Finite Group Databasebeta

← #11778517

Subgroups — #11778517

Order 1152.

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

normal subgroups only

This group has 489 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#10592732C211yesmaximal, characteristic
3#10591353C211yesmaximal, characteristic, complemented
4#10591126C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71886—31nomaximal
9#68296—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—
20C2×Dic3⋊Dic3—21no—
21#63659—21no—
22#63657C2211yescharacteristic
23#63634—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63573—21no—
28#63566—21no—
29C3×#539—31no—
30#5602D311yescharacteristic
31#5043—31no—
32#5033—31no—
33#5033—31no—
34#5033—61no—
35#4981—31no—
36#4721—31no—
37#4661—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—
71Dic3⋊Dic3—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—
84#935—21no—
85#935—21no—
86D4×Dic3—21no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3—61no—
91#924C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4C2×D311yescharacteristic
94#889—21no—
95#879—21no—
96#878—21no—
97C3×C22⋊C8—31no—
98C3×#95—31no—
99#835—61no—
100#832—62no—
101#832—61no—
102#832—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#817—61no—
111#816—61no—
112#808—61no—
113#807—62no—
114#807—61no—
115#807—61no—
116C23×C32—21no—
117C23×C32C2×D411yescharacteristic
118C32×D4—41no—
119C32×D4—41no—
120C32×D4—41no—
121C2×C32×C4—21no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—81no—
139C3×Dic6—41no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142#539—31no—
143#483—91no—
144#480—91no—
145#398—91no—
146#328—91no—
147#327—31no—
148#324—91no—
149C2×C3×Q8—31no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—41no—
154C2×C3×D4D1211yescharacteristic
155C2×C3×D4#6711yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3#6711yescharacteristic
169C22×Dic3#6711yescharacteristic
170C2×Dic6#6711yescharacteristic
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—31no—
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⋊C4D1211yescharacteristic
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—62no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—121no—
201C4⋊Dic3—122no—
202C4⋊Dic3#6711yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—122no—
209C4×Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32#12011yescharacteristic
220C22×C32#13511yescharacteristic
221C22×C32AGL(1,ℤ/8)11yescharacteristic
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C3⋊Dic3—81no—
226C3×Dic3—42no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231#126—61no—
232#125—61no—
233#123—61no—
234#123—61no—
235C22⋊Q8—31no—
236C22⋊Q8—61no—
237#121D3211yescharacteristic
238C4×D4—61no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—181no—
242#107—181no—
243#106—181no—
244#103—181no—
245#102—181no—
246C22⋊C8—31no—
247C22⋊C8—91no—
248#95—31no—
249#95—181no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—41no—
254C23×C3D3×D411yescharacteristic
255C23×C3C2×#6711yescharacteristic
256C3×Q8—121no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—42no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—81no—
265C3×D4—81no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—42no—
274C2×C3×C4—62no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—241no—
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×Dic3—22no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—81no—
300C2×Dic3—122no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—241no—
308C2×Dic3—241no—
309Dic6—41no—
310C3×C8—121no—
311C3⋊C8—41no—
312C3⋊C8—122no—
313C3⋊C8—121no—
314C3⋊C8—121no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32—81no—
318C2×C32#44911yescharacteristic
319C2×C32#45611yescharacteristic
320C2×C32#45811yescharacteristic
321C2×Q8—31no—
322C2×D4—21no—
323C2×D4#62611yescharacteristic
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4—181no—
329C22×C4C2×D3211yescharacteristic
330C2×C8—61no—
331C2×C8—181no—
332C4⋊C4—31no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C4⋊C4—362no—
342C4⋊C4#62611yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C42—61no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—81no—
365C22×C3—81no—
366C22×C3—81no—
367C22×C3#88211yescharacteristic
368C22×C3#91111yescharacteristic
369C22×C3#91611yescharacteristic
370C22×C3#94911yescharacteristic
371C22×C3#95011yescharacteristic
372C22×C3#95311yescharacteristic
373C3×C4—22no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—81no—
382C3×C4—122no—
383C3×C4—121no—
384C3×C4—121no—
385C3×C4—121no—
386C3×C4—121no—
387Dic3—42no—
388Dic3—41no—
389Dic3—41no—
390Dic3—41no—
391Dic3—41no—
392Dic3—242no—
393Dic3—241no—
394Dic3—241no—
395C32#160911yescharacteristic, complemented, Sylow
396C23—21no—
397C23D3×#6711yescharacteristic
398Q8—121no—
399D4—41no—
400D4—41no—
401D4—41no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—121no—
414C2×C4—241no—
415C2×C4—361no—
416C2×C4—361no—
417C2×C4—361no—
418C2×C4C2×#62611yescharacteristic
419C2×C4D3×#6711yescharacteristic
420C8—121no—
421C8—361no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3—81no—
432C2×C3—81no—
433C2×C3—161no—
434C2×C3#474211yescharacteristic
435C2×C3#478111yescharacteristic
436C2×C3#482611yescharacteristic
437C2×C3#523811yescharacteristic
438C2×C3#524311yescharacteristic
439C2×C3#524611yescharacteristic
440C22—21no—
441C22—21no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22#6392511yescharacteristic
446C22#6393511yescharacteristic
447C22#6397711yescharacteristic
448C4—21no—
449C4—21no—
450C4—41no—
451C4—122no—
452C4—121no—
453C4—121no—
454C4—121no—
455C4—121no—
456C4—721no—
457C3—21no—
458C3#6829611yescharacteristic, complemented
459C3#7188611yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—81no—
463C2#1059145211yescharacteristic
464C2#1059153411yescharacteristic
465C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
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. #10591353C2semidirect
4. #10591126C2semidirect
6. #10589153C2semidirect
7. #10589147C2semidirect
395. C32#1609semidirect
458. C3#68296semidirect
459. C3#71886semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
#105927322
#105913532
#105911262
C3×#45372
#105891532
#105891472
#718863
#682963