Finite Group Databasebeta

← #30601663

Subgroups — #30601663

Order 15616.

640 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461673C211yesmaximal, characteristic
2#21461545C211yesmaximal, characteristic
3C2×#16840608C212yesmaximal
4C2×#16840607C212yesmaximal
5C2×#16839659C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420C2212yes—
8C2×C22⋊#92420C2212yes—
9C2×#14519832—21no—
10#16840628—21no—
11#16840628—21no—
12#16840608—24no—
13#16840607—24no—
14C22×C4⋊Dic61C2211yescharacteristic
15C22×#11758196C411yescharacteristic
16C22×#11758196C411yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19#16839659—21no—
20#16839659—21no—
21#16839659—21no—
22#16839659—21no—
23C2×#14519684C411yescharacteristic
24C2×#95×C61C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27C4⋊#92420—42no—
28C22⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31C22⋊#92420D414yes—
32#14519832—42no—
33C23×Dic61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2311yescharacteristic
37C2×C4⋊Dic61—22no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—22no—
41C2×#11758196—22no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—22no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—22no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×#11758196—22no—
51C2×#11758196—42no—
52C2×C4×Dic61—42no—
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57#14519684—21no—
58#14519684—21no—
59C23×C4×C61C2×C411yescharacteristic
60C23×C4×C61C2×C411yescharacteristic
61C23×C4×C61C2×C411yescharacteristic
62#95×C61—21no—
63#95×C61—21no—
64C24×C61C22×C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—22no—
67C22×C4×C61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—21no—
72C22×C4×C61—22no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61M1612yes—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—22no—
82C22×Dic61—22no—
83C22×Dic61—21no—
84C22×Dic61—22no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—21no—
88C22×Dic61—22no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61M1612yes—
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61C2×D411yescharacteristic
98C22×Dic61C2×D412yes—
99C22×Dic61#4112yes—
100C2×#92420—24no—
101C2×#92420—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104C2×#92420—42no—
105C2×#92420—42no—
106C4⋊Dic61—42no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109#11758196—24no—
110#11758196—24no—
111#11758196—42no—
112#11758196—42no—
113#11758196—42no—
114#11758196—41no—
115#11758196—41no—
116C4×Dic61—22no—
117C4×Dic61—22no—
118C4×Dic61—41no—
119C4×Dic61—41no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61C4×D412yes—
126C23×C61C2×M1611yescharacteristic
127C23×C61C2×M1611yescharacteristic
128C23×C61#13112yes—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—24no—
136C2×C4×C61—44no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—82no—
144C2×C4×C61#10112yes—
145C2×Dic61—24no—
146C2×Dic61—24no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—22no—
156C2×Dic61—24no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—42no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—82no—
166C2×Dic61#9912yes—
167C2×Dic61#10112yes—
168C2×Dic61#12112yes—
169C2×Dic61#12411yescharacteristic
170C2×Dic61#12711yescharacteristic
171#92420—44no—
172#92420—82no—
173#9654—611nomaximal, Sylow
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61#39011yescharacteristic
183C22×C61#40711yescharacteristic
184C22×C61#40811yescharacteristic
185C22×C61C2×#9911yescharacteristic
186C22×C61#41011yescharacteristic
187C22×C61C2×#10111yescharacteristic
188C22×C61C2×#10111yescharacteristic
189C22×C61#43512yes—
190C22×C61#43512yes—
191C4×C61—22no—
192C4×C61—42no—
193C4×C61—41no—
194C4×C61—81no—
195Dic61—22no—
196Dic61—21no—
197Dic61—21no—
198Dic61—22no—
199Dic61—22no—
200Dic61—42no—
201Dic61—81no—
202C2×#389—611no—
203#1797—611no—
204#1749—611no—
205C2×#324—612no—
206C2×#324—612no—
207C2×C61—22no—
208C2×C61—22no—
209C2×C61#146311yescharacteristic
210C2×C61#146711yescharacteristic
211C2×C61#147011yescharacteristic
212C2×C61#147211yescharacteristic
213C2×C61#195511yescharacteristic
214C2×C61#196411yescharacteristic
215C2×C61#196611yescharacteristic
216C22×C4⋊C4—611no—
217C22×C4⋊C4—611no—
218C22×C4⋊C4—611no—
219C22×C4⋊C4—611no—
220C22×C42—611no—
221C2×C4⋊C8—1221no—
222C2×C22⋊C8—612no—
223C2×C22⋊C8—612no—
224C2×#97—1221no—
225#389—1221no—
226#389—1221no—
227#389—1221no—
228#389—1221no—
229C2×#95—611no—
230C2×#95#692311yescharacteristic
231#336—1221no—
232#336—1221no—
233#324—1224no—
234#324—1224no—
235C61#965411yescharacteristic, complemented, Sylow
236C23×C4—611no—
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—611no—
240C23×C4C2×#692311yescharacteristic
241C23×C4C2×#692311yescharacteristic
242C23×C4C2×#692311yescharacteristic
243C22×C8—1222no—
244C22×C8—1222no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1222no—
248C2×C4⋊C4—1222no—
249C2×C4⋊C4—1222no—
250C2×C4⋊C4—1222no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1222no—
258C2×C4⋊C4—1222no—
259C2×C4⋊C4—2442no—
260C2×C42—611no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—2442no—
265C4⋊C8—2442no—
266C22⋊C8—614no—
267C22⋊C8—1222no—
268C22⋊C8—1222no—
269C22⋊C8—1222no—
270#97—2442no—
271#95—21no—
272#95—21no—
273#95—1221no—
274#95—1221no—
275C24C22×#692311yescharacteristic
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1222no—
300C22×C4—1221no—
301C22×C4—1222no—
302C22×C4—1222no—
303C22×C4—1221no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4#1175821312yes—
309C22×C4C22⋊#692311yescharacteristic
310C22×C4C22⋊#692311yescharacteristic
311C2×C8—1224no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C2×C8—2442no—
317C4⋊C4—1224no—
318C4⋊C4—1224no—
319C4⋊C4—2442no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C4⋊C4—2442no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C4⋊C4—2442no—
326C4⋊C4—2442no—
327C42—1222no—
328C42—1222no—
329C42—2441no—
330C42—2441no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23C2×C22⋊#692311yescharacteristic
336C23D4×#692312yes—
337C23D61⋊M1611yescharacteristic
338C23C2×#1175821311yescharacteristic
339C23#1451986412yes—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—24no—
347C2×C4—44no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—82no—
355C2×C4—612no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—612no—
359C2×C4—612no—
360C2×C4—1224no—
361C2×C4—1224no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1222no—
371C2×C4—1224no—
372C2×C4—4882no—
373C2×C4—2442no—
374C2×C4—2442no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2442no—
381C2×C4#1451983812yes—
382C8—4882no—
383C8—2444no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22#1684071411yescharacteristic
393C22#1684073311yescharacteristic
394C22#1684073511yescharacteristic
395C22D61⋊#9911yescharacteristic
396C22#1684074111yescharacteristic
397C22C2×#1451983811yescharacteristic
398C22D61⋊#10111yescharacteristic
399C22#1684079112yes—
400C22#1684079412yes—
401C4—22no—
402C4—41no—
403C4—42no—
404C4—81no—
405C4—1222no—
406C4—1222no—
407C4—1221no—
408C4—1222no—
409C4—1221no—
410C4—4881no—
411C4—2442no—
412C2—22no—
413C2—22no—
414C2#2146106811yescharacteristic
415C2#2146108111yescharacteristic
416C2#2146109111yescharacteristic
417C2#2146109811yescharacteristic
418C2#2146194411yescharacteristic
419C2#2146196011yescharacteristic
420C2#2146196211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#9654
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
235. C61#9654semidirect

Maximal subgroups

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

subgroupindex
#214616732
#214615452
C2×#168406082
C2×#168406072
C2×#168396592
#965461