Finite Group Databasebeta

← #11778333

Subgroups — #11778333

Order 1152.

711 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 711 conjugacy classes of subgroups — too many to draw. Only its 82 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
1#10596068C211yesmaximal, characteristic
2C3×#5040C211yesmaximal, characteristic, complemented
3#10591346C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589148C211yesmaximal, characteristic, complemented
8#70975—31nomaximal
9#68295—31nomaximal
10C2×#3830—21no—
11C22×C3×Dic6C2211yescharacteristic
12C32×#121C2211yescharacteristic
13#64148—21no—
14#64148—21no—
15#64139C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17#64105—21no—
18#64093—21no—
19#64087—21no—
20C2×C3×#214—21no—
21C2×Dic3⋊Dic3—21no—
22C2×#3717—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#810—21no—
27#63579—21no—
28#63566—21no—
29#5597—31no—
30#5597—31no—
31#5597—61no—
32C3×#448—31no—
33#5230—31no—
34#5227—31no—
35#5040D311yescharacteristic, complemented
36#4738—31no—
37#4656—31no—
38C3×#327—31no—
39#4537D311yescharacteristic, complemented
40#4470—31no—
41#4469—31no—
42#4469—31no—
43#4451—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53#3830—42no—
54#3830—42no—
55C2×C4⋊(C3⋊D3)D411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—42no—
63C32×C4⋊C4D411yescharacteristic
64C32×C22⋊C4—21no—
65#3757—21no—
66#3752—21no—
67#3752—21no—
68C4⋊(C3⋊Dic3)D411yescharacteristic
69#3750—21no—
70#3750—21no—
71#3750—21no—
72C3×#214—42no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75Dic3⋊Dic3—42no—
76#3717—42no—
77#1604—91noSylow
78C22×C3×Q8—31no—
79C2×#237—61no—
80C2×#237—61no—
81C2×#237—62no—
82C22×Dic6C2×D311yescharacteristic
83C2×C3×SD16—61no—
84C3×#121—21no—
85C3×#121C2×D311yescharacteristic
86C3×#121C2×D311yescharacteristic
87C2×#215—61no—
88#939—61no—
89#939—61no—
90#939—62no—
91#939—62no—
92#939—61no—
93#939—61no—
94C2×#214—21no—
95#930—31no—
96#930—31no—
97#930—61no—
98C2×C4⋊Dic3—61no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—31no—
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C2×#204—61no—
104#896—62no—
105#896—61no—
106#896—61no—
107#884—61no—
108#884—61no—
109#884—62no—
110#878—61no—
111#878—61no—
112#878—62no—
113C3×#103—61no—
114C3×C22⋊C8—31no—
115C3×C22⋊C8—31no—
116C3×#95—31no—
117#835—61no—
118C3⋊#95—61no—
119C3⋊#95—61no—
120C3⋊#95C2×D311yescharacteristic
121#830C2×D311yescharacteristic
122#830C2×D311yescharacteristic
123#816—61no—
124#810—21no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C32×D4—41no—
129C32×D4—41no—
130C32×D4—41no—
131C2×C32×C4—21no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135#638—42no—
136#638—41no—
137#638—41no—
138#638—81no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3SD1612yescomplemented
146C4⋊(C3⋊D3)—41no—
147C4×C3⋊D3—42no—
148#634—42no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C3×C3⋊C8—41no—
160C3×C3⋊C8—41no—
161#537—91no—
162#448—31no—
163#448—91no—
164#395—91no—
165#327—31no—
166#327—91no—
167#324—91no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—122no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4D1211yescharacteristic
176C2×C3×D4#6711yescharacteristic
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—62no—
183C2×#67—61no—
184C2×#67—61no—
185C2×#67—62no—
186C2×#67—61no—
187C2×#67—61no—
188C2×#67—62no—
189C2×#67—61no—
190C2×#67—61no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202#237—122no—
203#237—122no—
204#237—124no—
205#237—124no—
206#237—122no—
207#237—122no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—61no—
211C2×C4×D3—62no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—42no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C3×SD16—122no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4D1211yescharacteristic
225C3×C4⋊C4#6711yescharacteristic
226C3×C22⋊C4—22no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229#217—62no—
230#217—61no—
231#217—61no—
232#215—122no—
233#214—42no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—61no—
236(C2×D3)⋊C4—61no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—61no—
239(C2×D3)⋊C4—61no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—61no—
243C4⋊Dic3—122no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248Dic3⋊C4—62no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252Dic3⋊C4—61no—
253Dic3⋊C4—122no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256#204—122no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32#12011yescharacteristic
263C22×C32C2×SD1611yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C32×C4—21no—
269C32×C4—21no—
270C32×C4—41no—
271C3⋊Dic3—22no—
272C3⋊Dic3—41no—
273C3⋊Dic3—41no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C2×#41—181no—
277C22×Q8—31no—
278C2×SD16—61no—
279C2×SD16—181no—
280C22⋊Q8—181no—
281C22⋊Q8—181no—
282#121—91no—
283#121—181no—
284#121—181no—
285#121—181no—
286#121D3211yescharacteristic
287C2×C4⋊C4—91no—
288C2×C4⋊C4—181no—
289#103—61no—
290#103—181no—
291C22⋊C8—31no—
292C22⋊C8—31no—
293#95—31no—
294#95—181no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3D3×D411yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—62no—
302C22×D3—61no—
303C22×D3—61no—
304C3×Q8—62no—
305C3×Q8—62no—
306C3×Q8—121no—
307C3×Q8—121no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—81no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—81no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335#67—124no—
336#67—122no—
337#67—122no—
338#67—122no—
339#67—122no—
340#67—121no—
341#67—121no—
342#67—121no—
343#67—121no—
344#67—242no—
345#67—241no—
346#67—241no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—124no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—241no—
374D12—121no—
375D12—121no—
376D12—241no—
377C4×D3—124no—
378C4×D3—122no—
379C4×D3—122no—
380Dic6—22no—
381Dic6—22no—
382Dic6—41no—
383Dic6—41no—
384Dic6—124no—
385Dic6—122no—
386Dic6—122no—
387C3×C8—121no—
388C3×C8—121no—
389C3⋊C8—41no—
390C3⋊C8—41no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—81no—
394C2×C32#45011yescharacteristic
395C2×C32#45611yescharacteristic
396C2×C32B(4,𝔽2)11yescharacteristic
397C3⋊D3—81no—
398#41—362no—
399#41—362no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—122no—
403C2×Q8—181no—
404C2×D4—21no—
405C2×D4—91no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4—181no—
409C2×D4#62611yescharacteristic
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—181no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417SD16—122no—
418SD16—362no—
419C2×C8—61no—
420C2×C8—61no—
421C4⋊C4—91no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—362no—
426C4⋊C4#62611yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3#88211yescharacteristic
450C22×C3#91111yescharacteristic
451C22×C3D3×SD1611yescharacteristic
452C22×C3D3×SD1611yescharacteristic
453C22×C3#91411yescharacteristic
454C22×C3#93711yescharacteristic
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—121no—
463C2×D3—121no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—42no—
471C3×C4—41no—
472C3×C4—41no—
473C3×C4—122no—
474C3×C4—122no—
475Dic3—42no—
476Dic3—42no—
477Dic3—64no—
478Dic3—62no—
479Dic3—62no—
480Dic3—122no—
481Dic3—122no—
482Dic3—121no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486C32#160411yescharacteristic, complemented, Sylow
487C23—21no—
488C23—181no—
489C23#381111yescharacteristic
490Q8—62no—
491Q8—62no—
492Q8—121no—
493Q8—121no—
494Q8—362no—
495D4—41no—
496D4—41no—
497D4—41no—
498D4—361no—
499D4—362no—
500D4—361no—
501D4—361no—
502D4—721no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—92no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—362no—
517C2×C4—362no—
518C2×C4—361no—
519C2×C4C2×#62611yescharacteristic
520C2×C4#381111yescharacteristic
521C8—121no—
522C8—121no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—41no—
531C2×C3—41no—
532C2×C3—82no—
533C2×C3—81no—
534C2×C3—81no—
535C2×C3#474111yescharacteristic
536C2×C3#477611yescharacteristic
537C2×C3#482611yescharacteristic
538C2×C3#503211yescharacteristic
539C2×C3#516911yescharacteristic
540C2×C3#520511yescharacteristic
541D3—242no—
542D3—241no—
543D3—241no—
544C22—21no—
545C22—21no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22#6393011yescharacteristic
553C22#6393711yescharacteristic
554C22#6398111yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—122no—
559C4—122no—
560C4—182no—
561C4—361no—
562C4—361no—
563C3—21no—
564C3#6829511yescharacteristic, complemented
565C3#7097511yescharacteristic, complemented
566C2—21no—
567C2—21no—
568C2—81no—
569C2—721no—
570C2#1059146711yescharacteristic
571C2#1059153211yescharacteristic
572C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radical#10596068C2
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. C3×#5040C2semidirect
3. #10591346C2semidirect
4. #10591174C2semidirect
5. C3×#4537C2semidirect
6. #10589151C2semidirect
7. #10589148C2semidirect
35. #5040D3semidirect
39. #4537D3semidirect
145. C2×C3⋊Dic3SD16semidirect
486. C32#1604semidirect
564. C3#68295semidirect
565. C3#70975semidirect

Maximal subgroups

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

subgroupindex
#105960682
C3×#50402
#105913462
#105911742
C3×#45372
#105891512
#105891482
#709753
#682953