Finite Group Databasebeta

← #11778332

Subgroups — #11778332

Order 1152.

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

normal subgroups only

This group has 643 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×#5597C211yesmaximal, characteristic
2#10592739C211yesmaximal, characteristic, complemented
3#10591354C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71880—31nomaximal
9#68295—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#237—21no—
12C32×#121C2211yescharacteristic
13C2×#3754—21no—
14C3×#939—21no—
15C3×#939—21no—
16C3×#930C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#896—21no—
19C3×#884—21no—
20C3×#878—21no—
21C2×Dic3⋊Dic3—21no—
22C2×#3716—21no—
23#63657C2211yescharacteristic
24#63637—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29C3×#537—31no—
30#5597D311yescharacteristic
31#5040—31no—
32#5040—31no—
33#5040—31no—
34#5040—61no—
35#4979—31no—
36#4738—31no—
37#4656—31no—
38C3×#327—31no—
39#4537—31no—
40#4537D311yescharacteristic, complemented
41#4528—31no—
42#4469—31no—
43#4451—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—42no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C22×C3×Dic3D411yescharacteristic
58C3×#237—42no—
59C3×#237—42no—
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6—21no—
63C32×C4⋊C4D411yescharacteristic
64C32×C22⋊C4—21no—
65#3754—42no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#217—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×C4⋊Dic3D411yescharacteristic
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—21no—
73C3×Dic3⋊C4—21no—
74C2×C3×C3⋊C8—21no—
75Dic3⋊Dic3—42no—
76#3716—42no—
77#1604—91noSylow
78C2×C3×#41—61no—
79C2×#237—21no—
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C3×C22⋊Q8—61no—
84C3×C22⋊Q8—61no—
85C3×#121—21no—
86C3×#121—31no—
87C3×#121—61no—
88C3×#121—61no—
89C3×#121—61no—
90C3×#121C2×D311yescharacteristic
91C3×#121C2×D311yescharacteristic
92C2×C3×C4⋊C4—31no—
93#939—21no—
94#939—21no—
95C2×#214—61no—
96C2×#214—62no—
97C2×#214—61no—
98C2×#214—61no—
99#930C2×D311yescharacteristic
100C2×C4⋊Dic3—61no—
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4C2×D311yescharacteristic
103C2×#204—61no—
104#896—21no—
105#884—21no—
106#878—21no—
107C3×C22⋊C8—31no—
108C3×#95—31no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#830C2×D311yescharacteristic
116#816—61no—
117#810—61no—
118#810—62no—
119#810—61no—
120#810—61no—
121C23×C32—21no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C32×D4—41no—
125C32×D4—41no—
126C32×D4—41no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134#634—22no—
135#634—22no—
136#634—41no—
137#634—41no—
138C3×#67—42no—
139C3×#67—41no—
140C3×#67—41no—
141C3×#67—81no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3SD1612yescomplemented
152C3×D12—41no—
153C3×C4×D3—42no—
154C3×Dic6—42no—
155C3⋊(C3⋊C8)—41no—
156C3×C3⋊C8—41no—
157#537—31no—
158#448—91no—
159#448—91no—
160#395—91no—
161#327—31no—
162#327—91no—
163#324—91no—
164C3×#41—122no—
165C3×#41—122no—
166C2×C3×Q8—61no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—31no—
171C2×C3×D4—41no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4D1211yescharacteristic
176C2×C3×D4#6711yescharacteristic
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—21no—
186C2×#67—21no—
187C2×#67—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3#6711yescharacteristic
194C22×Dic3#6711yescharacteristic
195#237—42no—
196#237—42no—
197C2×D12#6711yescharacteristic
198C2×C4×D3—21no—
199C2×Dic6—21no—
200C2×Dic6—62no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—121no—
206C2×Dic6—122no—
207C2×Dic6—122no—
208C2×Dic6—124no—
209C2×C3×C8—61no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—31no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4D1211yescharacteristic
216C3×C4⋊C4#6711yescharacteristic
217C3×C22⋊C4—21no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—41no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4—61no—
223#217—21no—
224#214—122no—
225#214—122no—
226#214—122no—
227#214—124no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—21no—
230C4⋊Dic3—122no—
231C4⋊Dic3#6711yescharacteristic
232Dic3⋊C4—21no—
233Dic3⋊C4—21no—
234Dic3⋊C4—21no—
235Dic3⋊C4—122no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240#204—122no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32#12011yescharacteristic
247C22×C32C2×SD1611yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C32×C4—21no—
253C32×C4—21no—
254C32×C4—41no—
255C3⋊Dic3—42no—
256C3×Dic3—22no—
257C3×Dic3—42no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C2×#41—61no—
261C22×Q8—91no—
262C2×SD16—181no—
263C2×SD16—181no—
264C22⋊Q8—61no—
265C22⋊Q8—61no—
266#121—31no—
267#121—61no—
268#121—61no—
269#121—61no—
270#121D3211yescharacteristic
271C2×C4⋊C4—31no—
272C2×C4⋊C4—181no—
273#103—181no—
274#103—181no—
275C22⋊C8—31no—
276C22⋊C8—91no—
277#95—31no—
278#95—181no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—21no—
282C23×C3—41no—
283C23×C3—61no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—21no—
287C3×Q8—122no—
288C3×D4—41no—
289C3×D4—41no—
290C3×D4—42no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—81no—
296C3×D4—81no—
297C3×D4—121no—
298C3×D4—122no—
299C3×D4—121no—
300C3×D4—121no—
301C3×D4—241no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—32no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—42no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—62no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—122no—
317C2×C3×C4—122no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325#67—42no—
326#67—41no—
327#67—41no—
328#67—81no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—22no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—42no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—122no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3#21412yescomplemented
348D12—41no—
349C4×D3—42no—
350Dic6—42no—
351Dic6—62no—
352Dic6—64no—
353Dic6—62no—
354Dic6—62no—
355Dic6—62no—
356Dic6—122no—
357Dic6—122no—
358Dic6—121no—
359Dic6—121no—
360Dic6—121no—
361Dic6—121no—
362Dic6—122no—
363C3×C8—121no—
364C3⋊C8—41no—
365C3⋊C8—122no—
366C3⋊C8—121no—
367C3⋊C8—121no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32—81no—
371C2×C32#45011yescharacteristic
372C2×C32#45611yescharacteristic
373C2×C32B(4,𝔽2)11yescharacteristic
374C3×D3—81no—
375#41—122no—
376#41—122no—
377C2×Q8—61no—
378C2×Q8—181no—
379C2×Q8—181no—
380C2×Q8—362no—
381C2×D4—21no—
382C2×D4—31no—
383C2×D4—61no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4#62611yescharacteristic
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—181no—
393C22×C4C2×D3211yescharacteristic
394SD16—362no—
395SD16—362no—
396C2×C8—61no—
397C2×C8—181no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—362no—
403C4⋊C4#62611yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—61no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3—121no—
429C22×C3#88211yescharacteristic
430C22×C3#91111yescharacteristic
431C22×C3D3×SD1611yescharacteristic
432C22×C3#93211yescharacteristic
433C22×C3C2×#21411yescharacteristic
434C22×C3#95311yescharacteristic
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—41no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—62no—
447C3×C4—81no—
448C3×C4—122no—
449C3×C4—121no—
450C3×C4—121no—
451Dic3—22no—
452Dic3—42no—
453Dic3—41no—
454Dic3—41no—
455Dic3—124no—
456Dic3—122no—
457Dic3—122no—
458C32#160411yescharacteristic, complemented, Sylow
459C23—21no—
460C23—61no—
461C23D3×#6711yescharacteristic
462Q8—122no—
463Q8—182no—
464Q8—182no—
465Q8—361no—
466Q8—361no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—121no—
471D4—122no—
472D4—121no—
473D4—121no—
474D4—241no—
475C2×C4—21no—
476C2×C4—32no—
477C2×C4—41no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—62no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—122no—
484C2×C4—122no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—182no—
489C2×C4—361no—
490C2×C4—361no—
491C2×C4C2×#62611yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C8—121no—
494C8—361no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—81no—
505C2×C3—81no—
506C2×C3—161no—
507C2×C3—241no—
508C2×C3#474111yescharacteristic
509C2×C3#477611yescharacteristic
510C2×C3#482611yescharacteristic
511C2×C3#521811yescharacteristic
512C2×C3#524411yescharacteristic
513C2×C3#524611yescharacteristic
514D3—81no—
515C22—21no—
516C22—21no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—121no—
521C22—121no—
522C22—121no—
523C22D3×#21411yescharacteristic
524C22#6393211yescharacteristic
525C22#6397711yescharacteristic
526C4—21no—
527C4—21no—
528C4—41no—
529C4—62no—
530C4—122no—
531C4—121no—
532C4—121no—
533C4—362no—
534C3—21no—
535C3#6829511yescharacteristic, complemented
536C3#7188011yescharacteristic, complemented
537C2—21no—
538C2—21no—
539C2—81no—
540C2—241no—
541C2#1059145911yescharacteristic
542C2#1059153111yescharacteristic
543C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radicalC3×#5597C2
hypercenter#121D32
hypocenterC32#1604
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
2. #10592739C2semidirect
3. #10591354C2semidirect
4. #10591181C2semidirect
5. C3×#4537C2semidirect
6. #10589149C2semidirect
7. #10589147C2semidirect
40. #4537D3semidirect
151. C2×C3×Dic3SD16semidirect
347. C2×Dic3#214semidirect
458. C32#1604semidirect
535. C3#68295semidirect
536. C3#71880semidirect

Maximal subgroups

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

subgroupindex
C3×#55972
#105927392
#105913542
#105911812
C3×#45372
#105891492
#105891472
#718803
#682953