Finite Group Databasebeta

← #29580869

Subgroups — #29580869

Order 15616.

696 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 101 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#21455823C211yesmaximal, characteristic, complemented
2#21449098C211yesmaximal, characteristic
3#21446801C211yesmaximal, characteristic, complemented
4#21444245C211yesmaximal, characteristic, complemented
5#21444244C211yesmaximal, characteristic, complemented
6#21443647C211yesmaximal, characteristic, complemented
7C61×#3101C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×C4×C22⋊D61—22no—
10#16840090—21no—
11#16840049—21no—
12#16839964—21no—
13#16839912—21no—
14C4×#11758201—22no—
15#16839815C2211yescharacteristic
16#16839786C2211yescharacteristic
17#16839698—21no—
18#16839697—21no—
19#16839671—21no—
20#16839670—21no—
21#16839608C2211yescharacteristic
22#16839521—22no—
23#16839491—22no—
24D4⋊#92418—22no—
25C61×#533C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#483—21no—
28C61×#476—21no—
29C61×#461—21no—
30C61×#450—21no—
31C4×SD16×C61—22no—
32C61×#431C2211yescharacteristic
33C22×D244D411yescharacteristic
34C22×C22⋊D61—22no—
35C22×C4×D61—21no—
36C2×#11758201—22no—
37C2×#11758194—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×C22⋊D61—44no—
43C4×C22⋊D61—44no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—22no—
46C2×C22⋊Dic61—22no—
47C2×#11758198—22no—
48C2×#11758198—21no—
49C2×C4×Dic61D412yes—
50#14519708—22no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54#14519701—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57C4×#92418D412yescomplemented
58#14519684—21no—
59#14519684—21no—
60C22×D4×C61D411yescharacteristic
61C23×C4×C61—21no—
62C2×SD16×C61—22no—
63C4⋊Q8×C61D411yescharacteristic, complemented
64C4⋊Q8×C61D411yescharacteristic, complemented
65#125×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74#117×C61—21no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C42×C61C2311yescharacteristic
78#106×C61—22no—
79C4⋊C8×C61—21no—
80#103×C61—22no—
81#102×C61—22no—
82C22⋊C8×C61—21no—
83C4×C8×C61D412yescomplemented
84C24×C61—21no—
85C23×D61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—42no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—42no—
95C22×C4×C61—42no—
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C2×C22⋊D61—44no—
100C2×C22⋊D61—44no—
101C2×C22⋊D61—44no—
102C22×Dic61—22no—
103C22×Dic61—21no—
104C2×D244—21no—
105C2×D244—21no—
106C2×D244—42no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111SD16×C61—44no—
112C2×C8×C61—22no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C42×C61—41no—
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61#4111yescharacteristic
129C22⋊Dic61—44no—
130#11758201—44no—
131#11758198—44no—
132#11758198—41no—
133#11758198—41no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136#11758196—44no—
137C4×Dic61—22no—
138C4×Dic61SD1614yescomplemented
139#11758194—42no—
140C2×#92418—22no—
141C2×#92418—41no—
142C23×C61—22no—
143C23×C61—42no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—42no—
147C23×C61#12011yescharacteristic
148C22×D61—22no—
149C22×D61—41no—
150C22×D61—42no—
151C22×D61—41no—
152C22×D61—42no—
153Q8×C61—42no—
154Q8×C61—42no—
155D4×C61—22no—
156D4×C61—22no—
157D4×C61—41no—
158D4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—82no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12711yescharacteristic
174C2×C4×C61C2×SD1612yes—
175C2×C4×C61AGL(1,ℤ/8)12yes—
176C22⋊D61—416no—
177C2×Dic61—24no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—42no—
182D244—22no—
183D244—22no—
184D244—41no—
185D244—41no—
186C4×D61—82no—
187C4×D61—81no—
188C4×D61—81no—
189C8×C61—42no—
190#92418—42no—
191#92418—81no—
192#10015—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—44no—
196C22×C61—42no—
197C22×C61—82no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61#39211yescharacteristic
201C22×C61#45012yes—
202C2×D61—44no—
203C2×D61—42no—
204C2×D61—82no—
205C2×D61—81no—
206C2×D61—81no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—81no—
212C4×C61—81no—
213C4×C61—81no—
214C4×C61#46012yes—
215C4×C61#49211yescharacteristic
216C4×C61#49611yescharacteristic
217Dic61—44no—
218Dic61—81no—
219#3101—611no—
220#3101D6111yescharacteristic, complemented
221#2397—611no—
222#1995—611no—
223#1486—611no—
224#1486—611no—
225#1274—611no—
226C2×C61—22no—
227C2×C61—82no—
228C2×C61#201011yescharacteristic
229C2×C61#201011yescharacteristic
230C2×C61#201411yescharacteristic
231D61—82no—
232#533C2×D6111yescharacteristic
233C2×C4×D4—611no—
234C2×C4×D4—1222no—
235C2×C4×D4C2×D6111yescharacteristic
236#483—21no—
237#483—1221no—
238#476—21no—
239#476—1221no—
240#461—21no—
241#461—1221no—
242#450—21no—
243#450—1221no—
244C4×SD16—22no—
245C4×SD16—1222no—
246#431—611no—
247#431C2×D6111yescharacteristic
248#423—611no—
249#399—1221no—
250#399—1221no—
251#392—1221no—
252#392—1221no—
253#376—611no—
254#339—1222no—
255D4⋊C8—1222no—
256D4⋊C8—1222no—
257C61#1001511yescharacteristic, complemented, Sylow
258C22×D4—611no—
259C22×D4—1222no—
260C22×D4C22⋊D6111yescharacteristic
261C23×C4—21no—
262C23×C4—1221no—
263C2×SD16—22no—
264C2×SD16—1222no—
265C2×M16—1221no—
266C4⋊Q8C22⋊D6111yescharacteristic, complemented
267C4⋊Q8C22⋊D6111yescharacteristic, complemented
268#125—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—1221no—
278C4×D4—1221no—
279C4×D4—1221no—
280C4×D4—1221no—
281C4×D4—2444no—
282C4×D4—2444no—
283#117—21no—
284C2×C4⋊C4—611no—
285C2×C4⋊C4—1222no—
286C2×C4⋊C4C22⋊D6111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—1222no—
289C2×C22⋊C4—1222no—
290C2×C22⋊C4—1221no—
291C2×C42—612no—
292C2×C42C22×D6111yescharacteristic
293#106—22no—
294#106—1222no—
295C4⋊C8—21no—
296C4⋊C8—1221no—
297C4⋊C8—1221no—
298C4⋊C8—1221no—
299#103—22no—
300#103—1222no—
301#102—22no—
302#102—1222no—
303C22⋊C8—21no—
304C22⋊C8—1221no—
305C4×C8—612no—
306C4×C8C22⋊D6112yescomplemented
307#95—1221no—
308#95—1221no—
309C24—21no—
310C24—1221no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—42no—
316C2×D4—1221no—
317C2×D4—1221no—
318C2×D4—2442no—
319C2×D4—2444no—
320C2×D4—2444no—
321C2×D4—2444no—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—1222no—
328C22×C4—1221no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2442no—
332C22×C4—2442no—
333C22×C4D4×D6111yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4C2×C22⋊D6111yescharacteristic
336SD16—44no—
337SD16—2444no—
338M16—2442no—
339C2×C8—22no—
340C2×C8—1222no—
341C2×C8—2441no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—2444no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—2444no—
357C22⋊C4—2444no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—41no—
361C42—614no—
362C42—1222no—
363C42D4×D6111yescharacteristic
364C42#1175822411yescharacteristic
365C42C2×C22⋊D6111yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C23—22no—
368C23—41no—
369C23—42no—
370C23—42no—
371C23—41no—
372C23—1222no—
373C23—2441no—
374C23—2442no—
375C23—2442no—
376C23—2441no—
377C23#1451974511yescharacteristic
378Q8—42no—
379Q8—42no—
380D4—22no—
381D4—22no—
382D4—41no—
383D4—41no—
384D4—1222no—
385D4—1222no—
386D4—2441no—
387D4—2441no—
388D4—24416no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—1224no—
399C2×C4—4882no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—2442no—
403C2×C4—2441no—
404C2×C4—2442no—
405C2×C4—2442no—
406C2×C4#1451974511yescharacteristic
407C2×C4#1451974611yescharacteristic
408C2×C4#1451974811yescharacteristic
409C2×C4#1451974911yescharacteristic
410C2×C4#1451974911yescharacteristic
411C2×C4#1451977311yescharacteristic
412C2×C4SD16×D6112yes—
413C2×C4#1451980412yes—
414C8—42no—
415C8—4881no—
416C8—2442no—
417C22—21no—
418C22—21no—
419C22—44no—
420C22—42no—
421C22—82no—
422C22—81no—
423C22—81no—
424C22—4882no—
425C22—4881no—
426C22—4881no—
427C22—2444no—
428C22—2442no—
429C22#1683967011yescharacteristic
430C22#1683991112yes—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—4881no—
439C4—2444no—
440C4#1683996012yes—
441C4#1684013311yescharacteristic
442C4#1684014811yescharacteristic
443C2—22no—
444C2—82no—
445C2—4882no—
446C2#2144688311yescharacteristic
447C2#2144688411yescharacteristic
448C2#2144690511yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3101C2
socleC22×C61#392
prime radical#21449098C2
hypercenter#3101D61
hypocenterC61#10015
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #21455823C2semidirect
3. #21446801C2semidirect
4. #21444245C2semidirect
5. #21444244C2semidirect
6. #21443647C2semidirect
7. C61×#3101C2semidirect
57. C4×#92418D4semidirect
63. C4⋊Q8×C61D4semidirect
64. C4⋊Q8×C61D4semidirect
83. C4×C8×C61D4semidirect
138. C4×Dic61SD16semidirect
220. #3101D61semidirect
257. C61#10015semidirect
266. C4⋊Q8C22⋊D61semidirect
267. C4⋊Q8C22⋊D61semidirect
306. C4×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214558232
#214490982
#214468012
#214442452
#214442442
#214436472
C61×#31012
#1001561