Finite Group Databasebeta

← #29595988

Subgroups — #29595988

Order 15616.

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

normal subgroups only

This group has 512 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#21448484C211yesmaximal, characteristic
2C2×#16839551C212yesmaximal
3#21445811C211yesmaximal, characteristic
4#21443936C212yesmaximal
5C61×#1799C211yesmaximal, characteristic
6C2×#14519758C2211yescharacteristic
7C22×#11758196C411yescharacteristic, complemented
8#16839786—21no—
9C2×#14519694C2212yes—
10#16839657—21no—
11#16839656—21no—
12#16839646—21no—
13#16839642C2211yescharacteristic
14#16839635—21no—
15#16839634C411yescharacteristic, complemented
16#16839623C411yescharacteristic, complemented
17C4×C22⋊Dic61C411yescharacteristic, complemented
18#16839551—24no—
19#16839531—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C2×#99×C61C2212yes—
22C61×#380—21no—
23C61×#342—21no—
24C23×Dic61C2×C411yescharacteristic
25C23×Dic61C2×C411yescharacteristic
26C2×#11758194—22no—
27#14519758—21no—
28#14519758—21no—
29#14519758D412yes—
30#14519758Q812yes—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—41no—
36C2×#11758196—41no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61C2×C411yescharacteristic
41C2×C4×Dic61—21no—
42C4⋊#92418—41no—
43C4⋊#92418—41no—
44#14519694—22no—
45#14519694—22no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61C2311yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C23×C4×C61D411yescharacteristic
54C4×D4×C61—41no—
55C4×D4×C61—41no—
56C2×C4⋊C4×C61—41no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C22⋊C4×C61—22no—
59C2×C22⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62#99×C61—22no—
63#99×C61—22no—
64#95×C61—41no—
65C24×C61C22×C411yescharacteristic
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×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—81no—
94C22×Dic61C4⋊C412yescomplemented
95C4⋊C4×C61—41no—
96C4⋊C4×C61—82no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—42no—
101C42×C61—21no—
102C42×C61—21no—
103C22⋊Dic61—21no—
104C22⋊Dic61—22no—
105C22⋊Dic61—22no—
106C22⋊Dic61—41no—
107C22⋊Dic61—81no—
108C22⋊Dic61C4⋊C412yescomplemented
109#11758196—22no—
110#11758196—22no—
111#11758196—42no—
112#11758196—41no—
113#11758196—41no—
114#11758196—81no—
115C4×Dic61—81no—
116#11758194—42no—
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×C22⋊C411yescharacteristic
128C23×C61C2×C4⋊C411yescharacteristic
129C23×C61#11711yescharacteristic
130C23×C61#12111yescharacteristic
131C23×C61C22⋊Q811yescharacteristic
132D4×C61—41no—
133D4×C61—41no—
134D4×C61—41no—
135D4×C61—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
149C2×C4×C61—82no—
150C2×C4×C61—82no—
151C2×C4×C61—82no—
152C2×C4×C61#9911yescharacteristic
153C2×C4×C61#9911yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61C22⋊Q811yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—42no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—82no—
171#92418—82no—
172#12796—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—42no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—81no—
189C22×C61#38011yescharacteristic
190C22×C61C2×#9911yescharacteristic
191C22×C61#41011yescharacteristic
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—162no—
200Dic61—42no—
201Dic61—42no—
202Dic61—81no—
203Dic61—81no—
204#2322—611no—
205C2×#352—612no—
206#1800—611no—
207#1799D6111yescharacteristic
208#1390—612no—
209C2×C61—21no—
210C2×C61—21no—
211C2×C61—41no—
212C2×C61—41no—
213C2×C61—41no—
214C2×C61—41no—
215C2×C61#179911yescharacteristic
216C2×C61#212111yescharacteristic
217C2×C61#212311yescharacteristic
218C2×#123—611no—
219C2×C4×D4C2×D6111yescharacteristic
220C22×C4⋊C4—611no—
221#423—1221no—
222C2×#100—612no—
223C2×#99C2×D6112yes—
224#389—1221no—
225#388—1221no—
226#387—1221no—
227#386—611no—
228#385—611no—
229#385—1221no—
230#381—611no—
231#380—21no—
232C4×C22⋊C4—611no—
233#352—1224no—
234#343—1221no—
235#342—21no—
236C61#1279611yescharacteristic, complemented, Sylow
237C22×D4C22×D6111yescharacteristic
238C23×C4—611no—
239C23×C4—611no—
240C23×C4C4×D6111yescharacteristic
241C23×C4C22⋊D6111yescharacteristic
242C2×M16—1222no—
243#123—612no—
244#123—612no—
245#123—1221no—
246#123—1221no—
247C4×D4—41no—
248C4×D4—41no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—2441no—
255C2×C4⋊C4—2441no—
256C2×C4⋊C4D24411yescharacteristic
257C2×C22⋊C4—22no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4C4×D6111yescharacteristic
263C2×C22⋊C4C22⋊D6111yescharacteristic
264C2×C42—1221no—
265C2×C42D24411yescharacteristic
266C4⋊C8—2441no—
267C4⋊C8—2441no—
268#100—1222no—
269#100—1222no—
270#99—22no—
271#99—22no—
272#95—41no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276#95—1221no—
277#95—1221no—
278C24C2×C4×D6111yescharacteristic
279C24C2×C22⋊D6111yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4D4×D6111yescharacteristic
283C2×D4#1175822411yescharacteristic
284C2×D4Q8×D6111yescharacteristic
285C2×D4#1175822611yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—612no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—4881no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4#1175819811yescharacteristic
304C22×C4#1175819811yescharacteristic
305C22×C4#1175819811yescharacteristic
306C22×C4#1175819811yescharacteristic
307C22×C4C2×D24411yescharacteristic
308M16—2442no—
309M16—2442no—
310C2×C8—2442no—
311C4⋊C4—41no—
312C4⋊C4—82no—
313C4⋊C4—1222no—
314C4⋊C4—1222no—
315C4⋊C4—4881no—
316C4⋊C4—2442no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—612no—
324C22⋊C4—1221no—
325C22⋊C4—1222no—
326C22⋊C4—1222no—
327C22⋊C4—4881no—
328C22⋊C4—2441no—
329C42—21no—
330C42—21no—
331C42—4881no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C2×#1175819811yescharacteristic
341C23C4⋊C4×D6111yescharacteristic
342C23#1451973511yescharacteristic
343C23#1451974811yescharacteristic
344C23#1451975311yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—1222no—
366C2×C4—1222no—
367C2×C4—4882no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2442no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2442no—
380C2×C4#1451969111yescharacteristic
381C2×C4#1451969111yescharacteristic
382C2×C4#1451975211yescharacteristic
383C2×C4#1451975711yescharacteristic
384C8—4882no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22#1683961911yescharacteristic
402C22C2×#1451969111yescharacteristic
403C22#1683973511yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—162no—
412C4—4881no—
413C4—4881no—
414C4—2442no—
415C4—2442no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2—41no—
421C2—41no—
422C2#2144580411yescharacteristic
423C2#2144746311yescharacteristic
424C2#2144747211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1799C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenter#1799D61
hypocenterC61#12796
LCSG ▷ C24×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. C22×#11758196C4semidirect
15. #16839634C4semidirect
16. #16839623C4semidirect
17. C4×C22⋊Dic61C4semidirect
94. C22×Dic61C4⋊C4semidirect
108. C22⋊Dic61C4⋊C4semidirect
236. C61#12796semidirect

Maximal subgroups

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

subgroupindex
#214484842
C2×#168395512
#214458112
#214439362
C61×#17992
#1279661