Finite Group Databasebeta

← #11778633

Subgroups — #11778633

Order 1152.

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

normal subgroups only

This group has 549 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×#5494C211yesmaximal, characteristic
2#10592652C211yesmaximal, characteristic, complemented
3#10591126C211yesmaximal, characteristic, complemented
4#10591094C211yesmaximal, characteristic, complemented
5C3×#4525C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#71882—31nomaximal
9#68111—31nomaximal
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×#3757—21no—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C3×#953—21no—
14C3×#930C2211yescharacteristic
15C3×C4×#67—21no—
16C3×#924C2211yescharacteristic
17C3×#885—21no—
18C3×#884—21no—
19C3×#883—21no—
20C3×#879—21no—
21#63658—21no—
22#63658C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63566—21no—
28#63563—21no—
29C3×#538—31no—
30#5494D311yescharacteristic
31#5043—31no—
32#5033—31no—
33#4953—31no—
34#4953—31no—
35#4953—61no—
36#4736—31no—
37#4721—31no—
38C3×#323—31no—
39#4538—31no—
40#4537—31no—
41#4525D311yescharacteristic, complemented
42#4470—31no—
43#4467—31no—
44C24×C32D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×Dic6D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C22⋊C4—21no—
57#3757—42no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72#1612—91noSylow
73C3×#126—61no—
74C3×#124—61no—
75C3×#123—61no—
76C3×C22⋊Q8—31no—
77C3×#121—31no—
78C3×#121—61no—
79C3×#120—61no—
80C3×C4×D4—61no—
81C2×C3×C22⋊C4—21no—
82C2×C3×C22⋊C4C2×D311yescharacteristic
83C2×C3×C22⋊C4C2×D311yescharacteristic
84#953—21no—
85C2×#217—62no—
86C2×#217—61no—
87C2×#217—61no—
88#930C2×D311yescharacteristic
89C4×#67—21no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93#924C2×D311yescharacteristic
94#885—21no—
95#884—21no—
96#883—21no—
97#879—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8—31no—
100#835—61no—
101#832—61no—
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—61no—
105C3⋊#95—62no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108#830C2×D311yescharacteristic
109#830C2×D311yescharacteristic
110#821—61no—
111#818—61no—
112#817—61no—
113#816—61no—
114#808—61no—
115#807—61no—
116C23×C32—21no—
117C23×C32—21no—
118C23×C32—21no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—21no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C3×#67—41no—
135C3×#67—41no—
136C3×#67—81no—
137C3×#67—81no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C3×D12—41no—
142C3×C4×D3—81no—
143C3×Dic6—41no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146#538—31no—
147#483—91no—
148#480—91no—
149#397—91no—
150#328—91no—
151#327—91no—
152#323—31no—
153C24×C3—21no—
154C24×C3D1211yescharacteristic
155C24×C3#6711yescharacteristic
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C2×#67—21no—
170C2×#67—21no—
171C22×Dic3—62no—
172C22×Dic3—62no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C2×D12#6711yescharacteristic
178C2×C4×D3—21no—
179C2×Dic6#6711yescharacteristic
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—41no—
191C3×C22⋊C4—41no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C42—61no—
198#217—21no—
199#217—21no—
200#217—21no—
201#217—124no—
202#217—122no—
203#217—122no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—21no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—121no—
211C4⋊Dic3—121no—
212C4⋊Dic3#6711yescharacteristic
213C4⋊Dic3#6711yescharacteristic
214Dic3⋊C4—21no—
215Dic3⋊C4—21no—
216C4×Dic3—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32—42no—
222C22×C32—41no—
223C22×C32—41no—
224C22×C32—41no—
225C22×C32—81no—
226C22×C32#12011yescharacteristic
227C22×C32#13511yescharacteristic
228C22×C32AGL(1,ℤ/8)11yescharacteristic
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—41no—
235C3⋊Dic3—81no—
236C3⋊Dic3—81no—
237C3×Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240#126—61no—
241#124—61no—
242#123—61no—
243C22⋊Q8—31no—
244#121—31no—
245#121—61no—
246#120—61no—
247C4×D4—61no—
248C2×C4⋊C4—91no—
249C2×C22⋊C4—181no—
250C2×C22⋊C4D3211yescharacteristic
251#107—181no—
252#106—181no—
253#103—181no—
254#102—181no—
255C22⋊C8—31no—
256C22⋊C8—31no—
257#95—91no—
258#95—181no—
259C23×C3—22no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—41no—
268C23×C3—41no—
269C23×C3—41no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—61no—
276C23×C3C2×D1211yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—21no—
279C3×Q8—121no—
280C3×D4—121no—
281C3×D4—121no—
282C3×D4—121no—
283C3×D4—241no—
284C3×D4—241no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—42no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—241no—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304#67—41no—
305#67—41no—
306#67—81no—
307#67—81no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—122no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329D12—41no—
330C4×D3—81no—
331Dic6—41no—
332C3×C8—121no—
333C3×C8—121no—
334C3⋊C8—41no—
335C3⋊C8—41no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32—81no—
339C2×C32#44911yescharacteristic
340C2×C32#45511yescharacteristic
341C2×C32#45811yescharacteristic
342C3×D3—81no—
343C24#62611yescharacteristic
344C2×Q8—31no—
345C2×D4—31no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C22×C4—61no—
350C22×C4—181no—
351C22×C4—181no—
352C22×C4#62611yescharacteristic
353C22×C4C2×D3211yescharacteristic
354C2×C8—61no—
355C2×C8—61no—
356C4⋊C4—31no—
357C4⋊C4—31no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—362no—
370C42—61no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—44no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—81no—
391C22×C3—81no—
392C22×C3—81no—
393C22×C3—81no—
394C22×C3—82no—
395C22×C3—121no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3#88211yescharacteristic
399C22×C3#90411yescharacteristic
400C22×C3#90811yescharacteristic
401C22×C3#94911yescharacteristic
402C22×C3#95011yescharacteristic
403C22×C3#95311yescharacteristic
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—81no—
416C3×C4—121no—
417C3×C4—121no—
418C3×C4—121no—
419Dic3—41no—
420Dic3—41no—
421Dic3—41no—
422Dic3—242no—
423Dic3—241no—
424Dic3—241no—
425Dic3—242no—
426Dic3—241no—
427Dic3—241no—
428C32#161211yescharacteristic, complemented, Sylow
429C23—21no—
430C23—21no—
431C23—21no—
432C23—41no—
433C23—41no—
434C23—61no—
435C23C2×#62611yescharacteristic
436Q8—121no—
437D4—121no—
438D4—121no—
439D4—121no—
440D4—241no—
441D4—241no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—241no—
449C2×C4—361no—
450C2×C4—361no—
451C2×C4—361no—
452C2×C4—361no—
453C2×C4—361no—
454C2×C4—361no—
455C2×C4D3×#6711yescharacteristic
456C2×C4D3×#6711yescharacteristic
457C8—121no—
458C8—121no—
459C2×C3—22no—
460C2×C3—22no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—82no—
469C2×C3—81no—
470C2×C3—81no—
471C2×C3—241no—
472C2×C3#473411yescharacteristic
473C2×C3#474211yescharacteristic
474C2×C3#474611yescharacteristic
475C2×C3#523811yescharacteristic
476C2×C3#524211yescharacteristic
477C2×C3#524311yescharacteristic
478D3—81no—
479C22—21no—
480C22—21no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—81no—
486C22—121no—
487C22—121no—
488C22—121no—
489C22#6382511yescharacteristic
490C22#6382911yescharacteristic
491C22#6397711yescharacteristic
492C4—21no—
493C4—21no—
494C4—41no—
495C4—121no—
496C4—121no—
497C4—121no—
498C4—721no—
499C4—721no—
500C3—21no—
501C3#6811111yescharacteristic, complemented
502C3#7188211yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—81no—
506C2—241no—
507C2#1059116311yescharacteristic
508C2#1059151311yescharacteristic
509C2#1059153411yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC3×#5494C2
hypercenterC2×C22⋊C4D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592652C2semidirect
3. #10591126C2semidirect
4. #10591094C2semidirect
5. C3×#4525C2semidirect
6. #10589152C2semidirect
7. #10589150C2semidirect
41. #4525D3semidirect
428. C32#1612semidirect
501. C3#68111semidirect
502. C3#71882semidirect

Maximal subgroups

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

subgroupindex
C3×#54942
#105926522
#105911262
#105910942
C3×#45252
#105891522
#105891502
#718823
#681113