Finite Group Databasebeta

← #29596005

Subgroups — #29596005

Order 15616.

524 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448531C211yesmaximal, characteristic
2C2×#16839556C212yesmaximal
3#21445807C211yesmaximal, characteristic
4#21443943C212yesmaximal
5C61×#1799C211yesmaximal, characteristic
6C2×#14519764C2211yescharacteristic
7C2×C4×Dic122C411yescharacteristic, complemented
8C2×#14519692C2212yes—
9#16839667C411yescharacteristic, complemented
10#16839665C2211yescharacteristic
11#16839650—21no—
12#16839650—21no—
13#16839635—21no—
14#16839635—21no—
15#16839631C411yescharacteristic, complemented
16#16839622—21no—
17#16839608C411yescharacteristic, complemented
18#16839556—24no—
19#16839529—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×#99×C61C2212yes—
22C61×#380—21no—
23C61×#342—21no—
24C22×Dic122C2×C411yescharacteristic
25#14519764—21no—
26#14519764—21no—
27#14519764D412yes—
28#14519764Q812yes—
29C4×Dic122—41no—
30C4×Dic122—41no—
31C2×C4⋊Dic61—41no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44#14519692—22no—
45#14519692—22no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—41no—
51C22×D4×C61C2311yescharacteristic
52C23×C4×C61D411yescharacteristic
53C23×C4×C61D411yescharacteristic
54C4×D4×C61—41no—
55C4×D4×C61—41no—
56C2×C4⋊C4×C61—41no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—22no—
59C2×C22⋊C4×C61D411yescharacteristic
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62#99×C61—22no—
63#99×C61—22no—
64#95×C61—41no—
65C24×C61C2×D411yescharacteristic
66C24×C61C2×D411yescharacteristic
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61C2×D411yescharacteristic
70C2×D4×C61C2×Q811yescharacteristic
71C2×D4×C61#4111yescharacteristic
72C2×D4×C61#4111yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—42no—
78C22×C4×C61—81no—
79C22×C4×C61—81no—
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22×C411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—42no—
90C2×Dic122—21no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122C4⋊C412yescomplemented
94C4⋊C4×C61—41no—
95C4⋊C4×C61—82no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C42×C61—21no—
101C42×C61—21no—
102C22⋊Dic61—22no—
103C22⋊Dic61—22no—
104C22⋊Dic61—22no—
105C22⋊Dic61—22no—
106C22⋊Dic61—42no—
107C22⋊Dic61—42no—
108C22⋊Dic61—81no—
109C22⋊Dic61—81no—
110C4⋊Dic61—41no—
111C4⋊Dic61—82no—
112#11758196—41no—
113#11758196—41no—
114#11758196—81no—
115#11758196—81no—
116C4×Dic61—21no—
117C4×Dic61—42no—
118C4×Dic61—41no—
119C4×Dic61C4⋊C412yescomplemented
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×C61#12111yescharacteristic
130C23×C61#12111yescharacteristic
131C23×C61C22⋊Q811yescharacteristic
132C23×C61C22⋊Q811yescharacteristic
133D4×C61—41no—
134D4×C61—41no—
135D4×C61—41no—
136D4×C61—41no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—81no—
149C2×C4×C61—81no—
150C2×C4×C61—82no—
151C2×C4×C61—82no—
152C2×C4×C61—82no—
153C2×C4×C61#9911yescharacteristic
154C2×C4×C61#9911yescharacteristic
155C2×C4×C61C2×C4⋊C411yescharacteristic
156C2×C4×C61#11711yescharacteristic
157C2×Dic61—22no—
158C2×Dic61—22no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—82no—
170C2×Dic61—82no—
171C2×Dic61—82no—
172Dic122—42no—
173Dic122—42no—
174#12800—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61#38011yescharacteristic
192C22×C61C2×#9911yescharacteristic
193C22×C61#41011yescharacteristic
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—162no—
202Dic61—42no—
203Dic61—42no—
204Dic61—81no—
205Dic61—81no—
206Dic61—162no—
207#2326—611no—
208C2×#354—612no—
209#1799—611no—
210#1799D6111yescharacteristic
211#1393—612no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—41no—
215C2×C61—41no—
216C2×C61—41no—
217C2×C61—41no—
218C2×C61#179911yescharacteristic
219C2×C61#212711yescharacteristic
220C2×C61#212911yescharacteristic
221C2×#124—611no—
222C2×C4×Q8—611no—
223C2×C4×D4C2×D6111yescharacteristic
224C2×#99—612no—
225C2×#99C2×D6112yes—
226#391—611no—
227#390—611no—
228#388—1221no—
229#388—1221no—
230#385—1221no—
231#385—1221no—
232#384—611no—
233#380—21no—
234#380—1221no—
235#376—611no—
236#354—1224no—
237#342—21no—
238#342—1221no—
239C61#1280011yescharacteristic, complemented, Sylow
240C22×Q8—611no—
241C22×D4C22×D6111yescharacteristic
242C23×C4D24411yescharacteristic
243C23×C4C22⋊D6111yescharacteristic
244#124—612no—
245#124—612no—
246#124—1221no—
247#124—1221no—
248C4×Q8—2441no—
249C4×Q8—2441no—
250C4×D4—41no—
251C4×D4—41no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—2441no—
258C2×C4⋊C4C4×D6111yescharacteristic
259C2×C22⋊C4—22no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1222no—
265C2×C22⋊C4D24411yescharacteristic
266C2×C22⋊C4C22⋊D6111yescharacteristic
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—1221no—
270C2×C42C4×D6111yescharacteristic
271#99—22no—
272#99—22no—
273#99—1222no—
274#99—1222no—
275#95—41no—
276#95—1221no—
277#95—1221no—
278#95—1221no—
279#95—1221no—
280#95—2441no—
281C24C2×D24411yescharacteristic
282C24C2×C22⋊D6111yescharacteristic
283C2×Q8—612no—
284C2×Q8—1221no—
285C2×Q8—2441no—
286C2×Q8—2441no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4D4×D6111yescharacteristic
290C2×D4#1175822411yescharacteristic
291C2×D4Q8×D6111yescharacteristic
292C2×D4#1175822611yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—2442no—
305C22×C4#1175819811yescharacteristic
306C22×C4#1175819811yescharacteristic
307C22×C4#1175819811yescharacteristic
308C22×C4#1175819811yescharacteristic
309C22×C4C2×C4×D6111yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—82no—
312C4⋊C4—4882no—
313C4⋊C4—4881no—
314C4⋊C4—4881no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—1222no—
323C22⋊C4—1222no—
324C22⋊C4—1222no—
325C22⋊C4—1222no—
326C22⋊C4—4881no—
327C22⋊C4—4881no—
328C22⋊C4—2442no—
329C22⋊C4—2442no—
330C42—21no—
331C42—21no—
332C42—612no—
333C42—1221no—
334C42—2441no—
335C42—2442no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23C2×#1175819811yescharacteristic
345C23#1451974811yescharacteristic
346C23#1451975211yescharacteristic
347C23#1451975311yescharacteristic
348C23#1451975711yescharacteristic
349Q8—2442no—
350Q8—2442no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—1222no—
372C2×C4—1222no—
373C2×C4—4882no—
374C2×C4—4882no—
375C2×C4—4882no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4#1451969111yescharacteristic
387C2×C4#1451969111yescharacteristic
388C2×C4C4⋊C4×D6111yescharacteristic
389C2×C4#1451973511yescharacteristic
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22#1683961911yescharacteristic
407C22C2×#1451969111yescharacteristic
408C22#1683973511yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—162no—
417C4—9762no—
418C4—4881no—
419C4—4881no—
420C4—2442no—
421C4—2442no—
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2—41no—
427C2—41no—
428C2#2144580411yescharacteristic
429C2#2144748611yescharacteristic
430C2#2144749311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1799C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenter#1799D61
hypocenterC61#12800
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic122C4semidirect
9. #16839667C4semidirect
15. #16839631C4semidirect
17. #16839608C4semidirect
93. C2×Dic122C4⋊C4semidirect
119. C4×Dic61C4⋊C4semidirect
239. C61#12800semidirect

Maximal subgroups

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

subgroupindex
#214485312
C2×#168395562
#214458072
#214439432
C61×#17992
#1280061