Finite Group Databasebeta

← #29583159

Subgroups — #29583159

Order 15616.

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

normal subgroups only

This group has 508 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#21450831C211yesmaximal, characteristic, complemented
2#21446656C211yesmaximal, characteristic
3C2×#16839496C211yesmaximal, characteristic
4#21443699C211yesmaximal, characteristic, complemented
5#21443686C211yesmaximal, characteristic, complemented
6#21443666C211yesmaximal, characteristic, complemented
7C61×#1519C211yesmaximal, characteristic
8C2×#14519754—21no—
9C2×#14519692—21no—
10C2×#14519692—21no—
11C2×C22⋊#92418C2211yescharacteristic
12#16839695—21no—
13#16839682—21no—
14#16839666—21no—
15#16839659—21no—
16#16839634—21no—
17#16839622C2211yescharacteristic
18C4×C22⋊Dic61C2211yescharacteristic
19C2×#14519684C2211yescharacteristic
20#16839496—21no—
21#16839496—21no—
22C2×#121×C61C2211yescharacteristic
23C2×C22⋊C8×C61C2211yescharacteristic
24C61×#380C2211yescharacteristic
25C61×#327—21no—
26C61×#327—21no—
27C22×Dic122—21no—
28C23×Dic61—21no—
29C22×#92418—21no—
30#14519754—42no—
31#14519754—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61D411yescharacteristic
40C2×C22⋊Dic61D411yescharacteristic
41C2×C4×Dic61—21no—
42#14519692—42no—
43#14519692—42no—
44C22⋊#92418—21no—
45C22⋊#92418—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684D411yescharacteristic
52#14519684D411yescharacteristic
53C22×D4×C61—21no—
54C22×D4×C61Q811yescharacteristic, complemented
55C23×C4×C61C2311yescharacteristic
56C22×C8×C61—21no—
57#121×C61—21no—
58#121×C61—21no—
59#121×C61—21no—
60#121×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61Q811yescharacteristic, complemented
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67#95×C61D411yescharacteristic
68#95×C61D411yescharacteristic
69C24×C61—21no—
70C24×C61C2×D411yescharacteristic
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—81no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—81no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×Q811yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—42no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61—81no—
99C2×Dic122—42no—
100C2×Dic122—42no—
101C2×Dic122—81no—
102C2×C8×C61—41no—
103C2×C8×C61—81no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—81no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊Dic61—21no—
112C22⋊Dic61—21no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115C22⋊Dic61D812yes—
116C22⋊Dic61SD1612yes—
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—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—81no—
132C23×C61—81no—
133C23×C61#12011yescharacteristic
134C23×C61C22⋊Q811yescharacteristic
135C23×C61#12411yescharacteristic
136C23×C61C2×D811yescharacteristic
137C23×C61C2×SD1611yescharacteristic
138C23×C61AGL(1,ℤ/8)11yescharacteristic
139C23×C61#13711yescharacteristic
140D4×C61—81no—
141D4×C61—81no—
142D4×C61—81no—
143D4×C61—81no—
144D4×C61—81no—
145D4×C61—81no—
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—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61C22⋊Q811yescharacteristic
162C2×C4×C61C22⋊Q811yescharacteristic
163C2×C4×C61#12411yescharacteristic
164C2×C4×C61#12411yescharacteristic
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61—22no—
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—82no—
178C2×Dic61—82no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61—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—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—161no—
200C22×C61—161no—
201C22×C61#39311yescharacteristic
202C22×C61#44711yescharacteristic
203C22×C61#44811yescharacteristic
204C22×C61#47411yescharacteristic
205C22×C61#47611yescharacteristic
206C22×C61#48611yescharacteristic
207C22×C61#48911yescharacteristic
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—81no—
213C4×C61—81no—
214C4×C61—81no—
215Dic61—42no—
216Dic61—42no—
217Dic61—42no—
218Dic61—81no—
219Dic61—161no—
220#2549—611no—
221#1964—611no—
222#1519D6111yescharacteristic
223C2×#327—611no—
224#1294—611no—
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—161no—
234C2×C61#202311yescharacteristic
235C2×C61#203111yescharacteristic
236C2×C61#203211yescharacteristic
237C2×C22⋊Q8—1221no—
238C2×#121C2×D6111yescharacteristic
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×#95—611no—
252#327—21no—
253#327—21no—
254#327—1221no—
255#327—1221no—
256C61#1037411yescharacteristic, complemented, Sylow
257C22×Q8—1221no—
258C22×D4—21no—
259C22×D4Dic12211yescharacteristic, complemented
260C23×C4—1221no—
261C23×C4C22×D6111yescharacteristic
262C22×C8—21no—
263C22×C8—1221no—
264C22⋊Q8—2442no—
265C22⋊Q8—2442no—
266#121—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4Dic12211yescharacteristic, complemented
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
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—611no—
291#95—611no—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297#95C22⋊D6111yescharacteristic
298#95C22⋊D6111yescharacteristic
299C24—21no—
300C24D4×D6111yescharacteristic
301C2×Q8—4881no—
302C2×Q8—2442no—
303C2×Q8—2442no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—81no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—81no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—4881no—
322C22×C4—2442no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4—2441no—
326C22×C4C2×Dic12211yescharacteristic
327C22×C4#1175822211yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C22×C4#1175822411yescharacteristic
330C22×C4#1175822411yescharacteristic
331C22×C4C2×C22⋊D6111yescharacteristic
332C2×C8—41no—
333C2×C8—81no—
334C2×C8—4881no—
335C2×C8—2441no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—81no—
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—41no—
348C22⋊C4—41no—
349C22⋊C4—612no—
350C22⋊C4—612no—
351C22⋊C4—1221no—
352C22⋊C4—1221no—
353C22⋊C4—2441no—
354C22⋊C4—2441no—
355C42—4881no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—81no—
362C23—81no—
363C23#1451974511yescharacteristic
364C23#1451975411yescharacteristic
365C23#1451976311yescharacteristic
366C23D8×D6111yescharacteristic
367C23SD16×D6111yescharacteristic
368C23#1451980111yescharacteristic
369C23#1451980611yescharacteristic
370Q8—4884no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—41no—
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—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—1222no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—4881no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—4882no—
399C2×C4—4882no—
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#1451975411yescharacteristic
410C2×C4#1451975611yescharacteristic
411C2×C4#1451976311yescharacteristic
412C2×C4#1451976411yescharacteristic
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—81no—
426C22—81no—
427C22—81no—
428C22—161no—
429C22—161no—
430C22#1683967411yescharacteristic
431C22#1683989411yescharacteristic
432C22#1683989911yescharacteristic
433C22#1684004011yescharacteristic
434C22#1684005011yescharacteristic
435C22#1684010711yescharacteristic
436C22#1684012011yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—9761no—
445C4—4881no—
446C4—2442no—
447C4—2442no—
448C4—2442no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—161no—
456C2#2144695311yescharacteristic
457C2#2144698911yescharacteristic
458C2#2144699611yescharacteristic
subgroupG/H
centerC22#16839674
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1519C2
socleC22×C61#393
prime radicalC2×#121×C61C22
hypercenter#1519D61
hypocenterC61#10374
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
1. #21450831C2semidirect
4. #21443699C2semidirect
5. #21443686C2semidirect
6. #21443666C2semidirect
54. C22×D4×C61Q8semidirect
62. C2×C4⋊C4×C61Q8semidirect
256. C61#10374semidirect
259. C22×D4Dic122semidirect
277. C2×C4⋊C4Dic122semidirect

Maximal subgroups

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

subgroupindex
#214508312
#214466562
C2×#168394962
#214436992
#214436862
#214436662
C61×#15192
#1037461