Finite Group Databasebeta

← #29577829

Subgroups — #29577829

Order 15616.

838 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 93 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#21449134C211yesmaximal, characteristic
2#21448414C211yesmaximal, characteristic, complemented
3#21445763C211yesmaximal, characteristic, complemented
4#21444145C211yesmaximal, characteristic, complemented
5#21443673C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1789C211yesmaximal, characteristic, complemented
8C2×#14519745—21no—
9C22×#11758198C2211yescharacteristic
10C2×#14519704—22no—
11#16839726C2211yescharacteristic
12#16839673C412yescomplemented
13#16839670C412yescomplemented
14#16839653—22no—
15#16839651—22no—
16#16839642—21no—
17#16839641—22no—
18#16839625C2211yescharacteristic
19#16839620—21no—
20#16839617—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839485—22no—
23C22×#41×C61C2211yescharacteristic
24C2×#104×C61—22no—
25C61×#407C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×C22⋊D61—22no—
29C23×Dic61D411yescharacteristic
30C2×#11758194—21no—
31#14519745—44no—
32C2×#11758196—22no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—22no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198—22no—
43C2×#11758198C2×C412yes—
44C2×#11758198D412yes—
45C2×C4×Dic61D412yescomplemented
46#14519704—44no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49#14519684—22no—
50#14519684—21no—
51#14519684—21no—
52#14519684—22no—
53#14519684C2×C412yes—
54C2×#41×C61—21no—
55C2×#41×C61—21no—
56C2×#41×C61—21no—
57C2×#41×C61—21no—
58C2×#41×C61—44no—
59C22×Q8×C61C2×C411yescharacteristic
60C22×D4×C61—21no—
61C22×D4×C61C2×C411yescharacteristic
62C23×C4×C61—21no—
63C23×C4×C61C2311yescharacteristic
64C2×M16×C61—21no—
65C2×C22⋊C4×C61—21no—
66C2×C42×C61D412yescomplemented
67#104×C61—44no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70#95×C61—21no—
71C24×C61—21no—
72C24×C61C2×D411yescharacteristic
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—42no—
76C23×D61—42no—
77C23×D61—81no—
78C23×D61C22⋊C412yes—
79#41×C61—24no—
80#41×C61—24no—
81#41×C61—42no—
82#41×C61—42no—
83#41×C61—42no—
84#41×C61—42no—
85#41×C61—42no—
86#41×C61—42no—
87C2×Q8×C61—21no—
88C2×Q8×C61—21no—
89C2×Q8×C61—42no—
90C2×D4×C61—24no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—42no—
94C2×D4×C61—42no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C22×C4×C61—21no—
98C22×C4×C61—22no—
99C22×C4×C61—42no—
100C22×C4×C61—42no—
101C22×C4×C61—42no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61C22×C411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C2×C22⋊D61—44no—
111C2×C22⋊D61—44no—
112C2×C22⋊D61—82no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—81no—
118C22×Dic61C22⋊C412yes—
119M16×C61—42no—
120C2×C8×C61—41no—
121C22⋊C4×C61—42no—
122C42×C61—42no—
123C22⋊Dic61—42no—
124C22⋊Dic61—42no—
125C22⋊Dic61—82no—
126#11758198—22no—
127#11758198—22no—
128#11758198—22no—
129#11758198—22no—
130#11758198—44no—
131#11758198—82no—
132#11758198—82no—
133#11758196—82no—
134C4×Dic61—42no—
135#11758194—42no—
136C2×#92418—41no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61—41no—
141C23×C61—42no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—42no—
145C23×C61C2×C22⋊C411yescharacteristic
146C23×C61#12011yescharacteristic
147C23×C61#12311yescharacteristic
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—42no—
152C22×D61—42no—
153C22×D61—42no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—42no—
157C22×D61—81no—
158C22×D61—81no—
159C22×D61—88no—
160Q8×C61—22no—
161Q8×C61—22no—
162Q8×C61—41no—
163Q8×C61—41no—
164D4×C61—22no—
165D4×C61—22no—
166D4×C61—41no—
167D4×C61—41no—
168D4×C61—44no—
169D4×C61—44no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—44no—
178C2×C4×C61—44no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61C4×D411yescharacteristic
185C2×C4×C61C4×D411yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C22⋊D61—88no—
189C2×Dic61—22no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—81no—
199C8×C61—81no—
200#92418—81no—
201#9479—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—44no—
210C22×C61—44no—
211C22×C61—42no—
212C22×C61—82no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#38611yescharacteristic
216C22×C61#42112yes—
217C22×C61B(4,𝔽2)12yes—
218C2×D61—44no—
219C2×D61—42no—
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—84no—
223C2×D61—84no—
224C2×D61—82no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—42no—
230C4×C61—82no—
231Dic61—42no—
232Dic61—82no—
233Dic61—82no—
234#2404—611no—
235#2312—611no—
236#1789—611no—
237#1789D6111yescharacteristic, complemented
238#1462—611no—
239#1284—611no—
240#1284—611no—
241C2×C61—22no—
242C2×C61—22no—
243C2×C61—41no—
244C2×C61—82no—
245C2×C61#188911yescharacteristic
246C2×C61#189711yescharacteristic
247C2×C61#191111yescharacteristic
248D61—82no—
249C22×#41C2×D6111yescharacteristic
250C2×#120—1221no—
251C22×C22⋊C4—611no—
252C2×#104—22no—
253C2×#104—1222no—
254#407—611no—
255#407C2×D6111yescharacteristic
256#393—612no—
257#392—612no—
258#388—1222no—
259#388—1222no—
260#386—1222no—
261#386—1221no—
262#381—611no—
263#380—1221no—
264#379—1221no—
265C4×C22⋊C4—611no—
266C4×C22⋊C4C2×D6111yescharacteristic
267#323—1222no—
268C61#947911yescharacteristic, complemented, Sylow
269C25—611no—
270C2×#41—21no—
271C2×#41—21no—
272C2×#41—21no—
273C2×#41—21no—
274C2×#41—44no—
275C22×Q8C4×D6111yescharacteristic
276C22×D4—21no—
277C22×D4—1222no—
278C22×D4C4×D6111yescharacteristic
279C23×C4—21no—
280C23×C4—611no—
281C23×C4C22×D6111yescharacteristic
282C2×M16—21no—
283C2×M16—1221no—
284#120—2444no—
285C2×C4⋊C4—1222no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—612no—
288C2×C22⋊C4—612no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1222no—
294C2×C22⋊C4—1222no—
295C2×C22⋊C4—1222no—
296C2×C22⋊C4—1222no—
297C2×C22⋊C4—1221no—
298C2×C22⋊C4—1221no—
299C2×C42—612no—
300C2×C42C22⋊D6112yescomplemented
301#104—44no—
302#104—2444no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—1221no—
306C22⋊C8—1221no—
307#95—21no—
308#95—612no—
309#95—1222no—
310#95—1222no—
311#95—1221no—
312#95—1221no—
313C24—21no—
314C24—612no—
315C24—1221no—
316C24—1221no—
317C24—4881no—
318C24—2442no—
319C24—2442no—
320C24D4×D6111yescharacteristic
321#41—24no—
322#41—24no—
323#41—42no—
324#41—42no—
325#41—42no—
326#41—42no—
327#41—42no—
328#41—42no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—42no—
332C2×D4—24no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—4882no—
340C2×D4—2444no—
341C2×D4—2444no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—612no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—4881no—
355C22×C4C2×C4×D6111yescharacteristic
356C22×C4#1175822211yescharacteristic
357C22×C4D4×D6111yescharacteristic
358C22×C4D4×D6111yescharacteristic
359C22×C4#1175822411yescharacteristic
360C22×C4C2×C22⋊D6111yescharacteristic
361M16—42no—
362M16—2442no—
363C2×C8—41no—
364C2×C8—2441no—
365C4⋊C4—4882no—
366C22⋊C4—42no—
367C22⋊C4—1222no—
368C22⋊C4—1222no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C22⋊C4—4882no—
372C22⋊C4—4882no—
373C22⋊C4—4882no—
374C22⋊C4—2444no—
375C22⋊C4—2442no—
376C22⋊C4—2442no—
377C42—42no—
378C42—2442no—
379C23—22no—
380C23—22no—
381C23—22no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—1222no—
388C23—1222no—
389C23—1222no—
390C23—4881no—
391C23—4881no—
392C23—4888no—
393C23—2442no—
394C23—2442no—
395C23—2442no—
396C23—2442no—
397C23—2442no—
398C23—2442no—
399C23C22⋊C4×D6111yescharacteristic
400C23#1451974511yescharacteristic
401C23#1451975911yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—41no—
405Q8—41no—
406D4—22no—
407D4—22no—
408D4—41no—
409D4—41no—
410D4—44no—
411D4—44no—
412D4—4888no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—1222no—
428C2×C4—4881no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4#1451973711yescharacteristic
438C2×C4C4×C22⋊D6111yescharacteristic
439C2×C4#1451974811yescharacteristic
440C2×C4#1451975011yescharacteristic
441C8—81no—
442C8—4881no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—44no—
451C22—44no—
452C22—42no—
453C22—82no—
454C22—81no—
455C22—81no—
456C22—4882no—
457C22—4884no—
458C22—4884no—
459C22—2444no—
460C22—2442no—
461C22—2442no—
462C22—2442no—
463C22#1683963811yescharacteristic
464C22#1683977712yes—
465C22#1683994812yes—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—42no—
471C4—82no—
472C4—4882no—
473C4—4882no—
474C4—2442no—
475C2—22no—
476C2—22no—
477C2—41no—
478C2—82no—
479C2—4882no—
480C2#2144622411yescharacteristic
481C2#2144626411yescharacteristic
482C2#2144634811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1789C2
socleC22×C61#386
prime radical#21449134C2
cosocleC23×C4×C61C23
hypercenter#1789D61
hypocenterC61#9479
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #21448414C2semidirect
3. #21445763C2semidirect
4. #21444145C2semidirect
5. #21443673C2semidirect
6. #21443672C2semidirect
7. C61×#1789C2semidirect
12. #16839673C4semidirect
13. #16839670C4semidirect
45. C2×C4×Dic61D4semidirect
66. C2×C42×C61D4semidirect
237. #1789D61semidirect
268. C61#9479semidirect
300. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214491342
#214484142
#214457632
#214441452
#214436732
#214436722
C61×#17892
#947961