Finite Group Databasebeta

← #29583162

Subgroups — #29583162

Order 15616.

508 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 97 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#21450825C211yesmaximal, characteristic, complemented
2#21446655C211yesmaximal, characteristic
3#21444388C211yesmaximal, characteristic
4C2×#16839497C211yesmaximal, characteristic
5#21443699C211yesmaximal, characteristic, complemented
6#21443687C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C2×#14519754—21no—
9C2×#14519751C2211yescharacteristic
10C2×#14519691—21no—
11C2×#14519691—21no—
12#16839694—21no—
13#16839683—21no—
14#16839668—21no—
15#16839660—21no—
16#16839637—21no—
17#16839622C2211yescharacteristic
18#16839622C2211yescharacteristic
19C2×#14519684C2211yescharacteristic
20#16839497—21no—
21#16839497—21no—
22#16839497—21no—
23#16839497—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244Q811yescharacteristic, complemented
29C22×C22⋊D61—21no—
30C23×Dic61—21no—
31#14519754—42no—
32#14519754—42no—
33#14519751—21no—
34#14519751—21no—
35#14519751—21no—
36#14519751—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61Q811yescharacteristic, complemented
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48#14519691—42no—
49#14519691—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684D411yescharacteristic
55#14519684D411yescharacteristic
56#14519684D411yescharacteristic
57#14519684D411yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C2×C22⋊C4×C61D411yescharacteristic
62C2×C22⋊C4×C61D411yescharacteristic
63C2×C42×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68#95×C61—21no—
69C24×C61C2×D411yescharacteristic
70C23×D61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—81no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×Q811yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—42no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61—81no—
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—41no—
104C2×C8×C61—81no—
105C2×C8×C61—81no—
106C22⋊C4×C61—21no—
107C22⋊C4×C61—21no—
108C22⋊C4×C61D812yes—
109C22⋊C4×C61SD1612yes—
110C42×C61—81no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—42no—
120C4⋊Dic61—42no—
121C4⋊Dic61—81no—
122C4⋊Dic61—81no—
123C4⋊Dic61—81no—
124#11758196—42no—
125#11758196—42no—
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—22no—
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×C61C22⋊Q811yescharacteristic
153C2×C4×C61C22⋊Q811yescharacteristic
154C2×C4×C61#12411yescharacteristic
155C2×C4×C61#12411yescharacteristic
156C22⋊D61—81no—
157C22⋊D61—81no—
158C22⋊D61—81no—
159C22⋊D61—81no—
160C2×Dic61—22no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
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—82no—
176C2×Dic61—82no—
177C2×Dic61—81no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180D244—81no—
181D244—81no—
182Dic122—84no—
183C8×C61—81no—
184C8×C61—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—42no—
214Dic61—42no—
215Dic61—81no—
216Dic61—81no—
217Dic61—81no—
218Dic61—81no—
219Dic61—161no—
220#2549—611no—
221#1964—611no—
222#1519—611no—
223C2×#327—611no—
224#1294—611no—
225#1289—611no—
226#1282D6111yescharacteristic, complemented
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⋊C8C2×D6111yescharacteristic
242C2×C22⋊C8C2×D6111yescharacteristic
243#398—1221no—
244#395—1221no—
245#391—1221no—
246#389—1221no—
247#385—1221no—
248#380—611no—
249#380—611no—
250C4×C22⋊C4C2×D6111yescharacteristic
251C2×#95—611no—
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—1221no—
261C23×C4C22×D6111yescharacteristic
262C22×C8—21no—
263C22×C8—21no—
264C22⋊Q8—2442no—
265C22⋊Q8—2442no—
266#121—1221no—
267#121—1221no—
268#121—1221no—
269#121—1221no—
270C2×C4⋊C4—611no—
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⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4D24411yescharacteristic
282C2×C22⋊C4D24411yescharacteristic
283C2×C42—21no—
284#99—2442no—
285#99—2442no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290#95—21no—
291#95—611no—
292#95—611no—
293#95—611no—
294#95—611no—
295#95—1221no—
296#95—1221no—
297#95—1221no—
298#95—1221no—
299C24—1221no—
300C24C2×D24411yescharacteristic
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—81no—
316C22×C4—1221no—
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×C4#1175822211yescharacteristic
327C22×C4#1175822211yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C22×C4D4×D6111yescharacteristic
330C22×C4#1175822411yescharacteristic
331C22×C4Q8×D6111yescharacteristic
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—81no—
335C2×C8—81no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—4881no—
339C4⋊C4—4881no—
340C4⋊C4—4881no—
341C4⋊C4—2442no—
342C4⋊C4—2442no—
343C4⋊C4—2442no—
344C4⋊C4—2442no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C22⋊C4#1175819012yes—
354C22⋊C4D48812yes—
355C42—81no—
356C23—41no—
357C23—41no—
358C23—4881no—
359C23—4881no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23#1451974711yescharacteristic
364C23#1451975711yescharacteristic
365C23#1451976511yescharacteristic
366C23C2×D48811yescharacteristic
367C23C2×#1175819011yescharacteristic
368C23#1451980511yescharacteristic
369C23#1451981011yescharacteristic
370Q8—4884no—
371D4—4881no—
372D4—4881no—
373D4—4881no—
374D4—4881no—
375D4—4881no—
376D4—4881no—
377C2×C4—22no—
378C2×C4—22no—
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—1222no—
390C2×C4—4881no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4882no—
394C2×C4—4882no—
395C2×C4—2441no—
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#1451975511yescharacteristic
411C2×C4#1451976311yescharacteristic
412C2×C4#1451976311yescharacteristic
413C8—81no—
414C8—81no—
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#1683989811yescharacteristic
432C22#1683990311yescharacteristic
433C22#1684004311yescharacteristic
434C22#1684005311yescharacteristic
435C22#1684010911yescharacteristic
436C22#1684012211yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—9761no—
444C4—4881no—
445C4—4881no—
446C4—4881no—
447C4—4881no—
448C4—2442no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—9761no—
456C2#2144695611yescharacteristic
457C2#2144699411yescharacteristic
458C2#2144699711yescharacteristic
subgroupG/H
centerC22#16839675
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61#393
prime radicalC2×#14519751C22
hypercenter#1282D61
hypocenterC61#10374
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
1. #21450825C2semidirect
5. #21443699C2semidirect
6. #21443687C2semidirect
7. C61×#1282C2semidirect
28. C22×D244Q8semidirect
42. C2×C4⋊Dic61Q8semidirect
226. #1282D61semidirect
256. C61#10374semidirect

Maximal subgroups

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

subgroupindex
#214508252
#214466552
#214443882
C2×#168394972
#214436992
#214436872
C61×#12822
#1037461