Finite Group Databasebeta

← #30598218

Subgroups — #30598218

Order 15616.

908 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461711C211yesmaximal, characteristic, complemented
2C2×#16840616C212yesmaximal, complemented
3C2×#16840613C212yesmaximal
4#21460995C211yesmaximal, characteristic, complemented
5C2×#16840291C211yesmaximal, characteristic
6C2×#14519834C2212yes—
7C2×(C2×#6923)⋊C4—21no—
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840616—24no—
13#16840613—24no—
14#16840291—24no—
15#16840291—24no—
16C2×#14519770—21no—
17C2×#14519769C411yescharacteristic, complemented
18C2×#14519759—21no—
19C2×#14519753C2211yescharacteristic
20C2×#14519748C2211yescharacteristic
21C2×Q8×Dic61C411yescharacteristic, complemented
22C2×D4×Dic61C411yescharacteristic, complemented
23C2×#14519737—21no—
24C2×#14519733—21no—
25C2×C42×D61C2211yescharacteristic
26C2×#124×C61C411yescharacteristic, complemented
27C23×#6923—22no—
28C22×#92420—22no—
29#14519834—22no—
30#14519834—22no—
31(C2×#6923)⋊C4—24no—
32(C2×#6923)⋊C4—22no—
33(C2×#6923)⋊C4—22no—
34(C2×#6923)⋊C4—42no—
35C22×C22⋊D61—21no—
36C23×Dic61—21no—
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61C2311yescharacteristic
40#14519770—28no—
41#14519769—22no—
42#14519769—22no—
43#14519759—28no—
44#14519753—22no—
45#14519753D414yes—
46#14519748—22no—
47#14519748D414yes—
48Q8×Dic61—22no—
49Q8×Dic61—22no—
50D4×Dic61—22no—
51D4×Dic61—22no—
52#14519737—28no—
53#14519733—28no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61C2×C411yescharacteristic
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×#11758196—21no—
58C2×#11758196—21no—
59C2×#11758196—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×#11758198—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61C2×C411yescharacteristic
65C2×C4×Dic61D411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67C42×D61—22no—
68C42×D61—22no—
69C22×Q8×C61C2×C411yescharacteristic
70C22×D4×C61C2×C411yescharacteristic
71#124×C61—22no—
72#124×C61—22no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C42×C61C2×C411yescharacteristic
76C24×C61—21no—
77C23×D61C2×D411yescharacteristic
78C22×#6923—24no—
79C22×#6923—42no—
80C22×#6923—42no—
81C22×#6923—42no—
82C22×#6923—42no—
83C22×#6923—42no—
84C22×#6923—42no—
85C2×Q8×C61—21no—
86C2×Q8×C61—41no—
87C2×Q8×C61—41no—
88C2×Q8×C61C22⋊C412yes—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61C22⋊C412yes—
93C22×C4×C61—21no—
94C22×C4×C61C22⋊C411yescharacteristic
95C22×C4×C61C22⋊C411yescharacteristic
96C22×C4×C61C22×C411yescharacteristic
97C2×C22⋊D61—24no—
98C2×C22⋊D61—42no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C22×Dic61—24no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—42no—
105C22×Dic61—42no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C2×D411yescharacteristic
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61—22no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×C4×D61—22no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61C2×D412yes—
119C2×C4×D61C2×D412yes—
120C2×#92420—42no—
121C2×#92420—42no—
122C2×#92420—42no—
123C22⋊C4×C61—24no—
124C22⋊C4×C61—24no—
125C42×C61—21no—
126C42×C61—21no—
127C22⋊Dic61—24no—
128C22⋊Dic61—24no—
129#11758198—24no—
130C4⋊Dic61—24no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61C22⋊C412yes—
134C4⋊Dic61C22⋊C412yes—
135#11758196—24no—
136#11758196—24no—
137#11758196—24no—
138C4×Dic61—24no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—22no—
142C4×Dic61—22no—
143C23×C61—22no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61C2×C22⋊C411yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61#12012yes—
156C22×D61#13512yes—
157C22×D61AGL(1,ℤ/8)11yescharacteristic
158C22×D61#13711yescharacteristic
159C2×#6923—44no—
160C2×#6923—44no—
161C2×#6923—44no—
162C2×#6923—82no—
163C2×#6923—82no—
164C2×#6923—82no—
165C2×#6923—82no—
166Q8×C61—42no—
167Q8×C61—42no—
168D4×C61—42no—
169D4×C61—42no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—22no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×C4×C61C2×C22⋊C411yescharacteristic
183C22⋊D61—44no—
184C22⋊D61—44no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—48no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61#10412yes—
200C2×Dic61#12012yes—
201C4×D61—42no—
202C4×D61—42no—
203C4×D61—44no—
204C4×D61—42no—
205C4×D61—42no—
206#92420—82no—
207#8330—611nomaximal, Sylow
208C22×C61—42no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#37911yescharacteristic
216C22×C61#41011yescharacteristic
217C22×C61#41011yescharacteristic
218C22×C61#41611yescharacteristic
219C22×C61#41711yescharacteristic
220C22×C61C2×#10411yescharacteristic
221C22×C61#42111yescharacteristic
222C2×D61—22no—
223C2×D61—21no—
224C2×D61—21no—
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61#44912yes—
231C2×D61#45212yes—
232#6923—84no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—42no—
236C4×C61—41no—
237C4×C61—41no—
238Dic61—22no—
239Dic61—22no—
240Dic61—41no—
241Dic61—42no—
242Dic61—42no—
243C2×#529—611no—
244#1817—611no—
245C2×#328—612no—
246C2×#327—612no—
247#1434—611no—
248C2×C61—82no—
249C2×C61#150011yescharacteristic
250C2×C61#150911yescharacteristic
251C2×C61#151211yescharacteristic
252C2×C61#152111yescharacteristic
253C2×C61#178211yescharacteristic
254C2×C61#178811yescharacteristic
255C2×C61#178911yescharacteristic
256D61—22no—
257D61—22no—
258#529—1224no—
259#529—1224no—
260C2×#126—1221no—
261C2×#125—611no—
262C2×#124#692311yescharacteristic, complemented
263C2×#123—1221no—
264C2×C22⋊Q8—611no—
265C2×#121—611no—
266C2×C4×Q8—611no—
267C2×C4×D4—611no—
268C2×C4×D4—1221no—
269C2×#117—1221no—
270C22×C42—611no—
271C2×C22⋊C8—612no—
272C2×#95—612no—
273C2×#95—1221no—
274C2×#95—1221no—
275#336—1221no—
276#336—1221no—
277#328—1224no—
278#327—1224no—
279C61#833011yescharacteristic, complemented, Sylow
280C22×Q8C2×#692311yescharacteristic
281C22×D4—1221no—
282C22×D4C2×#692311yescharacteristic
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—1221no—
287C23×C4—1222no—
288C22×C8—1222no—
289#126—1228no—
290#125—1222no—
291#125—1222no—
292#124—22no—
293#124—22no—
294#123—1228no—
295C22⋊Q8—614no—
296C22⋊Q8—1222no—
297#121—614no—
298#121—1222no—
299C4×Q8—1222no—
300C4×Q8—1222no—
301C4×D4—1228no—
302C4×D4—1222no—
303C4×D4—1222no—
304#117—1228no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C42—611no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42—1222no—
320C2×C42—1222no—
321C2×C42—1221no—
322C2×C42C2×#692311yescharacteristic
323C22⋊C8—1222no—
324C22⋊C8—1222no—
325#95—1222no—
326#95—1222no—
327#95—1224no—
328#95—2442no—
329C24—21no—
330C24—611no—
331C2×Q8—21no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8C22⋊#692312yes—
335C2×D4—21no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—1224no—
339C2×D4—2442no—
340C2×D4—2441no—
341C2×D4—2441no—
342C2×D4C22⋊#692312yes—
343C22×C4—21no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—612no—
347C22×C4—612no—
348C22×C4—611no—
349C22×C4—1222no—
350C22×C4—1221no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1221no—
355C22×C4—1224no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1224no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4C22⋊#692311yescharacteristic
371C22×C4C22⋊#692311yescharacteristic
372C22×C4C22×#692311yescharacteristic
373C2×C8—2442no—
374C2×C8—2442no—
375C2×C8—2442no—
376C4⋊C4—612no—
377C4⋊C4—612no—
378C4⋊C4—1224no—
379C4⋊C4—1224no—
380C4⋊C4—1224no—
381C4⋊C4—1224no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—1224no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C42—21no—
390C42—21no—
391C42—1222no—
392C42—1222no—
393C42—1224no—
394C42—1221no—
395C42—1221no—
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—612no—
404C23—611no—
405C23—611no—
406C23—612no—
407C23—1221no—
408C23—1221no—
409C23—1221no—
410C23—1221no—
411C23C2×C22⋊#692311yescharacteristic
412Q8—42no—
413Q8—42no—
414D4—42no—
415D4—42no—
416D4—2444no—
417D4—2444no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—612no—
430C2×C4—612no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1222no—
439C2×C4—1222no—
440C2×C4—4882no—
441C2×C4—4882no—
442C2×C4—4882no—
443C2×C4—4882no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2444no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2448no—
450C2×C4—2444no—
451C2×C4—2444no—
452C2×C4—2444no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4C2×C22⋊#692311yescharacteristic
458C2×C4C2×C22⋊#692311yescharacteristic
459C8—4882no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—612no—
468C22—612no—
469C22—1222no—
470C22—1222no—
471C22—1222no—
472C22—1222no—
473C22—1221no—
474C22—1221no—
475C22—1221no—
476C22—1221no—
477C22#1684070311yescharacteristic
478C22#1684074211yescharacteristic
479C22#1684074211yescharacteristic
480C22#1684075211yescharacteristic
481C22#1684075311yescharacteristic
482C22D61⋊#10411yescharacteristic
483C22#1684075911yescharacteristic
484C4—21no—
485C4—21no—
486C4—42no—
487C4—41no—
488C4—41no—
489C4—1222no—
490C4—1222no—
491C4—4884no—
492C4—2441no—
493C4—2442no—
494C4—2442no—
495C2—82no—
496C2—1222no—
497C2—1222no—
498C2#2146119111yescharacteristic
499C2#2146122011yescharacteristic
500C2#2146123111yescharacteristic
501C2#2146126011yescharacteristic
502C2#2146164911yescharacteristic
503C2#2146165911yescharacteristic
504C2#2146166111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C22
cosocleC22×C4×D61C23
hypercenterC2×#124#6923
hypocenterC61#8330
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. C2×#16840616C2semidirect
4. #21460995C2semidirect
17. C2×#14519769C4semidirect
21. C2×Q8×Dic61C4semidirect
22. C2×D4×Dic61C4semidirect
26. C2×#124×C61C4semidirect
262. C2×#124#6923semidirect
279. C61#8330semidirect

Maximal subgroups

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

subgroupindex
#214617112
C2×#168406162
C2×#168406132
#214609952
C2×#168402912
#833061