Finite Group Databasebeta

← #30598236

Subgroups — #30598236

Order 15616.

846 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461546C211yesmaximal, characteristic, complemented
2#21461546C211yesmaximal, characteristic, complemented
3C2×#16840619C212yesmaximal, complemented
4C2×#16840617C212yesmaximal, complemented
5C2×#16840294C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×#14519832C2212yes—
9C2×#14519832C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840619—24no—
13#16840617—24no—
14#16840294—24no—
15#16840294—24no—
16C2×#14519770—21no—
17C2×#14519768C2211yescharacteristic
18C2×#14519764C2211yescharacteristic
19C2×#14519759—21no—
20C2×#14519757C411yescharacteristic
21C2×#14519748C411yescharacteristic
22C2×C4×Dic122C411yescharacteristic
23C2×C4×C22⋊D61—21no—
24C2×#14519736—21no—
25C2×C42×D61C2211yescharacteristic
26C2×C4×D4×C61C411yescharacteristic
27C22×#92420—22no—
28C22×#92420—22no—
29#14519834—24no—
30#14519834—24no—
31#14519832—22no—
32#14519832—22no—
33#14519832—22no—
34#14519832—22no—
35C22×Dic122C2×C411yescharacteristic
36C22×C22⋊D61—21no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40#14519770—28no—
41#14519768—22no—
42#14519768D414yes—
43#14519764—22no—
44#14519764D414yes—
45#14519759—28no—
46#14519757—22no—
47#14519757—22no—
48#14519748—22no—
49#14519748—22no—
50C4×Dic122—22no—
51C4×Dic122—22no—
52C4×C22⋊D61—28no—
53#14519736—28no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×#11758196—21no—
58C2×#11758196—21no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×#11758198—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61D411yescharacteristic
65C2×C4×Dic61D411yescharacteristic
66C2×C4×Dic61C2311yescharacteristic
67C42×D61—22no—
68C42×D61—22no—
69C22×D4×C61C2×C411yescharacteristic
70C23×C4×C61—21no—
71C4×D4×C61—22no—
72C4×D4×C61—22no—
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C42×C61C2×C411yescharacteristic
76C24×C61—21no—
77C23×D61C22⋊C411yescharacteristic
78C2×D4×C61—21no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61C22⋊C412yes—
82C22×C4×C61—24no—
83C22×C4×C61—21no—
84C22×C4×C61—42no—
85C22×C4×C61—42no—
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C2×C22⋊D61—24no—
90C2×C22⋊D61—42no—
91C2×C22⋊D61—42no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×D411yescharacteristic
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×Dic122—21no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122C22⋊C412yes—
111C2×#92420—24no—
112C2×#92420—24no—
113C2×#92420—42no—
114C2×#92420—42no—
115C2×#92420—42no—
116C2×#92420—42no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61C22⋊C412yes—
119C22⋊C4×C61—24no—
120C42×C61—21no—
121C42×C61—21no—
122C22⋊Dic61—24no—
123C22⋊Dic61—24no—
124C22⋊Dic61—24no—
125#11758198—24no—
126C4⋊Dic61—24no—
127C4⋊Dic61—21no—
128C4⋊Dic61—24no—
129C4⋊Dic61C22⋊C412yes—
130#11758196—24no—
131#11758196—24no—
132C4×Dic61—24no—
133C4×Dic61—22no—
134C4×Dic61—22no—
135C4×Dic61C2×D412yes—
136C4×Dic61C2×D412yes—
137C23×C61—22no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61C2×C22⋊C411yescharacteristic
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61#10412yes—
152D4×C61—42no—
153D4×C61—42no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—22no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—48no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61#10412yes—
166C2×C4×C61C2×C22⋊C411yescharacteristic
167C2×C4×C61C2×C22⋊C411yescharacteristic
168C22⋊D61—48no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61#12012yes—
183C2×Dic61#12012yes—
184C4×D61—44no—
185C4×D61—44no—
186C4×D61—42no—
187C4×D61—42no—
188Dic122—42no—
189Dic122—42no—
190#92420—44no—
191#92420—44no—
192#8336—611nomaximal, Sylow
193C22×C61—42no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61#37911yescharacteristic
201C22×C61#41311yescharacteristic
202C22×C61#41311yescharacteristic
203C22×C61C2×#10411yescharacteristic
204C22×C61C2×#10411yescharacteristic
205C22×C61#42111yescharacteristic
206C22×C61#42111yescharacteristic
207C2×D61—22no—
208C2×D61—22no—
209C2×D61—22no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—41no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—22no—
217C4×C61—41no—
218C4×C61—42no—
219Dic61—22no—
220Dic61—22no—
221Dic61—42no—
222Dic61—41no—
223Dic61—42no—
224C2×#529—611no—
225#1749—611no—
226#1749—611no—
227C2×#330—612no—
228C2×#329—612no—
229C2×C61—82no—
230C2×C61#152411yescharacteristic
231C2×C61#152911yescharacteristic
232C2×C61#153211yescharacteristic
233C2×C61#153511yescharacteristic
234C2×C61#178511yescharacteristic
235C2×C61#178911yescharacteristic
236C2×C61#178911yescharacteristic
237D61—42no—
238#529—1224no—
239#529—1224no—
240C2×#126—1221no—
241C2×#125—611no—
242C2×#124—611no—
243C2×#123—1221no—
244C2×C22⋊Q8—611no—
245C2×#121—611no—
246C2×C4×Q8—611no—
247C2×C4×D4—1221no—
248C2×C4×D4#692311yescharacteristic
249C2×#117—1221no—
250C22×C42—611no—
251C2×C22⋊C8—1221no—
252C2×C22⋊C8—1221no—
253C2×#97—612no—
254C2×#97—612no—
255#336—1221no—
256#336—1221no—
257#330—1224no—
258#329—1224no—
259C61#833611yescharacteristic, complemented, Sylow
260C22×Q8—611no—
261C22×D4—1221no—
262C22×D4C2×#692311yescharacteristic
263C23×C4—21no—
264C23×C4—611no—
265C23×C4—611no—
266C23×C4—611no—
267C22×C8—1222no—
268C22×C8—1222no—
269#126—1228no—
270#125—614no—
271#125—1222no—
272#124—614no—
273#124—1222no—
274#123—1228no—
275C22⋊Q8—1222no—
276C22⋊Q8—1222no—
277#121—1222no—
278#121—1222no—
279C4×Q8—1222no—
280C4×Q8—1222no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—1228no—
284#117—1228no—
285C2×C4⋊C4—611no—
286C2×C4⋊C4—1221no—
287C2×C4⋊C4—1221no—
288C2×C4⋊C4—1221no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4C2×#692311yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42—611no—
297C2×C42—611no—
298C2×C42—611no—
299C2×C42—1222no—
300C2×C42—1222no—
301C2×C42—1221no—
302C2×C42C2×#692311yescharacteristic
303C22⋊C8—1224no—
304C22⋊C8—1224no—
305#97—1222no—
306#97—1222no—
307#97—1222no—
308#97—1222no—
309C24—21no—
310C24—611no—
311C2×Q8—612no—
312C2×Q8—1221no—
313C2×Q8—2441no—
314C2×Q8—2441no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—1224no—
319C2×D4—2442no—
320C2×D4—2442no—
321C2×D4C22⋊#692312yes—
322C22×C4—24no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—1222no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1222no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4C22⋊#692311yescharacteristic
342C22×C4C22⋊#692311yescharacteristic
343C22×C4C22×#692311yescharacteristic
344C2×C8—1224no—
345C2×C8—1224no—
346C2×C8—2442no—
347C2×C8—2442no—
348C2×C8—2442no—
349C2×C8—2442no—
350C4⋊C4—21no—
351C4⋊C4—612no—
352C4⋊C4—1224no—
353C4⋊C4—1224no—
354C4⋊C4—1224no—
355C4⋊C4—1224no—
356C4⋊C4—1221no—
357C4⋊C4C22⋊#692312yes—
358C22⋊C4—24no—
359C22⋊C4—1224no—
360C22⋊C4—1224no—
361C22⋊C4—1224no—
362C22⋊C4—1224no—
363C42—21no—
364C42—21no—
365C42—612no—
366C42—612no—
367C42—1222no—
368C42—1222no—
369C42—1224no—
370C23—22no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—612no—
378C23—1221no—
379C23—1221no—
380C23—1221no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23C2×C22⋊#692311yescharacteristic
385Q8—2442no—
386Q8—2442no—
387D4—42no—
388D4—42no—
389D4—2448no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—48no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—612no—
402C2×C4—612no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1222no—
411C2×C4—1222no—
412C2×C4—2444no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2444no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4#1451984112yes—
421C2×C4C2×C22⋊#692311yescharacteristic
422C2×C4C2×C22⋊#692311yescharacteristic
423C8—2444no—
424C8—2444no—
425C22—42no—
426C22—42no—
427C22—42no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—1222no—
433C22—1222no—
434C22—1222no—
435C22—2441no—
436C22—2441no—
437C22—2441no—
438C22—2441no—
439C22#1684070311yescharacteristic
440C22#1684074811yescharacteristic
441C22#1684074811yescharacteristic
442C22C2×#1451984111yescharacteristic
443C22D61⋊#10411yescharacteristic
444C22#1684075911yescharacteristic
445C22#1684076011yescharacteristic
446C4—21no—
447C4—21no—
448C4—22no—
449C4—42no—
450C4—41no—
451C4—1222no—
452C4—1222no—
453C4—2441no—
454C4—2442no—
455C4—2442no—
456C2—82no—
457C2—2442no—
458C2#2146126911yescharacteristic
459C2#2146128411yescharacteristic
460C2#2146129411yescharacteristic
461C2#2146130311yescharacteristic
462C2#2146165511yescharacteristic
463C2#2146166011yescharacteristic
464C2#2146166111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#8336
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461546C2semidirect
2. #21461546C2semidirect
3. C2×#16840619C2semidirect
4. C2×#16840617C2semidirect
259. C61#8336semidirect

Maximal subgroups

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

subgroupindex
#214615462
C2×#168406192
C2×#168406172
C2×#168402942
#833661