Finite Group Databasebeta

← #29589645

Subgroups — #29589645

Order 15616.

494 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 71 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#21450793C211yesmaximal, characteristic
2#21444156C211yesmaximal, characteristic, complemented
3#21444136C211yesmaximal, characteristic, complemented
4#21443752C211yesmaximal, characteristic, complemented
5#21443752C211yesmaximal, characteristic, complemented
6#21443751C211yesmaximal, characteristic, complemented
7C61×#1318C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic
9C2×#14519765C411yescharacteristic
10C2×#14519764C411yescharacteristic
11C2×#14519739C2211yescharacteristic
12#16839724—21no—
13C22⋊C8×D61—21no—
14#16839677—21no—
15#16839677—21no—
16#16839667C2211yescharacteristic
17#16839638—21no—
18#16839638—21no—
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839485—21no—
23#16839485—21no—
24C61×#390C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758189—41no—
34C2×C8×D61—41no—
35#14519773—42no—
36#14519765—42no—
37#14519764—41no—
38#14519764—41no—
39#14519739—41no—
40#14519739—41no—
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×D4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2×C411yescharacteristic
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C24×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—81no—
80C2×C22⋊D61—81no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C2×D244—22no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—41no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—81no—
94C2×C4×D61—81no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122—41no—
98C2×Dic122—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—81no—
103C22⋊C4×C61—81no—
104C42×C61—41no—
105C22⋊Dic61—42no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—42no—
111#11758198—42no—
112#11758196—42no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118#11758189—82no—
119C8×D61—82no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—21no—
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#10012yes—
138D4×C61—81no—
139D4×C61—81no—
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×C61#13111yescharacteristic
150C2×C4×C61#13111yescharacteristic
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—42no—
168C4×D61—81no—
169C4×D61—81no—
170Dic122—81no—
171Dic122—81no—
172C8×C61—81no—
173C8×C61—81no—
174#92418—81no—
175#92418—81no—
176#11566—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61#40811yescharacteristic
187C22×C61C2×#9911yescharacteristic
188C22×C61C2×#10011yescharacteristic
189C2×D61—22no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—42no—
193C2×D61—42no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—81no—
198C2×D61—81no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—41no—
202C4×C61—41no—
203C4×C61—81no—
204Dic61—21no—
205Dic61—21no—
206Dic61—42no—
207Dic61—41no—
208Dic61—81no—
209#2544—611no—
210#1465—611no—
211#1459—611no—
212#1319—611no—
213#1319—611no—
214#1318—611no—
215#1318D6111yescharacteristic, complemented
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—161no—
219C2×C61#147111yescharacteristic
220C2×C61#212711yescharacteristic
221C2×C61#213211yescharacteristic
222D61—42no—
223D61—81no—
224C2×#127—611no—
225C2×#124—611no—
226C2×#124—611no—
227C2×C4×D4—611no—
228#407—1221no—
229C2×C22⋊C8—1221no—
230#394—1221no—
231#394—1221no—
232#391—611no—
233#390C2×D6111yescharacteristic
234#386—1221no—
235#386—1221no—
236C4×C4⋊C4—611no—
237#324—611no—
238#324—611no—
239#324C2×D6111yescharacteristic
240#324C2×D6111yescharacteristic
241#323—1221no—
242#323—1221no—
243C61#1156611yescharacteristic, complemented, Sylow
244C22×Q8—611no—
245C22×D4—611no—
246C22×D4—1221no—
247C22×D4—1221no—
248C22×D4C4×D6111yescharacteristic
249C23×C4—611no—
250C23×C4—611no—
251C2×M16—2441no—
252C22×C8—2441no—
253#127—2442no—
254#124—2442no—
255#124—2441no—
256#124—2441no—
257C4×D4—2441no—
258C4×D4—2441no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4C22×D6111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C42—611no—
270C2×C42—611no—
271C2×C42C4×D6111yescharacteristic
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—1221no—
275C22⋊C8—1221no—
276C22⋊C8—2441no—
277C22⋊C8—2441no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281C24—21no—
282C24—611no—
283C24—611no—
284C2×Q8—1221no—
285C2×Q8—1221no—
286C2×Q8—2441no—
287C2×Q8—2441no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—1222no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—4881no—
296C2×D4—4881no—
297C2×D4—2441no—
298C2×D4—2442no—
299C2×D4—2442no—
300C2×D4—2442no—
301C2×D4—2442no—
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—4881no—
312C22×C4—4881no—
313C22×C4C2×C4×D6111yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4D4×D6111yescharacteristic
316M16—4882no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—4882no—
320C2×C8—2441no—
321C2×C8—2441no—
322C4⋊C4—41no—
323C4⋊C4—2442no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C22⋊C4—2442no—
329C22⋊C4—2442no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C22⋊C4—2442no—
333C42—41no—
334C42—1221no—
335C42—1221no—
336C42—2441no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—612no—
345C23—1221no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23C22⋊C4×D6111yescharacteristic
355Q8—4881no—
356Q8—4881no—
357D4—81no—
358D4—81no—
359D4—4884no—
360D4—4884no—
361D4—2442no—
362D4—2442no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—611no—
373C2×C4—611no—
374C2×C4—1222no—
375C2×C4—1221no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4#1451978311yescharacteristic
388C2×C4#1451978511yescharacteristic
389C8—81no—
390C8—81no—
391C8—4881no—
392C8—4881no—
393C22—21no—
394C22—21no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—1222no—
403C22—4881no—
404C22—4881no—
405C22—2442no—
406C22—2442no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22—2441no—
412C22#1683972711yescharacteristic
413C22#99×D6111yescharacteristic
414C22#100×D6111yescharacteristic
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—1221no—
421C4—1221no—
422C4—4881no—
423C4—2442no—
424C4—2441no—
425C2—21no—
426C2—21no—
427C2—161no—
428C2—4881no—
429C2—2442no—
430C2#2144417711yescharacteristic
431C2#2144748511yescharacteristic
432C2#2144750111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1318C2
socleC22×C61C2×#99
prime radicalC2×#14519773C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1318D61
hypocenterC61#11566
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #21444156C2semidirect
3. #21444136C2semidirect
4. #21443752C2semidirect
5. #21443752C2semidirect
6. #21443751C2semidirect
7. C61×#1318C2semidirect
215. #1318D61semidirect
243. C61#11566semidirect

Maximal subgroups

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

subgroupindex
#214507932
#214441562
#214441362
#214437522
#214437512
C61×#13182
#1156661