Finite Group Databasebeta

← #30599831

Subgroups — #30599831

Order 15616.

688 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 124 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×#16840783C211yesmaximal, characteristic, complemented
2C4×C22⋊#92420C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448325C211yesmaximal, characteristic
6#16840783—24no—
7C2×C4⋊#92420C2212yes—
8C2×C22⋊#92420—21no—
9C2×C22⋊#92420—21no—
10C2×#14519832—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13#16840610—24no—
14C2×#14519751C411yescharacteristic
15C2×#14519739C2211yescharacteristic
16C2×#14519737—21no—
17C22×C4×Dic61C2211yescharacteristic
18#16839663C411yescharacteristic
19#16839658C411yescharacteristic
20#16839651—21no—
21#16839639—21no—
22C4⋊C4×Dic61C2211yescharacteristic
23#16839609—21no—
24C61×#380C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27C4⋊#92420—22no—
28C4⋊#92420D414yescomplemented
29C22⋊#92420—24no—
30C22⋊#92420—24no—
31#14519832—24no—
32C4×#92420—22no—
33C4×#92420—22no—
34C22×D244C2×C411yescharacteristic
35C22×C22⋊D61—21no—
36C23×Dic61D411yescharacteristic
37C23×Dic61D411yescharacteristic
38C22×C4×D61—21no—
39#14519751—22no—
40#14519751—22no—
41#14519739—22no—
42#14519739—22no—
43#14519737—44no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—22no—
52C2×C4×Dic61—21no—
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61C2311yescharacteristic
57#14519684—21no—
58#14519684—21no—
59C23×C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—21no—
63#95×C61—21no—
64C24×C61C22⋊C411yescharacteristic
65C23×D61—21no—
66C22×C4×C61—22no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C2×C22⋊D61—24no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C22×Dic61—22no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—22no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—22no—
84C22×Dic61—41no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C2×D244—22no—
90C2×D244—22no—
91C2×D244—21no—
92C2×D244M1612yes—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—42no—
96C2×C4×D61—42no—
97C2×#92420—24no—
98C2×#92420—24no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—22no—
105C22⋊C4×C61—42no—
106#11758198—24no—
107#11758198—42no—
108#11758198—42no—
109#11758198—42no—
110C4⋊Dic61—21no—
111C4⋊Dic61M1612yes—
112#11758196—42no—
113C4×Dic61—22no—
114C4×Dic61—21no—
115C4×Dic61—22no—
116C4×Dic61—21no—
117C4×Dic61—42no—
118C4×Dic61C2×D412yes—
119C4×Dic61#4112yes—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61#10412yes—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—22no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61C4×D412yes—
147C2×C4×C61C2×M1611yescharacteristic
148C2×C4×C61C2×M1611yescharacteristic
149C2×C4×C61#13112yes—
150C22⋊D61—48no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—22no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—44no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61#12011yescharacteristic
166C2×Dic61#12112yes—
167C2×Dic61#12311yescharacteristic
168C2×Dic61#13512yes—
169C2×Dic61AGL(1,ℤ/8)12yes—
170D244—24no—
171D244—42no—
172C4×D61—82no—
173C4×D61—82no—
174#92420—44no—
175#92420—44no—
176#8943—611nomaximal, Sylow
177C22×C61—22no—
178C22×C61—22no—
179C22×C61—22no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61#38611yescharacteristic
185C22×C61#40711yescharacteristic
186C22×C61#40811yescharacteristic
187C22×C61#41611yescharacteristic
188C22×C61#41811yescharacteristic
189C22×C61C2×#10411yescharacteristic
190C22×C61#42111yescharacteristic
191C2×D61—42no—
192C2×D61—42no—
193C2×D61—42no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C4×C61—41no—
199C4×C61—81no—
200C4×C61—81no—
201C4×C61#43512yes—
202C4×C61#43612yes—
203Dic61—22no—
204Dic61—41no—
205Dic61—41no—
206Dic61—42no—
207Dic61#44912yes—
208Dic61#48212yes—
209C2×#432—611no—
210C4×#121—611no—
211C4×C22⋊C8—611no—
212C2×D4⋊C8—612no—
213#1279—612no—
214C2×C61—42no—
215C2×C61#148811yescharacteristic
216C2×C61#149011yescharacteristic
217C2×C61#149411yescharacteristic
218C2×C61#149611yescharacteristic
219C2×C61#187011yescharacteristic
220C2×C61#187111yescharacteristic
221C2×C61#187511yescharacteristic
222D61—82no—
223C2×#121—611no—
224C2×C4×D4—611no—
225C2×C4×D4—1221no—
226C22×C42—611no—
227#432—1224no—
228C2×C4⋊C8—612no—
229C2×C22⋊C8—1221no—
230C2×C22⋊C8—1221no—
231C2×#97—1221no—
232C2×C4×C8—612no—
233#390—611no—
234#389—611no—
235#388—1221no—
236#386—1221no—
237#380#692311yescharacteristic
238C4×C4⋊C4—611no—
239C4×C22⋊C4—1221no—
240#336—1221no—
241D4⋊C8—1224no—
242C61#894311yescharacteristic, complemented, Sylow
243C22×D4—611no—
244C22×D4—1221no—
245C23×C4—611no—
246C23×C4—611no—
247C23×C4—1221no—
248C23×C4C2×#692311yescharacteristic
249C22×C8—1222no—
250C22×C8—1222no—
251#121—1222no—
252#121—1222no—
253C4×D4—1222no—
254C4×D4—1222no—
255C4×D4—2444no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4C2×#692311yescharacteristic
259C2×C4⋊C4C2×#692311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C42—611no—
266C2×C42—611no—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—1222no—
270C2×C42—1222no—
271C2×C42—1221no—
272C4⋊C8—614no—
273C4⋊C8—1222no—
274C22⋊C8—1224no—
275C22⋊C8—1224no—
276#97—1224no—
277C4×C8—1222no—
278C4×C8—1222no—
279#95—21no—
280#95—1221no—
281#95—1221no—
282C24—1221no—
283C24C22⋊#692311yescharacteristic
284C2×D4—612no—
285C2×D4—1224no—
286C2×D4—1222no—
287C2×D4—1221no—
288C2×D4—1222no—
289C2×D4—2442no—
290C2×D4—2442no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—1221no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4—2441no—
313C22×C4C22⋊#692311yescharacteristic
314C22×C4C22×#692311yescharacteristic
315C2×C8—1224no—
316C2×C8—1224no—
317C2×C8—2442no—
318C2×C8—2442no—
319C2×C8—2442no—
320C2×C8—2442no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—612no—
324C4⋊C4—1221no—
325C4⋊C4—2442no—
326C22⋊C4—42no—
327C22⋊C4—1224no—
328C22⋊C4—2442no—
329C22⋊C4—2442no—
330C22⋊C4—2442no—
331C42—612no—
332C42—612no—
333C42—1221no—
334C42—1221no—
335C42—1222no—
336C42—1222no—
337C42—2442no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—1222no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23—2441no—
351C23#1451984212yes—
352C23C2×C22⋊#692311yescharacteristic
353D4—1224no—
354D4—2448no—
355D4—2442no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—612no—
370C2×C4—612no—
371C2×C4—612no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1222no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4882no—
382C2×C4—4882no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2444no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4D4×#692312yes—
389C2×C4D61⋊M1611yescharacteristic
390C2×C4D61⋊M1611yescharacteristic
391C2×C4#1451986412yes—
392C8—2444no—
393C8—2444no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—4881no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22—2442no—
406C22—2442no—
407C22—2442no—
408C22#1684071011yescharacteristic
409C22#1684073411yescharacteristic
410C22#1684073511yescharacteristic
411C22#1684075211yescharacteristic
412C22#1684075411yescharacteristic
413C22C2×#1451984211yescharacteristic
414C22#1684075911yescharacteristic
415C4—41no—
416C4—81no—
417C4—81no—
418C4—612no—
419C4—612no—
420C4—1222no—
421C4—2441no—
422C4—2441no—
423C4—2442no—
424C4#1684079412yes—
425C4#1684079512yes—
426C2—42no—
427C2—4882no—
428C2#2146115211yescharacteristic
429C2#2146116011yescharacteristic
430C2#2146117211yescharacteristic
431C2#2146117811yescharacteristic
432C2#2146179811yescharacteristic
433C2#2146180011yescharacteristic
434C2#2146180711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#8943
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#16840783C2semidirect
2. C4×C22⋊#92420C2semidirect
3. C2×#16840610C2semidirect
4. #21460655C2semidirect
28. C4⋊#92420D4semidirect
242. C61#8943semidirect

Maximal subgroups

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

subgroupindex
C2×#168407832
C4×C22⋊#924202
C2×#168406102
#214606552
#214483252
#894361