Finite Group Databasebeta

← #11778519

Subgroups — #11778519

Order 1152.

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

normal subgroups only

This group has 477 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×#5033C211yesmaximal, characteristic
3#10591214C211yesmaximal, characteristic, complemented
4#10591101C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic
6#10589152C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71886—31nomaximal
9#71166—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—
20C2×#3724—21no—
21#63658C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#832—21no—
24C3×#830C2211yescharacteristic
25C3×#807—21no—
26#63579—21no—
27#63574—21no—
28#63565—21no—
29C3×#539—31no—
30#5602D311yescharacteristic
31C3×#480—31no—
32#5043—31no—
33#5033D311yescharacteristic
34#4983—31no—
35#4981—31no—
36#4971—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#3724—42no—
72#1609—91noSylow
73C3×#126—61no—
74C3×#125—61no—
75C3×#123—61no—
76C3×#123—61no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—61no—
79C3×#121—21no—
80C3×#121C2×D311yescharacteristic
81C3×#121C2×D311yescharacteristic
82C3×C4×D4—61no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85#935—21no—
86#935—21no—
87D4×Dic3—21no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4—61no—
92C2×Dic3⋊C4C2×D311yescharacteristic
93#889—21no—
94#879—21no—
95#878—21no—
96C3×#107—61no—
97C3×#102—61no—
98C3×C22⋊C8—31no—
99#835—61no—
100#832—21no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#810—61no—
111#808—61no—
112#808—61no—
113#807—21no—
114C23×C32—21no—
115C23×C32C2×D411yescharacteristic
116C32×D4—41no—
117C32×D4—41no—
118C32×D4—41no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
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#483—91no—
142#480—31no—
143#398—91no—
144#328—91no—
145#327—91no—
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×D4#6711yescharacteristic
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⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4#6711yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C42—61no—
190#217—21no—
191#217—21no—
192#217—21no—
193#217—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3#6711yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—122no—
204Dic3⋊C4—122no—
205C4×Dic3—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32#12011yescharacteristic
216C22×C32#13511yescharacteristic
217C22×C32AGL(1,ℤ/8)11yescharacteristic
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C3⋊Dic3—42no—
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—31no—
237C2×C4⋊C4—181no—
238#107—61no—
239#106—181no—
240#103—181no—
241#102—61no—
242C22⋊C8—31no—
243C22⋊C8—91no—
244#95—91no—
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—41no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—81no—
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—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—81no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4—241no—
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
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—62no—
296C2×Dic3—62no—
297C2×Dic3—81no—
298C2×Dic3—122no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—241no—
304C2×Dic3—241no—
305Dic6—41no—
306C3×C8—121no—
307C3⋊C8—41no—
308C3⋊C8—121no—
309C3⋊C8—121no—
310C3⋊C8—241no—
311C2×C32—21no—
312C2×C32—21no—
313C2×C32—81no—
314C2×C32#44911yescharacteristic
315C2×C32#45611yescharacteristic
316C2×C32#45811yescharacteristic
317C2×Q8—31no—
318C2×D4—21no—
319C2×D4#62511yescharacteristic
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4—181no—
325C22×C4C2×D3211yescharacteristic
326C2×C8—61no—
327C2×C8—181no—
328C4⋊C4—31no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—362no—
338C4⋊C4#62511yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C42—61no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—81no—
361C22×C3—81no—
362C22×C3—81no—
363C22×C3#91111yescharacteristic
364C22×C3#91211yescharacteristic
365C22×C3#93711yescharacteristic
366C22×C3#94911yescharacteristic
367C22×C3#95011yescharacteristic
368C22×C3#95311yescharacteristic
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—81no—
378C3×C4—121no—
379C3×C4—121no—
380C3×C4—121no—
381C3×C4—121no—
382C3×C4—241no—
383Dic3—41no—
384Dic3—41no—
385Dic3—41no—
386Dic3—41no—
387Dic3—81no—
388Dic3—122no—
389Dic3—122no—
390Dic3—242no—
391C32#160911yescharacteristic, complemented, Sylow
392C23—21no—
393C23D3×#6711yescharacteristic
394Q8—121no—
395D4—41no—
396D4—41no—
397D4—41no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—182no—
411C2×C4—241no—
412C2×C4—361no—
413C2×C4—361no—
414C2×C4C2×#62511yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C8—121no—
417C8—361no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—81no—
428C2×C3—81no—
429C2×C3—161no—
430C2×C3#505311yescharacteristic
431C2×C3#515811yescharacteristic
432C2×C3#520511yescharacteristic
433C2×C3#523811yescharacteristic
434C2×C3#524311yescharacteristic
435C2×C3#524611yescharacteristic
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22#6392511yescharacteristic
442C22#6393311yescharacteristic
443C22#6397611yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—121no—
448C4—121no—
449C4—121no—
450C4—121no—
451C4—241no—
452C4—362no—
453C3—21no—
454C3#7116611yescharacteristic, complemented
455C3#7188611yescharacteristic, complemented
456C2—21no—
457C2—21no—
458C2—81no—
459C2#1059145011yescharacteristic
460C2#1059153311yescharacteristic
461C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1609
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. #10591214C2semidirect
4. #10591101C2semidirect
6. #10589152C2semidirect
7. #10589147C2semidirect
391. C32#1609semidirect
454. C3#71166semidirect
455. C3#71886semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C3×#50332
#105912142
#105911012
#105894032
#105891522
#105891472
#718863
#711663