Finite Group Databasebeta

← #29596802

Subgroups — #29596802

Order 15616.

416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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#21454877C211yesmaximal, characteristic
2#21447461C211yesmaximal, characteristic
3#21446235C211yesmaximal, characteristic
4#21446104C211yesmaximal, characteristic, complemented
5#21446041C211yesmaximal, characteristic, complemented
6#21443949C211yesmaximal, characteristic, complemented
7C61×#1392C211yesmaximal, characteristic, complemented
8#16840529C2211yescharacteristic
9#16840269C2211yescharacteristic
10#16839838—21no—
11#16839837—21no—
12#16839833—21no—
13#16839830—21no—
14#16839820—21no—
15#16839811—21no—
16#16839788—21no—
17#16839736C2211yescharacteristic
18#16839729C2211yescharacteristic
19#16839725—21no—
20#16839724—21no—
21#16839553C412yes—
22#16839550C412yes—
23#16839534—21no—
24#16839534—21no—
25#16839526—21no—
26C61×#413C2211yescharacteristic
27C61×#413C2211yescharacteristic
28C61×#408C2211yescharacteristic
29C22×C4×D61D411yescharacteristic
30#14519784—42no—
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758194D411yescharacteristic
35C2×#11758189—21no—
36C2×#11758189—21no—
37C22×#92418D411yescharacteristic
38#14519758C2×C411yescharacteristic
39#14519758Q811yescharacteristic
40#14519753—21no—
41#14519748—21no—
42#14519745C2×C411yescharacteristic
43#14519745Q811yescharacteristic
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46#14519736—21no—
47#14519736D411yescharacteristic
48#14519713—42no—
49#14519706—21no—
50#14519706—21no—
51#14519706—42no—
52#14519692—21no—
53#14519692C2×C412yes—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56#14519689—21no—
57#14519689—21no—
58#14519689—42no—
59#14519687—21no—
60C8×Dic61—21no—
61C2×#41×C61C2311yescharacteristic
62C2×M16×C61—21no—
63C2×M16×C61—21no—
64C2×M16×C61D411yescharacteristic
65C22×C8×C61D411yescharacteristic
66#101×C61—21no—
67#101×C61—21no—
68#100×C61—21no—
69#100×C61C2×C412yes—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C23×D61C4⋊C411yescharacteristic
73#41×C61—41no—
74#41×C61—41no—
75C2×Q8×C61#4111yescharacteristic
76C2×D4×C61C22×C411yescharacteristic
77C2×D4×C61C2×Q811yescharacteristic
78C2×D4×C61#4111yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—21no—
83C2×C22⋊D61—21no—
84C22×Dic61C4⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89M16×C61—22no—
90M16×C61—41no—
91M16×C61—41no—
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61—22no—
102C22⋊Dic61C4⋊C411yescharacteristic
103C22⋊Dic61C4⋊C411yescharacteristic
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—41no—
108#11758196—21no—
109#11758196—21no—
110C4×Dic61—21no—
111C4×Dic61—41no—
112#11758194—22no—
113#11758194—41no—
114#11758194—41no—
115#11758194—41no—
116#11758194—41no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—41no—
122C2×#92418—41no—
123#11758189—81no—
124#11758189—81no—
125C23×C61C2×C4⋊C411yescharacteristic
126C23×C61C4×D411yescharacteristic
127C23×C61C22⋊Q811yescharacteristic
128C22×D61—21no—
129C22×D61—41no—
130C22×D61—81no—
131Q8×C61—41no—
132D4×C61—41no—
133D4×C61—41no—
134D4×C61—41no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61C22⋊Q811yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C22⋊D61—81no—
146C22⋊D61—81no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—42no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—81no—
155C8×C61—42no—
156C8×C61—41no—
157C8×C61—41no—
158C8×C61—81no—
159#92418—41no—
160#92418—42no—
161#92418—41no—
162#12963—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61#38511yescharacteristic
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—42no—
173C2×D61—41no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61B(4,𝔽2)11yescharacteristic
179C4×C61#45811yescharacteristic
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183Dic61—82no—
184#2978—611no—
185#2120—611no—
186#1891—611no—
187#1868—611no—
188#1858—611no—
189#1395—611no—
190#1392D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—41no—
193C2×C61—41no—
194C2×C61—41no—
195C2×C61#186711yescharacteristic
196D61—81no—
197#568—611no—
198#525—611no—
199#436—1221no—
200#436—1221no—
201#435—1221no—
202#435—1221no—
203#433—1221no—
204#430—1221no—
205#424—1221no—
206#413C2×D6111yescharacteristic
207#413C2×D6111yescharacteristic
208#410—611no—
209#408—611no—
210#408C2×D6111yescharacteristic
211#407—1221no—
212#407—1221no—
213#352—612no—
214AΣL(1,𝔽16)—612no—
215#344—1221no—
216#344—1221no—
217#341—1221no—
218C61#1296311yescharacteristic, complemented, Sylow
219C2×#41C22×D6111yescharacteristic
220C23×C4—611no—
221#131—2442no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—611no—
225C2×M16—1221no—
226C2×M16—1221no—
227C2×M16—1221no—
228C2×M16—1221no—
229C2×M16—1221no—
230C2×M16D24411yescharacteristic
231C22×C8—611no—
232C22×C8D24411yescharacteristic
233#123—611no—
234#123—611no—
235C22⋊Q8—1221no—
236#121—1221no—
237#120—611no—
238#120—611no—
239C4×D4—1221no—
240C4×D4—1221no—
241#117—611no—
242#117—1221no—
243#108—2442no—
244C4⋊C8—1221no—
245C4⋊C8—1221no—
246C4⋊C8—2442no—
247#101—21no—
248#101—21no—
249#100—21no—
250#100C4×D6112yes—
251#99—612no—
252#99—1221no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—1221no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258C22⋊C8—1221no—
259C22⋊C8—2442no—
260#97—1221no—
261C4×C8—1221no—
262C24—611no—
263#41—41no—
264#41—41no—
265C2×Q8#1175822411yescharacteristic
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4C2×C4×D6111yescharacteristic
269C2×D4#1175822211yescharacteristic
270C2×D4Q8×D6111yescharacteristic
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4C2×D24411yescharacteristic
277C22×C4D4×D6111yescharacteristic
278C22×C4D4×D6111yescharacteristic
279M16—22no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—1222no—
285M16—4881no—
286M16—4881no—
287M16—2441no—
288M16—2441no—
289M16—2441no—
290M16—2441no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—1222no—
297C2×C8—1222no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—2441no—
301C2×C8—2441no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—2441no—
306C22⋊C4—611no—
307C22⋊C4—611no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1222no—
313C42—1221no—
314C42—2441no—
315C23—1221no—
316C23—4881no—
317C23—2441no—
318C23C4⋊C4×D6111yescharacteristic
319C23C4×D24411yescharacteristic
320C23#1451975511yescharacteristic
321Q8—41no—
322D4—41no—
323D4—41no—
324D4—41no—
325D4—4881no—
326D4—4881no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4#1451973711yescharacteristic
342C2×C4#1451974711yescharacteristic
343C2×C4#1451975711yescharacteristic
344C2×C4#1451975911yescharacteristic
345C8—42no—
346C8—41no—
347C8—41no—
348C8—81no—
349C8—2442no—
350C8—2441no—
351C8—2441no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—4881no—
359C22—2441no—
360C22—2441no—
361C22—2442no—
362C22—2441no—
363C22#1683963611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—4882no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4#1683995011yescharacteristic
372C4#1683995311yescharacteristic
373C2—21no—
374C2—41no—
375C2—41no—
376C2—41no—
377C2—4881no—
378C2#2144610111yescharacteristic
subgroupG/H
centerC4#16839950
commutatorC2×D4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#1392C2
socleC2×C61#1867
prime radical#16840269C22
cosocleC2×#41×C61C23
hypercenter#1392D61
hypocenterC61#12963
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
4. #21446104C2semidirect
5. #21446041C2semidirect
6. #21443949C2semidirect
7. C61×#1392C2semidirect
190. #1392D61semidirect
218. C61#12963semidirect

Maximal subgroups

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

subgroupindex
#214548772
#214474612
#214462352
#214461042
#214460412
#214439492
C61×#13922
#1296361