Finite Group Databasebeta

← #11778745

Subgroups — #11778745

Order 1152.

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

normal subgroups only

This group has 461 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×#5602C211yesmaximal, characteristic
2C3×#5034C211yesmaximal, characteristic
3#10591225C211yesmaximal, characteristic, complemented
4#10591132C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic
6#10589152C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71887—31nomaximal
9#71170—31nomaximal
10C32×#121C2211yescharacteristic
11C3×#935—21no—
12C3×#935—21no—
13C3×D4×Dic3—21no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4C2211yescharacteristic
17C3×#889—21no—
18C3×#879—21no—
19C3×#878—21no—
20#63658C2211yescharacteristic
21#63657C2211yescharacteristic
22C3×#832—21no—
23C3×#830C2211yescharacteristic
24C3×#808—21no—
25#63579—21no—
26#63579—21no—
27#63576—21no—
28#63565—21no—
29C3×#539—31no—
30#5602D311yescharacteristic
31C3×#481—31no—
32#5044—31no—
33#5034D311yescharacteristic
34#4986—31no—
35#4985—31no—
36#4970—31no—
37#4538—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4528—31no—
42#4469—31no—
43#4467—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
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—31no—
77C3×C22⋊Q8—61no—
78C3×#121—21no—
79C3×#121C2×D311yescharacteristic
80C3×#121C2×D311yescharacteristic
81C3×C4×D4—61no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84#935—21no—
85#935—21no—
86D4×Dic3—21no—
87C2×C4⋊Dic3C2×D311yescharacteristic
88#924C2×D311yescharacteristic
89C2×Dic3⋊C4C2×D311yescharacteristic
90#889—21no—
91#879—21no—
92#878—21no—
93C3×#106—61no—
94C3×#102—61no—
95C3×C22⋊C8—31no—
96#835—61no—
97#832—21no—
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#810—61no—
110#808—21no—
111#807—61no—
112#807—61no—
113C23×C32—21no—
114C23×C32C2×D411yescharacteristic
115C32×D4—41no—
116C32×D4—41no—
117C32×D4—41no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3×Dic3—21no—
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—
134C2×C3×Dic3—81no—
135C3×Dic6—41no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138#539—31no—
139#484—91no—
140#481—31no—
141#400—91no—
142#328—91no—
143#327—91no—
144#324—91no—
145C2×C3×Q8—31no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—41no—
150C2×C3×D4#6711yescharacteristic
151C2×C3×D4#6711yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×Dic3—21no—
160C22×Dic3—21no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3#6711yescharacteristic
165C22×Dic3#6711yescharacteristic
166C2×Dic6#6711yescharacteristic
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
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#6711yescharacteristic
179C3×C4⋊C4#6711yescharacteristic
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—41no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C42—61no—
188#217—21no—
189#217—21no—
190#217—21no—
191#217—21no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3#6711yescharacteristic
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
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—41no—
209C22×C32—41no—
210C22×C32—41no—
211C22×C32#12011yescharacteristic
212C22×C32#13511yescharacteristic
213C22×C32#13711yescharacteristic
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—41no—
217C3⋊Dic3—81no—
218C3×Dic3—41no—
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—31no—
228C22⋊Q8—61no—
229#121D3211yescharacteristic
230C4×D4—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233#107—181no—
234#106—61no—
235#103—181no—
236#102—61no—
237C22⋊C8—31no—
238C22⋊C8—91no—
239#95—91no—
240#95—181no—
241#95—181no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—41no—
246C23×C3D3×D411yescharacteristic
247C23×C3C2×#6711yescharacteristic
248C3×Q8—121no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—81no—
256C3×D4—81no—
257C3×D4—81no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—81no—
272C2×C3×C4—121no—
273C2×C3×C4—122no—
274C2×C3×C4—121no—
275C2×C3×C4—241no—
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—41no—
287C2×Dic3—42no—
288C2×Dic3—41no—
289C2×Dic3—81no—
290C2×Dic3—121no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3—121no—
294C2×Dic3—122no—
295C2×Dic3—121no—
296C2×Dic3—121no—
297C2×Dic3—241no—
298C2×Dic3—241no—
299Dic6—41no—
300C3×C8—121no—
301C3⋊C8—41no—
302C3⋊C8—121no—
303C3⋊C8—121no—
304C3⋊C8—241no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32—81no—
308C2×C32#45211yescharacteristic
309C2×C32#45411yescharacteristic
310C2×C32#45811yescharacteristic
311C2×Q8—31no—
312C2×D4—21no—
313C2×D4#62511yescharacteristic
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—61no—
317C22×C4—61no—
318C22×C4—181no—
319C22×C4C2×D3211yescharacteristic
320C2×C8—61no—
321C2×C8—181no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4#62511yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—61no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C42—61no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3#91511yescharacteristic
357C22×C3#91611yescharacteristic
358C22×C3#93711yescharacteristic
359C22×C3#95011yescharacteristic
360C22×C3#95111yescharacteristic
361C22×C3#95311yescharacteristic
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—81no—
371C3×C4—121no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—121no—
375C3×C4—241no—
376Dic3—41no—
377Dic3—41no—
378Dic3—41no—
379Dic3—41no—
380Dic3—81no—
381Dic3—241no—
382Dic3—241no—
383Dic3—242no—
384C32#161511yescharacteristic, complemented, Sylow
385C23—21no—
386C23D3×#6711yescharacteristic
387Q8—121no—
388D4—41no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—121no—
400C2×C4—122no—
401C2×C4—121no—
402C2×C4—241no—
403C2×C4—361no—
404C2×C4—361no—
405C2×C4—361no—
406C2×C4C2×#62511yescharacteristic
407C2×C4D3×#6711yescharacteristic
408C8—121no—
409C8—361no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—81no—
420C2×C3—81no—
421C2×C3—161no—
422C2×C3#505311yescharacteristic
423C2×C3#517311yescharacteristic
424C2×C3#520111yescharacteristic
425C2×C3#523911yescharacteristic
426C2×C3#524311yescharacteristic
427C2×C3#524511yescharacteristic
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22#6392911yescharacteristic
434C22#6393511yescharacteristic
435C22#6397611yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—121no—
440C4—121no—
441C4—121no—
442C4—121no—
443C4—241no—
444C4—721no—
445C3—21no—
446C3#7117011yescharacteristic, complemented
447C3#7188711yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—81no—
451C2#1059146111yescharacteristic
452C2#1059153311yescharacteristic
453C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
3. #10591225C2semidirect
4. #10591132C2semidirect
6. #10589152C2semidirect
7. #10589147C2semidirect
384. C32#1615semidirect
446. C3#71170semidirect
447. C3#71887semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C3×#50342
#105912252
#105911322
#105894032
#105891522
#105891472
#718873
#711703