Finite Group Databasebeta

← #29592654

Subgroups — #29592654

Order 15616.

484 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 59 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#21446950C211yesmaximal, characteristic, complemented
2#21444838C211yesmaximal, characteristic, complemented
3#21444736C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic, complemented
5#21443816C211yesmaximal, characteristic, complemented
6#21443749C211yesmaximal, characteristic, complemented
7C61×#2752C211yesmaximal, characteristic, complemented
8#16840324C2211yescharacteristic
9C2×#14519760—21no—
10#16840080—21no—
11#16839896—21no—
12C2×#14519691—21no—
13#16839529C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#399C2211yescharacteristic
19C61×#397—21no—
20C61×#394—21no—
21C61×#392C2211yescharacteristic
22C61×#390—21no—
23C61×#388—21no—
24C61×#387—21no—
25C61×#386—21no—
26C61×#381C2211yescharacteristic
27C22×C22⋊D61—21no—
28C2×#11758199—41no—
29#14519761—41no—
30#14519760—42no—
31#14519760—42no—
32#14519751—21no—
33#14519751—21no—
34#14519747—41no—
35C2×#11758196—41no—
36C2×C22⋊Dic61—21no—
37C2×#11758198—41no—
38#14519708—41no—
39#14519698—41no—
40#14519697—41no—
41#14519691—42no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22×D4×C61—21no—
45C22×D4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C2×C4⋊C4×C61—21no—
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×D4×C61—41no—
69C2×D4×C61—42no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—81no—
73C2×D4×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C22×Dic61—21no—
92C22×Dic61—41no—
93C2×D244—21no—
94C2×D244—21no—
95C4⋊C4×C61—42no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—81no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—81no—
102C22⋊C4×C61—81no—
103C22⋊C4×C61—81no—
104C22⋊C4×C61—81no—
105C22⋊C4×C61—81no—
106C42×C61—81no—
107C22⋊Dic61—22no—
108C22⋊Dic61—41no—
109#11758199—82no—
110#11758198—41no—
111#11758198—41no—
112#11758198—44no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115#11758196—44no—
116C2×#92418—41no—
117C2×#92418—41no—
118C23×C61—21no—
119C23×C61—21no—
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×C61—41no—
129C23×C61#12011yescharacteristic
130C23×C61#13511yescharacteristic
131C23×C61AGL(1,ℤ/8)11yescharacteristic
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—81no—
136C22×D61—81no—
137D4×C61—42no—
138D4×C61—82no—
139D4×C61—82no—
140D4×C61—81no—
141C2×C4×C61—22no—
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—42no—
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—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—81no—
162C22⋊D61—81no—
163C22⋊D61—81no—
164C22⋊D61—81no—
165C22⋊D61—81no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172D244—81no—
173D244—81no—
174#92418—81no—
175#92418—81no—
176#12191—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×C61#44911yescharacteristic
194C22×C61#45311yescharacteristic
195C22×C61B(4,𝔽2)11yescharacteristic
196C2×D61—82no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—161no—
201C4×C61—42no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61—81no—
205C4×C61—81no—
206C4×C61—81no—
207C4×C61—81no—
208Dic61—82no—
209Dic61—81no—
210#2752D6111yescharacteristic, complemented
211#2022—611no—
212#1613—611no—
213#1595—611no—
214#1352—611no—
215#1343—611no—
216#1317—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—41no—
220C2×C61—41no—
221C2×C61—161no—
222C2×C61#160011yescharacteristic
223C2×C61#219811yescharacteristic
224C2×C61#220011yescharacteristic
225D61—161no—
226#534—611no—
227C2×#123—1221no—
228#481—1221no—
229#447—1221no—
230C2×#99—1221no—
231#399C2×D6111yescharacteristic
232#397—21no—
233#394—21no—
234#392C2×D6111yescharacteristic
235#390—21no—
236#388—21no—
237#387—21no—
238#386—21no—
239#381C2×D6111yescharacteristic
240#342—611no—
241#327—1221no—
242#327—1221no—
243#323—611no—
244#323—611no—
245C61#1219111yescharacteristic, complemented, Sylow
246C22×D4—21no—
247C22×D4—1221no—
248C22×D4C22⋊D6111yescharacteristic
249C23×C4C22⋊D6111yescharacteristic
250C2×D8—2441no—
251#123—2441no—
252#123—2442no—
253#123—2442no—
254#121—1221no—
255#121—1221no—
256#120—2441no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—2441no—
260C2×C4⋊C4C22⋊D6111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—2441no—
269C2×C22⋊C4C22⋊D6111yescharacteristic
270C2×C22⋊C4C22×D6111yescharacteristic
271C2×C42—21no—
272#106—2441no—
273#102—2441no—
274#102—2441no—
275#99—2442no—
276C22⋊C8—1221no—
277C22⋊C8—1221no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95C22⋊D6111yescharacteristic
283#95C22⋊D6111yescharacteristic
284C24—21no—
285C24—1221no—
286C24C2×C22⋊D6111yescharacteristic
287C2×D4—41no—
288C2×D4—42no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—1221no—
311C22×C4—2441no—
312C22×C4C2×C22⋊D6111yescharacteristic
313C22×C4C2×C22⋊D6111yescharacteristic
314D8—4882no—
315C2×C8—2441no—
316C2×C8—2441no—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—81no—
320C4⋊C4—1221no—
321C4⋊C4—1221no—
322C4⋊C4—2444no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—41no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C22⋊C4—81no—
331C22⋊C4—1222no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2444no—
335C22⋊C4—2441no—
336C42—81no—
337C23—21no—
338C23—21no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—4881no—
349C23—4881no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23#1451974611yescharacteristic
354C23#1451979711yescharacteristic
355C23#1451980211yescharacteristic
356D4—42no—
357D4—82no—
358D4—82no—
359D4—81no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—4881no—
364D4—4881no—
365D4—4881no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—2442no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C8—4881no—
394C8—4881no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—9761no—
412C22—4882no—
413C22—4881no—
414C22—4881no—
415C22—4881no—
416C22#1683990711yescharacteristic
417C22#1683993011yescharacteristic
418C22#1683994911yescharacteristic
419C4—42no—
420C4—41no—
421C4—41no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—81no—
426C4—4882no—
427C4—4881no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—161no—
433C2—9761no—
434C2#2144476511yescharacteristic
435C2#2144781511yescharacteristic
436C2#2144782611yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2752C2
socleC22×C61B(4,𝔽2)
prime radical#21444736C2
hypercenter#2752D61
hypocenterC61#12191
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2752

Complements

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

NH ≅ G/Ntype
1. #21446950C2semidirect
2. #21444838C2semidirect
4. #21443843C2semidirect
5. #21443816C2semidirect
6. #21443749C2semidirect
7. C61×#2752C2semidirect
210. #2752D61semidirect
245. C61#12191semidirect

Maximal subgroups

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

subgroupindex
#214469502
#214448382
#214447362
#214438432
#214438162
#214437492
C61×#27522
#1219161