Finite Group Databasebeta

← #29576303

Subgroups — #29576303

Order 15616.

588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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#21455815C211yesmaximal, characteristic
2#21448280C211yesmaximal, characteristic, complemented
3#21446648C211yesmaximal, characteristic, complemented
4#21444245C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1502C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519734—21no—
10#16840073—21no—
11#16840039C412yescomplemented
12#16839954C412yescomplemented
13#16839895—21no—
14C4×#11758199—22no—
15#16839815C2211yescharacteristic
16#16839786C2211yescharacteristic
17C2×#14519704—21no—
18C2×#14519704—21no—
19#16839663—21no—
20#16839658—21no—
21#16839651—22no—
22C4×#11758198—21no—
23C42×Dic61C2211yescharacteristic
24#16839491—22no—
25C61×#532C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#327—22no—
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758199—22no—
32C2×#11758194—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244C2×C412yes—
36C4×D244D412yes—
37#14519734—42no—
38#14519734—42no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—22no—
41C2×#11758198—21no—
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519710—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418C2×C412yes—
52#14519704—42no—
53#14519704—42no—
54#14519698—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57C4×#92418—21no—
58#14519684—22no—
59C2×#41×C61—21no—
60C4⋊Q8×C61C2×C411yescharacteristic
61#127×C61C2×C411yescharacteristic
62#124×C61—21no—
63#121×C61—21no—
64#121×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C42×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C4×C8×C61—21no—
73#95×C61D412yes—
74C23×D61—21no—
75#41×C61—41no—
76#41×C61—41no—
77#41×C61—41no—
78#41×C61—41no—
79C2×Q8×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C22×C4×C61—22no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C2×D244—21no—
93C2×D244—42no—
94C2×D244C22⋊C412yes—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—42no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61C22×C411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113#11758199—44no—
114#11758198—22no—
115#11758198—22no—
116#11758198—44no—
117#11758198—44no—
118C4⋊Dic61—21no—
119C4⋊Dic61C22⋊C412yes—
120#11758196—44no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—42no—
125C4×Dic61—42no—
126C4×Dic61D812yescomplemented
127#11758194—41no—
128#11758194—41no—
129C2×#92418—22no—
130C2×#92418—41no—
131C23×C61—41no—
132C23×C61#12011yescharacteristic
133C22×D61—22no—
134C22×D61—42no—
135C22×D61—42no—
136C22×D61—41no—
137C22×D61—41no—
138Q8×C61—41no—
139Q8×C61—41no—
140D4×C61—42no—
141D4×C61—41no—
142D4×C61—41no—
143D4×C61—81no—
144D4×C61—81no—
145D4×C61—81no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—42no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61#13511yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×Dic61—22no—
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173D244—22no—
174D244—22no—
175D244—42no—
176C4×D61—42no—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—42no—
180C8×C61—81no—
181#92418—42no—
182#92418—81no—
183#9237—611nomaximal, Sylow
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61#38611yescharacteristic
190C22×C61#44711yescharacteristic
191C22×C61#44911yescharacteristic
192C2×D61—42no—
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—82no—
196C2×D61—82no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—82no—
201C4×C61—81no—
202C4×C61#42112yes—
203C4×C61C4×D811yescharacteristic
204C4×C61#44211yescharacteristic
205C4×C61#45911yescharacteristic
206C4×C61#46311yescharacteristic
207Dic61—42no—
208Dic61—42no—
209Dic61—42no—
210#3100—611no—
211#2293—611no—
212#1962—611no—
213#1502D6111yescharacteristic, complemented
214#1486—611no—
215#1303—611no—
216#1276—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—161no—
220C2×C61#187911yescharacteristic
221C2×C61#189711yescharacteristic
222C2×C61#190611yescharacteristic
223D61—82no—
224#532C2×D6111yescharacteristic
225C2×C4×D4—611no—
226C2×#117—1221no—
227#480—1221no—
228#474—612no—
229#459—612no—
230#447—1221no—
231C4×D8—1222no—
232#431—611no—
233#431C2×D6111yescharacteristic
234#423—611no—
235C2×#104—1221no—
236C2×#104—1221no—
237#390—1221no—
238#389—1221no—
239#388—1222no—
240C4×C4⋊C4C2×D6111yescharacteristic
241C4×C22⋊C4—1221no—
242C43—611no—
243#327—22no—
244D4⋊C8—1222no—
245C61#923711yescharacteristic, complemented, Sylow
246C2×#41—21no—
247C22×D4—611no—
248C23×C4—1221no—
249C2×D8—1222no—
250C2×M16—1221no—
251C4⋊Q8C4×D6111yescharacteristic
252#127C4×D6111yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—612no—
259C4×D4—612no—
260C4×D4—1221no—
261C4×D4—1221no—
262#117—2442no—
263#117—2442no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—1222no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1222no—
269C2×C22⋊C4—1222no—
270C2×C42—21no—
271C2×C42—611no—
272C2×C42—611no—
273C2×C42—1221no—
274C2×C42—1221no—
275C2×C42C22×D6111yescharacteristic
276#107—1222no—
277C4⋊C8—21no—
278C4⋊C8—612no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281#104—2442no—
282#104—2442no—
283#102—1222no—
284#102—1222no—
285C22⋊C8—21no—
286C22⋊C8—1221no—
287C4×C8—21no—
288C4×C8—1221no—
289#95—1222no—
290#95C22⋊D6112yes—
291C24—1221no—
292#41—41no—
293#41—41no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—41no—
301C2×D4—612no—
302C2×D4—1221no—
303C2×D4—2442no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4D4×D6111yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4C2×C22⋊D6111yescharacteristic
318D8—2444no—
319M16—2441no—
320M16—2441no—
321C2×C8—41no—
322C2×C8—1222no—
323C2×C8—2441no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—612no—
328C4⋊C4—1221no—
329C4⋊C4—2444no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—1222no—
333C22⋊C4—1222no—
334C22⋊C4—2444no—
335C22⋊C4—2444no—
336C42—41no—
337C42—41no—
338C42—612no—
339C42—1221no—
340C42—1221no—
341C42—1221no—
342C42—2442no—
343C42—2442no—
344C42C2×C4×D6111yescharacteristic
345C42#1175822211yescharacteristic
346C42D4×D6111yescharacteristic
347C42#1175822411yescharacteristic
348C23—41no—
349C23—1222no—
350C23—2442no—
351C23—2442no—
352C23—2441no—
353C23—2441no—
354C23#1451974511yescharacteristic
355Q8—41no—
356Q8—41no—
357D4—42no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—1222no—
364D4—1222no—
365D4—2442no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—1222no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4C22⋊C4×D6111yescharacteristic
388C2×C4#1451973711yescharacteristic
389C2×C4C4×C22⋊D6111yescharacteristic
390C2×C4#1451974811yescharacteristic
391C2×C4#1451975011yescharacteristic
392C2×C4#1451975911yescharacteristic
393C2×C4D8×D6111yescharacteristic
394C2×C4#1451979811yescharacteristic
395C2×C4#1451980111yescharacteristic
396C2×C4#1451980411yescharacteristic
397C8—81no—
398C8—4881no—
399C8—2442no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—4882no—
406C22—4882no—
407C22—2442no—
408C22—2442no—
409C22—2442no—
410C22#1683963811yescharacteristic
411C22#1683989411yescharacteristic
412C22#1683990611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—82no—
417C4—81no—
418C4—2442no—
419C4—2442no—
420C4—2442no—
421C4#1683977712yes—
422C4#1683984211yescharacteristic
423C4#1683987111yescharacteristic
424C4#1683995611yescharacteristic
425C4#1683997611yescharacteristic
426C2—21no—
427C2—21no—
428C2—161no—
429C2—4882no—
430C2#2144616411yescharacteristic
431C2#2144626411yescharacteristic
432C2#2144631711yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1502C2
socleC22×C61#386
prime radical#21455815C2
cosocleC2×C42×C61C23
hypercenter#1502D61
hypocenterC61#9237
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #21448280C2semidirect
3. #21446648C2semidirect
4. #21444245C2semidirect
5. #21443722C2semidirect
6. #21443651C2semidirect
7. C61×#1502C2semidirect
11. #16840039C4semidirect
12. #16839954C4semidirect
126. C4×Dic61D8semidirect
213. #1502D61semidirect
245. C61#9237semidirect

Maximal subgroups

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

subgroupindex
#214558152
#214482802
#214466482
#214442452
#214437222
#214436512
C61×#15022
#923761