Finite Group Databasebeta

← #29583158

Subgroups — #29583158

Order 15616.

508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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#21446655C211yesmaximal, characteristic
2#21444386C211yesmaximal, characteristic
3C2×#16839495C211yesmaximal, characteristic
4#21443698C211yesmaximal, characteristic, complemented
5#21443686C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#2549C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519691—21no—
10C2×#14519691—21no—
11C2×C22⋊#92418C2211yescharacteristic
12C2×C22⋊#92418C2211yescharacteristic
13#16839622C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839495—21no—
17#16839495—21no—
18C2×C22⋊Q8×C61—21no—
19C61×#398—21no—
20C61×#395—21no—
21C61×#391—21no—
22C61×#389—21no—
23C61×#385—21no—
24C61×#380C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×D244Q811yescharacteristic, complemented
28C22×C22⋊D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519751—21no—
32#14519751—21no—
33#14519751—21no—
34#14519751—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61Q811yescharacteristic, complemented
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39#14519691—42no—
40#14519691—42no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22⋊#92418—21no—
45#14519684—21no—
46C22×Q8×C61—21no—
47C23×C4×C61—21no—
48C23×C4×C61C2311yescharacteristic
49C22⋊Q8×C61—42no—
50C22⋊Q8×C61—42no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61D411yescharacteristic
60C2×C42×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61—21no—
64#95×C61—21no—
65#95×C61D411yescharacteristic
66#95×C61D411yescharacteristic
67#95×C61D411yescharacteristic
68#95×C61D411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C23×D61—21no—
71C2×Q8×C61—42no—
72C2×Q8×C61—42no—
73C2×Q8×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—42no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—81no—
84C22×C4×C61—81no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×Q811yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C22×Dic61—21no—
98C22×Dic61—41no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—81no—
102C4⋊C4×C61—42no—
103C4⋊C4×C61—42no—
104C4⋊C4×C61—42no—
105C4⋊C4×C61—42no—
106C4⋊C4×C61—81no—
107C4⋊C4×C61—81no—
108C22⋊C4×C61—21no—
109C22⋊C4×C61—21no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61D812yes—
113C22⋊C4×C61SD1612yes—
114C42×C61—81no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117#11758198—41no—
118#11758198—41no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—81no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—81no—
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—
140Q8×C61—84no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
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—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×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—82no—
166C2×C4×C61—82no—
167C2×C4×C61C22⋊Q811yescharacteristic
168C2×C4×C61C22⋊Q811yescharacteristic
169C2×C4×C61#12411yescharacteristic
170C2×C4×C61#12411yescharacteristic
171C22⋊D61—81no—
172C22⋊D61—81no—
173C22⋊D61—81no—
174C22⋊D61—81no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181D244—81no—
182D244—81no—
183#92418—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—42no—
214C4×C61—42no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—81no—
218Dic61—81no—
219Dic61—161no—
220#2549D6111yescharacteristic, complemented
221#1964—611no—
222#1519—611no—
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#202311yescharacteristic
234C2×C61#203111yescharacteristic
235C2×C61#203211yescharacteristic
236D61—161no—
237C2×C22⋊Q8—21no—
238C2×#121—611no—
239C2×#99—1221no—
240C2×#99—1221no—
241C2×C22⋊C8—611no—
242C2×C22⋊C8—611no—
243#398—21no—
244#395—21no—
245#391—21no—
246#389—21no—
247#385—21no—
248#380—611no—
249#380C2×D6111yescharacteristic
250C4×C22⋊C4C2×D6111yescharacteristic
251C2×#95C2×D6111yescharacteristic
252#327—1221no—
253#327—1221no—
254#327—1221no—
255#327—1221no—
256C61#1037411yescharacteristic, complemented, Sylow
257C22×Q8—21no—
258C22×D4—611no—
259C22×D4—1221no—
260C23×C4—21no—
261C23×C4C22×D6111yescharacteristic
262C22×C8—1221no—
263C22×C8—1221no—
264C22⋊Q8—42no—
265C22⋊Q8—42no—
266#121—1221no—
267#121—1221no—
268#121—1221no—
269#121—1221no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4C22⋊D6111yescharacteristic
282C2×C22⋊C4C22⋊D6111yescharacteristic
283C2×C42—21no—
284#99—2442no—
285#99—2442no—
286C22⋊C8—1221no—
287C22⋊C8—1221no—
288C22⋊C8—1221no—
289C22⋊C8—1221no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—1221no—
295#95C22⋊D6111yescharacteristic
296#95C22⋊D6111yescharacteristic
297#95C22⋊D6111yescharacteristic
298#95C22⋊D6111yescharacteristic
299C24—1221no—
300C24C2×C22⋊D6111yescharacteristic
301C2×Q8—42no—
302C2×Q8—42no—
303C2×Q8—81no—
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—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—81no—
323C22×C4—81no—
324C22×C4—1221no—
325C22×C4—2441no—
326C22×C4Q8×D6111yescharacteristic
327C22×C4#1175822611yescharacteristic
328C22×C4#1175822611yescharacteristic
329C22×C4#1175822611yescharacteristic
330C22×C4C2×C22⋊D6111yescharacteristic
331C22×C4C2×C22⋊D6111yescharacteristic
332C2×C8—4881no—
333C2×C8—4881no—
334C2×C8—2441no—
335C2×C8—2441no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—81no—
341C4⋊C4—81no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—4881no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C22⋊C4#1175819912yes—
354C22⋊C4#1175820112yes—
355C42—81no—
356C23—41no—
357C23—41no—
358C23—4881no—
359C23—4881no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23#1451974611yescharacteristic
364C23#1451975311yescharacteristic
365C23#1451976611yescharacteristic
366C23C2×#1175819911yescharacteristic
367C23C2×#1175820111yescharacteristic
368C23#1451980311yescharacteristic
369C23#1451980811yescharacteristic
370Q8—84no—
371D4—4881no—
372D4—4881no—
373D4—4881no—
374D4—4881no—
375D4—4881no—
376D4—4881no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
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—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—4881no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4#1451975311yescharacteristic
410C2×C4#1451975311yescharacteristic
411C2×C4#1451976611yescharacteristic
412C2×C4#1451976611yescharacteristic
413C8—4881no—
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#1683967311yescharacteristic
431C22#1683989611yescharacteristic
432C22#1683990111yescharacteristic
433C22#1684003911yescharacteristic
434C22#1684004911yescharacteristic
435C22#1684011011yescharacteristic
436C22#1684012411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—9761no—
448C4—4881no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—9761no—
456C2#2144695211yescharacteristic
457C2#2144698811yescharacteristic
458C2#2144699511yescharacteristic
subgroupG/H
centerC22#16839673
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2549C2
socleC22×C61#393
prime radicalC2×#14519751C22
hypercenter#2549D61
hypocenterC61#10374
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2549

Complements

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

NH ≅ G/Ntype
4. #21443698C2semidirect
5. #21443686C2semidirect
6. #21443667C2semidirect
7. C61×#2549C2semidirect
27. C22×D244Q8semidirect
36. C2×C4⋊Dic61Q8semidirect
220. #2549D61semidirect
256. C61#10374semidirect

Maximal subgroups

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

subgroupindex
#214466552
#214443862
C2×#168394952
#214436982
#214436862
#214436672
C61×#25492
#1037461