Finite Group Databasebeta

← #29592414

Subgroups — #29592414

Order 15616.

492 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447070C211yesmaximal, characteristic, complemented
2#21444804C211yesmaximal, characteristic, complemented
3#21444736C211yesmaximal, characteristic
4#21443819C211yesmaximal, characteristic, complemented
5#21443816C211yesmaximal, characteristic, complemented
6#21443767C211yesmaximal, characteristic, complemented
7C61×#2712C211yesmaximal, characteristic, complemented
8#16840324C2211yescharacteristic
9#16840075—21no—
10#16839896—21no—
11C2×#14519691—21no—
12#16839641—21no—
13#16839529C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C2×#124×C61—21no—
19C61×#397C2211yescharacteristic
20C61×#394—21no—
21C61×#393—21no—
22C61×#392C2211yescharacteristic
23C61×#391—21no—
24C61×#388—21no—
25C61×#386—21no—
26C61×#385C2211yescharacteristic
27C22×C22⋊D61—21no—
28C2×#11758199—41no—
29#14519761—41no—
30#14519751—21no—
31#14519751—21no—
32#14519747—41no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—41no—
35#14519710—41no—
36#14519698—41no—
37#14519697—41no—
38#14519691—42no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41#14519684—41no—
42C22×Q8×C61—21no—
43C22×D4×C61—21no—
44C22×D4×C61D411yescharacteristic
45C23×C4×C61D411yescharacteristic
46#124×C61—42no—
47#124×C61—42no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61C2311yescharacteristic
58C2×C42×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C24×C61—21no—
66C24×C61C2×D411yescharacteristic
67C23×D61—21no—
68C2×Q8×C61—42no—
69C2×Q8×C61—42no—
70C2×Q8×C61—81no—
71C2×D4×C61—41no—
72C2×D4×C61—42no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—81no—
76C2×D4×C61—81no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61—81no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C22×Dic61—21no—
93C22×Dic61—41no—
94C2×D244—21no—
95C2×D244—21no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—81no—
98C22⋊C4×C61—21no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—42no—
102C22⋊C4×C61—42no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—81no—
106C22⋊C4×C61—81no—
107C22⋊C4×C61D812yescomplemented
108C42×C61—42no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111#11758199—82no—
112#11758198—41no—
113#11758198—41no—
114#11758198—82no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C2×#92418—41no—
118C2×#92418—41no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61#12011yescharacteristic
131C23×C61C2×D811yescharacteristic
132C23×C61AGL(1,ℤ/8)11yescharacteristic
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—81no—
137C22×D61—81no—
138Q8×C61—84no—
139D4×C61—42no—
140D4×C61—82no—
141D4×C61—82no—
142D4×C61—81no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C22⋊D61—81no—
165C22⋊D61—81no—
166C22⋊D61—81no—
167C22⋊D61—81no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174D244—81no—
175D244—81no—
176#92418—81no—
177#92418—81no—
178#12151—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61#44711yescharacteristic
196C22×C61#45411yescharacteristic
197C22×C61B(4,𝔽2)11yescharacteristic
198C2×D61—82no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—161no—
203C4×C61—42no—
204C4×C61—42no—
205C4×C61—41no—
206C4×C61—41no—
207C4×C61—81no—
208C4×C61—81no—
209C4×C61—81no—
210Dic61—81no—
211Dic61—161no—
212#2712D6111yescharacteristic, complemented
213#2044—611no—
214#1607—611no—
215#1595—611no—
216#1344—611no—
217#1343—611no—
218#1326—611no—
219C2×C61—21no—
220C2×C61—21no—
221C2×C61—41no—
222C2×C61—41no—
223C2×C61—161no—
224C2×C61#159811yescharacteristic
225C2×C61#219811yescharacteristic
226C2×C61#219911yescharacteristic
227D61—161no—
228#534—611no—
229C2×#124—21no—
230#480—1221no—
231#447—1221no—
232C2×#99—1221no—
233#397C2×D6111yescharacteristic
234#394—21no—
235#393—21no—
236#392C2×D6111yescharacteristic
237#391—21no—
238#388—21no—
239#386—21no—
240#386—1221no—
241#385C2×D6111yescharacteristic
242#342—611no—
243#327—1221no—
244#327—1221no—
245#323—611no—
246#323—611no—
247C61#1215111yescharacteristic, complemented, Sylow
248C22×Q8—21no—
249C22×D4—21no—
250C22×D4—1221no—
251C22×D4C22⋊D6111yescharacteristic
252C23×C4C22⋊D6111yescharacteristic
253C2×D8—2441no—
254#124—42no—
255#124—42no—
256#123—2441no—
257#121—1221no—
258#121—1221no—
259#120—2441no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22⋊D6111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—2441no—
270C2×C22⋊C4C22⋊D6111yescharacteristic
271C2×C22⋊C4C22×D6111yescharacteristic
272C2×C42—21no—
273#107—2441no—
274#102—2441no—
275#102—2441no—
276#99—2442no—
277C22⋊C8—1221no—
278C22⋊C8—1221no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—2441no—
284#95C22⋊D6111yescharacteristic
285#95C22⋊D6111yescharacteristic
286C24—21no—
287C24—1221no—
288C24C2×C22⋊D6111yescharacteristic
289C2×Q8—42no—
290C2×Q8—42no—
291C2×Q8—81no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—2441no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2441no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—81no—
313C22×C4—1221no—
314C22×C4—2441no—
315C22×C4C2×C22⋊D6111yescharacteristic
316C22×C4C2×C22⋊D6111yescharacteristic
317D8—4882no—
318C2×C8—2441no—
319C2×C8—2441no—
320C4⋊C4—41no—
321C4⋊C4—81no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C22⋊C4—21no—
325C22⋊C4—41no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—4882no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4#1175819912yescomplemented
339C42—42no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—4881no—
352C23—4881no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23#1451974611yescharacteristic
357C23C2×#1175819911yescharacteristic
358C23#1451980311yescharacteristic
359Q8—84no—
360D4—42no—
361D4—82no—
362D4—82no—
363D4—81no—
364D4—4881no—
365D4—4881no—
366D4—4881no—
367D4—4881no—
368D4—4881no—
369D4—4881no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C8—4881no—
398C8—4881no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—9761no—
416C22—4882no—
417C22—4881no—
418C22—4881no—
419C22—4881no—
420C22#1683989611yescharacteristic
421C22#1683993511yescharacteristic
422C22#1683994911yescharacteristic
423C4—42no—
424C4—42no—
425C4—41no—
426C4—41no—
427C4—81no—
428C4—81no—
429C4—81no—
430C4—9761no—
431C4—4881no—
432C2—21no—
433C2—21no—
434C2—41no—
435C2—41no—
436C2—161no—
437C2—9761no—
438C2#2144475411yescharacteristic
439C2#2144781511yescharacteristic
440C2#2144782011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2712C2
socleC22×C61B(4,𝔽2)
prime radical#21444736C2
hypercenter#2712D61
hypocenterC61#12151
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2712

Complements

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

NH ≅ G/Ntype
1. #21447070C2semidirect
2. #21444804C2semidirect
4. #21443819C2semidirect
5. #21443816C2semidirect
6. #21443767C2semidirect
7. C61×#2712C2semidirect
107. C22⋊C4×C61D8semidirect
212. #2712D61semidirect
247. C61#12151semidirect
338. C22⋊C4#11758199semidirect

Maximal subgroups

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

subgroupindex
#214470702
#214448042
#214447362
#214438192
#214438162
#214437672
C61×#27122
#1215161