
216C8×C61—41no—
217#92418—22no—
218#92418—22no—
219#92418—42no—
220#25315—611nomaximal, Sylow
221C22×C61—21no—
222C22×C61—21no—
223C22×C61C2×#12111yescharacteristic
224C22×C61#52911yescharacteristic
225C22×C61#54211yescharacteristic
226C2×D61—82no—
227C2×D61—82no—
228C2×D61—82no—
229C2×D61—162no—
230C2×D61—162no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—42no—
235C4×C61—81no—
236C4×C61#47112yes—
237C4×C61#54611yescharacteristic
238C4×C61#54811yescharacteristic
239C4×C61#54811yescharacteristic
240C4×C61#55011yescharacteristic
241Dic61—42no—
242Dic61—42no—
243#3138—611no—
244#3078—611no—
245C2×#460—611no—
246#2962—611no—
247#2063—612no—
248#2046—612no—
249#1977—612no—
250#1965—611no—
251#1950—611no—
252#1931—612no—
253C4×#101D6111yescharacteristic, complemented
254C2×C61—21no—
255C2×C61—21no—
256C2×C61#242611yescharacteristic
257C2×C61C2×#47111yescharacteristic
258C2×C61#306811yescharacteristic
259D61—162no—
260C22×SD16—612no—
261#533—611no—
262C2×#127—611no—
263C2×C4×Q8C2×D6111yescharacteristic
264#490—1222no—
265#486—1221no—
266#486—1221no—
267#479—1222no—
268#477—1221no—
269#475—1221no—
270#460—1221no—
271#460—1222no—
272#460—1221no—
273#446—1221no—
274#446—1222no—
275C8×Q8—1221no—
276C2×#108—612no—
277#428—612no—
278#424—612no—
279#423—611no—
280C2×C4⋊C8—611no—
281#419—612no—
282#418—612no—
283#418—612no—
284C2×#102—612no—
285C2×#101C2×D6111yescharacteristic
286C2×#101C2×D6111yescharacteristic
287C2×#100—612no—
288C2×#100—612no—
289#405—612no—
290C4×M16C2×D6111yescharacteristic
291C4×M16C2×D6111yescharacteristic
292#343C2×D6111yescharacteristic
293#343C2×D6111yescharacteristic
294#341—612no—
295C61#2531511yescharacteristic, complemented, Sylow
296C22×Q8C22×D6111yescharacteristic
297C22×D4—612no—
298C22×D4—1221no—
299C22×D4—1221no—
300C2×SD16—1222no—
301C2×SD16—1222no—
302C2×SD16—1224no—
303C2×SD16—2442no—
304C2×M16—612no—
305C2×M16C22×D6111yescharacteristic
306C2×M16C22×D6111yescharacteristic
307C2×M16C22×D6111yescharacteristic
308C2×M16C22×D6111yescharacteristic
309C22×C8—612no—
310C4⋊Q8—611no—
311C4⋊Q8—611no—
312#127—1221no—
313#127—1221no—
314#127—1221no—
315#127—1221no—
316#125—612no—
317C22⋊Q8—1221no—
318C22⋊Q8—1221no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—1221no—
324C4×Q8—1221no—
325#117—612no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4C22×D6111yescharacteristic
328C2×C42—21no—
329C2×C42C22×D6111yescharacteristic
330#108—2442no—
331#107—1222no—
332#106—1222no—
333C4⋊C8—611no—
334C4⋊C8—611no—
335C4⋊C8—612no—
336C4⋊C8—1222no—
337C4⋊C8—1222no—
338C4⋊C8—1221no—
339C4⋊C8—1221no—
340#103—1222no—
341#103—1222no—
342#102—1222no—
343#102—1222no—
344#102—1222no—
345#102—1222no—
346#102—1222no—
347#102—1222no—
348#101—22no—
349#101—22no—
350#100—1224no—
351#100—2442no—
352#97—21no—
353#97—21no—
354#97—1222no—
355C4×C8—21no—
356C4×C8—21no—
357C4×C8—1222no—
358C24—1222no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—1221no—
365C2×Q8—1221no—
366C2×Q8#1175822212yes—
367C2×D4—1222no—
368C2×D4—1222no—
369C2×D4—1222no—
370C2×D4—1222no—
371C2×D4—1222no—
372C2×D4—1222no—
373C2×D4—4882no—
374C2×D4—4882no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4#1175822211yescharacteristic
382C22×C4#1175822211yescharacteristic
383C22×C4C23×D6111yescharacteristic
384SD16—2444no—
385SD16—2444no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—21no—
391M16—21no—
392M16—21no—
393M16—1222no—
394M16—1222no—
395M16#1175822212yes—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—612no—
401C2×C8—612no—
402C2×C8—1222no—
403C2×C8—1222no—
404C2×C8—1222no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—612no—
410C4⋊C4—612no—
411C4⋊C4—1222no—
412C4⋊C4—1222no—
413C4⋊C4—1221no—
414C4⋊C4—1221no—
415C22⋊C4—1222no—
416C42—41no—
417C42—41no—
418C42—1222no—
419C42D4×D6111yescharacteristic
420C42D4×D6111yescharacteristic
421C42D4×D6111yescharacteristic
422C42D4×D6111yescharacteristic
423C23—4882no—
424C23—4882no—
425C23—2442no—
426C23—2442no—
427C23—2442no—
428C23C2×#1175822211yescharacteristic
429Q8—22no—
430Q8—22no—
431Q8—41no—
432Q8—41no—
433Q8—4881no—
434Q8—2442no—
435D4—4882no—
436D4—4882no—
437D4—4882no—
438D4—4882no—
439D4—2442no—
440D4—2442no—
441D4—2442no—
442D4—2442no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—81no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4#1451975011yescharacteristic
453C2×C4#1451975011yescharacteristic
454C2×C4#1451975011yescharacteristic
455C2×C4#1451975011yescharacteristic
456C2×C4C2×D4×D6111yescharacteristic
457C2×C4C2×D4×D6111yescharacteristic
458C2×C4C2×#1175822211yescharacteristic
459C2×C4C2×#1175822211yescharacteristic
460C2×C4#1451982311yescharacteristic
461C2×C4#1451982411yescharacteristic
462C8—22no—
463C8—41no—
464C8—41no—
465C8—41no—
466C8—1222no—
467C8—1222no—
468C8—2442no—
469C22—21no—
470C22—21no—
471C22—9762no—
472C22—9762no—
473C22—4882no—
474C22—4882no—
475C22—4882no—
476C22C2×#1451975011yescharacteristic
477C22#1684029611yescharacteristic
478C22#1684038311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—2442no—
485C4—2442no—
486C4#1684002812yes—
487C4#1684040811yescharacteristic
488C4#1684042111yescharacteristic
489C4#1684042111yescharacteristic
490C4#1684043311yescharacteristic
491C2—21no—
492C2—21no—
493C2—9762no—
494C2#2144938511yescharacteristic
495C2C2×#1684002811yescharacteristic
496C2#2145555011yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×#101×C61C2
socleC22×C61C2×#121
prime radicalC2×#14519774C22
hypercenterC4×#101D61
hypocenterC61#25315
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #21455624C2semidirect
4. #21454766C2semidirect
5. #21447180C2semidirect
6. #21447078C2semidirect
7. #21446723C2semidirect
9. #21446594C2semidirect
10. #21446479C2semidirect
11. C4×#101×C61C2semidirect
253. C4×#101D61semidirect
295. C61#25315semidirect

Maximal subgroups

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

subgroupindex
#214561942
#214556242
C2×#168399622
#214547662
#214471802
#214470782
#214467232
#214466592
#214465942
#214464792
C4×#101×C612
#2531561