Finite Group Databasebeta

← #30599309

Subgroups — #30599309

Order 15616.

622 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#16840606C211yesmaximal, characteristic
2C2×#16840606C211yesmaximal, characteristic
3#21460662C212yesmaximal, complemented
4#21460662C212yesmaximal, complemented
5#21448171C211yesmaximal, characteristic
6C2×C22⋊#92420C2212yes—
7C2×C22⋊#92420C2212yes—
8#16840606—21no—
9#16840606—21no—
10#16840606—21no—
11#16840606—21no—
12C22×#11758198C2211yescharacteristic
13C2×C22⋊C4×D61C411yescharacteristic
14C2×C22⋊C4×D61C411yescharacteristic
15C22⋊C4×Dic61C2211yescharacteristic
16C22⋊C4×Dic61C2211yescharacteristic
17C4×#11758198—21no—
18C4×#11758198—21no—
19C4×C22⋊Dic61C411yescharacteristic
20#16839609—21no—
21#16839609—21no—
22C4×C22⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C24×D61C2×C411yescharacteristic
30C23×Dic61C2311yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C2×C22⋊Dic61C2×C411yescharacteristic
34C2×C22⋊Dic61C2×C411yescharacteristic
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198D411yescharacteristic
40C2×#11758198D411yescharacteristic
41C2×#11758198D411yescharacteristic
42C2×#11758198D411yescharacteristic
43C22⋊C4×D61—22no—
44C22⋊C4×D61—22no—
45C22⋊C4×D61—22no—
46C22⋊C4×D61C814yescomplemented
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C23×C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61—21no—
57#95×C61—21no—
58C24×C61C22×C411yescharacteristic
59C23×D61—21no—
60C23×D61—21no—
61C23×D61—21no—
62C23×D61—21no—
63C23×D61—81no—
64C23×D61—81no—
65C23×D61C22⋊C411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
67C23×D61C2×C812yes—
68C23×D61M1612yes—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—81no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—81no—
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61#4112yes—
82C22×Dic61#4112yes—
83C2×C4×D61—24no—
84C2×C4×D61—24no—
85C2×C4×D61—81no—
86C2×C4×D61—81no—
87C2×C4×D61—81no—
88C2×C4×D61—81no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—82no—
92C2×#92420—82no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61C2×C812yes—
96C22⋊C4×C61M1612yes—
97C42×C61—81no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61C2×C812yes—
101C22⋊Dic61M1612yes—
102#11758198—24no—
103#11758198—24no—
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108C4×Dic61—81no—
109C4×Dic61—81no—
110C4×Dic61—81no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61#11711yescharacteristic
115C23×C61#11711yescharacteristic
116C23×C61C22×C811yescharacteristic
117C23×C61C2×M1611yescharacteristic
118C23×C61C2×M1611yescharacteristic
119C23×C61C2×M1611yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—22no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61—81no—
135C22×D61—81no—
136C22×D61—82no—
137C22×D61—82no—
138C22×D61—82no—
139C22×D61—82no—
140C22×D61C22⋊C812yes—
141C22×D61C22⋊C812yes—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
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—81no—
153C2×C4×C61—81no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61#12312yes—
165C2×Dic61#12312yes—
166C4×D61—84no—
167C4×D61—84no—
168#92420—82no—
169#92420—82no—
170#8734—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61#38111yescharacteristic
182C22×C61C2×C22⋊C811yescharacteristic
183C22×C61#40711yescharacteristic
184C22×C61#43111yescharacteristic
185C22×C61#43111yescharacteristic
186C22×C61#43211yescharacteristic
187C22×C61#43211yescharacteristic
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—82no—
199C2×D61—82no—
200C2×D61—82no—
201C2×D61—82no—
202C4×C61—42no—
203C4×C61—42no—
204C4×C61—41no—
205C4×C61—41no—
206Dic61—22no—
207Dic61—22no—
208Dic61—42no—
209Dic61—42no—
210#2273—611no—
211C2×#323—611no—
212C2×#323—611no—
213#1282—612no—
214#1282—612no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—21no—
220C2×C61—21no—
221C2×C61#181711yescharacteristic
222C2×C61#182811yescharacteristic
223C2×C61#182911yescharacteristic
224D61—42no—
225D61—42no—
226C22×C22⋊C4—611no—
227C22×C22⋊C4—611no—
228C22×C22⋊C4—611no—
229C2×C22⋊C8—612no—
230C2×C22⋊C8—612no—
231C4×C22⋊C4—611no—
232C4×C22⋊C4—611no—
233C4×C22⋊C4—611no—
234C4×C22⋊C4—1221no—
235C4×C22⋊C4—1221no—
236C4×C22⋊C4—1221no—
237C4×C22⋊C4—1221no—
238C4×C22⋊C4#692311yescharacteristic
239#323—1221no—
240#323—1221no—
241#323—1221no—
242#323—1221no—
243C61#873411yescharacteristic, complemented, Sylow
244C25—611no—
245C23×C4—611no—
246C23×C4—1221no—
247C23×C4—1221no—
248C23×C4C2×#692311yescharacteristic
249C22×C8—1222no—
250C22×C8—1222no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—614no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—1222no—
259C2×C22⋊C4—1222no—
260C2×C22⋊C4—1222no—
261C2×C22⋊C4—1222no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1222no—
265C2×C22⋊C4C2×#692311yescharacteristic
266C2×C22⋊C4C2×#692311yescharacteristic
267C2×C42—21no—
268C2×C42—1221no—
269C2×C42—1221no—
270C2×C42—1221no—
271C22⋊C8—1222no—
272C22⋊C8—1222no—
273C22⋊C8—1222no—
274C22⋊C8—1222no—
275#95—21no—
276#95—1221no—
277#95—1221no—
278#95—1221no—
279C24—612no—
280C24—612no—
281C24—611no—
282C24—611no—
283C24—1221no—
284C24—1221no—
285C24—1221no—
286C24—1221no—
287C24—4881no—
288C24—4881no—
289C24C22×#692311yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—81no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—612no—
298C22×C4—612no—
299C22×C4—1224no—
300C22×C4—1224no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—4881no—
304C22×C4—4881no—
305C22×C4—4881no—
306C22×C4—4881no—
307C22×C4—4881no—
308C22×C4C22⋊#692311yescharacteristic
309C22×C4C22⋊#692311yescharacteristic
310C2×C8—4882no—
311C2×C8—4882no—
312C2×C8—2442no—
313C2×C8—2442no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—612no—
317C22⋊C4—612no—
318C22⋊C4—1222no—
319C22⋊C4—1222no—
320C22⋊C4—1222no—
321C22⋊C4—1222no—
322C22⋊C4—1224no—
323C22⋊C4—1224no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4D61⋊C812yes—
327C22⋊C4#1175821312yes—
328C42—81no—
329C42—4881no—
330C42—4881no—
331C42—4881no—
332C23—41no—
333C23—41no—
334C23—612no—
335C23—612no—
336C23—1222no—
337C23—1222no—
338C23—1222no—
339C23—1222no—
340C23—1221no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—4881no—
345C23—4881no—
346C23—4881no—
347C23—4881no—
348C23—4882no—
349C23—4882no—
350C23—4882no—
351C23—4882no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23C2×C22⋊#692311yescharacteristic
357C23#1451985611yescharacteristic
358C23#1451985611yescharacteristic
359C23C2×D61⋊C811yescharacteristic
360C23D61⋊M1611yescharacteristic
361C23D61⋊M1611yescharacteristic
362C23C2×#1175821311yescharacteristic
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—612no—
376C2×C4—612no—
377C2×C4—1222no—
378C2×C4—1222no—
379C2×C4—4884no—
380C2×C4—4884no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C8—4882no—
390C8—4882no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—1222no—
402C22—1222no—
403C22—4882no—
404C22—4882no—
405C22—4882no—
406C22—4882no—
407C22—2442no—
408C22—2442no—
409C22—2442no—
410C22—2442no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22#1684070511yescharacteristic
416C22D61⋊(C22⋊C8)11yescharacteristic
417C22#1684073311yescharacteristic
418C22#1684078011yescharacteristic
419C22#1684078111yescharacteristic
420C22#1684078411yescharacteristic
421C22#1684078511yescharacteristic
422C4—42no—
423C4—42no—
424C4—41no—
425C4—41no—
426C4—1222no—
427C4—1222no—
428C4—2442no—
429C4—2442no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2—21no—
435C2—21no—
436C2—2442no—
437C2—2442no—
438C2#2146171111yescharacteristic
439C2#2146173111yescharacteristic
440C2#2146173211yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8734
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460662C2semidirect
4. #21460662C2semidirect
46. C22⋊C4×D61C8semidirect
243. C61#8734semidirect

Maximal subgroups

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

subgroupindex
C2×#168406062
#214606622
#214481712
#873461