Finite Group Databasebeta

← D61×#1345 #29590204

Subgroups — D61×#1345 #29590204

Order 15616.

824 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 91 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#394×D61C211yesmaximal, characteristic
2#343×D61C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443823C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C22×D4×D61C411yescharacteristic
9C2×M16×D61—21no—
10C2×C4⋊C4×D61C2211yescharacteristic
11C2×C22⋊C4×D61—21no—
12C2×C22⋊C4×D61—21no—
13C22⋊C8×D61—21no—
14#16839680C411yescharacteristic
15#16839679C2211yescharacteristic
16#16839678—21no—
17#16839677—21no—
18#16839676C411yescharacteristic
19#95×D61C411yescharacteristic
20#16839531C2211yescharacteristic, complemented
21#16839530—21no—
22#16839488C2211yescharacteristic, complemented
23#16839487—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic, complemented
26C61×#324C2211yescharacteristic, complemented
27C24×D61—21no—
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C2×D4×D61—41no—
31C2×D4×D61—41no—
32C2×D4×D61—44no—
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C2×#11758194—21no—
38C2×#11758189—41no—
39M16×D61—24no—
40M16×D61—42no—
41C2×C8×D61—41no—
42C2×C8×D61—41no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196C2×C411yescharacteristic
45C2×#11758196D411yescharacteristic
46C4⋊C4×D61—41no—
47C4⋊C4×D61—41no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C22⋊C4×D61—44no—
55C22⋊C4×D61—42no—
56C22⋊C4×D61—42no—
57C22⋊#92418—21no—
58#14519689—41no—
59#14519684—21no—
60#14519684C2×C411yescharacteristic
61C22×D4×C61C2×C411yescharacteristic
62C2×M16×C61—21no—
63C2×C4⋊C4×C61C2311yescharacteristic
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61—21no—
66C22⋊C8×C61—21no—
67#95×C61C2×C411yescharacteristic
68C24×C61—21no—
69C23×D61—24no—
70C23×D61—21no—
71C23×D61—42no—
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—41no—
75C23×D61—41no—
76C23×D61—42no—
77C23×D61—42no—
78C23×D61C22⋊C411yescharacteristic
79C2×D4×C61—41no—
80C2×D4×C61—42no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—42no—
86C2×C22⋊D61—42no—
87C2×C22⋊D61—42no—
88C22×Dic61—21no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92D4×D61—44no—
93D4×D61—44no—
94D4×D61—44no—
95D4×D61—44no—
96C2×D244—41no—
97C2×D244—42no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—22no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61D812yes—
111C2×C4×D61SD1612yes—
112M16×C61—22no—
113M16×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C4⋊C4×C61—41no—
117C22⋊C4×C61—42no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊Dic61—42no—
121C22⋊Dic61—42no—
122#11758198—42no—
123#11758198—42no—
124#11758198—41no—
125#11758198—41no—
126#11758198—42no—
127C4⋊Dic61—41no—
128#11758196—41no—
129#11758196—41no—
130#11758194—22no—
131#11758194—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134#11758189—44no—
135C8×D61—44no—
136C8×D61—82no—
137C23×C61—22no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61C2×C22⋊C411yescharacteristic
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—44no—
149C22×D61—48no—
150C22×D61—48no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—44no—
158C22×D61—82no—
159C22×D61—84no—
160C22×D61—84no—
161C22×D61—82no—
162C22×D61—82no—
163C22×D61—82no—
164C22×D61#9911yescharacteristic
165C22×D61#9911yescharacteristic
166C22×D61#10212yes—
167C22×D61#10412yes—
168D4×C61—42no—
169D4×C61—42no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C2×SD1611yescharacteristic
181C22⋊D61—48no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61#10212yes—
192D244—42no—
193D244—42no—
194C4×D61—22no—
195C4×D61—22no—
196C4×D61—22no—
197C4×D61—22no—
198C4×D61—42no—
199C4×D61—42no—
200C4×D61—42no—
201C4×D61—81no—
202C4×D61—84no—
203C8×C61—42no—
204C8×C61—81no—
205#92418—42no—
206#92418—81no—
207C2×#1345—611nomaximal, Sylow
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—42no—
211C22×C61—42no—
212C22×C61—42no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61C2×#9911yescharacteristic
218C22×C61C2×#10211yescharacteristic
219C22×C61C2×#10411yescharacteristic
220C2×D61—21no—
221C2×D61—21no—
222C2×D61—24no—
223C2×D61—24no—
224C2×D61—42no—
225C2×D61—42no—
226C2×D61—42no—
227C2×D61—88no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61—88no—
233C2×D61#32712yes—
234C2×D61#32712yes—
235C2×D61AΣL(1,𝔽16)12yes—
236C2×D61#35512yes—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—41no—
240C4×C61—41no—
241C4×C61—81no—
242Dic61—22no—
243Dic61—41no—
244Dic61—41no—
245Dic61—81no—
246C2×#394—611no—
247C2×#343—611no—
248C2×#324—611no—
249#1345—611no—
250#1345—611no—
251#1345—611no—
252#1345D6111yescharacteristic, direct product factor
253C2×C61—21no—
254C2×C61—21no—
255C2×C61—82no—
256C2×C61C2×#32711yescharacteristic
257C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
258C2×C61C2×#35511yescharacteristic
259D61—22no—
260D61—82no—
261D61#134514yesdirect product factor
262C23×D4—611no—
263C22×M16—1221no—
264C22×C4⋊C4—611no—
265C22×C22⋊C4—1221no—
266C22×C22⋊C4—1221no—
267C2×C22⋊C8—1221no—
268#394—611no—
269#394—611no—
270#394—611no—
271#394—1221no—
272#394—1221no—
273#394C2×D6111yescharacteristic
274C2×#95—611no—
275#343—611no—
276#343—1221no—
277#343C2×D6111yescharacteristic, complemented
278#324—611no—
279#324—1221no—
280#324C2×D6111yescharacteristic, complemented
281C61C2×#134511yescharacteristic, complemented, Sylow
282C25—1221no—
283C22×D4—611no—
284C22×D4—1221no—
285C22×D4—2441no—
286C22×D4—2441no—
287C22×D4—2444no—
288C22×D4C4×D6111yescharacteristic
289C23×C4—611no—
290C23×C4—611no—
291C23×C4—611no—
292C23×C4—1221no—
293C2×M16—21no—
294C2×M16—1224no—
295C2×M16—1221no—
296C2×M16—2441no—
297C2×M16—2442no—
298C22×C8—2441no—
299C22×C8—2441no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—2441no—
304C2×C4⋊C4—2441no—
305C2×C4⋊C4C22×D6111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—2442no—
315C2×C22⋊C4—2442no—
316C2×C22⋊C4—2444no—
317C22⋊C8—21no—
318C22⋊C8—1221no—
319C22⋊C8—2441no—
320#95—611no—
321#95—1221no—
322#95C4×D6111yescharacteristic
323C24—21no—
324C24—611no—
325C24—1224no—
326C24—1221no—
327C24—2442no—
328C24—2441no—
329C24—2441no—
330C24—2442no—
331C24—2442no—
332C24—2442no—
333C24—2442no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—2441no—
337C2×D4—2442no—
338C2×D4—2442no—
339C2×D4—2444no—
340C2×D4—2444no—
341C2×D4—2444no—
342C2×D4—2444no—
343C2×D4—2442no—
344C2×D4—2442no—
345C22×C4—21no—
346C22×C4—611no—
347C22×C4—612no—
348C22×C4—612no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1222no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4C2×C4×D6111yescharacteristic
365C22×C4D4×D6111yescharacteristic
366C22×C4D4×D6111yescharacteristic
367M16—22no—
368M16—41no—
369M16—1222no—
370M16—2444no—
371M16—2441no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—4882no—
375C2×C8—2444no—
376C2×C8—2441no—
377C2×C8—2441no—
378C4⋊C4—41no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C22⋊C4—42no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—2442no—
386C22⋊C4—2442no—
387C22⋊C4—2442no—
388C22⋊C4—2442no—
389C22⋊C4—2442no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C23—22no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—611no—
400C23—611no—
401C23—612no—
402C23—612no—
403C23—1222no—
404C23—1222no—
405C23—1222no—
406C23—4882no—
407C23—4882no—
408C23—4882no—
409C23—4884no—
410C23—4884no—
411C23—4882no—
412C23—2441no—
413C23—2441no—
414C23—2441no—
415C23—2444no—
416C23—2444no—
417C23—2448no—
418C23—2448no—
419C23—2441no—
420C23—2441no—
421C23—2441no—
422C23C22⋊C4×D6111yescharacteristic
423D4—42no—
424D4—42no—
425D4—2442no—
426D4—2442no—
427D4—2448no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—612no—
438C2×C4—1222no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—4881no—
447C2×C4—4884no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4D8×D6111yescharacteristic
457C2×C4SD16×D6111yescharacteristic
458C8—42no—
459C8—81no—
460C8—4881no—
461C8—2442no—
462C22—21no—
463C22—21no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—612no—
472C22—612no—
473C22—612no—
474C22—612no—
475C22—1224no—
476C22—1224no—
477C22—1221no—
478C22—1221no—
479C22—4881no—
480C22—4881no—
481C22—4888no—
482C22—4888no—
483C22—4881no—
484C22—4881no—
485C22—2442no—
486C22—2442no—
487C22—2442no—
488C22#99×D6111yescharacteristic
489C22#102×D6111yescharacteristic
490C22#104×D6111yescharacteristic
491C4—21no—
492C4—21no—
493C4—41no—
494C4—41no—
495C4—81no—
496C4—1222no—
497C4—4881no—
498C4—2441no—
499C4—2441no—
500C2—21no—
501C2—21no—
502C2—82no—
503C2—614no—
504C2—1222no—
505C2—4882no—
506C2#327×D6111yescharacteristic
507C2AΣL(1,𝔽16)×D6111yescharacteristic
508C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radicalC22×D4×D61C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61C2×#1345
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #343×D61C2semidirect
3. #324×D61C2semidirect
4. #21443823C2semidirect
5. #21443822C2semidirect
6. #21443821C2semidirect
7. C61×#1345C2semidirect
20. #16839531C22semidirect
22. #16839488C22semidirect
25. C61×#343C22semidirect
26. C61×#324C22semidirect
252. #1345D61direct (N × H)
261. D61#1345direct (N × H)
277. #343C2×D61semidirect
280. #324C2×D61semidirect
281. C61C2×#1345semidirect

Maximal subgroups

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

subgroupindex
#394×D612
#343×D612
#324×D612
#214438232
#214438222
#214438212
C61×#13452
C2×#134561