Finite Group Databasebeta

← #29595161

Subgroups — #29595161

Order 15616.

636 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 123 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#21448473C211yesmaximal, characteristic
2C2×#16839548C212yesmaximal
3C4×#14519694C211yesmaximal, characteristic, complemented
4#21443936C212yesmaximal, complemented
5C4×#99×C61C211yesmaximal, characteristic, complemented
6C2×#14519745C2211yescharacteristic
7C22×#11758198C411yescharacteristic, complemented
8C2×#14519694C2212yes—
9C4×#11758194—21no—
10#16839662—21no—
11#16839653—21no—
12#16839652—21no—
13#16839642C2211yescharacteristic
14#16839641—21no—
15#16839634C411yescharacteristic, complemented
16#16839617C411yescharacteristic, complemented
17C4×C22⋊Dic61C411yescharacteristic, complemented
18#16839548C418yescomplemented
19#16839531—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×#99×C61C2212yes—
22C4×C22⋊C4×C61—21no—
23C61×#342—21no—
24C24×D61C2×C411yescharacteristic
25C22×C22⋊D61—21no—
26C23×Dic61C2×C411yescharacteristic
27C2×#11758194—22no—
28#14519745—22no—
29#14519745C2×C414yes—
30C2×#11758196—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61C2×C411yescharacteristic
33C2×C22⋊Dic61C2×C411yescharacteristic
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—41no—
40C2×#11758198—41no—
41C2×C4×Dic61—21no—
42#14519694—22no—
43#14519694C2×C414yes—
44#14519688—41no—
45C4×#92418—41no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×D4×C61C2311yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C4×D4×C61—41no—
53C4×D4×C61—41no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61—22no—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C42×C61—41no—
59C2×C42×C61D411yescharacteristic
60#99×C61—22no—
61#99×C61C2×C414yes—
62#95×C61—41no—
63C24×C61C22×C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C23×D61—21no—
66C23×D61—21no—
67C23×D61—41no—
68C23×D61—41no—
69C23×D61—81no—
70C23×D61—81no—
71C23×D61C4212yescomplemented
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61C22×C412yes—
75C2×D4×C61#4112yes—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—42no—
81C22×C4×C61—81no—
82C22×C4×C61—81no—
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C2×C22⋊D61—24no—
89C2×C22⋊D61—81no—
90C2×C22⋊D61—81no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—41no—
95C22×Dic61—81no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—24no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—42no—
101C42×C61—21no—
102C42×C61—21no—
103C42×C61—82no—
104C22⋊Dic61—21no—
105C22⋊Dic61—41no—
106C22⋊Dic61—81no—
107C22⋊Dic61C4212yescomplemented
108#11758198—24no—
109#11758198—42no—
110#11758198—41no—
111#11758198—41no—
112#11758198—81no—
113#11758198—81no—
114#11758196—81no—
115C4×Dic61—81no—
116#11758194—24no—
117#11758194—42no—
118C2×#92418—42no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61C2×C4211yescharacteristic
128C23×C61C2×C22⋊C411yescharacteristic
129C23×C61#11711yescharacteristic
130C23×C61C4×D412yes—
131C22×D61—22no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—42no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—42no—
140C22×D61—82no—
141C22×D61—82no—
142C22×D61—84no—
143C22×D61—82no—
144C22×D61—82no—
145D4×C61—42no—
146D4×C61—42no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—44no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61—82no—
162C2×C4×C61—82no—
163C2×C4×C61#9911yescharacteristic
164C2×C4×C61#9911yescharacteristic
165C2×C4×C61C4×D412yes—
166C22⋊D61—84no—
167C2×Dic61—22no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—82no—
177#92418—44no—
178#12622—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—22no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—42no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—42no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—81no—
193C22×C61C4×C22⋊C411yescharacteristic
194C22×C61C2×#9911yescharacteristic
195C22×C61#41011yescharacteristic
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—42no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—84no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—84no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—22no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61—84no—
212Dic61—42no—
213Dic61—81no—
214Dic61—81no—
215#2321—611no—
216C2×AΣL(1,𝔽16)—612no—
217C4×#100—611no—
218C4×#99D6111yescharacteristic, complemented
219#1390—612no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—42no—
223C2×C61—41no—
224C2×C61—41no—
225C2×C61C4×#9911yescharacteristic
226C2×C61#212111yescharacteristic
227C2×C61#212211yescharacteristic
228D61—82no—
229C2×#120—611no—
230C2×C4×D4C2×D6111yescharacteristic
231C22×C22⋊C4—611no—
232C2×#100—612no—
233C2×#99C2×D6112yes—
234C4×M16—1221no—
235#390—1221no—
236#388—1221no—
237#388—1221no—
238#386—611no—
239#386—1221no—
240#385—611no—
241#379—611no—
242C4×C22⋊C4—21no—
243C4×C22⋊C4—611no—
244AΣL(1,𝔽16)—618no—
245#343—1221no—
246#342—21no—
247C61#1262211yescharacteristic, complemented, Sylow
248C25—611no—
249C22×D4—1221no—
250C22×D4C22×D6111yescharacteristic
251C23×C4—611no—
252C23×C4C4×D6111yescharacteristic
253C23×C4C22⋊D6111yescharacteristic
254C2×M16—1222no—
255#120—614no—
256#120—1222no—
257C4×D4—41no—
258C4×D4—41no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4D24411yescharacteristic
261C2×C22⋊C4—22no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—2441no—
271C2×C22⋊C4—2441no—
272C2×C22⋊C4C4×D6111yescharacteristic
273C2×C22⋊C4C22⋊D6111yescharacteristic
274C2×C42—41no—
275C2×C42—1221no—
276C2×C42D24411yescharacteristic
277#100—614no—
278#100—1222no—
279#99—22no—
280#99C4×D6114yes—
281#97—2441no—
282C4×C8—2441no—
283#95—41no—
284#95—1221no—
285#95—1221no—
286#95—1221no—
287C24—612no—
288C24—1221no—
289C24—1221no—
290C24—4881no—
291C24—4881no—
292C24—2441no—
293C24—2441no—
294C24C2×C4×D6111yescharacteristic
295C24C2×C22⋊D6111yescharacteristic
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—1224no—
299C2×D4—4881no—
300C2×D4—4881no—
301C2×D4C2×C4×D6112yes—
302C2×D4#1175822212yes—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—4881no—
314C22×C4—2441no—
315C22×C4#1175819811yescharacteristic
316C22×C4#1175819811yescharacteristic
317C22×C4#1175819811yescharacteristic
318C22×C4#1175819811yescharacteristic
319C22×C4C2×D24411yescharacteristic
320M16—1224no—
321M16—2442no—
322C2×C8—2442no—
323C4⋊C4—41no—
324C4⋊C4—4881no—
325C22⋊C4—24no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C22⋊C4—612no—
330C22⋊C4—1221no—
331C22⋊C4—1224no—
332C22⋊C4—4881no—
333C22⋊C4—4881no—
334C22⋊C4—4881no—
335C22⋊C4—2442no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C42—21no—
340C42—21no—
341C42—82no—
342C42—4881no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—1222no—
352C23—4882no—
353C23—4882no—
354C23—4884no—
355C23—4882no—
356C23—4882no—
357C23—2442no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2442no—
363C23—2441no—
364C23—2441no—
365C23C42×D6111yescharacteristic
366C23C2×#1175819811yescharacteristic
367C23#1451973411yescharacteristic
368C23C4×C22⋊D6112yes—
369D4—42no—
370D4—42no—
371D4—4884no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—44no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—1222no—
389C2×C4—4882no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4#1451969111yescharacteristic
399C2×C4#1451969111yescharacteristic
400C2×C4C4×D24412yes—
401C8—2444no—
402C22—21no—
403C22—21no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—41no—
409C22—41no—
410C22—42no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—81no—
416C22—4881no—
417C22—4881no—
418C22—4884no—
419C22—4884no—
420C22—4881no—
421C22—4881no—
422C22—2442no—
423C22—2442no—
424C22—2442no—
425C22C4×#1175819811yescharacteristic
426C22C2×#1451969111yescharacteristic
427C22#1683973511yescharacteristic
428C4—21no—
429C4—21no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—84no—
435C4—4881no—
436C4—4881no—
437C4—2442no—
438C2—21no—
439C2—21no—
440C2—42no—
441C2—41no—
442C2—41no—
443C2—4882no—
444C2C4×#1451969111yescharacteristic
445C2#2144746311yescharacteristic
446C2#2144746811yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC23×C61C2×C42
FrattiniC22×D4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radicalC2×#14519745C22
cosocleC22×D4×C61C23
hypercenterC4×#99D61
hypocenterC61#12622
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. C4×#14519694C2semidirect
4. #21443936C2semidirect
5. C4×#99×C61C2semidirect
7. C22×#11758198C4semidirect
15. #16839634C4semidirect
16. #16839617C4semidirect
17. C4×C22⋊Dic61C4semidirect
18. #16839548C4semidirect
71. C23×D61C42semidirect
107. C22⋊Dic61C42semidirect
218. C4×#99D61semidirect
247. C61#12622semidirect

Maximal subgroups

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

subgroupindex
#214484732
C2×#168395482
C4×#145196942
#214439362
C4×#99×C612
#1262261