Finite Group Databasebeta

← #29568784

Subgroups — #29568784

Order 15616.

492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 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#21447053C211yesmaximal, characteristic
2#21447053C211yesmaximal, characteristic
3#21446906C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443642C211yesmaximal, characteristic, complemented
7C61×#2805C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519774C2211yescharacteristic
10C2×#14519697—21no—
11C2×#14519697—21no—
12C2×#14519697—21no—
13C2×#14519697—21no—
14C2×#14519697—21no—
15#16839517C2211yescharacteristic
16#16839517C2211yescharacteristic
17#16839517C2211yescharacteristic
18C61×#400—21no—
19C61×#400—21no—
20C61×#395—21no—
21C61×#391C2211yescharacteristic
22C61×#389—21no—
23C61×#389C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#387—21no—
26C61×#387—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C2×#11758201—42no—
31C2×#11758201—42no—
32C2×#11758201—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519774—42no—
37#14519697—42no—
38#14519697—42no—
39#14519697—42no—
40#14519697—42no—
41#14519697—42no—
42C22×Q8×C61D411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63C23×D61—41no—
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—22no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—81no—
106C4⋊C4×C61—81no—
107C4⋊C4×C61SD1612yescomplemented
108C42×C61—41no—
109C42×C61—81no—
110#11758201—48no—
111C2×#92418—22no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61#12011yescharacteristic
121C22×D61—42no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61—81no—
128Q8×C61—42no—
129Q8×C61—81no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
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×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61#13711yescharacteristic
160D244—42no—
161D244—42no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—42no—
166D244—81no—
167D244—81no—
168D244—81no—
169D244—81no—
170D244—81no—
171D244—81no—
172#92418—42no—
173#92418—81no—
174#92418—81no—
175#7747—611nomaximal, Sylow
176C22×C61#44811yescharacteristic
177C22×C61#44911yescharacteristic
178C22×C61#44911yescharacteristic
179C22×C61#45311yescharacteristic
180C22×C61#45411yescharacteristic
181C22×C61#45411yescharacteristic
182C22×C61B(4,𝔽2)11yescharacteristic
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—161no—
187C2×D61—161no—
188C2×D61—161no—
189C2×D61—161no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—81no—
198C4×C61—81no—
199C4×C61—81no—
200C4×C61—81no—
201C4×C61—81no—
202#2805D6111yescharacteristic, complemented
203#2041—611no—
204#2041—611no—
205#2014—611no—
206#1272—611no—
207#1271—611no—
208#1271—611no—
209C2×C61#159711yescharacteristic
210C2×C61#159911yescharacteristic
211C2×C61#160011yescharacteristic
212C2×C61#162211yescharacteristic
213C2×C61#162611yescharacteristic
214C2×C61#162811yescharacteristic
215C2×C61#165711yescharacteristic
216D61—162no—
217C22×SD16—1221no—
218C2×#127—611no—
219C2×#102—1221no—
220C2×#102—1221no—
221C2×#102—1221no—
222C2×#102—1221no—
223C2×#102—1221no—
224#400—21no—
225#400—21no—
226#395—21no—
227#391C2×D6111yescharacteristic
228#389—21no—
229#389C2×D6111yescharacteristic
230#389C2×D6111yescharacteristic
231#387—21no—
232#387—21no—
233#336—611no—
234#336—611no—
235#336—611no—
236C61#774711yescharacteristic, complemented, Sylow
237C22×Q8C22⋊D6111yescharacteristic
238C22×D4—1221no—
239C22×D4—1221no—
240C22×D4—1221no—
241C2×SD16—2442no—
242C2×SD16—2442no—
243C2×SD16—2442no—
244C22×C8—1221no—
245C22×C8—1221no—
246C22×C8—1221no—
247#127—2442no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D6111yescharacteristic
253C2×C4⋊C4C22⋊D6111yescharacteristic
254C2×C4⋊C4C22⋊D6111yescharacteristic
255C2×C4⋊C4C22⋊D6111yescharacteristic
256C2×C4⋊C4C22⋊D6111yescharacteristic
257C2×C42—21no—
258C2×C42C22×D6111yescharacteristic
259#102—2442no—
260#102—2442no—
261#102—2442no—
262#102—2442no—
263#102—2442no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273C24—2441no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×D4—1222no—
279C2×D4—1222no—
280C2×D4—1222no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2441no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4C2×C22⋊D6111yescharacteristic
303C22×C4C2×C22⋊D6111yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305SD16—2448no—
306C2×C8—1222no—
307C2×C8—2441no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2441no—
311C2×C8—2441no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C4⋊C4—81no—
327C4⋊C4#1175820112yescomplemented
328C42—41no—
329C42—81no—
330C23—4881no—
331C23—4881no—
332C23—4881no—
333C23—4881no—
334C23—4881no—
335C23—4881no—
336C23—2442no—
337C23#1451974611yescharacteristic
338Q8—42no—
339Q8—81no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—4881no—
345D4—4881no—
346D4—2442no—
347D4—2442no—
348D4—2442no—
349D4—2442no—
350D4—2442no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4C2×#1175820111yescharacteristic
377C2×C4#1451979711yescharacteristic
378C2×C4#1451979711yescharacteristic
379C2×C4#1451980211yescharacteristic
380C2×C4#1451980211yescharacteristic
381C2×C4#1451980811yescharacteristic
382C8—4881no—
383C8—4881no—
384C8—2442no—
385C22—9761no—
386C22—9761no—
387C22—9761no—
388C22—9761no—
389C22—4882no—
390C22—4882no—
391C22—4882no—
392C22#1683990111yescharacteristic
393C22#1683990711yescharacteristic
394C22#1683990711yescharacteristic
395C22#1683993011yescharacteristic
396C22#1683993511yescharacteristic
397C22#1683993511yescharacteristic
398C22#1683994911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—42no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C2—9762no—
412C2#2144474811yescharacteristic
413C2#2144475911yescharacteristic
414C2#2144476511yescharacteristic
415C2#2144489111yescharacteristic
416C2#2144491511yescharacteristic
417C2#2144492911yescharacteristic
418C2#2144511711yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2805C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenter#2805D61
hypocenterC61#7747
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
4. #21443645C2semidirect
5. #21443642C2semidirect
6. #21443642C2semidirect
7. C61×#2805C2semidirect
107. C4⋊C4×C61SD16semidirect
202. #2805D61semidirect
236. C61#7747semidirect
327. C4⋊C4#11758201semidirect

Maximal subgroups

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

subgroupindex
#214470532
#214469062
#214436452
#214436422
C61×#28052
#774761