Finite Group Databasebeta

← #11778479

Subgroups — #11778479

Order 1152.

496 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5634C211yesmaximal, characteristic
2C3×#5043C211yesmaximal, characteristic, complemented
3#10591314C211yesmaximal, characteristic
4#10591101C211yesmaximal, characteristic, complemented
5#10589404C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic
8#71890—31nomaximal
9#71172—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×(C2×D3)⋊C4C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C3×#924C2211yescharacteristic
15C3×#897—21no—
16C3×#896—21no—
17C3×#896—21no—
18C3×D3×C22⋊C4—21no—
19C3×#878—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63658C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#835—21no—
24C3×#830C2211yescharacteristic
25C3×#808—21no—
26#63579—21no—
27#63574—21no—
28#63565—21no—
29C3×#543—31no—
30#5634D311yescharacteristic
31C3×#483—31no—
32#5043—31no—
33#5043D311yescharacteristic, complemented
34#4992—31no—
35#4971—31no—
36#4953—31no—
37#4538—31no—
38#4538—31no—
39#4538—31no—
40#4538—61no—
41#4525—31no—
42#4468—31no—
43#4467—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71(C2×D3)⋊Dic3—42no—
72#1608—91noSylow
73C3×C22⋊Q8—21no—
74C3×C22⋊Q8—31no—
75C3×C22⋊Q8—61no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C2×D311yescharacteristic
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—31no—
84C2×C3×C22⋊C4—61no—
85C2×#217—61no—
86#946—21no—
87C2×(C2×D3)⋊C4—61no—
88C2×(C2×D3)⋊C4C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90#924C2×D311yescharacteristic
91#897—21no—
92#896—21no—
93#896—21no—
94D3×C22⋊C4—21no—
95#878—21no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—31no—
99#835—21no—
100#835—61no—
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—21no—
112#808—61no—
113#808—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3SD1612yes—
120C32×Q8—41no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
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—
136C3×C4×D3—81no—
137C3×C4×D3—81no—
138C3×Dic6—41no—
139C3×Dic6—81no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142#543—31no—
143#483—31no—
144#483—91no—
145#397—91no—
146#328—91no—
147#328—91no—
148#323—91no—
149C24×C3—31no—
150C23×D3#6711yescharacteristic
151C2×C3×Q8—21no—
152C2×C3×Q8—31no—
153C2×C3×Q8—61no—
154C2×C3×Q8#6711yescharacteristic
155C2×C3×Q8#6711yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—121no—
167C22×Dic3#6711yescharacteristic
168C2×C4×D3—21no—
169C2×C4×D3—21no—
170C2×Dic6—21no—
171C2×Dic6#6711yescharacteristic
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—41no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4#6711yescharacteristic
185C3×C4⋊C4#6711yescharacteristic
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194#217—21no—
195#217—122no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—122no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3#6711yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—121no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32#12011yescharacteristic
215C22×C32C2×SD1611yescharacteristic
216C22×C32#13711yescharacteristic
217C2×C3×D3—22no—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—42no—
221C2×C3×D3—81no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—41no—
226C3⋊Dic3—81no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—81no—
231C22⋊Q8—31no—
232C22⋊Q8—61no—
233C22⋊Q8—61no—
234C22⋊Q8—61no—
235C22⋊Q8—61no—
236C22⋊Q8—61no—
237C22⋊Q8D3211yescharacteristic
238C2×C4⋊C4—31no—
239C2×C22⋊C4—31no—
240C2×C22⋊C4—61no—
241C2×C22⋊C4—181no—
242#106—61no—
243#106—181no—
244#103—61no—
245#103—181no—
246C22⋊C8—31no—
247C22⋊C8—91no—
248#95—91no—
249#95—181no—
250C23×C3—21no—
251C23×C3—32no—
252C23×C3—61no—
253C23×C3—61no—
254C23×C3—121no—
255C23×C3—121no—
256C23×C3D3×D411yescharacteristic
257C23×C3C2×#6711yescharacteristic
258C22×D3—21no—
259C22×D3—21no—
260C22×D3—41no—
261C22×D3—41no—
262C22×D3#21512yes—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×Q8—81no—
266C3×Q8—121no—
267C3×Q8—241no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—241no—
287C2×C3×C4—241no—
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291C2×C3×C4C2×#6711yescharacteristic
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—122no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—241no—
307C2×Dic3—241no—
308C4×D3—81no—
309C4×D3—81no—
310Dic6—41no—
311Dic6—81no—
312C3×C8—121no—
313C3⋊C8—41no—
314C3⋊C8—121no—
315C3⋊C8—121no—
316C3⋊C8—241no—
317C2×C32—21no—
318C2×C32—21no—
319C2×C32#44811yescharacteristic
320C2×C32#45511yescharacteristic
321C2×C32#45811yescharacteristic
322C3×D3—42no—
323C24—31no—
324C2×Q8—31no—
325C2×Q8—61no—
326C2×Q8#62511yescharacteristic
327C22×C4—31no—
328C22×C4—61no—
329C22×C4—61no—
330C22×C4—61no—
331C22×C4—181no—
332C22×C4C2×D3211yescharacteristic
333C2×C8—61no—
334C2×C8—181no—
335C4⋊C4—21no—
336C4⋊C4—31no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4#62511yescharacteristic
344C22⋊C4—21no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C22⋊C4—61no—
350C22⋊C4—362no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—62no—
361C22×C3—122no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3—241no—
365C22×C3D3×SD1611yescharacteristic
366C22×C3#91511yescharacteristic
367C22×C3#93711yescharacteristic
368C22×C3C2×#21511yescharacteristic
369C22×C3#94211yescharacteristic
370C22×C3#95311yescharacteristic
371C2×D3—22no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—42no—
375C2×D3—81no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—81no—
387C3×C4—81no—
388C3×C4—121no—
389C3×C4—121no—
390C3×C4—121no—
391C3×C4—241no—
392Dic3—41no—
393Dic3—41no—
394Dic3—41no—
395Dic3—81no—
396Dic3—241no—
397Dic3—241no—
398Dic3—242no—
399C32#160811yescharacteristic, complemented, Sylow
400C23—32no—
401C23—61no—
402C23—61no—
403C23—121no—
404C23—121no—
405C23D3×#6711yescharacteristic
406Q8—41no—
407Q8—121no—
408Q8—241no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—241no—
420C2×C4—241no—
421C2×C4—361no—
422C2×C4—361no—
423C2×C4—361no—
424C2×C4C2×#62511yescharacteristic
425C2×C4D3×#6711yescharacteristic
426C8—121no—
427C8—361no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—122no—
438C2×C3#505311yescharacteristic
439C2×C3#517011yescharacteristic
440C2×C3#520211yescharacteristic
441C2×C3#522711yescharacteristic
442C2×C3#524211yescharacteristic
443C2×C3#524311yescharacteristic
444D3—42no—
445C22—21no—
446C22—21no—
447C22—62no—
448C22—122no—
449C22—121no—
450C22—121no—
451C22—241no—
452C22D3×#21511yescharacteristic
453C22#6394611yescharacteristic
454C22#6397611yescharacteristic
455C4—21no—
456C4—21no—
457C4—41no—
458C4—41no—
459C4—121no—
460C4—121no—
461C4—121no—
462C4—241no—
463C4—721no—
464C3—21no—
465C3#7117211yescharacteristic, complemented
466C3#7189011yescharacteristic, complemented
467C2—21no—
468C2—21no—
469C2—122no—
470C2#1059153311yescharacteristic
471C2#1059158311yescharacteristic
472C2#1059166411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenterC22⋊Q8D32
hypocenterC32#1608
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5043C2semidirect
4. #10591101C2semidirect
5. #10589404C2semidirect
6. #10589152C2semidirect
33. #5043D3semidirect
399. C32#1608semidirect
465. C3#71172semidirect
466. C3#71890semidirect

Maximal subgroups

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

subgroupindex
C3×#56342
C3×#50432
#105913142
#105911012
#105894042
#105891522
#105891452
#718903
#711723