Finite Group Databasebeta

← #30604258

Subgroups — #30604258

Order 15616.

496 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461067C211yesmaximal, characteristic, complemented
2C2×#16840607C211yesmaximal, characteristic, complemented
3#21460761C212yesmaximal, complemented
4#21460748C212yesmaximal, complemented
5#21450290C211yesmaximal, characteristic
6#16840732—21no—
7C2×C22⋊#92420—21no—
8#16840607—21no—
9#16840607—21no—
10#16840607C2212yes—
11#16840607C2212yes—
12C2×#14519761—21no—
13C2×#14519761—21no—
14C2×#14519751C411yescharacteristic
15C22×C4⋊Dic61C2211yescharacteristic
16#16839699—21no—
17#16839699—21no—
18#16839664C411yescharacteristic
19#16839664C2211yescharacteristic
20#16839632C411yescharacteristic
21#16839632C2211yescharacteristic
22C4×C22⋊C4×C61C411yescharacteristic
23C2×#11758217—41no—
24C22×#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C22⋊#92420—41no—
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519761—44no—
34#14519761—44no—
35#14519751—41no—
36#14519751—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—41no—
42C2×C4⋊Dic61—41no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×C4⋊Dic61C2311yescharacteristic
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C23×C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58C24×C61C22⋊C411yescharacteristic
59C23×D61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—41no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C2×D244—22no—
84C2×D244—41no—
85C2×D244—41no—
86#11758217—82no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—82no—
90C22⋊C4×C61—24no—
91C42×C61—22no—
92C42×C61—41no—
93#11758198—42no—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—42no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—42no—
103C4⋊Dic61—42no—
104C4⋊Dic61—42no—
105C4⋊Dic61—42no—
106C4⋊Dic61—41no—
107C23×C61—22no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—41no—
111C23×C61#9911yescharacteristic
112C23×C61#9911yescharacteristic
113C23×C61C2×C22⋊C411yescharacteristic
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61#13112yes—
135C22⋊D61—82no—
136C22⋊D61—82no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152D244—82no—
153#92420—82no—
154#92420—82no—
155#11549—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61#35312yes—
166C22×C61#40811yescharacteristic
167C22×C61C2×#9911yescharacteristic
168C22×C61#41311yescharacteristic
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—22no—
177C4×C61—42no—
178C4×C61—42no—
179C4×C61—41no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184Dic61—81no—
185#2501—611no—
186#1463—611no—
187C2×#324—611no—
188#1325—612no—
189#1318—612no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—22no—
193C2×C61—41no—
194C2×C61#146811yescharacteristic
195C2×C61C2×#35311yescharacteristic
196C2×C61#213311yescharacteristic
197D61—161no—
198C2×#123—1221no—
199C2×#123—1221no—
200C2×#121—611no—
201C22×C4⋊C4—611no—
202#407—1221no—
203C2×C22⋊C8—1221no—
204#399—1221no—
205#399—1221no—
206#390—611no—
207#390—611no—
208#384—611no—
209#384—611no—
210C4×C22⋊C4#692311yescharacteristic
211#324—612no—
212#324—612no—
213#324—1221no—
214#324—1221no—
215C61#1154911yescharacteristic, complemented, Sylow
216C22×D4—611no—
217C22×D4—1221no—
218C23×C4—611no—
219C23×C4—611no—
220C23×C4C2×#692311yescharacteristic
221C2×M16—2441no—
222C22×C8—2441no—
223#123—2444no—
224#123—2444no—
225#121—2441no—
226#121—2441no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—2441no—
237C2×C4⋊C4—2441no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42C2×#692311yescharacteristic
245C2×C42C2×#692311yescharacteristic
246C22⋊C8—1222no—
247C22⋊C8—1222no—
248C22⋊C8—2441no—
249C22⋊C8—2441no—
250#95—21no—
251C24—1221no—
252C24C22⋊#692311yescharacteristic
253C2×D4—1222no—
254C2×D4—2441no—
255C2×D4—2441no—
256C2×D4—2442no—
257C2×D4—2442no—
258C2×D4—2441no—
259C2×D4—2441no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—2442no—
276C22×C4—2442no—
277C22×C4C22⋊#692311yescharacteristic
278C22×C4C22×#692311yescharacteristic
279M16—4882no—
280C2×C8—4882no—
281C2×C8—2442no—
282C2×C8—2442no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2442no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C4⋊C4—2442no—
292C22⋊C4—24no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2442no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C42—22no—
299C42—41no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23#1451983611yescharacteristic
312C23#1451983611yescharacteristic
313C23C2×C22⋊#692311yescharacteristic
314D4—4882no—
315D4—4882no—
316D4—4882no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4#1451986412yes—
346C8—4882no—
347C8—4882no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22—4881no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22#1684066712yes—
365C22#1684073511yescharacteristic
366C22C2×#1451983611yescharacteristic
367C22#1684074911yescharacteristic
368C4—22no—
369C4—42no—
370C4—42no—
371C4—41no—
372C4—4881no—
373C4—2441no—
374C4—2441no—
375C4—2441no—
376C4—2441no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—9761no—
382C2#2146108611yescharacteristic
383C2C2×#1684066711yescharacteristic
384C2#2146211611yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC2×#14519751C4
cosocleC2×C4⋊Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#11549
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461067C2semidirect
2. C2×#16840607C2semidirect
3. #21460761C2semidirect
4. #21460748C2semidirect
215. C61#11549semidirect

Maximal subgroups

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

subgroupindex
#214610672
C2×#168406072
#214607612
#214607482
#214502902
#1154961