Finite Group Databasebeta

← #29592330

Subgroups — #29592330

Order 15616.

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

normal subgroups only

This group has 404 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#21447070C211yesmaximal, characteristic
2#21444804C211yesmaximal, characteristic
3#21444770C211yesmaximal, characteristic
4#21443840C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443767C211yesmaximal, characteristic, complemented
7C61×#2835C211yesmaximal, characteristic, complemented
8#16840324C2211yescharacteristic
9#16840075—21no—
10#16839901—21no—
11C2×#14519691—21no—
12#16839641—21no—
13#16839529C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#400—21no—
19C61×#400—21no—
20C61×#400—21no—
21C61×#397—21no—
22C61×#397C2211yescharacteristic
23C61×#395—21no—
24C61×#393C2211yescharacteristic
25C61×#385—21no—
26C61×#385C2211yescharacteristic
27C22×C22⋊D61—21no—
28C2×#11758201—41no—
29#14519761—41no—
30#14519751—21no—
31#14519751—21no—
32#14519747—41no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—41no—
35#14519710—41no—
36#14519701—41no—
37#14519697—41no—
38#14519691—42no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41#14519684—41no—
42C22×Q8×C61D411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61C2311yescharacteristic
53#95×C61—21no—
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×C61D411yescharacteristic
62#95×C61D411yescharacteristic
63C24×C61C2×D411yescharacteristic
64C23×D61—21no—
65C2×Q8×C61—41no—
66C2×Q8×C61—81no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61—81no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C22×Dic61—21no—
84C22×Dic61—41no—
85C2×D244—21no—
86C2×D244—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—81no—
89C4⋊C4×C61—81no—
90C4⋊C4×C61—81no—
91C4⋊C4×C61—81no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—81no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100#11758201—82no—
101#11758198—41no—
102#11758198—41no—
103#11758198—82no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C2×#92418—41no—
107C2×#92418—41no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61#12011yescharacteristic
113C23×C61#13511yescharacteristic
114C23×C61AGL(1,ℤ/8)11yescharacteristic
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—81no—
119C22×D61—81no—
120Q8×C61—42no—
121Q8×C61—81no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—42no—
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—81no—
146C22⋊D61—81no—
147C22⋊D61—81no—
148C22⋊D61—81no—
149C22⋊D61—81no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61—81no—
156D244—81no—
157D244—81no—
158#92418—81no—
159#92418—81no—
160#12139—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—81no—
170C22×C61#44911yescharacteristic
171C22×C61#45411yescharacteristic
172C22×C61B(4,𝔽2)11yescharacteristic
173C2×D61—82no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—161no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61—81no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—81no—
187Dic61—161no—
188#2835D6111yescharacteristic, complemented
189#2044—611no—
190#1607—611no—
191#1601—611no—
192#1351—611no—
193#1344—611no—
194#1326—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—41no—
198C2×C61—41no—
199C2×C61#159711yescharacteristic
200C2×C61#219911yescharacteristic
201C2×C61#220111yescharacteristic
202D61—161no—
203#534—611no—
204#480—1221no—
205#448—1221no—
206C2×#99—1221no—
207#400—21no—
208#400—21no—
209#400—21no—
210#397—21no—
211#397C2×D6111yescharacteristic
212#395—21no—
213#393C2×D6111yescharacteristic
214#386—1221no—
215#385—21no—
216#385C2×D6111yescharacteristic
217#342—611no—
218#327—1221no—
219#327—1221no—
220#323—611no—
221#323—611no—
222C61#1213911yescharacteristic, complemented, Sylow
223C22×Q8C22⋊D6111yescharacteristic
224C22×D4—1221no—
225C23×C4C22⋊D6111yescharacteristic
226C2×SD16—2441no—
227#123—2441no—
228#121—1221no—
229#121—1221no—
230#120—2441no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C22⋊D6111yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—2441no—
240C2×C22⋊C4C22⋊D6111yescharacteristic
241C2×C22⋊C4C22×D6111yescharacteristic
242#107—2441no—
243#103—2441no—
244#102—2441no—
245#99—2442no—
246C22⋊C8—1221no—
247C22⋊C8—1221no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—2441no—
257#95C22⋊D6111yescharacteristic
258#95C22⋊D6111yescharacteristic
259C24—1221no—
260C24C2×C22⋊D6111yescharacteristic
261C2×Q8—41no—
262C2×Q8—81no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—81no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4C2×C22⋊D6111yescharacteristic
282C22×C4C2×C22⋊D6111yescharacteristic
283SD16—4882no—
284C2×C8—2441no—
285C2×C8—2441no—
286C4⋊C4—41no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—4882no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—4881no—
309C23—4881no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23#1451974611yescharacteristic
314C23#1451979711yescharacteristic
315C23#1451980211yescharacteristic
316Q8—42no—
317Q8—81no—
318D4—4881no—
319D4—4881no—
320D4—4881no—
321D4—4881no—
322D4—4881no—
323D4—4881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C8—4881no—
355C8—4881no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—9761no—
366C22—4882no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22#1683990711yescharacteristic
371C22#1683993511yescharacteristic
372C22#1683994911yescharacteristic
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4—9761no—
382C4—4881no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—9761no—
388C2#2144474811yescharacteristic
389C2#2144782011yescharacteristic
390C2#2144783211yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2835C2
socleC22×C61B(4,𝔽2)
prime radical#16840324C22
hypercenter#2835D61
hypocenterC61#12139
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2835

Complements

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

NH ≅ G/Ntype
4. #21443840C2semidirect
5. #21443819C2semidirect
6. #21443767C2semidirect
7. C61×#2835C2semidirect
188. #2835D61semidirect
222. C61#12139semidirect

Maximal subgroups

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

subgroupindex
#214470702
#214448042
#214447702
#214438402
#214438192
#214437672
C61×#28352
#1213961