Finite Group Databasebeta

← #29710003

Subgroups — #29710003

Order 15616.

880 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448226C211yesmaximal, characteristic, complemented
2#21447377C211yesmaximal, characteristic, complemented
3#21447347C211yesmaximal, characteristic, complemented
4#21447290C211yesmaximal, characteristic, complemented
5#21447245C212yesmaximal, complemented
6#21447222C211yesmaximal, characteristic, complemented
7#21446998C212yesmaximal
8C4×#14519710C212yesmaximal, complemented
9C4×#14519698C212yesmaximal, complemented
10C4×C22⋊#92418C211yesmaximal, characteristic, complemented
11C4×#121×C61C211yesmaximal, characteristic
12C2×#14519736—21no—
13C2×#14519710C2212yes—
14C2×#14519710C2212yes—
15C2×#14519698C2212yes—
16C2×#14519698C2212yes—
17C2×C22⋊#92418C2212yes—
18C2×C4×#92418C2212yes—
19#16839632C2211yescharacteristic
20#16839632C2211yescharacteristic
21#16839628—21no—
22#16839622—21no—
23#16839622C2212yes—
24C4×C4⋊Dic61—21no—
25C4×C4⋊Dic61C2212yes—
26#16839524C2212yes—
27#16839524C2212yes—
28#16839524C2212yes—
29#16839524C2212yes—
30#16839517C2211yescharacteristic
31#16839517C2211yescharacteristic
32C2×#121×C61C2211yescharacteristic
33C2×C4×D4×C61—21no—
34C2×C4×D4×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C61×#390C2211yescharacteristic
37C61×#389C2211yescharacteristic
38C61×#388—21no—
39C61×#386—21no—
40C61×#380C2211yescharacteristic
41C4×C4⋊C4×C61C2211yescharacteristic
42C4×C22⋊C4×C61—21no—
43C22×#92418C2312yes—
44C22×#92418C2312yes—
45#14519736—44no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61C2312yes—
51C2×C4⋊Dic61C2312yes—
52C2×C22⋊Dic61—22no—
53C2×C4×Dic61—22no—
54#14519710—24no—
55#14519710—24no—
56#14519698—24no—
57#14519698—24no—
58C22⋊#92418—24no—
59C4×#92418—24no—
60#14519684—22no—
61#14519684—22no—
62C22×D4×C61—21no—
63C22×D4×C61C2311yescharacteristic
64C23×C4×C61—21no—
65C23×C4×C61D411yescharacteristic
66C23×C4×C61D411yescharacteristic
67C23×C4×C61C2311yescharacteristic
68#121×C61—22no—
69#121×C61—22no—
70C4×D4×C61—24no—
71C4×D4×C61—44no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61C2311yescharacteristic
74C2×C4⋊C4×C61C2311yescharacteristic
75C2×C4⋊C4×C61C2311yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61—21no—
81C2×C42×C61—24no—
82C2×C42×C61—21no—
83C2×C42×C61D411yescharacteristic
84C2×C42×C61D411yescharacteristic
85C2×C42×C61C2311yescharacteristic
86C2×C42×C61C2311yescharacteristic
87#95×C61—21no—
88#95×C61—21no—
89#95×C61—21no—
90C24×C61—21no—
91C24×C61C2×D411yescharacteristic
92C2×D4×C61—24no—
93C2×D4×C61—22no—
94C2×D4×C61—22no—
95C2×D4×C61—21no—
96C2×D4×C61—42no—
97C2×D4×C61—42no—
98C2×D4×C61#4112yes—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—21no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—22no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—41no—
111C22×C4×C61—42no—
112C22×C4×C61—42no—
113C22×C4×C61—42no—
114C22×C4×C61D814yes—
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2411yescharacteristic
121C22×Dic61—22no—
122C22×Dic61—22no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—42no—
127C4⋊C4×C61#4112yes—
128C22⋊C4×C61—24no—
129C22⋊C4×C61—42no—
130C22⋊C4×C61—42no—
131C22⋊C4×C61—42no—
132C22⋊C4×C61—42no—
133C42×C61—22no—
134C42×C61—22no—
135C42×C61—22no—
136C42×C61—42no—
137C42×C61#4114yes—
138C22⋊Dic61—44no—
139C4⋊Dic61—22no—
140C4⋊Dic61—22no—
141C4⋊Dic61—22no—
142C4⋊Dic61—22no—
143C4⋊Dic61—42no—
144C4⋊Dic61—42no—
145C4⋊Dic61—42no—
146C4⋊Dic61—42no—
147C4×Dic61—44no—
148C2×#92418—22no—
149C2×#92418—22no—
150C2×#92418—22no—
151C2×#92418—22no—
152C2×#92418—22no—
153C2×#92418#4114yes—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—22no—
161C23×C61—41no—
162C23×C61—41no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61C2×D812yes—
168C23×C61C22×D411yescharacteristic
169D4×C61—24no—
170D4×C61—48no—
171D4×C61—42no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—28no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—22no—
182C2×C4×C61—21no—
183C2×C4×C61—44no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—84no—
195C2×C4×C61#12312yes—
196C2×C4×C61#12312yes—
197C2×C4×C61C2×D812yes—
198C2×C4×C61C2×D812yes—
199C2×C4×C61#13512yes—
200C2×C4×C61#13712yes—
201C2×C4×C61C2×#4112yes—
202C2×C4×C61C2×#4112yes—
203C2×C4×C61C2×#4111yescharacteristic
204C2×C4×C61C2×#4111yescharacteristic
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211#92418—24no—
212#92418—42no—
213#23754—611nomaximal, Sylow
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—22no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—42no—
222C22×C61—42no—
223C22×C61—42no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61C2×#12311yescharacteristic
229C22×C61#52511yescharacteristic
230C22×C61#53211yescharacteristic
231C22×C61C22×D811yescharacteristic
232C22×C61C2×#13511yescharacteristic
233C22×C61C2×#13711yescharacteristic
234C22×C61#57511yescharacteristic
235C4×C61—22no—
236C4×C61—22no—
237C4×C61—22no—
238C4×C61—42no—
239C4×C61—41no—
240C4×C61—81no—
241C4×C61—81no—
242C4×C61#48014yes—
243C4×C61#52912yes—
244C4×C61#52912yes—
245Dic61—82no—
246Dic61—82no—
247C4×#121D6111yescharacteristic
248#2285—611no—
249#2099—611no—
250#2093—611no—
251#2083—611no—
252#2075—612no—
253#2071—611no—
254#2033—612no—
255C4×#107—612no—
256C4×#102—612no—
257C4×C22⋊C8—611no—
258C2×C61—42no—
259C2×C61—82no—
260C2×C61#239511yescharacteristic
261C2×C61C2×#48011yescharacteristic
262C2×C61#309111yescharacteristic
263C2×C61#310011yescharacteristic
264C2×C61#310711yescharacteristic
265C2×C61#316911yescharacteristic
266C2×C61#317211yescharacteristic
267C2×#121C2×D6111yescharacteristic
268C2×C4×D4—21no—
269C2×C4×D4C2×D6111yescharacteristic
270C2×#117—1221no—
271C22×C42C2×D6111yescharacteristic
272C2×#107—612no—
273C2×#107—612no—
274C2×#102—612no—
275C2×#102—612no—
276C2×C22⋊C8—612no—
277C2×C4×C8—612no—
278#390C2×D6111yescharacteristic
279#389C2×D6111yescharacteristic
280#388—21no—
281#386—21no—
282#384—611no—
283#384—611no—
284#382—1221no—
285#380—612no—
286#380—1221no—
287#380C2×D6111yescharacteristic
288C4×C4⋊C4—612no—
289C4×C4⋊C4—1221no—
290C4×C4⋊C4C2×D6111yescharacteristic
291C4×C22⋊C4—21no—
292#340—612no—
293#340—612no—
294#340—612no—
295#340—612no—
296#336—611no—
297#336—611no—
298C61#2375411yescharacteristic, complemented, Sylow
299C22×D4—21no—
300C22×D4C22×D6111yescharacteristic
301C23×C4—21no—
302C23×C4C22⋊D6111yescharacteristic
303C23×C4C22⋊D6111yescharacteristic
304C23×C4C22×D6111yescharacteristic
305C22×C8—612no—
306C22×C8—612no—
307#121—22no—
308#121—22no—
309C4×D4—24no—
310C4×D4—44no—
311#117—2444no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—612no—
314C2×C4⋊C4—612no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4C22×D6111yescharacteristic
320C2×C4⋊C4C22×D6111yescharacteristic
321C2×C4⋊C4C22×D6111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—1222no—
328C2×C42—24no—
329C2×C42—21no—
330C2×C42—1222no—
331C2×C42C22⋊D6111yescharacteristic
332C2×C42C22⋊D6111yescharacteristic
333C2×C42C22×D6111yescharacteristic
334C2×C42C22×D6111yescharacteristic
335#107—1224no—
336#107—1224no—
337#102—1224no—
338#102—1224no—
339C22⋊C8—1224no—
340C4×C8—1224no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—1222no—
345#95—1222no—
346C24—21no—
347C24C2×C22⋊D6111yescharacteristic
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4#1175822212yes—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—41no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—1222no—
371C22×C4—1222no—
372C22×C4#1175819914yes—
373C22×C4C2×C22⋊D6111yescharacteristic
374C22×C4C2×C22⋊D6111yescharacteristic
375C22×C4C2×C22⋊D6111yescharacteristic
376C22×C4C2×C22⋊D6111yescharacteristic
377C22×C4C2×C22⋊D6111yescharacteristic
378C22×C4C23×D6111yescharacteristic
379C2×C8—614no—
380C2×C8—1222no—
381C2×C8—1222no—
382C2×C8—1222no—
383C2×C8—1222no—
384C2×C8—1222no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4—1222no—
392C4⋊C4—1222no—
393C4⋊C4—2442no—
394C4⋊C4—2442no—
395C4⋊C4—2442no—
396C4⋊C4—2442no—
397C4⋊C4#1175822212yes—
398C22⋊C4—24no—
399C22⋊C4—42no—
400C22⋊C4—42no—
401C22⋊C4—42no—
402C22⋊C4—42no—
403C22⋊C4—2444no—
404C42—22no—
405C42—22no—
406C42—22no—
407C42—42no—
408C42—2444no—
409C42#1175822414yes—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23C2×#1175819912yes—
424C23C22×C22⋊D6111yescharacteristic
425D4—24no—
426D4—48no—
427D4—42no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—28no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—44no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—84no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4—2442no—
457C2×C4#1451975812yes—
458C2×C4#1451975812yes—
459C2×C4C2×#1175819912yes—
460C2×C4C2×#1175819912yes—
461C2×C4#1451979712yes—
462C2×C4#1451980712yes—
463C2×C4#41×D6112yes—
464C2×C4C2×#1175822412yes—
465C2×C4C2×#1175822211yescharacteristic
466C2×C4C2×#1175822211yescharacteristic
467C8—1224no—
468C8—2442no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C2×#1451975811yescharacteristic
484C22#1684027311yescharacteristic
485C22#1684030811yescharacteristic
486C22C22×#1175819911yescharacteristic
487C22C2×#1451979711yescharacteristic
488C22C2×#1451980711yescharacteristic
489C22#1684056011yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—41no—
494C4—42no—
495C4—81no—
496C4—81no—
497C4—4882no—
498C4—4882no—
499C4#1684007314yes—
500C4#1684029212yes—
501C4#1684029412yes—
502C2—42no—
503C2—82no—
504C2#2144907811yescharacteristic
505C2C2×#1684007311yescharacteristic
506C2#2145572811yescharacteristic
507C2#2145581911yescharacteristic
508C2#2145589011yescharacteristic
509C2#2145639411yescharacteristic
510C2#2145642611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×#121×C61C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC4×#121D61
hypocenterC61#23754
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #21448226C2semidirect
2. #21447377C2semidirect
3. #21447347C2semidirect
4. #21447290C2semidirect
5. #21447245C2semidirect
6. #21447222C2semidirect
8. C4×#14519710C2semidirect
9. C4×#14519698C2semidirect
10. C4×C22⋊#92418C2semidirect
298. C61#23754semidirect

Maximal subgroups

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

subgroupindex
#214482262
#214473772
#214473472
#214472902
#214472452
#214472222
#214469982
C4×#145197102
C4×#145196982
C4×C22⋊#924182
C4×#121×C612
#2375461