Finite Group Databasebeta

← #29590359

Subgroups — #29590359

Order 15616.

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

normal subgroups only

This group has 500 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#21451676C211yesmaximal, characteristic
2#21445606C211yesmaximal, characteristic, complemented
3#21444134C211yesmaximal, characteristic, complemented
4#21443841C211yesmaximal, characteristic, complemented
5#21443839C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic, complemented
7C61×#1343C211yesmaximal, characteristic, complemented
8C2×#14519764C411yescharacteristic, complemented
9C2×#14519737C2211yescharacteristic
10C2×#14519691—21no—
11C22⋊C8×D61—21no—
12#16839690—21no—
13#16839675C411yescharacteristic, complemented
14#16839674C2211yescharacteristic
15#16839670—21no—
16#16839670C411yescharacteristic, complemented
17#16839642—21no—
18#16839638—21no—
19#16839629C411yescharacteristic, complemented
20C22⋊C4×Dic61—21no—
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×C8×D61—41no—
33#14519764—41no—
34#14519764—41no—
35#14519737—41no—
36#14519737—41no—
37C2×#11758196D411yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198C2×C411yescharacteristic
45C2×C4×Dic61—41no—
46C2×C4×Dic61C2×C411yescharacteristic
47#14519691—24no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684C2×C411yescharacteristic
56C22×D4×C61—21no—
57C22×D4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61—21no—
64C24×C61C2×D411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—81no—
70C2×D4×C61—81no—
71C2×D4×C61—81no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—81no—
82C2×C22⋊D61—81no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—41no—
88C22×Dic61—81no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—81no—
95C2×Dic122—41no—
96C2×Dic122—81no—
97C2×C8×C61—41no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—81no—
102C22⋊Dic61—22no—
103C22⋊Dic61—42no—
104C22⋊Dic61—41no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61—81no—
108C22⋊Dic61—81no—
109#11758198—41no—
110#11758198—81no—
111#11758196—41no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—82no—
115C2×#92418—41no—
116C8×D61—82no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—41no—
120C23×C61—41no—
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
129C23×C61#13511yescharacteristic
130C23×C61#13511yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61#10412yes—
136D4×C61—82no—
137D4×C61—82no—
138D4×C61—82no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
149C22⋊D61—42no—
150C22⋊D61—42no—
151C22⋊D61—84no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—42no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169C2×Dic61#9911yescharacteristic
170C2×Dic61#9911yescharacteristic
171C4×D61—42no—
172C4×D61—81no—
173Dic122—82no—
174C8×C61—81no—
175#92418—81no—
176#11730—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61C2×#9911yescharacteristic
194C22×C61#41611yescharacteristic
195C22×C61C2×#10411yescharacteristic
196C2×D61—22no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—42no—
200C2×D61—81no—
201C4×C61—41no—
202C4×C61—41no—
203C4×C61—81no—
204C4×C61—82no—
205Dic61—21no—
206Dic61—21no—
207Dic61—41no—
208Dic61—41no—
209Dic61—81no—
210Dic61—82no—
211Dic61—81no—
212#2631—611no—
213C4×#99—611no—
214#1459—611no—
215#1351—611no—
216#1351—611no—
217#1343—611no—
218#1343D6111yescharacteristic, complemented
219C2×C61—21no—
220C2×C61—21no—
221C2×C61—41no—
222C2×C61—41no—
223C2×C61—161no—
224C2×C61#150111yescharacteristic
225C2×C61#212211yescharacteristic
226C2×C61#212711yescharacteristic
227D61—42no—
228C2×#124—611no—
229C2×C4×D4—611no—
230C2×#99—1221no—
231C2×C22⋊C8—1221no—
232#397—1221no—
233#393—611no—
234#393—611no—
235#392—611no—
236#392—1221no—
237#392C2×D6111yescharacteristic
238#386—1221no—
239#386—1221no—
240#383—611no—
241C4×C22⋊C4—1221no—
242#342—611no—
243#342C2×D6111yescharacteristic
244#324—1221no—
245#323—611no—
246#323C2×D6111yescharacteristic
247C61#1173011yescharacteristic, complemented, Sylow
248C22×Q8—611no—
249C22×D4—21no—
250C22×D4—611no—
251C22×D4—1221no—
252C22×D4C4×D6111yescharacteristic
253C23×C4—611no—
254C23×C4—611no—
255C22×C8—2441no—
256#124—2441no—
257#124—2441no—
258C4×D4—2441no—
259C4×D4—2441no—
260C2×C4⋊C4—611no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4C22×D6111yescharacteristic
271C2×C42—611no—
272C2×C42—2441no—
273#99—1224no—
274C22⋊C8—21no—
275C22⋊C8—1221no—
276C22⋊C8—2441no—
277#95—611no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282#95—2441no—
283#95C4×D6111yescharacteristic
284C24—21no—
285C24—611no—
286C24D4×D6111yescharacteristic
287C2×Q8—4881no—
288C2×Q8—2441no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4—1222no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—4881no—
299C2×D4—4881no—
300C2×D4—2441no—
301C2×D4—2442no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—4881no—
314C22×C4—4881no—
315C22×C4—2441no—
316C22×C4C2×C4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C2×C8—41no—
319C2×C8—4882no—
320C2×C8—2441no—
321C4⋊C4—2441no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—81no—
326C22⋊C4—1222no—
327C22⋊C4—4881no—
328C22⋊C4—4881no—
329C22⋊C4—4881no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2442no—
334C22⋊C4—2441no—
335C42—1221no—
336C42—1221no—
337C42—4882no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—612no—
350C23—1221no—
351C23—1221no—
352C23—2441no—
353C23—2441no—
354C23C22⋊C4×D6111yescharacteristic
355C23#1451979611yescharacteristic
356C23#1451979811yescharacteristic
357Q8—4882no—
358D4—82no—
359D4—82no—
360D4—82no—
361D4—4884no—
362D4—2442no—
363D4—2442no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—4881no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C8—81no—
396C8—4881no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—1222no—
414C22—4881no—
415C22—2442no—
416C22—2441no—
417C22—2441no—
418C22#99×D6111yescharacteristic
419C22#1683975511yescharacteristic
420C22#104×D6111yescharacteristic
421C4—41no—
422C4—41no—
423C4—81no—
424C4—82no—
425C4—1221no—
426C4—1221no—
427C4—4881no—
428C4—4882no—
429C4—4881no—
430C4—2441no—
431C4—2441no—
432C2—21no—
433C2—21no—
434C2—41no—
435C2—41no—
436C2—161no—
437C2—2442no—
438C2#2144430711yescharacteristic
439C2#2144746711yescharacteristic
440C2#2144748511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radical#21451676C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11730
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445606C2semidirect
3. #21444134C2semidirect
4. #21443841C2semidirect
5. #21443839C2semidirect
6. #21443816C2semidirect
7. C61×#1343C2semidirect
8. C2×#14519764C4semidirect
13. #16839675C4semidirect
16. #16839670C4semidirect
19. #16839629C4semidirect
218. #1343D61semidirect
247. C61#11730semidirect

Maximal subgroups

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

subgroupindex
#214516762
#214456062
#214441342
#214438412
#214438392
#214438162
C61×#13432
#1173061