Finite Group Databasebeta

← #29584404

Subgroups — #29584404

Order 15616.

532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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#21456576C211yesmaximal, characteristic
2#21446803C211yesmaximal, characteristic, complemented
3#21446656C211yesmaximal, characteristic
4#21446242C211yesmaximal, characteristic, complemented
5#21445997C211yesmaximal, characteristic, complemented
6#21443686C211yesmaximal, characteristic, complemented
7C61×#1893C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840092—21no—
10#16840078—21no—
11#16839989—21no—
12#16839989—21no—
13#16839913—21no—
14#16839900—21no—
15C2×#14519706—21no—
16C2×#14519702—21no—
17C2×#14519692—21no—
18C2×#14519692—21no—
19C2×C22⋊#92418C2211yescharacteristic
20#16839622C2211yescharacteristic
21C4×C22⋊Dic61C2211yescharacteristic
22#16839528—21no—
23#16839528—21no—
24#16839525—21no—
25#16839516—21no—
26C23×C8×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×#102×C61—21no—
29C61×#380C2211yescharacteristic
30C61×#340—21no—
31C22×Dic122D411yescharacteristic
32C2×#11758200—21no—
33C2×#11758200—21no—
34C22×#92418D411yescharacteristic
35C22×#92418D411yescharacteristic
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61D411yescharacteristic
46C2×C22⋊Dic61D411yescharacteristic
47C2×C4×Dic61—21no—
48#14519708—21no—
49#14519708—21no—
50#14519706—42no—
51#14519702—42no—
52#14519700—21no—
53#14519700—21no—
54#14519698—21no—
55#14519698—21no—
56#14519692—42no—
57#14519692—42no—
58C22⋊#92418—21no—
59C22⋊#92418—21no—
60#14519684—21no—
61#14519684—21no—
62C22×D4×C61—21no—
63C22×D4×C61D411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—21no—
66C22×C8×C61—21no—
67C22×C8×C61—21no—
68C22×C8×C61—42no—
69#121×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77#102×C61—42no—
78#95×C61—21no—
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—41no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×C8×C61—22no—
111C2×C8×C61—22no—
112C2×C8×C61—22no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊Dic61—21no—
126C22⋊Dic61—21no—
127C22⋊Dic61—21no—
128C22⋊Dic61—41no—
129C22⋊Dic61—41no—
130C22⋊Dic61—41no—
131C22⋊Dic61—41no—
132C22⋊Dic61SD1612yescomplemented
133#11758200—81no—
134#11758200—81no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61—41no—
138C4⋊Dic61—41no—
139#11758196—41no—
140#11758196—41no—
141C4×Dic61—41no—
142C4×Dic61—41no—
143C2×#92418—21no—
144C2×#92418—21no—
145C2×#92418—41no—
146C2×#92418—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—81no—
153C23×C61—81no—
154C23×C61#12111yescharacteristic
155C23×C61#12111yescharacteristic
156C23×C61#12111yescharacteristic
157C23×C61C2×SD1611yescharacteristic
158C23×C61#13511yescharacteristic
159C23×C61AGL(1,ℤ/8)11yescharacteristic
160C23×C61#13711yescharacteristic
161D4×C61—42no—
162D4×C61—41no—
163D4×C61—41no—
164D4×C61—81no—
165D4×C61—81no—
166D4×C61—81no—
167D4×C61—81no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
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×C61—41no—
180C2×C4×C61—81no—
181C2×C4×C61—81no—
182C2×C4×C61—81no—
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12311yescharacteristic
185C2×C4×C61#12311yescharacteristic
186C2×C4×C61#12411yescharacteristic
187C2×Dic61—22no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198C2×Dic61—81no—
199C2×Dic61—81no—
200Dic122—42no—
201Dic122—41no—
202Dic122—41no—
203C8×C61—42no—
204#92418—41no—
205#92418—41no—
206#10565—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—161no—
221C22×C61—161no—
222C22×C61#39411yescharacteristic
223C22×C61#46011yescharacteristic
224C22×C61#46111yescharacteristic
225C22×C61#46311yescharacteristic
226C22×C61#46411yescharacteristic
227C22×C61#46511yescharacteristic
228C22×C61#46811yescharacteristic
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—81no—
233C4×C61—161no—
234C4×C61B(4,𝔽2)11yescharacteristic
235C4×C61#45811yescharacteristic
236Dic61—42no—
237Dic61—81no—
238Dic61—81no—
239Dic61—81no—
240Dic61—161no—
241#3187—611no—
242#1996—611no—
243#1964—611no—
244#1893D6111yescharacteristic
245#1892—611no—
246#1850—611no—
247#1289—611no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—161no—
255C2×C61#204411yescharacteristic
256C2×C61#205311yescharacteristic
257C2×C61#205511yescharacteristic
258C23×C8C2×D6111yescharacteristic
259C2×C22⋊Q8—611no—
260C2×#121C2×D6111yescharacteristic
261#483—1221no—
262#481—1221no—
263#465—1221no—
264#465—1221no—
265#450—1221no—
266#448—1221no—
267C2×C4⋊C8—1221no—
268C2×#103—1221no—
269C2×#102—21no—
270C2×#99—1221no—
271C2×#99—1221no—
272C2×C22⋊C8—611no—
273#380—611no—
274#380C2×D6111yescharacteristic
275C4×C22⋊C4—611no—
276#342—1221no—
277#342—1221no—
278#340—21no—
279#340—1221no—
280#336—1221no—
281C61#1056511yescharacteristic, complemented, Sylow
282C22×Q8—611no—
283C22×D4—21no—
284C22×D4C22⋊D6111yescharacteristic
285C23×C4C22×D6111yescharacteristic
286C2×SD16—1221no—
287C2×SD16—1221no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—42no—
292C22×C8—611no—
293C22×C8—611no—
294C22⋊Q8—1221no—
295C22⋊Q8—1221no—
296C22⋊Q8—1221no—
297C22⋊Q8—1221no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4C22⋊D6111yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—611no—
310C2×C22⋊C4—611no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C42—1221no—
314#106—1221no—
315#106—1221no—
316C4⋊C8—2442no—
317#103—1221no—
318#103—1221no—
319#103—2442no—
320#102—42no—
321#102—1221no—
322#102—1221no—
323#99—2442no—
324#99—2442no—
325C22⋊C8—1221no—
326C22⋊C8—1221no—
327#95—21no—
328#95—1221no—
329#95—1221no—
330C24—21no—
331C24D4×D6111yescharacteristic
332C2×Q8—1221no—
333C2×Q8—1221no—
334C2×Q8—2441no—
335C2×Q8—2441no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—2441no—
355C22×C4#1175822211yescharacteristic
356C22×C4#1175822211yescharacteristic
357C22×C4D4×D6111yescharacteristic
358C22×C4D4×D6111yescharacteristic
359C22×C4#1175822411yescharacteristic
360C22×C4C2×C22⋊D6111yescharacteristic
361SD16—4881no—
362SD16—4881no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—1221no—
371C2×C8—1221no—
372C2×C8—2441no—
373C2×C8—2441no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—612no—
389C22⋊C4—1221no—
390C22⋊C4—1221no—
391C22⋊C4—1221no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C42—2441no—
397C42—2441no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—81no—
404C23—81no—
405C23#1451974911yescharacteristic
406C23#1451975011yescharacteristic
407C23#1451975011yescharacteristic
408C23SD16×D6111yescharacteristic
409C23#1451979611yescharacteristic
410C23#1451980111yescharacteristic
411C23#1451980611yescharacteristic
412Q8—2442no—
413Q8—2441no—
414Q8—2441no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—81no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—1222no—
438C2×C4—4881no—
439C2×C4—4881no—
440C2×C4—4881no—
441C2×C4—4881no—
442C2×C4—4881no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4#1451974511yescharacteristic
451C2×C4#1451975911yescharacteristic
452C2×C4#1451976011yescharacteristic
453C2×C4#1451976311yescharacteristic
454C8—42no—
455C8—2441no—
456C8—2441no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—161no—
471C22—161no—
472C22#1683967711yescharacteristic
473C22#1683996111yescharacteristic
474C22#1683996511yescharacteristic
475C22#1683997511yescharacteristic
476C22#1683998311yescharacteristic
477C22#1683999011yescharacteristic
478C22#1684000711yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—161no—
484C4—9761no—
485C4—4881no—
486C4—4881no—
487C4—4881no—
488C4—2442no—
489C4#1683994811yescharacteristic
490C4#1683995111yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—161no—
498C2#2144706811yescharacteristic
499C2#2144712311yescharacteristic
500C2#2144713511yescharacteristic
subgroupG/H
centerC22#16839677
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1893C2
socleC22×C61#394
prime radicalC2×#121×C61C22
hypercenter#1893D61
hypocenterC61#10565
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. #21446803C2semidirect
4. #21446242C2semidirect
5. #21445997C2semidirect
6. #21443686C2semidirect
132. C22⋊Dic61SD16semidirect
281. C61#10565semidirect

Maximal subgroups

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

subgroupindex
#214565762
#214468032
#214466562
#214462422
#214459972
#214436862
C61×#18932
#1056561