Finite Group Databasebeta

← #29568745

Subgroups — #29568745

Order 15616.

546 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 81 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#21452779C211yesmaximal, characteristic, complemented
2#21447050C211yesmaximal, characteristic, complemented
3#21446890C211yesmaximal, characteristic
4#21443642C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#2041C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×#14519772—21no—
10C2×#14519698—21no—
11C2×#14519698—21no—
12C2×#14519698—21no—
13#16839697—21no—
14#16839684—21no—
15#16839680—21no—
16#16839664C2211yescharacteristic
17#16839660C2211yescharacteristic
18#16839659—21no—
19#16839652—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#127×C61C2211yescharacteristic
23C2×#102×C61—21no—
24C2×#102×C61—21no—
25C61×#389C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C2×#11758199—42no—
29C2×#11758199—42no—
30C2×#11758199—42no—
31C22×#92418—21no—
32C22×#92418—21no—
33#14519772—42no—
34#14519772—42no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48#14519698—42no—
49#14519698—42no—
50#14519698—42no—
51#14519684—21no—
52#14519684—21no—
53C22×D4×C61—21no—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C22×C8×C61—21no—
57#127×C61—42no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#102×C61—42no—
63#102×C61—42no—
64#95×C61—21no—
65C24×C61—41no—
66C23×D61—21no—
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61—22no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—41no—
96C2×D244—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61—41no—
106#11758199—48no—
107#11758198—42no—
108#11758198—42no—
109#11758198—41no—
110#11758198—41no—
111#11758198—41no—
112#11758198—41no—
113#11758198—81no—
114#11758198—81no—
115C4⋊Dic61—21no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61D812yescomplemented
119#11758196—42no—
120#11758196—41no—
121#11758196—41no—
122#11758196—81no—
123C4×Dic61—42no—
124C2×#92418—22no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C23×C61—42no—
131C23×C61—81no—
132C23×C61—81no—
133C23×C61—81no—
134C23×C61—81no—
135C23×C61—81no—
136C23×C61—81no—
137C23×C61#12011yescharacteristic
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145D4×C61—42no—
146D4×C61—42no—
147D4×C61—42no—
148D4×C61—42no—
149D4×C61—42no—
150D4×C61—42no—
151D4×C61—81no—
152D4×C61—81no—
153D4×C61—81no—
154D4×C61—81no—
155D4×C61—81no—
156D4×C61—81no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
175C2×Dic61—22no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184D244—42no—
185D244—81no—
186C8×C61—81no—
187#92418—42no—
188#92418—81no—
189#7740—611nomaximal, Sylow
190C22×C61—82no—
191C22×C61—82no—
192C22×C61—82no—
193C22×C61—161no—
194C22×C61—161no—
195C22×C61—161no—
196C22×C61—161no—
197C22×C61#44711yescharacteristic
198C22×C61#44911yescharacteristic
199C22×C61#44911yescharacteristic
200C22×C61#45311yescharacteristic
201C22×C61#45411yescharacteristic
202C22×C61#45411yescharacteristic
203C22×C61B(4,𝔽2)11yescharacteristic
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—81no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—81no—
218C4×C61—81no—
219Dic61—42no—
220Dic61—81no—
221Dic61—81no—
222#2727—611no—
223#2041—611no—
224#2041D6111yescharacteristic, complemented
225#2011—611no—
226#1271—611no—
227#1271—611no—
228#1270—611no—
229C2×C61—162no—
230C2×C61#159711yescharacteristic
231C2×C61#159811yescharacteristic
232C2×C61#160011yescharacteristic
233C2×C61#162111yescharacteristic
234C2×C61#162511yescharacteristic
235C2×C61#162811yescharacteristic
236C2×C61#165711yescharacteristic
237D61—161no—
238C22×D8—1221no—
239C2×#127C2×D6111yescharacteristic
240C2×#126—1221no—
241C2×#102—21no—
242C2×#102—21no—
243C2×#102—1221no—
244C2×#102—1221no—
245C2×#102—1221no—
246#399—1221no—
247#396—1221no—
248#394—1221no—
249#390—611no—
250#389—611no—
251#389—1221no—
252#389C2×D6111yescharacteristic
253#388—1221no—
254#336—611no—
255#336—611no—
256#336C2×D6111yescharacteristic
257C61#774011yescharacteristic, complemented, Sylow
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—611no—
262C2×D8—2442no—
263C2×D8—2442no—
264C2×D8—2442no—
265C22×C8—21no—
266C22×C8—1221no—
267C22×C8—1221no—
268#127—42no—
269#126—2442no—
270#126—2442no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4C22⋊D6111yescharacteristic
279C2×C4⋊C4C22⋊D6111yescharacteristic
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C42—1221no—
287C2×C42C22×D6111yescharacteristic
288#102—42no—
289#102—42no—
290#102—2442no—
291#102—2442no—
292#102—2442no—
293#95—21no—
294#95—1221no—
295#95—1221no—
296C24—41no—
297C24—1221no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4—2441no—
319C2×D4—2441no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4D4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C22×C4C2×C22⋊D6111yescharacteristic
328D8—2448no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—1222no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8—2441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—612no—
344C4⋊C4—1221no—
345C4⋊C4—4881no—
346C4⋊C4—2441no—
347C4⋊C4—2441no—
348C4⋊C4—2442no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C22⋊C4—4881no—
352C22⋊C4—4881no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C22⋊C4—2441no—
356C22⋊C4—2441no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C42—41no—
360C42—2442no—
361C23—42no—
362C23—81no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23—81no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23#1451974511yescharacteristic
376D4—42no—
377D4—42no—
378D4—42no—
379D4—42no—
380D4—42no—
381D4—42no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—81no—
388D4—4881no—
389D4—2442no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—1222no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4D8×D6111yescharacteristic
412C2×C4#1451979711yescharacteristic
413C2×C4#1451979811yescharacteristic
414C2×C4#1451980111yescharacteristic
415C2×C4#1451980311yescharacteristic
416C2×C4#1451980411yescharacteristic
417C8—81no—
418C8—4881no—
419C8—2442no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22—161no—
424C22—161no—
425C22—161no—
426C22—161no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22—4881no—
431C22—4881no—
432C22—4881no—
433C22—4881no—
434C22#1683989411yescharacteristic
435C22#1683990511yescharacteristic
436C22#1683990611yescharacteristic
437C22#1683992811yescharacteristic
438C22#1683993311yescharacteristic
439C22#1683993411yescharacteristic
440C22#1683994811yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—81no—
448C4—81no—
449C4—4881no—
450C4—4881no—
451C4—2442no—
452C2—162no—
453C2—9761no—
454C2#2144474611yescharacteristic
455C2#2144475211yescharacteristic
456C2#2144476411yescharacteristic
457C2#2144488311yescharacteristic
458C2#2144490511yescharacteristic
459C2#2144492811yescharacteristic
460C2#2144511611yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2041C2
socleC23×C61#120
prime radical#21446890C2
hypercenter#2041D61
hypocenterC61#7740
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
1. #21452779C2semidirect
2. #21447050C2semidirect
4. #21443642C2semidirect
5. #21443641C2semidirect
6. #21443639C2semidirect
7. C61×#2041C2semidirect
118. C4⋊Dic61D8semidirect
224. #2041D61semidirect
257. C61#7740semidirect

Maximal subgroups

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

subgroupindex
#214527792
#214470502
#214468902
#214436422
#214436412
#214436392
C61×#20412
#774061