Finite Group Databasebeta

← #29596254

Subgroups — #29596254

Order 15616.

656 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448304C211yesmaximal, characteristic
2#21445744C211yesmaximal, characteristic
3#21445735C211yesmaximal, characteristic
4#21443938C211yesmaximal, characteristic, complemented
5#21443937C211yesmaximal, characteristic, complemented
6#21443936C211yesmaximal, characteristic, complemented
7C61×#1390C211yesmaximal, characteristic, complemented
8C22×#11758224C2211yescharacteristic
9C2×#14519733C411yescharacteristic, complemented
10C22×C4×Dic61C411yescharacteristic, complemented
11C2×#14519695—21no—
12C2×#14519694C2211yescharacteristic
13C2×#14519692C2211yescharacteristic
14C2×#14519691—21no—
15#16839725—21no—
16#16839666—21no—
17#16839662—21no—
18#16839642C2211yescharacteristic
19#16839641C411yescharacteristic, complemented
20#16839639C411yescharacteristic, complemented
21#16839623—21no—
22C22⋊C4×Dic61—21no—
23#16839609—21no—
24C2×#100×C61C2211yescharacteristic
25C2×#99×C61C2211yescharacteristic
26C61×#386C2211yescharacteristic
27C2×#11758224—21no—
28C2×#11758224—21no—
29C2×#11758224—21no—
30C2×#11758224—21no—
31C2×#11758224—42no—
32C2×#11758224—42no—
33C22×Dic122D411yescharacteristic
34C22×C22⋊D61C2×C411yescharacteristic
35C22×C22⋊D61D411yescharacteristic
36C23×Dic61C2×C411yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C2×#11758194—21no—
41#14519733—42no—
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61—42no—
52#14519695—42no—
53#14519694—21no—
54#14519694—21no—
55#14519692—21no—
56#14519692—21no—
57#14519691—42no—
58#14519689—42no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—42no—
63C22×D4×C61C2311yescharacteristic
64C23×C4×C61C2×C411yescharacteristic
65C2×M16×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61C2×C411yescharacteristic
69#100×C61—21no—
70#100×C61—21no—
71#99×C61—21no—
72#99×C61—21no—
73#95×C61—21no—
74C24×C61C22×C411yescharacteristic
75C24×C61C2×D411yescharacteristic
76C23×D61C22⋊C411yescharacteristic
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61#4111yescharacteristic
80C2×D4×C61#4111yescharacteristic
81C2×D4×C61#4111yescharacteristic
82C2×D4×C61#4111yescharacteristic
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—42no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C2×C22⋊D61—21no—
90C2×C22⋊D61—21no—
91C2×C22⋊D61—21no—
92C2×C22⋊D61—21no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—22no—
105C22×Dic61—21no—
106C22×Dic61—41no—
107C22×Dic61—42no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C22⋊C411yescharacteristic
113#11758224—44no—
114#11758224—44no—
115#11758224—44no—
116#11758224—44no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61—22no—
120C2×C4×D61—41no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—22no—
124C2×Dic122—41no—
125M16×C61—41no—
126M16×C61—41no—
127C2×C8×C61—41no—
128C22⋊C4×C61—42no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊Dic61—42no—
133C22⋊Dic61—41no—
134C22⋊Dic61—41no—
135C22⋊Dic61—41no—
136#11758198—42no—
137#11758198—42no—
138#11758196—42no—
139C4×Dic61—42no—
140C4×Dic61—42no—
141C4×Dic61—42no—
142#11758194—41no—
143#11758194—41no—
144C2×#92418—41no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61C2×C22⋊C411yescharacteristic
154C23×C61#11711yescharacteristic
155C23×C61#11711yescharacteristic
156C23×C61#12311yescharacteristic
157C23×C61#12311yescharacteristic
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—41no—
162C22×D61—41no—
163D4×C61—41no—
164D4×C61—41no—
165D4×C61—41no—
166D4×C61—41no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—22no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—81no—
178C2×C4×C61—81no—
179C2×C4×C61—81no—
180C2×C4×C61#12311yescharacteristic
181C2×C4×C61#12311yescharacteristic
182C22⋊D61—42no—
183C22⋊D61—42no—
184C22⋊D61—42no—
185C22⋊D61—42no—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—22no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—41no—
199C2×Dic61—42no—
200C2×Dic61—41no—
201C2×Dic61—42no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—81no—
206C2×Dic61—81no—
207C2×Dic61—81no—
208C2×Dic61#9912yes—
209C2×Dic61#9912yes—
210C4×D61—42no—
211C4×D61—42no—
212Dic122—42no—
213Dic122—42no—
214C8×C61—81no—
215#92418—81no—
216#12853—611nomaximal, Sylow
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—41no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—42no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61—81no—
233C22×C61#38111yescharacteristic
234C22×C61C2×#9911yescharacteristic
235C22×C61C2×#9911yescharacteristic
236C2×D61—42no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—81no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—42no—
244C4×C61—81no—
245C4×C61—161no—
246Dic61—22no—
247Dic61—22no—
248Dic61—41no—
249Dic61—42no—
250Dic61—81no—
251Dic61—161no—
252#2297—611no—
253#1785—611no—
254#1782—611no—
255#1390—611no—
256#1390—611no—
257#1390—611no—
258#1390D6111yescharacteristic, complemented
259C2×C61—21no—
260C2×C61—21no—
261C2×C61—41no—
262C2×C61—41no—
263C2×C61—41no—
264C2×C61—41no—
265C2×C61#181911yescharacteristic
266C2×C61#212011yescharacteristic
267C2×C61#212011yescharacteristic
268D61—81no—
269C22×#41—611no—
270C2×#117—611no—
271C22×C42—611no—
272C2×#101—1221no—
273C2×#100—611no—
274C2×#100C2×D6111yescharacteristic
275C2×#99—611no—
276C2×#99—1221no—
277C2×#99C2×D6111yescharacteristic
278#407—1221no—
279#391—1221no—
280#390—1221no—
281#386—611no—
282#386—611no—
283#386—611no—
284#386C2×D6111yescharacteristic
285#381—1221no—
286C4×C22⋊C4—1221no—
287C4×C22⋊C4—1221no—
288C61#1285311yescharacteristic, complemented, Sylow
289C2×#41—1221no—
290C2×#41—1221no—
291C2×#41—1221no—
292C2×#41—1221no—
293C2×#41—2442no—
294C2×#41—2442no—
295C22×Q8—611no—
296C22×D4—611no—
297C22×D4—611no—
298C22×D4C22×D6111yescharacteristic
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4C4×D6111yescharacteristic
304C2×M16—21no—
305C2×M16—1221no—
306#117—2442no—
307C2×C4⋊C4—1221no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—611no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4C4×D6111yescharacteristic
316C2×C42—1221no—
317C2×C42—1221no—
318C2×C42—1221no—
319C2×C42—2442no—
320#101—2442no—
321#100—21no—
322#100—21no—
323#100—1221no—
324#100—1221no—
325#99—21no—
326#99—21no—
327#99—1221no—
328#99—1221no—
329#99—2442no—
330C22⋊C8—2442no—
331#95—21no—
332#95—1221no—
333#95—1221no—
334#95—1221no—
335#95—2442no—
336C24—611no—
337C24C2×C4×D6111yescharacteristic
338C24D4×D6111yescharacteristic
339#41—2444no—
340#41—2444no—
341#41—2444no—
342#41—2444no—
343C2×Q8—1222no—
344C2×Q8—1221no—
345C2×Q8—1221no—
346C2×Q8—2441no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—1222no—
350C2×D4—1221no—
351C2×D4—1221no—
352C2×D4—1221no—
353C2×D4—1221no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4#1175822211yescharacteristic
358C2×D4#1175822211yescharacteristic
359C2×D4#1175822411yescharacteristic
360C2×D4#1175822611yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—42no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—1222no—
372C22×C4—1222no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2442no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4D4×D6111yescharacteristic
387M16—41no—
388M16—41no—
389M16—2441no—
390M16—2441no—
391C2×C8—41no—
392C2×C8—2441no—
393C4⋊C4—2442no—
394C22⋊C4—42no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—2442no—
399C22⋊C4—2442no—
400C22⋊C4—2442no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C42—2442no—
405C42—2442no—
406C42—2442no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—1221no—
416C23—1221no—
417C23—1221no—
418C23—2441no—
419C23—2441no—
420C23C22⋊C4×D6111yescharacteristic
421C23#1451973411yescharacteristic
422C23#1451973511yescharacteristic
423C23#1451975911yescharacteristic
424C23#1451976211yescharacteristic
425Q8—2442no—
426Q8—2442no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—41no—
431D4—2442no—
432D4—2442no—
433D4—2442no—
434D4—2442no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—612no—
449C2×C4—612no—
450C2×C4—1224no—
451C2×C4—1224no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—1222no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—4881no—
461C2×C4—4881no—
462C2×C4—4881no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4—2442no—
467C2×C4—2441no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4—2441no—
471C2×C4—2442no—
472C2×C4—2441no—
473C2×C4—2442no—
474C2×C4#1451975911yescharacteristic
475C2×C4#1451976211yescharacteristic
476C8—81no—
477C8—4881no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—81no—
494C22—4881no—
495C22—2442no—
496C22—2441no—
497C22—2441no—
498C22—2441no—
499C22#1683962411yescharacteristic
500C22#99×D6111yescharacteristic
501C22#99×D6111yescharacteristic
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—161no—
507C4—1222no—
508C4—1222no—
509C4—9761no—
510C4—4881no—
511C4—2441no—
512C4—2442no—
513C2—21no—
514C2—21no—
515C2—41no—
516C2—41no—
517C2—41no—
518C2—41no—
519C2—4881no—
520C2#2144589211yescharacteristic
521C2#2144745711yescharacteristic
522C2#2144745911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1390C2
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×D4×C61C23
hypercenter#1390D61
hypocenterC61#12853
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
4. #21443938C2semidirect
5. #21443937C2semidirect
6. #21443936C2semidirect
7. C61×#1390C2semidirect
9. C2×#14519733C4semidirect
10. C22×C4×Dic61C4semidirect
19. #16839641C4semidirect
20. #16839639C4semidirect
258. #1390D61semidirect
288. C61#12853semidirect

Maximal subgroups

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

subgroupindex
#214483042
#214457442
#214457352
#214439382
#214439372
#214439362
C61×#13902
#1285361