Finite Group Databasebeta

← #29595188

Subgroups — #29595188

Order 15616.

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

normal subgroups only

This group has 628 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#21448541C211yesmaximal, characteristic
2C2×#16839554C212yesmaximal
3C4×#14519692C211yesmaximal, characteristic, complemented
4#21443943C212yesmaximal, complemented
5C4×#99×C61C211yesmaximal, characteristic, complemented
6C2×#14519773C2211yescharacteristic
7C2×C4×D244C411yescharacteristic, complemented
8C2×#14519692C2212yes—
9#16839665C2211yescharacteristic
10#16839663C411yescharacteristic, complemented
11#16839641—21no—
12#16839641—21no—
13#16839638—21no—
14#16839638—21no—
15#16839627C411yescharacteristic, complemented
16C4×C22⋊Dic61—21no—
17#16839608C411yescharacteristic, complemented
18#16839554C418yescomplemented
19#16839529—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×#99×C61C2212yes—
22C4×C22⋊C4×C61—21no—
23C61×#342—21no—
24C22×D244C2×C411yescharacteristic
25C22×C22⋊D61—21no—
26C22×C22⋊D61—21no—
27C22×C4×D61—21no—
28#14519773—22no—
29#14519773C2×C414yes—
30C4×D244—41no—
31C4×D244—41no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C22⋊Dic61—22no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×C4×Dic61—41no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42#14519692—22no—
43#14519692C2×C414yescomplemented
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—41no—
49C22×D4×C61C2311yescharacteristic
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C4×D4×C61—41no—
53C4×D4×C61—41no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—22no—
56C2×C22⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C42×C61—41no—
59C2×C42×C61C2×C411yescharacteristic
60#99×C61—22no—
61#99×C61C2×C414yescomplemented
62#95×C61—41no—
63C24×C61C2×D411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C23×D61—21no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61C22×C412yes—
69C2×D4×C61#4112yes—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—42no—
75C22×C4×C61—81no—
76C22×C4×C61—81no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61C22×C411yescharacteristic
82C2×C22⋊D61—24no—
83C2×C22⋊D61—24no—
84C2×C22⋊D61—81no—
85C2×C22⋊D61—81no—
86C2×C22⋊D61—81no—
87C2×C22⋊D61—81no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—42no—
92C2×D244—21no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244C4212yescomplemented
96C2×C4×D61—42no—
97C2×C4×D61—81no—
98C2×C4×D61—81no—
99C4⋊C4×C61—41no—
100C22⋊C4×C61—24no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—42no—
104C42×C61—21no—
105C42×C61—21no—
106C42×C61—82no—
107C22⋊Dic61—24no—
108C22⋊Dic61—42no—
109C22⋊Dic61—81no—
110C22⋊Dic61—81no—
111#11758198—41no—
112#11758198—41no—
113#11758198—81no—
114#11758198—81no—
115C4⋊Dic61—41no—
116C4×Dic61—21no—
117C4×Dic61—41no—
118C4×Dic61—82no—
119C4×Dic61C4212yescomplemented
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C2×C22⋊C411yescharacteristic
129C23×C61C4×D412yes—
130C23×C61C4×D412yes—
131C22×D61—22no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138D4×C61—42no—
139D4×C61—42no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—44no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61—82no—
155C2×C4×C61—82no—
156C2×C4×C61#9911yescharacteristic
157C2×C4×C61#9911yescharacteristic
158C2×C4×C61C2×C4211yescharacteristic
159C2×C4×C61#11711yescharacteristic
160C22⋊D61—84no—
161C22⋊D61—84no—
162C2×Dic61—22no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—44no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—82no—
173C2×Dic61—82no—
174D244—42no—
175D244—42no—
176C4×D61—84no—
177#12628—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—42no—
183C22×C61—42no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61C4×C22⋊C411yescharacteristic
191C22×C61C2×#9911yescharacteristic
192C22×C61#41011yescharacteristic
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—42no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61—41no—
207C4×C61—84no—
208Dic61—42no—
209Dic61—81no—
210Dic61—84no—
211Dic61—81no—
212#2328—611no—
213C2×#353—612no—
214C4×#99—611no—
215C4×#99D6111yescharacteristic, complemented
216#1393—612no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—42no—
220C2×C61—42no—
221C2×C61C4×#9911yescharacteristic
222C2×C61#212711yescharacteristic
223C2×C61#212811yescharacteristic
224D61—82no—
225C2×#127—611no—
226C2×C4×D4—611no—
227C2×C4×D4C2×D6111yescharacteristic
228C2×#99—612no—
229C2×#99C2×D6112yes—
230#390—611no—
231#390—611no—
232#386—1221no—
233#386—1221no—
234#386—1221no—
235#386—1221no—
236#382—611no—
237C4×C22⋊C4—21no—
238C4×C22⋊C4—1221no—
239#376—611no—
240#353—618no—
241#342—21no—
242#342—1221no—
243C61#1262811yescharacteristic, complemented, Sylow
244C22×D4—611no—
245C22×D4—1221no—
246C22×D4—1221no—
247C22×D4C22×D6111yescharacteristic
248C23×C4—1221no—
249C23×C4D24411yescharacteristic
250C23×C4C22⋊D6111yescharacteristic
251#127—614no—
252#127—1222no—
253C4×D4—41no—
254C4×D4—41no—
255C4×D4—2441no—
256C4×D4—2441no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4C4×D6111yescharacteristic
259C2×C22⋊C4—22no—
260C2×C22⋊C4—1222no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4D24411yescharacteristic
267C2×C22⋊C4C22⋊D6111yescharacteristic
268C2×C42—41no—
269C2×C42—611no—
270C2×C42—611no—
271C2×C42—2441no—
272C2×C42C4×D6111yescharacteristic
273#99—22no—
274#99—614no—
275#99—1222no—
276#99C4×D6114yescomplemented
277#95—41no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282#95—2441no—
283C24—1221no—
284C24C2×D24411yescharacteristic
285C24C2×C22⋊D6111yescharacteristic
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—612no—
289C2×D4—1224no—
290C2×D4—1224no—
291C2×D4—1221no—
292C2×D4—4881no—
293C2×D4—4881no—
294C2×D4—4881no—
295C2×D4—4881no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4C2×C4×D6112yes—
299C2×D4#1175822212yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—81no—
306C22×C4—81no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—4881no—
311C22×C4—4881no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4#1175819811yescharacteristic
315C22×C4#1175819811yescharacteristic
316C22×C4#1175819811yescharacteristic
317C22×C4#1175819811yescharacteristic
318C22×C4C2×C4×D6111yescharacteristic
319C4⋊C4—41no—
320C4⋊C4—2441no—
321C22⋊C4—24no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—1224no—
326C22⋊C4—4881no—
327C22⋊C4—4881no—
328C22⋊C4—4881no—
329C22⋊C4—4881no—
330C22⋊C4—2442no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C42—21no—
334C42—21no—
335C42—82no—
336C42—612no—
337C42—1221no—
338C42—4882no—
339C42—2441no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—1222no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23C2×#1175819811yescharacteristic
356C23C4×C22⋊D6112yes—
357C23C4×D24412yes—
358D4—42no—
359D4—42no—
360D4—4884no—
361D4—4884no—
362D4—2442no—
363D4—2442no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—44no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—1222no—
381C2×C4—4884no—
382C2×C4—4882no—
383C2×C4—4882no—
384C2×C4—2444no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4#1451969111yescharacteristic
394C2×C4#1451969111yescharacteristic
395C2×C4C42×D6111yescharacteristic
396C2×C4#1451973411yescharacteristic
397C22—21no—
398C22—21no—
399C22—22no—
400C22—22no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—81no—
408C22—81no—
409C22—4881no—
410C22—4881no—
411C22—4881no—
412C22—4881no—
413C22—2442no—
414C22—2442no—
415C22—2442no—
416C22C4×#1175819811yescharacteristic
417C22C2×#1451969111yescharacteristic
418C22#1683973511yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—41no—
424C4—41no—
425C4—41no—
426C4—84no—
427C4—4881no—
428C4—4884no—
429C4—4881no—
430C4—2442no—
431C2—21no—
432C2—21no—
433C2—42no—
434C2—42no—
435C2—4882no—
436C2C4×#1451969111yescharacteristic
437C2#2144748611yescharacteristic
438C2#2144749011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radicalC2×#14519773C22
cosocleC22×D4×C61C23
hypercenterC4×#99D61
hypocenterC61#12628
LCSG ▷ C2×C4×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×#14519692C2semidirect
4. #21443943C2semidirect
5. C4×#99×C61C2semidirect
7. C2×C4×D244C4semidirect
10. #16839663C4semidirect
15. #16839627C4semidirect
17. #16839608C4semidirect
18. #16839554C4semidirect
43. #14519692C2×C4semidirect
61. #99×C61C2×C4semidirect
95. C2×D244C42semidirect
119. C4×Dic61C42semidirect
215. C4×#99D61semidirect
243. C61#12628semidirect
276. #99C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214485412
C2×#168395542
C4×#145196922
#214439432
C4×#99×C612
#1262861