Finite Group Databasebeta

← #29575089

Subgroups — #29575089

Order 15616.

670 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454847C211yesmaximal, characteristic, complemented
2#21449098C211yesmaximal, characteristic
3C4×#14519693C211yesmaximal, characteristic, complemented
4#21444262C211yesmaximal, characteristic, complemented
5#21443713C211yesmaximal, characteristic, complemented
6#21443711C211yesmaximal, characteristic, complemented
7C61×#1490C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×C4×C22⋊D61—21no—
10C2×C4×C22⋊D61—21no—
11#16839835—22no—
12#16839832—22no—
13#16839819C2211yescharacteristic
14C2×#14519693—21no—
15#16839724—21no—
16C22⋊C8×D61—21no—
17C4×#11758194C2211yescharacteristic
18#16839698—21no—
19#16839697C411yescharacteristic
20#16839697C411yescharacteristic
21#16839671—21no—
22#16839670C411yescharacteristic
23#16839670C411yescharacteristic
24#16839608C2211yescharacteristic
25#16839530—21no—
26D4⋊#92418—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758194—21no—
37C2×#11758189—22no—
38C2×C8×D61—22no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×C22⋊D61—44no—
44C4×C22⋊D61—44no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198C2×C411yescharacteristic
53C2×#11758198C2×C411yescharacteristic
54C2×C4×Dic61—21no—
55C4⋊#92418D412yescomplemented
56#14519693—24no—
57C22⋊#92418—21no—
58#14519689—22no—
59#14519689—22no—
60#14519688—21no—
61#14519688—21no—
62C4×#92418—21no—
63#14519684—21no—
64#14519684C2×C411yescharacteristic
65#14519684C2×C411yescharacteristic
66C22×D4×C61C2×C411yescharacteristic
67C23×C4×C61—21no—
68C2×M16×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61D412yescomplemented
77C22⋊C8×C61—21no—
78#97×C61—21no—
79#97×C61—21no—
80C4×C8×C61—21no—
81C24×C61—21no—
82C23×D61C22⋊C411yescharacteristic
83C23×D61C22⋊C411yescharacteristic
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—42no—
87C22×C4×C61—21no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C2×C22⋊D61—42no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C2×C22⋊D61—42no—
99C2×C22⋊D61—42no—
100C2×C22⋊D61—42no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C2×D244—22no—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244—41no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
115M16×C61—22no—
116M16×C61—41no—
117C2×C8×C61—22no—
118C2×C8×C61—41no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61#4111yescharacteristic
126C42×C61#4111yescharacteristic
127C22⋊Dic61—42no—
128C22⋊Dic61—42no—
129#11758198—21no—
130#11758198—21no—
131#11758198—21no—
132#11758198—21no—
133#11758198—42no—
134#11758198—42no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137#11758196—42no—
138#11758196—42no—
139C4×Dic61—24no—
140#11758194—22no—
141#11758194—41no—
142C2×#92418—22no—
143C2×#92418—41no—
144#11758189—82no—
145C8×D61—82no—
146C23×C61—22no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61C2×C22⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61#10412yes—
164D4×C61—22no—
165D4×C61—22no—
166D4×C61—41no—
167D4×C61—41no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—22no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—82no—
176C2×C4×C61—82no—
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61C4×D411yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12311yescharacteristic
183C22⋊D61—48no—
184C22⋊D61—48no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195D244—42no—
196D244—42no—
197C4×D61—42no—
198C4×D61—42no—
199C4×D61—81no—
200C4×D61—81no—
201C8×C61—42no—
202C8×C61—42no—
203#92418—42no—
204#92418—42no—
205#9031—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—42no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#38611yescharacteristic
216C22×C61C2×#10411yescharacteristic
217C22×C61#42111yescharacteristic
218C2×D61—22no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—42no—
222C2×D61—42no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—81no—
227C2×D61—81no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—81no—
234C4×C61#45312yes—
235Dic61—42no—
236Dic61—42no—
237Dic61—41no—
238Dic61—41no—
239#2973—611no—
240#2397—611no—
241C4×#100—611no—
242#1490—611no—
243#1490D6111yescharacteristic, complemented
244#1300—611no—
245#1300—611no—
246C2×C61—21no—
247C2×C61—21no—
248C2×C61—82no—
249C2×C61#187111yescharacteristic
250C2×C61#188711yescharacteristic
251C2×C61#189111yescharacteristic
252D61—42no—
253D61—81no—
254C2×C4×D4—611no—
255C2×C4×D4—1221no—
256C2×C4×D4—1221no—
257C2×C4×D4C2×D6111yescharacteristic
258#435—1222no—
259#435—1222no—
260#432—611no—
261#432C2×D6111yescharacteristic
262C2×#100—1221no—
263#407—1221no—
264C2×C22⋊C8—1221no—
265C4×M16—611no—
266C4×M16C2×D6111yescharacteristic
267#399—611no—
268#399—611no—
269#399—1221no—
270#392—611no—
271#392—611no—
272#392—1221no—
273#376—611no—
274#343—1221no—
275D4⋊C8—22no—
276D4⋊C8—1222no—
277C61#903111yescharacteristic, complemented, Sylow
278C22×D4—611no—
279C22×D4—1221no—
280C22×D4—1221no—
281C22×D4C4×D6111yescharacteristic
282C23×C4—21no—
283C23×C4—611no—
284C23×C4—611no—
285C2×M16—21no—
286C2×M16—1222no—
287C2×M16—1221no—
288C22×C8—1222no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—1221no—
294C4×D4—1221no—
295C4×D4—1221no—
296C4×D4—1221no—
297C4×D4—2444no—
298C4×D4—2444no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4C4×D6111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C42—1221no—
311C2×C42C22×D6111yescharacteristic
312C4⋊C8—612no—
313C4⋊C8C22⋊D6112yescomplemented
314#100—1224no—
315C22⋊C8—21no—
316C22⋊C8—1222no—
317C22⋊C8—1222no—
318C22⋊C8—1221no—
319#97—21no—
320#97—21no—
321#97—1221no—
322#97—1221no—
323C4×C8—21no—
324C4×C8—1221no—
325#95—611no—
326#95—611no—
327#95—1221no—
328C24—21no—
329C24—611no—
330C24—611no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—42no—
334C2×D4—1222no—
335C2×D4—1221no—
336C2×D4—1221no—
337C2×D4—2441no—
338C2×D4—2442no—
339C2×D4—2442no—
340C2×D4—2442no—
341C2×D4—2442no—
342C2×D4—2442no—
343C2×D4—2442no—
344C22×C4—21no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—2442no—
358C22×C4—2442no—
359C22×C4C2×C4×D6111yescharacteristic
360C22×C4D4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362M16—22no—
363M16—41no—
364M16—1222no—
365M16—4882no—
366M16—2441no—
367C2×C8—22no—
368C2×C8—41no—
369C2×C8—1222no—
370C2×C8—4882no—
371C2×C8—2441no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—2442no—
377C4⋊C4—2442no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—1221no—
381C22⋊C4—1221no—
382C22⋊C4—1221no—
383C22⋊C4—1221no—
384C22⋊C4—2442no—
385C22⋊C4—2442no—
386C22⋊C4—2442no—
387C22⋊C4—2442no—
388C42—1224no—
389C42#1175822211yescharacteristic
390C42D4×D6111yescharacteristic
391C42#1175822411yescharacteristic
392C42C2×C22⋊D6111yescharacteristic
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—612no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—2441no—
407C23—2441no—
408C23—2441no—
409C23—2441no—
410C23C22⋊C4×D6111yescharacteristic
411D4—22no—
412D4—22no—
413D4—41no—
414D4—41no—
415D4—2442no—
416D4—2442no—
417D4—2448no—
418D4—2448no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—1222no—
429C2×C4—1222no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—4881no—
433C2×C4—4881no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4#1451973711yescharacteristic
443C2×C4C4×C22⋊D6111yescharacteristic
444C2×C4#1451974511yescharacteristic
445C2×C4#1451974811yescharacteristic
446C2×C4#1451975011yescharacteristic
447C2×C4#1451975911yescharacteristic
448C8—42no—
449C8—42no—
450C8—2442no—
451C8—2442no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—1222no—
462C22—4881no—
463C22—4881no—
464C22—2442no—
465C22—2442no—
466C22—2441no—
467C22—2441no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22#1683963811yescharacteristic
472C22#104×D6111yescharacteristic
473C22#1683977711yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—81no—
480C4—2442no—
481C4—2442no—
482C4—2441no—
483C4—2441no—
484C4#1683992812yes—
485C2—21no—
486C2—21no—
487C2—82no—
488C2—4881no—
489C2—2442no—
490C2#2144611811yescharacteristic
491C2#2144621411yescharacteristic
492C2#2144623411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1490C2
socleC22×C61#386
prime radical#21449098C2
cosocleC2×C42×C61C23
hypercenter#1490D61
hypocenterC61#9031
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
1. #21454847C2semidirect
3. C4×#14519693C2semidirect
4. #21444262C2semidirect
5. #21443713C2semidirect
6. #21443711C2semidirect
7. C61×#1490C2semidirect
55. C4⋊#92418D4semidirect
76. C4⋊C8×C61D4semidirect
243. #1490D61semidirect
277. C61#9031semidirect
313. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214548472
#214490982
C4×#145196932
#214442622
#214437132
#214437112
C61×#14902
#903161