Finite Group Databasebeta

← #30599830

Subgroups — #30599830

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×#16840784C211yesmaximal, characteristic, complemented
2C4×#14519834C211yesmaximal, characteristic, complemented
3C2×D4⋊#92420C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448335C211yesmaximal, characteristic
6#16840784—24no—
7C2×C4⋊#92420C2212yes—
8C2×#14519834—21no—
9C2×#14519834—21no—
10C2×#14519832—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13D4⋊#92420—24no—
14C2×#14519748C411yescharacteristic
15C2×D4×Dic61C2211yescharacteristic
16C2×#14519737—21no—
17C2×C42×D61C2211yescharacteristic
18#16839660C411yescharacteristic
19#16839656—21no—
20#16839638—21no—
21#16839619C411yescharacteristic
22C4⋊C4×Dic61C2211yescharacteristic
23C22⋊C4×Dic61—21no—
24C61×#390C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27C4⋊#92420—22no—
28C4⋊#92420D414yescomplemented
29#14519834—24no—
30#14519834—24no—
31#14519832—24no—
32C4×#92420—22no—
33C4×#92420—22no—
34C22×C22⋊D61—21no—
35C23×Dic61—21no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39#14519748—22no—
40#14519748—22no—
41D4×Dic61—22no—
42D4×Dic61—22no—
43#14519737—44no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C42×D61—22no—
55C42×D61—22no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59C22×D4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C42×C61C2×C411yescharacteristic
64C24×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C2×D4×C61—22no—
67C2×D4×C61—21no—
68C2×D4×C61—22no—
69C2×D4×C61M1612yes—
70C22×C4×C61—21no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C2×C22⋊D61—24no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—22no—
91C2×C4×D61—21no—
92C2×C4×D61—22no—
93C2×C4×D61—21no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C2×#92420—24no—
98C2×#92420—24no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C4⋊C4×C61—22no—
104C22⋊C4×C61—42no—
105C22⋊C4×C61—42no—
106C42×C61—22no—
107C22⋊Dic61—24no—
108C22⋊Dic61—42no—
109#11758198—42no—
110C4⋊Dic61—21no—
111C4⋊Dic61—22no—
112C4⋊Dic61M1612yes—
113#11758196—42no—
114C4×Dic61—21no—
115C4×Dic61—22no—
116C4×Dic61—21no—
117C4×Dic61—42no—
118C4×Dic61C2×D412yes—
119C4×Dic61#4112yes—
120C23×C61—22no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61#10412yes—
135D4×C61—24no—
136D4×C61—42no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
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—22no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—82no—
163C2×Dic61—82no—
164C2×Dic61#12011yescharacteristic
165C2×Dic61#12112yes—
166C2×Dic61#12311yescharacteristic
167C2×Dic61#13512yes—
168C2×Dic61AGL(1,ℤ/8)12yes—
169C4×D61—44no—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—42no—
173C4×D61—42no—
174#92420—44no—
175#92420—44no—
176#8943—611nomaximal, Sylow
177C22×C61—42no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61#38611yescharacteristic
185C22×C61#40711yescharacteristic
186C22×C61#40811yescharacteristic
187C22×C61#41611yescharacteristic
188C22×C61#41811yescharacteristic
189C22×C61C2×#10411yescharacteristic
190C22×C61#42111yescharacteristic
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—22no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—81no—
201C4×C61#43512yes—
202C4×C61#43612yes—
203Dic61—22no—
204Dic61—41no—
205Dic61—42no—
206Dic61—81no—
207Dic61#44912yes—
208Dic61#48212yes—
209C2×#432—611no—
210C4×#121—611no—
211C4×C22⋊C8—611no—
212C2×D4⋊C8—612no—
213#1279—612no—
214C2×C61—82no—
215C2×C61#148811yescharacteristic
216C2×C61#149011yescharacteristic
217C2×C61#149411yescharacteristic
218C2×C61#149611yescharacteristic
219C2×C61#187011yescharacteristic
220C2×C61#187111yescharacteristic
221C2×C61#187511yescharacteristic
222D61—42no—
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#692311yescharacteristic
234#389—611no—
235#388—1221no—
236#386—1221no—
237#380—611no—
238C4×C4⋊C4—611no—
239C4×C22⋊C4—1221no—
240#336—1221no—
241D4⋊C8—1224no—
242C61#894311yescharacteristic, complemented, Sylow
243C22×D4—1221no—
244C22×D4C2×#692311yescharacteristic
245C23×C4—611no—
246C23×C4—611no—
247C23×C4—611no—
248C23×C4—1221no—
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—611no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4C2×#692311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C42—611no—
266C2×C42—611no—
267C2×C42—611no—
268C2×C42—1222no—
269C2×C42—1222no—
270C2×C42—1221no—
271C2×C42C2×#692311yescharacteristic
272C4⋊C8—614no—
273C4⋊C8—1222no—
274C22⋊C8—1224no—
275C22⋊C8—1224no—
276#97—1224no—
277C4×C8—1222no—
278C4×C8—1222no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282C24—21no—
283C24—611no—
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—22no—
287C2×D4—1224no—
288C2×D4—2442no—
289C2×D4—2442no—
290C2×D4#1175821312yes—
291C22×C4—21no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—1222no—
300C22×C4—1222no—
301C22×C4—1221no—
302C22×C4—1222no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1222no—
306C22×C4—1221no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4C22⋊#692311yescharacteristic
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—612no—
323C4⋊C4—1221no—
324C4⋊C4—1222no—
325C4⋊C4—2442no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—1224no—
329C22⋊C4—2442no—
330C22⋊C4—2442no—
331C42—22no—
332C42—612no—
333C42—612no—
334C42—1221no—
335C42—1221no—
336C42—1222no—
337C42—2442no—
338C23—22no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—612no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23C2×C22⋊#692311yescharacteristic
353D4—24no—
354D4—42no—
355D4—2448no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—612no—
368C2×C4—612no—
369C2×C4—612no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1222no—
375C2×C4—1221no—
376C2×C4—4882no—
377C2×C4—4882no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2444no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4D4×#692312yes—
389C2×C4D61⋊M1611yescharacteristic
390C2×C4C2×#1175821311yescharacteristic
391C2×C4#1451986412yes—
392C8—2444no—
393C8—2444no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—1222no—
402C22—1222no—
403C22—1222no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22#1684071011yescharacteristic
409C22#1684073311yescharacteristic
410C22#1684073611yescharacteristic
411C22#1684075211yescharacteristic
412C22#1684075411yescharacteristic
413C22D61⋊#10411yescharacteristic
414C22#1684076011yescharacteristic
415C4—41no—
416C4—41no—
417C4—81no—
418C4—612no—
419C4—612no—
420C4—1222no—
421C4—4881no—
422C4—2441no—
423C4—2442no—
424C4#1684079112yes—
425C4#1684079512yes—
426C2—82no—
427C2—2442no—
428C2#2146115111yescharacteristic
429C2#2146115911yescharacteristic
430C2#2146117111yescharacteristic
431C2#2146117911yescharacteristic
432C2#2146179711yescharacteristic
433C2#2146180311yescharacteristic
434C2#2146180711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#8943
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16840784C2semidirect
2. C4×#14519834C2semidirect
3. C2×D4⋊#92420C2semidirect
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×#168407842
C4×#145198342
C2×D4⋊#924202
#214606552
#214483352
#894361