Finite Group Databasebeta

← #29590191

Subgroups — #29590191

Order 15616.

670 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451552C211yesmaximal, characteristic
2#342×D61C211yesmaximal, characteristic, complemented
3#323×D61C211yesmaximal, characteristic, complemented
4#21443820C211yesmaximal, characteristic, complemented
5#21443818C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic, complemented
7C61×#1343C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic, complemented
9C2×#14519745—21no—
10C2×C22⋊C4×D61—21no—
11C2×C22⋊C4×D61C2211yescharacteristic
12C22⋊C8×D61—21no—
13#16839689C411yescharacteristic, complemented
14#16839687C2211yescharacteristic
15#16839677—21no—
16#16839676—21no—
17#16839670C411yescharacteristic, complemented
18#16839638—21no—
19#16839621C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C22×C4×D61—41no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×C8×D61—41no—
34#14519748—41no—
35#14519748—41no—
36#14519745—42no—
37#14519745—42no—
38C2×C4⋊Dic61C2×C411yescharacteristic, complemented
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—41no—
48C2×#11758198C2×C411yescharacteristic
49C2×#11758198D411yescharacteristic
50C22⋊C4×D61—24no—
51C22⋊C4×D61—41no—
52C22⋊C4×D61—41no—
53C22⋊C4×D61—42no—
54C22⋊#92418—21no—
55#14519689—41no—
56#14519684—21no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic, complemented
59C22×D4×C61—21no—
60C22×D4×C61C2×C411yescharacteristic, complemented
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61C2311yescharacteristic
64C22⋊C8×C61—21no—
65#95×C61C2×C411yescharacteristic, complemented
66C24×C61—21no—
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C23×D61—21no—
70C23×D61—22no—
71C23×D61—81no—
72C23×D61—81no—
73C23×D61C22⋊C411yescharacteristic
74C23×D61C22⋊C411yescharacteristic
75C23×D61D812yes—
76C23×D61SD1612yes—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—81no—
81C2×D4×C61—81no—
82C2×D4×C61—81no—
83C22×C4×C61—21no—
84C22×C4×C61—41no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—42no—
90C2×C22⋊D61—42no—
91C2×C22⋊D61—42no—
92C2×C22⋊D61—81no—
93C2×C22⋊D61—81no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—41no—
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—44no—
104C2×C4×D61—81no—
105C2×C4×D61—82no—
106C2×C4×D61—82no—
107C2×C4×D61—81no—
108C2×C8×C61—41no—
109C22⋊C4×C61—22no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—81no—
113C22⋊Dic61—22no—
114C22⋊Dic61—41no—
115C22⋊Dic61—42no—
116C22⋊Dic61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119C22⋊Dic61—81no—
120#11758198—41no—
121#11758198—41no—
122#11758198—44no—
123#11758198—42no—
124#11758198—42no—
125C4⋊Dic61—41no—
126#11758196—81no—
127C2×#92418—41no—
128C8×D61—82no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61C2×C22⋊C411yescharacteristic
141C23×C61C2×D811yescharacteristic
142C23×C61C2×SD1611yescharacteristic
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—42no—
152C22×D61—42no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—81no—
156C22×D61—81no—
157C22×D61—82no—
158C22×D61—82no—
159C22×D61—84no—
160C22×D61#9911yescharacteristic
161C22×D61#9911yescharacteristic
162C22×D61#10212yes—
163C22×D61#10212yes—
164C22×D61#10412yes—
165D4×C61—82no—
166D4×C61—82no—
167D4×C61—82no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—81no—
177C2×C4×C61—81no—
178C22⋊D61—84no—
179C22⋊D61—82no—
180C22⋊D61—82no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—42no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—81no—
193C2×Dic61—81no—
194C4×D61—42no—
195C4×D61—81no—
196C4×D61—81no—
197C4×D61—81no—
198C4×D61—88no—
199C8×C61—81no—
200#92418—81no—
201#11692—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61C2×#9911yescharacteristic
219C22×C61C2×#10211yescharacteristic
220C22×C61C2×#10411yescharacteristic
221C2×D61—21no—
222C2×D61—21no—
223C2×D61—21no—
224C2×D61—21no—
225C2×D61—22no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—44no—
229C2×D61—44no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—42no—
233C2×D61—82no—
234C2×D61—82no—
235C2×D61—81no—
236C2×D61#32712yes—
237C2×D61#32712yes—
238C4×C61—41no—
239C4×C61—41no—
240C4×C61—81no—
241C4×C61—82no—
242Dic61—41no—
243Dic61—41no—
244Dic61—81no—
245Dic61—82no—
246Dic61—81no—
247#2617—611no—
248C2×#342—611no—
249C2×#323—611no—
250#1344—611no—
251#1344—611no—
252#1343—611no—
253#1343D6111yescharacteristic, complemented
254C2×C61—21no—
255C2×C61—21no—
256C2×C61—41no—
257C2×C61—41no—
258C2×C61—161no—
259C2×C61C2×#32711yescharacteristic
260C2×C61#212111yescharacteristic
261C2×C61#212711yescharacteristic
262D61—22no—
263D61—22no—
264D61—42no—
265C2×#121—611no—
266C2×#120—1221no—
267C22×C22⋊C4—611no—
268C22×C22⋊C4—1221no—
269C2×C22⋊C8—1221no—
270#397—611no—
271#397—611no—
272#394—1221no—
273#394—1221no—
274#392—611no—
275#392C2×D6111yescharacteristic
276#386—1221no—
277#380—611no—
278#342—611no—
279#342—1221no—
280#342C2×D6111yescharacteristic
281#323—611no—
282#323—1221no—
283#323C2×D6111yescharacteristic
284C61#1169211yescharacteristic, complemented, Sylow
285C25—611no—
286C22×D4—21no—
287C22×D4—1221no—
288C22×D4—1221no—
289C22×D4C4×D6111yescharacteristic, complemented
290C23×C4—611no—
291C23×C4—611no—
292C23×C4—2441no—
293C22×C8—2441no—
294#121—2441no—
295#121—2441no—
296#120—2442no—
297#120—2442no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—1221no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—1224no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—2441no—
313C2×C22⋊C4—2441no—
314C2×C22⋊C4—2442no—
315C2×C22⋊C4—2441no—
316C2×C22⋊C4C22×D6111yescharacteristic
317C22⋊C8—21no—
318C22⋊C8—1221no—
319C22⋊C8—2441no—
320#95—611no—
321#95—1221no—
322#95—1221no—
323#95C4×D6111yescharacteristic, complemented
324C24—21no—
325C24—611no—
326C24—612no—
327C24—612no—
328C24—611no—
329C24—1222no—
330C24—1221no—
331C24—1221no—
332C24—4881no—
333C24—4881no—
334C24D4×D6111yescharacteristic
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—81no—
339C2×D4—81no—
340C2×D4—81no—
341C2×D4—4881no—
342C2×D4—4881no—
343C2×D4—2442no—
344C2×D4—2442no—
345C2×D4—2441no—
346C2×D4—2441no—
347C2×D4—2442no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—4881no—
359C22×C4—4881no—
360C22×C4—4882no—
361C22×C4—4882no—
362C22×C4—2444no—
363C22×C4—2441no—
364C22×C4C2×C4×D6111yescharacteristic
365C22×C4D4×D6111yescharacteristic
366C2×C8—41no—
367C2×C8—4882no—
368C2×C8—2441no—
369C4⋊C4—4881no—
370C4⋊C4—2441no—
371C22⋊C4—22no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—81no—
375C22⋊C4—1222no—
376C22⋊C4—4881no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C22⋊C4—2442no—
380C22⋊C4—2442no—
381C22⋊C4—2444no—
382C22⋊C4—2441no—
383C22⋊C4—2442no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C23—21no—
388C23—21no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—611no—
399C23—611no—
400C23—612no—
401C23—612no—
402C23—612no—
403C23—1222no—
404C23—1222no—
405C23—1222no—
406C23—1222no—
407C23—1221no—
408C23—1221no—
409C23—4881no—
410C23—4881no—
411C23—4882no—
412C23—4882no—
413C23—4884no—
414C23—2441no—
415C23—2441no—
416C23—2441no—
417C23—2441no—
418C23—2442no—
419C23—2442no—
420C23C22⋊C4×D6111yescharacteristic
421C23D8×D6111yescharacteristic
422C23SD16×D6111yescharacteristic
423D4—82no—
424D4—82no—
425D4—82no—
426D4—4882no—
427D4—4882no—
428D4—4884no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—4881no—
442C2×C4—4881no—
443C2×C4—4881no—
444C2×C4—4888no—
445C2×C4—4881no—
446C2×C4—4881no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C8—81no—
458C8—4881no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—612no—
476C22—612no—
477C22—1221no—
478C22—1221no—
479C22—1221no—
480C22—1221no—
481C22—1222no—
482C22—4881no—
483C22—4882no—
484C22—4882no—
485C22—2442no—
486C22—2442no—
487C22—2442no—
488C22—2444no—
489C22—2444no—
490C22—2441no—
491C22—2441no—
492C22#99×D6111yescharacteristic
493C22#102×D6111yescharacteristic
494C22#104×D6111yescharacteristic
495C4—41no—
496C4—41no—
497C4—81no—
498C4—82no—
499C4—4881no—
500C4—4882no—
501C4—4881no—
502C4—2441no—
503C4—2441no—
504C2—21no—
505C2—21no—
506C2—41no—
507C2—41no—
508C2—161no—
509C2—1222no—
510C2—1222no—
511C2—2442no—
512C2#327×D6111yescharacteristic
513C2#2144746211yescharacteristic
514C2#2144748511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radical#21451552C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11692
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #342×D61C2semidirect
3. #323×D61C2semidirect
4. #21443820C2semidirect
5. #21443818C2semidirect
6. #21443816C2semidirect
7. C61×#1343C2semidirect
8. C2×#14519748C4semidirect
13. #16839689C4semidirect
17. #16839670C4semidirect
19. #16839621C4semidirect
38. C2×C4⋊Dic61C2×C4semidirect
58. #14519684C2×C4semidirect
60. C22×D4×C61C2×C4semidirect
65. #95×C61C2×C4semidirect
253. #1343D61semidirect
284. C61#11692semidirect
289. C22×D4C4×D61semidirect
323. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214515522
#342×D612
#323×D612
#214438202
#214438182
#214438162
C61×#13432
#1169261