Finite Group Databasebeta

← #29577949

Subgroups — #29577949

Order 15616.

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

normal subgroups only

This group has 880 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#21454846C211yesmaximal, characteristic, complemented
2#21449169C211yesmaximal, characteristic
3#21445740C211yesmaximal, characteristic, complemented
4#21444155C211yesmaximal, characteristic, complemented
5#21443726C211yesmaximal, characteristic, complemented
6#21443724C211yesmaximal, characteristic, complemented
7C61×#1783C211yesmaximal, characteristic, complemented
8C2×#14519748—21no—
9C2×#14519746C412yes—
10C2×C4×C22⋊D61C2211yescharacteristic
11#16839836—22no—
12#16839831—22no—
13#16839816—21no—
14C2×#14519694—22no—
15#16839726C2211yescharacteristic
16#16839726C2211yescharacteristic
17C22⋊C8×D61—21no—
18#16839676—21no—
19#16839670—21no—
20#16839665—21no—
21#16839622C2211yescharacteristic
22#16839618C412yes—
23#16839487—21no—
24#16839485—21no—
25C23×D4×C61C2211yescharacteristic
26C2×#100×C61—22no—
27C61×#407C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C22×C22⋊D61—22no—
30C22×C22⋊D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194D412yescomplemented
34C2×C8×D61—22no—
35#14519748—44no—
36#14519746—44no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41C2×C4⋊Dic61—21no—
42C2×#11758196D411yescharacteristic
43C2×C22⋊Dic61—22no—
44C2×C22⋊Dic61—22no—
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61C2×C411yescharacteristic
47C2×C22⋊Dic61C2×C412yes—
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519706—22no—
51#14519694—44no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56#14519689—22no—
57#14519687—22no—
58#14519684—21no—
59C25×C61C2×C412yes—
60C22×D4×C61—21no—
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—44no—
67C23×C4×C61C2311yescharacteristic
68C2×M16×C61—21no—
69C2×M16×C61D412yescomplemented
70#100×C61—44no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C24×C61—22no—
76C24×C61—22no—
77C24×C61—22no—
78C24×C61—44no—
79C24×C61—42no—
80C24×C61—42no—
81C24×C61—82no—
82C24×C61C22×C411yescharacteristic
83C23×D61C22⋊C411yescharacteristic
84C2×D4×C61—24no—
85C2×D4×C61—24no—
86C2×D4×C61—24no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C2×D4×C61—42no—
90C2×D4×C61—44no—
91C2×D4×C61—44no—
92C2×D4×C61—44no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C22×C4×C61—42no—
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×C4×C61#4111yescharacteristic
104C2×C22⋊D61—21no—
105C2×C22⋊D61—21no—
106C2×C22⋊D61—22no—
107C2×C22⋊D61—41no—
108C2×C22⋊D61—44no—
109C2×C22⋊D61—44no—
110C2×C22⋊D61—82no—
111C22×Dic61—22no—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C22⋊C411yescharacteristic
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—42no—
118M16×C61—42no—
119M16×C61—42no—
120C2×C8×C61—22no—
121C2×C8×C61—41no—
122C22⋊Dic61—21no—
123C22⋊Dic61—21no—
124C22⋊Dic61—44no—
125C22⋊Dic61—44no—
126C22⋊Dic61—42no—
127C22⋊Dic61—82no—
128#11758198—21no—
129#11758198—21no—
130C4⋊Dic61—42no—
131#11758196—21no—
132#11758196—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135#11758194—42no—
136#11758194—42no—
137C2×#92418—22no—
138C2×#92418—41no—
139C8×D61—82no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61—24no—
143C23×C61—24no—
144C23×C61—24no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61—42no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61—42no—
153C23×C61—42no—
154C23×C61—42no—
155C23×C61—82no—
156C23×C61—82no—
157C23×C61—82no—
158C23×C61—82no—
159C23×C61—88no—
160C23×C61—88no—
161C23×C61C2×C22⋊C411yescharacteristic
162C23×C61C4×D411yescharacteristic
163C23×C61C4×D411yescharacteristic
164C22×D61—21no—
165C22×D61—21no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61#10012yescomplemented
169D4×C61—44no—
170D4×C61—44no—
171D4×C61—44no—
172D4×C61—44no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12311yescharacteristic
183C22⋊D61—42no—
184C22⋊D61—42no—
185C22⋊D61—88no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C4×D61—42no—
197C4×D61—81no—
198C8×C61—42no—
199C8×C61—81no—
200#92418—42no—
201#92418—81no—
202#9503—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—42no—
212C22×C61—42no—
213C22×C61—44no—
214C22×C61—44no—
215C22×C61—44no—
216C22×C61—82no—
217C22×C61—82no—
218C22×C61—84no—
219C22×C61—84no—
220C22×C61—84no—
221C22×C61—84no—
222C22×C61—82no—
223C22×C61—82no—
224C22×C61#38611yescharacteristic
225C22×C61C2×#10011yescharacteristic
226C22×C61#41311yescharacteristic
227C2×D61—22no—
228C2×D61—41no—
229C2×D61—41no—
230C2×D61—42no—
231C2×D61—81no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61B(4,𝔽2)12yes—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239Dic61—82no—
240#2973—611no—
241#2408—611no—
242#1783—611no—
243#1783D6111yescharacteristic, complemented
244#1465—611no—
245#1305—611no—
246#1305—611no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61—41no—
250C2×C61—41no—
251C2×C61—84no—
252C2×C61#188911yescharacteristic
253C2×C61#190011yescharacteristic
254C2×C61#191411yescharacteristic
255D61—42no—
256C23×D4C2×D6111yescharacteristic
257C2×#121—1221no—
258C2×#120—612no—
259C2×C4×D4—611no—
260#435—1222no—
261#435—1222no—
262#432—1221no—
263C2×#100—22no—
264C2×#100—1222no—
265#407—611no—
266#407—611no—
267#407C2×D6111yescharacteristic
268#407C2×D6111yescharacteristic
269C2×C22⋊C8—1221no—
270#394—1221no—
271#392—1221no—
272#390—1221no—
273#380—611no—
274#379—612no—
275#324—1221no—
276#323—1221no—
277C61#950311yescharacteristic, complemented, Sylow
278C25C4×D6112yes—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—44no—
286C22×D4—611no—
287C22×D4—1222no—
288C23×C4—611no—
289C23×C4C22×D6111yescharacteristic
290C2×M16—21no—
291C2×M16—612no—
292C2×M16—1221no—
293C2×M16C22⋊D6112yescomplemented
294C22×C8—1222no—
295#121—2444no—
296#120—2444no—
297C4×D4—1221no—
298C4×D4—1221no—
299C4×D4—1221no—
300C4×D4—1221no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—1221no—
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—612no—
306C2×C22⋊C4—1222no—
307C2×C22⋊C4—1222no—
308C2×C22⋊C4—1222no—
309C2×C42—611no—
310C4⋊C8—1222no—
311#100—44no—
312#100—2444no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—1222no—
318C22⋊C8—1221no—
319C22⋊C8—1221no—
320C22⋊C8—1221no—
321C22⋊C8—1221no—
322#97—1222no—
323#95—1221no—
324C24—22no—
325C24—22no—
326C24—22no—
327C24—44no—
328C24—42no—
329C24—42no—
330C24—82no—
331C24—611no—
332C24C2×C4×D6111yescharacteristic
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—1222no—
347C2×D4—1221no—
348C2×D4—1221no—
349C2×D4—4882no—
350C2×D4—2441no—
351C2×D4—2444no—
352C2×D4—2444no—
353C22×C4—42no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1222no—
360C22×C4—2442no—
361C22×C4#1175822211yescharacteristic
362C22×C4D4×D6111yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365C22×C4#1175822411yescharacteristic
366C22×C4C2×C22⋊D6111yescharacteristic
367M16—42no—
368M16—42no—
369M16—2442no—
370M16—2442no—
371C2×C8—22no—
372C2×C8—41no—
373C2×C8—1222no—
374C2×C8—4882no—
375C2×C8—2441no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—2442no—
379C22⋊C4—1221no—
380C22⋊C4—1221no—
381C22⋊C4—1221no—
382C22⋊C4—1221no—
383C22⋊C4—4882no—
384C22⋊C4—2444no—
385C22⋊C4—2444no—
386C22⋊C4—2442no—
387C42—1221no—
388C42—1221no—
389C23—21no—
390C23—21no—
391C23—24no—
392C23—24no—
393C23—24no—
394C23—41no—
395C23—41no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—82no—
405C23—82no—
406C23—82no—
407C23—82no—
408C23—88no—
409C23—88no—
410C23—612no—
411C23—1221no—
412C23—1221no—
413C23—2441no—
414C23—2441no—
415C23C22⋊C4×D6111yescharacteristic
416C23#1451973711yescharacteristic
417C23C4×C22⋊D6111yescharacteristic
418D4—44no—
419D4—44no—
420D4—44no—
421D4—44no—
422D4—4888no—
423D4—2442no—
424D4—2442no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—4881no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4#1451974511yescharacteristic
444C2×C4#1451974811yescharacteristic
445C2×C4#1451975011yescharacteristic
446C2×C4#1451975911yescharacteristic
447C8—42no—
448C8—81no—
449C8—4881no—
450C8—2442no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—42no—
460C22—42no—
461C22—44no—
462C22—44no—
463C22—44no—
464C22—82no—
465C22—82no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—84no—
470C22—82no—
471C22—82no—
472C22—1222no—
473C22—4881no—
474C22—2442no—
475C22—2441no—
476C22—2441no—
477C22#1683963811yescharacteristic
478C22#100×D6111yescharacteristic
479C22#1683974311yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—4882no—
484C4—2441no—
485C4—2441no—
486C4—2441no—
487C4#1683994812yes—
488C2—21no—
489C2—21no—
490C2—41no—
491C2—41no—
492C2—84no—
493C2—2442no—
494C2#2144622411yescharacteristic
495C2#2144627911yescharacteristic
496C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1783C2
socleC22×C61#386
prime radical#21449169C2
cosocleC23×C4×C61C23
hypercenter#1783D61
hypocenterC61#9503
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1783

Complements

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

NH ≅ G/Ntype
1. #21454846C2semidirect
3. #21445740C2semidirect
4. #21444155C2semidirect
5. #21443726C2semidirect
6. #21443724C2semidirect
7. C61×#1783C2semidirect
33. C2×#11758194D4semidirect
69. C2×M16×C61D4semidirect
168. C22×D61#100semidirect
243. #1783D61semidirect
277. C61#9503semidirect
293. C2×M16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214548462
#214491692
#214457402
#214441552
#214437262
#214437242
C61×#17832
#950361