Finite Group Databasebeta

← #11778757

Subgroups — #11778757

Order 1152.

456 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#5645C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic, complemented
3#10591225C211yesmaximal, characteristic, complemented
4#10591091C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71887—31nomaximal
9#71178—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#946—21no—
12C3×#930C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#898—21no—
16C3×#894—21no—
17C3×#890—21no—
18C3×#886—21no—
19C3×#67⋊C4—21no—
20#63658C2211yescharacteristic
21#63657C2211yescharacteristic
22C3×#835—21no—
23C3×#830C2211yescharacteristic
24C3×#807—21no—
25#63579—21no—
26#63579—21no—
27#63574—21no—
28#63562—21no—
29C3×#539—31no—
30#5645D311yescharacteristic
31C3×#484—31no—
32#5044D311yescharacteristic, complemented
33#5034—31no—
34#4986—31no—
35#4985—31no—
36#4968—31no—
37#4538—31no—
38#4538—31no—
39#4538—61no—
40#4537—31no—
41#4528—31no—
42#4470—31no—
43#4469—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#1615—91noSylow
72C3×#126—61no—
73C3×#125—61no—
74C3×#123—61no—
75C3×#123—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8C2×D311yescharacteristic
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×#121—31no—
81C3×C4×D4—61no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84#946—21no—
85#930C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4C2×D311yescharacteristic
88#898—21no—
89#894—21no—
90#890—21no—
91#886—21no—
92#67⋊C4—21no—
93C3×#107—61no—
94C3×#103—61no—
95C3×C22⋊C8—31no—
96#835—21no—
97#832—61no—
98C3⋊#95—31no—
99C3⋊#95—31no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic
109#809—61no—
110#808—61no—
111#808—61no—
112#807—21no—
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—21no—
115C32×Q8—41no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C3×#67—41no—
125C3×#67—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—41no—
134C3×D12—41no—
135C3×C4×D3—81no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138#539—31no—
139#484—31no—
140#481—91no—
141#400—91no—
142#328—91no—
143#327—91no—
144#324—91no—
145C2×C3×Q8—21no—
146C2×C3×Q8#6711yescharacteristic
147C2×C3×Q8#6711yescharacteristic
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—21no—
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—121no—
162C22×Dic3#6711yescharacteristic
163C22×Dic3#6711yescharacteristic
164C2×D12#6711yescharacteristic
165C2×C4×D3—21no—
166C2×C3×C8—61no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4#6711yescharacteristic
180C3×C4⋊C4#6711yescharacteristic
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—41no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—61no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3#6711yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201C4×Dic3—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#12011yescharacteristic
209C22×C32#13511yescharacteristic
210C22×C32#13711yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—41no—
217C32×C4—41no—
218C3⋊Dic3—81no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223#126—61no—
224#125—61no—
225#123—61no—
226#123—61no—
227C22⋊Q8—61no—
228C22⋊Q8D3211yescharacteristic
229#121—31no—
230C4×D4—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233#107—61no—
234#106—181no—
235#103—61no—
236#102—181no—
237C22⋊C8—31no—
238C22⋊C8—91no—
239#95—91no—
240#95—181no—
241#95—181no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3D3×D411yescharacteristic
245C23×C3C2×#6711yescharacteristic
246C22×D3—21no—
247C3×Q8—41no—
248C3×Q8—41no—
249C3×Q8—81no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—81no—
269C2×C3×C4—121no—
270C2×C3×C4—122no—
271C2×C3×C4—121no—
272C2×C3×C4—241no—
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—41no—
278#67—41no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—41no—
285C2×Dic3—42no—
286C2×Dic3—41no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—122no—
292C2×Dic3—121no—
293C2×Dic3—121no—
294C2×Dic3—241no—
295C2×Dic3—241no—
296D12—41no—
297C4×D3—81no—
298C3×C8—121no—
299C3⋊C8—41no—
300C3⋊C8—121no—
301C3⋊C8—121no—
302C3⋊C8—241no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32#45211yescharacteristic
306C2×C32#45411yescharacteristic
307C2×C32#45811yescharacteristic
308C3×D3—81no—
309C2×Q8#62511yescharacteristic
310C2×D4—31no—
311C2×D4—61no—
312C22×C4—31no—
313C22×C4—31no—
314C22×C4—61no—
315C22×C4—61no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318C2×C8—61no—
319C2×C8—181no—
320C4⋊C4—21no—
321C4⋊C4—31no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4#62511yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—61no—
332C22⋊C4—61no—
333C22⋊C4—61no—
334C22⋊C4—61no—
335C42—61no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—121no—
346C22×C3—121no—
347C22×C3—121no—
348C22×C3#91811yescharacteristic
349C22×C3#91911yescharacteristic
350C22×C3#93711yescharacteristic
351C22×C3#95011yescharacteristic
352C22×C3#95111yescharacteristic
353C22×C3#95311yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—81no—
368C3×C4—81no—
369C3×C4—121no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4—241no—
373Dic3—41no—
374Dic3—41no—
375Dic3—41no—
376Dic3—81no—
377Dic3—241no—
378Dic3—241no—
379Dic3—242no—
380C32#161511yescharacteristic, complemented, Sylow
381C23—61no—
382C23D3×#6711yescharacteristic
383Q8—41no—
384D4—121no—
385D4—121no—
386D4—121no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—121no—
396C2×C4—122no—
397C2×C4—121no—
398C2×C4—241no—
399C2×C4—361no—
400C2×C4—361no—
401C2×C4—361no—
402C2×C4C2×#62511yescharacteristic
403C2×C4D3×#6711yescharacteristic
404C8—121no—
405C8—361no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—241no—
416C2×C3#505311yescharacteristic
417C2×C3#518711yescharacteristic
418C2×C3#520111yescharacteristic
419C2×C3#523911yescharacteristic
420C2×C3#524311yescharacteristic
421C2×C3#524511yescharacteristic
422D3—81no—
423C22—21no—
424C22—21no—
425C22—121no—
426C22—121no—
427C22—121no—
428C22#6394311yescharacteristic
429C22#6394911yescharacteristic
430C22#6397611yescharacteristic
431C4—21no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—121no—
436C4—121no—
437C4—121no—
438C4—241no—
439C4—721no—
440C3—21no—
441C3#7117811yescharacteristic, complemented
442C3#7188711yescharacteristic, complemented
443C2—21no—
444C2—21no—
445C2—241no—
446C2#1059153311yescharacteristic
447C2#1059159711yescharacteristic
448C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊Q8D32
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5044C2semidirect
3. #10591225C2semidirect
5. #10589404C2semidirect
7. #10589147C2semidirect
32. #5044D3semidirect
380. C32#1615semidirect
441. C3#71178semidirect
442. C3#71887semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
C3×#50442
#105912252
#105910912
#105894042
#105891502
#105891472
#718873
#711783