Finite Group Databasebeta

← #29591073

Subgroups — #29591073

Order 15616.

510 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 77 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#21450782C211yesmaximal, characteristic
2#21445810C211yesmaximal, characteristic, complemented
3#21444136C211yesmaximal, characteristic, complemented
4#21443826C211yesmaximal, characteristic, complemented
5#21443824C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C2×#14519750—21no—
9C2×#14519748C411yescharacteristic
10C2×#14519739C2211yescharacteristic
11#16839785—21no—
12C2×#14519693—21no—
13C22⋊C8×D61—21no—
14#16839692C2211yescharacteristic
15#16839689C411yescharacteristic
16#16839670C411yescharacteristic
17#16839656—21no—
18#16839638—21no—
19#16839638—21no—
20#95×D61C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C22×C4×D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758194—21no—
34C2×C8×D61—41no—
35#14519750—42no—
36#14519750—42no—
37#14519748—41no—
38#14519748—41no—
39#14519739—41no—
40#14519739—41no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50#14519706—41no—
51#14519693—42no—
52C22⋊#92418—21no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C22×D4×C61C2×C411yescharacteristic
59C2×M16×C61—21no—
60C2×C4⋊C4×C61C2311yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C23×D61C22⋊C411yescharacteristic
67C23×D61C22⋊C411yescharacteristic
68C2×D4×C61—41no—
69C2×D4×C61—81no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—81no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×D244—41no—
85C2×D244—41no—
86C2×D244D812yes—
87C2×D244SD1612yes—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—81no—
95C2×C4×D61—81no—
96C2×C4×D61—81no—
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—81no—
105C22⋊Dic61—42no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—42no—
111C4⋊Dic61—41no—
112#11758196—41no—
113#11758196—41no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116#11758194—41no—
117#11758194—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C8×D61—82no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61#10212yes—
138C22×D61#10212yes—
139D4×C61—82no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61C2×SD1611yescharacteristic
151C22⋊D61—84no—
152C22⋊D61—84no—
153C2×Dic61—22no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61#9911yescharacteristic
163C2×Dic61#9911yescharacteristic
164D244—42no—
165D244—42no—
166C4×D61—42no—
167C4×D61—81no—
168C4×D61—81no—
169C4×D61—81no—
170C4×D61—84no—
171C8×C61—81no—
172C8×C61—81no—
173#92418—81no—
174#92418—81no—
175#11884—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61C2×#9911yescharacteristic
186C22×C61C2×#10211yescharacteristic
187C22×C61#42111yescharacteristic
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—42no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—81no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—41no—
201C4×C61—41no—
202C4×C61—81no—
203Dic61—21no—
204Dic61—21no—
205Dic61—42no—
206Dic61—41no—
207Dic61—81no—
208#2543—611no—
209#1800—611no—
210#1459—611no—
211#1346—611no—
212#1346—611no—
213#1345—611no—
214#1345D6111yescharacteristic, complemented
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—161no—
218C2×C61#151911yescharacteristic
219C2×C61#212111yescharacteristic
220C2×C61#213211yescharacteristic
221D61—42no—
222D61—42no—
223C2×#121—611no—
224C2×#121—1221no—
225C2×C4×D4—611no—
226#423—1221no—
227C2×#100—1221no—
228C2×C22⋊C8—1221no—
229#398—611no—
230#397—611no—
231#394C2×D6111yescharacteristic
232#392—611no—
233#388—1221no—
234#386—1221no—
235#386—1221no—
236C2×#95—611no—
237#343—611no—
238#343C2×D6111yescharacteristic
239#324—611no—
240#324C2×D6111yescharacteristic
241#323—1221no—
242C61#1188411yescharacteristic, complemented, Sylow
243C22×D4—611no—
244C22×D4—1221no—
245C22×D4—1221no—
246C22×D4C4×D6111yescharacteristic
247C23×C4—611no—
248C23×C4—611no—
249C23×C4—1221no—
250C2×M16—21no—
251C2×M16—1221no—
252C22×C8—2441no—
253#121—2442no—
254#121—2442no—
255#121—2441no—
256#121—2441no—
257C4×D4—2441no—
258C4×D4—2441no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4C22×D6111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C42—611no—
270C4⋊C8—2441no—
271C4⋊C8—2441no—
272#100—2442no—
273C22⋊C8—21no—
274C22⋊C8—1221no—
275C22⋊C8—2441no—
276#95—611no—
277#95—1221no—
278#95—1221no—
279#95—1221no—
280#95C4×D6111yescharacteristic
281C24—21no—
282C24—611no—
283C24—611no—
284C2×D4—41no—
285C2×D4—81no—
286C2×D4—612no—
287C2×D4—612no—
288C2×D4—4881no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2442no—
292C2×D4—2442no—
293C2×D4—2442no—
294C2×D4—2442no—
295C2×D4—2442no—
296C22×C4—21no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—4881no—
306C22×C4—4881no—
307C22×C4—4881no—
308C22×C4—2442no—
309C22×C4—2442no—
310C22×C4C2×C4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313M16—41no—
314M16—41no—
315M16—2441no—
316M16—2441no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—4882no—
320C2×C8—2441no—
321C2×C8—2441no—
322C4⋊C4—41no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—81no—
329C22⋊C4—2441no—
330C22⋊C4—2441no—
331C22⋊C4—2442no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2442no—
335C42—1221no—
336C42—1221no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—612no—
345C23—612no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23C22⋊C4×D6111yescharacteristic
355D4—82no—
356D4—4884no—
357D4—4884no—
358D4—2442no—
359D4—2442no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—1222no—
372C2×C4—1221no—
373C2×C4—4881no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—4884no—
377C2×C4—2442no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4D8×D6111yescharacteristic
386C2×C4SD16×D6111yescharacteristic
387C8—81no—
388C8—81no—
389C8—4881no—
390C8—4881no—
391C22—21no—
392C22—21no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—1222no—
401C22—1222no—
402C22—4881no—
403C22—2442no—
404C22—2442no—
405C22—2442no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22#99×D6111yescharacteristic
411C22#102×D6111yescharacteristic
412C22#1683977711yescharacteristic
413C4—21no—
414C4—21no—
415C4—41no—
416C4—41no—
417C4—81no—
418C4—1221no—
419C4—1221no—
420C4—4881no—
421C4—2442no—
422C4—2441no—
423C2—21no—
424C2—21no—
425C2—161no—
426C2—2442no—
427C2—2442no—
428C2#2144438511yescharacteristic
429C2#2144746211yescharacteristic
430C2#2144750111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radical#21450782C2
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11884
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. #21445810C2semidirect
3. #21444136C2semidirect
4. #21443826C2semidirect
5. #21443824C2semidirect
6. #21443822C2semidirect
7. C61×#1345C2semidirect
214. #1345D61semidirect
242. C61#11884semidirect

Maximal subgroups

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

subgroupindex
#214507822
#214458102
#214441362
#214438262
#214438242
#214438222
C61×#13452
#1188461