Finite Group Databasebeta

← #11778743

Subgroups — #11778743

Order 1152.

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

normal subgroups only

This group has 473 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
2#10592733C211yesmaximal, characteristic
3#10591226C211yesmaximal, characteristic, complemented
4#10591103C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71887—31nomaximal
9#68298—31nomaximal
10C32×#121C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#935—21no—
13C3×#935—21no—
14C3×D4×Dic3—21no—
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4C2211yescharacteristic
17C3×#889—21no—
18C3×#879—21no—
19C3×#878—21no—
20#63659—21no—
21#63657C2211yescharacteristic
22#63635—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63575—21no—
28#63566—21no—
29C3×#539—31no—
30#5602D311yescharacteristic
31#5044—31no—
32#5034—31no—
33#5034—31no—
34#5034—61no—
35#4986—31no—
36#4722—31no—
37#4659—31no—
38C3×#327—31no—
39#4538—31no—
40#4537D311yescharacteristic
41#4528—31no—
42#4469—31no—
43#4452—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—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—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—
83#935—21no—
84#935—21no—
85D4×Dic3—21no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4C2×D311yescharacteristic
91#889—21no—
92#879—21no—
93#878—21no—
94C3×C22⋊C8—31no—
95C3×#95—31no—
96#835—61no—
97#832—62no—
98#832—61no—
99#832—61no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95C2×D311yescharacteristic
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic
109#818—61no—
110#816—61no—
111#808—62no—
112#808—61no—
113#808—61no—
114#807—61no—
115C23×C32—21no—
116C23×C32C2×D411yescharacteristic
117C32×D4—41no—
118C32×D4—41no—
119C32×D4—41no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—42no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—81no—
137C3×Dic6—41no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140#539—31no—
141#484—91no—
142#481—91no—
143#400—91no—
144#328—91no—
145#327—31no—
146#324—91no—
147C2×C3×Q8—31no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—41no—
152C2×C3×D4D1211yescharacteristic
153C2×C3×D4#6711yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C22×Dic3#6711yescharacteristic
167C22×Dic3#6711yescharacteristic
168C2×Dic6#6711yescharacteristic
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—31no—
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⋊C4D1211yescharacteristic
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—62no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—121no—
199C4⋊Dic3#6711yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32#12011yescharacteristic
216C22×C32#13511yescharacteristic
217C22×C32#13711yescharacteristic
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C3⋊Dic3—81no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—61no—
228#125—61no—
229#123—61no—
230#123—61no—
231C22⋊Q8—31no—
232C22⋊Q8—61no—
233#121D3211yescharacteristic
234C4×D4—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—91no—
237#107—181no—
238#106—181no—
239#103—181no—
240#102—181no—
241C22⋊C8—31no—
242C22⋊C8—91no—
243#95—31no—
244#95—181no—
245#95—181no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—41no—
250C23×C3D3×D411yescharacteristic
251C23×C3C2×#6711yescharacteristic
252C3×Q8—121no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—81no—
261C3×D4—81no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4—241no—
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—81no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—242no—
302Dic6—41no—
303C3×C8—121no—
304C3⋊C8—41no—
305C3⋊C8—122no—
306C3⋊C8—121no—
307C3⋊C8—121no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—81no—
311C2×C32#45211yescharacteristic
312C2×C32#45411yescharacteristic
313C2×C32#45811yescharacteristic
314C2×Q8—31no—
315C2×D4—21no—
316C2×D4#62611yescharacteristic
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323C2×C8—61no—
324C2×C8—181no—
325C4⋊C4—31no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4#62611yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C42—61no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3#88211yescharacteristic
360C22×C3#91211yescharacteristic
361C22×C3#91511yescharacteristic
362C22×C3#95011yescharacteristic
363C22×C3#95111yescharacteristic
364C22×C3#95311yescharacteristic
365C3×C4—22no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—81no—
374C3×C4—121no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4—121no—
378C3×C4—241no—
379Dic3—41no—
380Dic3—41no—
381Dic3—41no—
382Dic3—41no—
383Dic3—81no—
384Dic3—242no—
385Dic3—241no—
386Dic3—241no—
387C32#161511yescharacteristic, complemented, Sylow
388C23—21no—
389C23D3×#6711yescharacteristic
390Q8—121no—
391D4—41no—
392D4—41no—
393D4—41no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—241no—
407C2×C4—362no—
408C2×C4—361no—
409C2×C4C2×#62611yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C8—121no—
412C8—361no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—81no—
423C2×C3—81no—
424C2×C3—161no—
425C2×C3#474211yescharacteristic
426C2×C3#478311yescharacteristic
427C2×C3#482711yescharacteristic
428C2×C3#523911yescharacteristic
429C2×C3#524311yescharacteristic
430C2×C3#524511yescharacteristic
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22#6392911yescharacteristic
437C22#6393311yescharacteristic
438C22#6397711yescharacteristic
439C4—21no—
440C4—21no—
441C4—41no—
442C4—121no—
443C4—121no—
444C4—121no—
445C4—121no—
446C4—241no—
447C4—721no—
448C3—21no—
449C3#6829811yescharacteristic, complemented
450C3#7188711yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—81no—
454C2#1059146311yescharacteristic
455C2#1059153411yescharacteristic
456C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
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. #10591226C2semidirect
4. #10591103C2semidirect
6. #10589153C2semidirect
7. #10589147C2semidirect
387. C32#1615semidirect
449. C3#68298semidirect
450. C3#71887semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
#105927332
#105912262
#105911032
C3×#45372
#105891532
#105891472
#718873
#682983