Finite Group Databasebeta

← #30601807

Subgroups — #30601807

Order 15616.

716 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 120 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#21461676C211yesmaximal, characteristic
2C2×#16840616C212yesmaximal
3C2×#16840615C212yesmaximal
4C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
5#21454168C211yesmaximal, characteristic
6C22×C4×#6923—21no—
7C2×#14519844—21no—
8C2×#14519834C2212yes—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4C2212yes—
11#16840628—21no—
12#16840616—24no—
13#16840615—24no—
14C2×#14519775C411yescharacteristic, complemented
15C2×#14519757C2211yescharacteristic
16C2×#14519753C2211yescharacteristic
17C2×C42×D61C2211yescharacteristic
18#16839668C411yescharacteristic, complemented
19#16839659—21no—
20#16839659—21no—
21#16839631C411yescharacteristic, complemented
22#16839621—21no—
23#16839621—21no—
24C61×#391C411yescharacteristic, complemented
25C23×#6923—22no—
26C22×#92420—22no—
27C2×C4×#6923—24no—
28C2×C4×#6923—42no—
29C2×C4×#6923—42no—
30#14519844—42no—
31#14519834—22no—
32#14519834—22no—
33(C2×#6923)⋊C4—24no—
34(C2×#6923)⋊C4—22no—
35(C2×#6923)⋊C4D414yes—
36C22×Dic122C2×C411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61C2311yescharacteristic
40#14519775—42no—
41#14519757—22no—
42#14519757—22no—
43#14519753—22no—
44#14519753—22no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×C4×Dic61C2×C411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C42×D61—42no—
58#14519684—21no—
59#14519684—21no—
60C22×Q8×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C42×C61C2×C411yescharacteristic
63#95×C61—21no—
64#95×C61—21no—
65C23×D61C2×D411yescharacteristic
66C22×#6923—24no—
67C22×#6923—24no—
68C22×#6923—24no—
69C22×#6923—42no—
70C22×#6923—42no—
71C22×#6923—42no—
72C22×#6923—42no—
73C2×Q8×C61—22no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C22×C411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61SD1612yes—
94C2×C4×D61Q1612yes—
95C2×C4×D61C2×D412yes—
96C2×C4×D61#4112yes—
97C2×Dic122—22no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C4×#6923—48no—
104C4⋊C4×C61—22no—
105C42×C61—41no—
106#11758198—42no—
107#11758198—42no—
108C4⋊Dic61—22no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111#11758196—42no—
112#11758196—42no—
113#11758196—42no—
114#11758196—42no—
115#11758196—41no—
116#11758196—41no—
117C4×Dic61—22no—
118C4×Dic61—22no—
119C4×Dic61—41no—
120C23×C61C2×C22⋊C411yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61#12112yes—
126C22×D61C2×SD1611yescharacteristic
127C22×D61C2×Q1611yescharacteristic
128C22×D61#13712yes—
129C2×#6923—28no—
130C2×#6923—44no—
131C2×#6923—44no—
132C2×#6923—44no—
133C2×#6923—44no—
134C2×#6923—44no—
135C2×#6923—44no—
136Q8×C61—82no—
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—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61#10312yes—
151C2×C4×C61C4×D412yes—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61#9912yes—
163C2×Dic61#10312yes—
164C2×Dic61#10412yes—
165C2×Dic61#10412yes—
166C2×Dic61#12411yescharacteristic
167C2×Dic61#12711yescharacteristic
168C4×D61—24no—
169C4×D61—24no—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—44no—
173Dic122—82no—
174#92420—82no—
175#9711—611nomaximal, Sylow
176C22×C61#39011yescharacteristic
177C22×C61C2×#9911yescharacteristic
178C22×C61#41011yescharacteristic
179C22×C61C2×#10311yescharacteristic
180C22×C61#41911yescharacteristic
181C22×C61C2×#10411yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61#46112yes—
192C2×D61#46212yes—
193#6923—48no—
194C4×C61—22no—
195C4×C61—22no—
196C4×C61—41no—
197C4×C61—81no—
198C4×C61—81no—
199Dic61—21no—
200Dic61—21no—
201Dic61—22no—
202Dic61—81no—
203Dic61—81no—
204Dic61#32814yescomplemented
205#2857—611no—
206#1797—611no—
207C2×#328—612no—
208C2×#328—612no—
209C4×#95—611no—
210C2×C61C2×#32811yescharacteristic
211C2×C61#150311yescharacteristic
212C2×C61#150611yescharacteristic
213C2×C61#150811yescharacteristic
214C2×C61#196211yescharacteristic
215C2×C61#196411yescharacteristic
216C2×C61#198111yescharacteristic
217D61—22no—
218D61—22no—
219C2×C4⋊Q8—611no—
220C2×C22⋊Q8—611no—
221C2×C22⋊Q8—611no—
222C22×C42—611no—
223C22×C42—1221no—
224C2×C4⋊C8—1221no—
225C2×C22⋊C8—612no—
226#391—611no—
227#391#692311yescharacteristic, complemented
228#389—1221no—
229#389—1221no—
230#384—611no—
231#380—1221no—
232#380—1221no—
233C2×#95—612no—
234C2×#95—1221no—
235#336—1221no—
236#328—1224no—
237#328—1224no—
238C61#971111yescharacteristic, complemented, Sylow
239C22×Q8—611no—
240C22×Q8C2×#692311yescharacteristic
241C23×C4—611no—
242C23×C4—611no—
243C23×C4—611no—
244C23×C4—1222no—
245C22×C8—1222no—
246C4⋊Q8—2442no—
247C22⋊Q8—1222no—
248C22⋊Q8—1222no—
249C22⋊Q8—1222no—
250C22⋊Q8—1222no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4C2×#692311yescharacteristic
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—1224no—
265C2×C42—2442no—
266C2×C42—2442no—
267C2×C42—2442no—
268C2×C42C2×#692311yescharacteristic
269C4⋊C8—2442no—
270C22⋊C8—1222no—
271C22⋊C8—1222no—
272#95—21no—
273#95—21no—
274#95—614no—
275#95—1222no—
276#95—1224no—
277#95—1221no—
278#95—1221no—
279C24—611no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—1222no—
284C2×Q8—2441no—
285C2×Q8—2441no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—612no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—1224no—
300C22×C4—1224no—
301C22×C4—1224no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2442no—
308C22×C4—2442no—
309C22×C4—2442no—
310C22×C4—2442no—
311C22×C4C22⋊#692311yescharacteristic
312C22×C4C22⋊#692311yescharacteristic
313C22×C4C22×#692311yescharacteristic
314C2×C8—2442no—
315C2×C8—2442no—
316C2×C8—2442no—
317C4⋊C4—22no—
318C4⋊C4—1222no—
319C4⋊C4—2442no—
320C4⋊C4—2442no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C4⋊C4—2442no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4—2442no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C42—41no—
330C42—1222no—
331C42—1222no—
332C42—2441no—
333C42—2448no—
334C23—612no—
335C23—611no—
336C23—611no—
337C23—612no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23C2×C22⋊#692311yescharacteristic
343Q8—82no—
344Q8—4882no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—612no—
359C2×C4—612no—
360C2×C4—612no—
361C2×C4—611no—
362C2×C4—611no—
363C2×C4—612no—
364C2×C4—1224no—
365C2×C4—1224no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1228no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2444no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2444no—
381C2×C4—2444no—
382C2×C4—2444no—
383C2×C4—2444no—
384C2×C4—2444no—
385C2×C4—2444no—
386C2×C4#1451984012yes—
387C2×C4D4×#692312yes—
388C8—4882no—
389C22—612no—
390C22—612no—
391C22—1222no—
392C22—1221no—
393C22—1221no—
394C22—1222no—
395C22—1221no—
396C22—1221no—
397C22—1222no—
398C22—1222no—
399C22#1684071411yescharacteristic
400C22D61⋊#9911yescharacteristic
401C22#1684074111yescharacteristic
402C22C2×#1451984011yescharacteristic
403C22#1684075511yescharacteristic
404C22D61⋊#10411yescharacteristic
405C22D61⋊#10411yescharacteristic
406C4—22no—
407C4—22no—
408C4—41no—
409C4—81no—
410C4—81no—
411C4—614no—
412C4—1221no—
413C4—1221no—
414C4—1222no—
415C4—4881no—
416C4—4881no—
417C4—2448no—
418C2—1222no—
419C2—1222no—
420C2D61⋊#32811yescharacteristic
421C2#2146120111yescharacteristic
422C2#2146121211yescharacteristic
423C2#2146121711yescharacteristic
424C2#2146195411yescharacteristic
425C2#2146196011yescharacteristic
426C2#2146198511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#391#6923
hypocenterC61#9711
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
14. C2×#14519775C4semidirect
18. #16839668C4semidirect
21. #16839631C4semidirect
24. C61×#391C4semidirect
204. Dic61#328semidirect
227. #391#6923semidirect
238. C61#9711semidirect

Maximal subgroups

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

subgroupindex
#214616762
C2×#168406162
C2×#168406152
C4×(C2×#6923)⋊C42
#214541682
#971161