Finite Group Databasebeta

← #29583164

Subgroups — #29583164

Order 15616.

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

normal subgroups only

This group has 508 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#21450830C211yesmaximal, characteristic, complemented
2#21446654C211yesmaximal, characteristic
3#21444388C211yesmaximal, characteristic
4C2×#16839495C211yesmaximal, characteristic
5#21443686C211yesmaximal, characteristic, complemented
6#21443666C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C2×#14519756—21no—
9C2×#14519751C2211yescharacteristic
10C2×#14519691—21no—
11C2×#14519691—21no—
12C2×C22⋊#92418C2211yescharacteristic
13#16839696—21no—
14#16839683—21no—
15#16839666—21no—
16#16839659—21no—
17#16839635—21no—
18#16839622C2211yescharacteristic
19C4×C22⋊Dic61C2211yescharacteristic
20#16839497—21no—
21#16839497—21no—
22#16839495—21no—
23#16839495—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244Q811yescharacteristic, complemented
29C22×C22⋊D61—21no—
30C22×#92418—21no—
31#14519756—42no—
32#14519756—42no—
33#14519751—21no—
34#14519751—21no—
35#14519751—21no—
36#14519751—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61Q811yescharacteristic, complemented
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61D411yescharacteristic
46C2×C22⋊Dic61D411yescharacteristic
47C2×#11758198—21no—
48C2×C4×Dic61—21no—
49#14519691—42no—
50#14519691—42no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684D411yescharacteristic
57#14519684D411yescharacteristic
58C23×C4×C61—21no—
59C23×C4×C61C2311yescharacteristic
60C22×C8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65#95×C61—21no—
66#95×C61—21no—
67#95×C61D411yescharacteristic
68#95×C61D411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C23×D61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—42no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61—81no—
78C22×C4×C61—81no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×Q811yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—81no—
99C2×Dic122—42no—
100C2×Dic122—42no—
101C2×Dic122—81no—
102C2×C8×C61—41no—
103C2×C8×C61—81no—
104C4⋊C4×C61—81no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊Dic61—21no—
108C22⋊Dic61—21no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111C22⋊Dic61D812yes—
112C22⋊Dic61SD1612yes—
113#11758198—41no—
114#11758198—41no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—42no—
118C4⋊Dic61—81no—
119#11758196—42no—
120#11758196—42no—
121#11758196—42no—
122#11758196—81no—
123C4×Dic61—81no—
124C2×#92418—41no—
125C2×#92418—81no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61#12011yescharacteristic
129C23×C61C22⋊Q811yescharacteristic
130C23×C61#12411yescharacteristic
131C23×C61C2×D811yescharacteristic
132C23×C61C2×SD1611yescharacteristic
133C23×C61AGL(1,ℤ/8)11yescharacteristic
134C23×C61#13711yescharacteristic
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—81no—
139C22×D61—81no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—82no—
153C2×C4×C61—82no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61C22⋊Q811yescharacteristic
158C2×C4×C61C22⋊Q811yescharacteristic
159C2×C4×C61#12411yescharacteristic
160C2×C4×C61#12411yescharacteristic
161C22⋊D61—81no—
162C22⋊D61—81no—
163C22⋊D61—81no—
164C22⋊D61—81no—
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180D244—81no—
181D244—81no—
182Dic122—84no—
183C8×C61—81no—
184#92418—81no—
185#10374—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61#39311yescharacteristic
197C22×C61#44711yescharacteristic
198C22×C61#44811yescharacteristic
199C22×C61#47411yescharacteristic
200C22×C61#47611yescharacteristic
201C22×C61#48611yescharacteristic
202C22×C61#48911yescharacteristic
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—161no—
207C2×D61—161no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—42no—
213C4×C61—81no—
214C4×C61—161no—
215Dic61—42no—
216Dic61—42no—
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220#2549—611no—
221#1964—611no—
222#1519—611no—
223C2×#327—611no—
224#1294D6111yescharacteristic, complemented
225#1289—611no—
226#1282—611no—
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—21no—
233C2×C61#202311yescharacteristic
234C2×C61#203111yescharacteristic
235C2×C61#203211yescharacteristic
236D61—161no—
237C2×C22⋊Q8—1221no—
238C2×#121—611no—
239C2×#99—1221no—
240C2×#99—1221no—
241C2×C22⋊C8—611no—
242C2×C22⋊C8C2×D6111yescharacteristic
243#398—1221no—
244#395—1221no—
245#391—1221no—
246#389—1221no—
247#385—1221no—
248#380—611no—
249#380C2×D6111yescharacteristic
250C4×C22⋊C4—611no—
251C2×#95C2×D6111yescharacteristic
252#327—1221no—
253#327—1221no—
254#327—1221no—
255#327—1221no—
256C61#1037411yescharacteristic, complemented, Sylow
257C22×Q8—1221no—
258C22×D4—611no—
259C22×D4—1221no—
260C23×C4—21no—
261C23×C4C22×D6111yescharacteristic
262C22×C8—21no—
263C22×C8—1221no—
264C22⋊Q8—2442no—
265C22⋊Q8—2442no—
266#121—1221no—
267#121—1221no—
268#121—1221no—
269#121—1221no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C42—1221no—
284#99—2442no—
285#99—2442no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—1221no—
289C22⋊C8—1221no—
290#95—21no—
291#95—21no—
292#95—611no—
293#95—611no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297#95D24411yescharacteristic
298#95D24411yescharacteristic
299C24—1221no—
300C24D4×D6111yescharacteristic
301C2×Q8—4881no—
302C2×Q8—2442no—
303C2×Q8—2442no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—4881no—
307C2×D4—2441no—
308C2×D4—2441no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—81no—
320C22×C4—81no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4C2×D24411yescharacteristic
327C22×C4#1175822211yescharacteristic
328C22×C4#1175822211yescharacteristic
329C22×C4D4×D6111yescharacteristic
330C22×C4#1175822411yescharacteristic
331C22×C4Q8×D6111yescharacteristic
332C2×C8—41no—
333C2×C8—81no—
334C2×C8—4881no—
335C2×C8—2441no—
336C4⋊C4—81no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C4⋊C4—4881no—
340C4⋊C4—4881no—
341C4⋊C4—2442no—
342C4⋊C4—2442no—
343C4⋊C4—2442no—
344C4⋊C4—2442no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—612no—
348C22⋊C4—612no—
349C22⋊C4—1221no—
350C22⋊C4—1221no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C22⋊C4—2441no—
355C42—4881no—
356C23—41no—
357C23—41no—
358C23—4881no—
359C23—4881no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23#1451974711yescharacteristic
364C23#1451975511yescharacteristic
365C23#1451976311yescharacteristic
366C23D8×D6111yescharacteristic
367C23SD16×D6111yescharacteristic
368C23#1451980411yescharacteristic
369C23#1451980911yescharacteristic
370Q8—4884no—
371D4—4881no—
372D4—4881no—
373D4—4881no—
374D4—4881no—
375D4—4881no—
376D4—4881no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4#1451975511yescharacteristic
410C2×C4#1451975711yescharacteristic
411C2×C4#1451976311yescharacteristic
412C2×C4#1451976511yescharacteristic
413C8—81no—
414C8—4881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—9761no—
426C22—9761no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22#1683967511yescharacteristic
431C22#1683989711yescharacteristic
432C22#1683990211yescharacteristic
433C22#1684004111yescharacteristic
434C22#1684005111yescharacteristic
435C22#1684010711yescharacteristic
436C22#1684012311yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—81no—
443C4—161no—
444C4—4881no—
445C4—4881no—
446C4—4881no—
447C4—2442no—
448C4—2442no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—9761no—
456C2#2144695411yescharacteristic
457C2#2144699211yescharacteristic
458C2#2144699711yescharacteristic
subgroupG/H
centerC22#16839675
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC22×C61#393
prime radicalC2×#14519751C22
hypercenter#1294D61
hypocenterC61#10374
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
1. #21450830C2semidirect
5. #21443686C2semidirect
6. #21443666C2semidirect
7. C61×#1294C2semidirect
28. C22×D244Q8semidirect
39. C2×C4⋊Dic61Q8semidirect
224. #1294D61semidirect
256. C61#10374semidirect

Maximal subgroups

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

subgroupindex
#214508302
#214466542
#214443882
C2×#168394952
#214436862
#214436662
C61×#12942
#1037461