Finite Group Databasebeta

← #11808452

Subgroups — #11808452

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×#63902C211yesmaximal, characteristic, complemented
3C2×#63881C212yesmaximal, complemented
4C3×#4994C212yesmaximal, complemented
5#10591394C211yesmaximal, characteristic, complemented
6#10591393C211yesmaximal, characteristic
7#10591392C212yesmaximal, complemented
8#10591368C212yesmaximal, complemented
9#10591274C211yesmaximal, characteristic, complemented
10#10591216C211yesmaximal, characteristic, complemented
11#10591215C211yesmaximal, characteristic, complemented
12#77281—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#626C2212yes—
15C22×#625C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64101—24no—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×#3724C2211yescharacteristic
30C2×#3722C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33#63902—24no—
34#63881—28no—
35C3×C3⋊#95C2212yes—
36#63579C2211yescharacteristic
37#63579C2211yescharacteristic
38#63579C2212yes—
39C2×#893—32no—
40C2×#892—32no—
41C2×#892—61no—
42C2×#67⋊C4—32no—
43C2×#67⋊C4—32no—
44C3×#396—32no—
45#4994D312yescomplemented
46#4991—32no—
47#4982—32no—
48Dic3×C4⋊C4—32no—
49#4961—32no—
50#4961—32no—
51#4960—32no—
52Dic3×C22⋊C4—32no—
53#4675—32no—
54#4666—32no—
55C23×C3⋊D3C2311yescharacteristic
56C23×C3×D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3D414yescomplemented
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×#626—24no—
70C2×#626—24no—
71C2×#626—24no—
72C2×#625—24no—
73C2×#625—22no—
74C2×D3×Dic3—24no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—24no—
77C32×C4⋊C4—22no—
78#3752—22no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—22no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3D414yescomplemented
83C3×(C2×D3)⋊C4—24no—
84C3×(C2×D3)⋊C4—24no—
85C3×(C2×D3)⋊C4—24no—
86C3×C4⋊Dic3—24no—
87C3×Dic3⋊C4—24no—
88#3724—22no—
89#3722—24no—
90(C2×D3)⋊Dic3—24no—
91Dic32—24no—
92#2392—91noSylow
93C22×#67—32no—
94C22×#67—32no—
95C23×Dic3—32no—
96C22×D12—32no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—61no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4C2×D312yes—
104C2×C3×C22⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—32no—
107C2×#217—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4C2×D312yes—
116C2×(C2×D3)⋊C4C2×D312yes—
117C2×(C2×D3)⋊C4C2×D312yes—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D312yes—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4C2×D312yes—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—61no—
128C2×C4×Dic3—61no—
129#893—68no—
130#892—68no—
131#892—68no—
132#67⋊C4—68no—
133#67⋊C4—68no—
134C3×#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95C2×D312yes—
140C23×C32C2411yescharacteristic
141C22×C3⋊D3—21no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3C2×D412yes—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3#4114yes—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C2×D412yes—
164C2×C3⋊Dic3C2×D412yes—
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3#4112yes—
167C4×C3⋊D3—28no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3#4114yes—
177#626—216no—
178#625—28no—
179D3×Dic3—48no—
180C2×C4×D4—91no—
181C2×C4×D4—92no—
182C2×#117—91no—
183#398—91no—
184#397—91no—
185#396—32no—
186#394—91no—
187#394—92no—
188#392—91no—
189C4×C4⋊C4—91no—
190C4×C22⋊C4—92no—
191C24×C3—32no—
192C23×D3—32no—
193C23×D3—61no—
194C23×D3C22×D312yes—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D312yes—
204C2×#67—64no—
205C2×#67—64no—
206C2×#67—64no—
207C2×#67—64no—
208C2×#67—64no—
209C2×#67—64no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—64no—
217C22×Dic3—64no—
218C22×Dic3—64no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C2×D12—64no—
223C2×D12—64no—
224C2×D12—64no—
225C2×C4×D3—38no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C3×C4⋊C4—24no—
235C3×C4⋊C4—24no—
236C3×C4⋊C4—64no—
237C3×C4⋊C4—64no—
238C3×C22⋊C4—64no—
239C3×C22⋊C4—64no—
240C3×C22⋊C4—64no—
241#217—64no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—24no—
244(C2×D3)⋊C4—24no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—24no—
253C4⋊Dic3—64no—
254C4⋊Dic3—64no—
255Dic3⋊C4—24no—
256Dic3⋊C4—64no—
257C4×Dic3—38no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C22×C32C22×D411yescharacteristic
264C22×C32C22×D411yescharacteristic
265C22×C32C2×#4112yes—
266C22×C32C2×#4112yes—
267C22×C32C2×#4111yescharacteristic
268C2×C3⋊D3—22no—
269C2×C3⋊D3—24no—
270C2×C3⋊D3—41no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—41no—
273C2×C3×D3—24no—
274C2×C3×D3—24no—
275C2×C3×D3—24no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—22no—
281C32×C4—22no—
282C32×C4—41no—
283C3⋊Dic3—22no—
284C3⋊Dic3—41no—
285C3⋊Dic3#12114yes—
286C3×Dic3—24no—
287C3×Dic3—42no—
288C3×Dic3—42no—
289C22×D4—92no—
290C22×D4—91no—
291C23×C4—92no—
292C23×C4—91no—
293C4×D4—184no—
294C4×D4—188no—
295#117—184no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4D3211yescharacteristic
301C2×C22⋊C4—32no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—32no—
304C2×C22⋊C4—92no—
305C2×C22⋊C4—92no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C42—91no—
309C2×C42—92no—
310C2×C42—91no—
311#95—32no—
312#95—92no—
313#95—91no—
314#95—91no—
315C23×C3—21no—
316C23×C3—34no—
317C23×C3—62no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3—62no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3C23×D312yes—
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—22no—
330C22×D3—34no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3#23914yes—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—34no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4D3×D414yes—
367C2×C3×C4D3×D414yes—
368#67—616no—
369#67—616no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3—128no—
395C2×Dic3#23714yes—
396D12—616no—
397C4×D3—616no—
398C4×D3—616no—
399C4×D3—128no—
400C2×C32C2×#12111yescharacteristic
401C2×C32#52512yes—
402C2×C32#52511yescharacteristic
403C2×C32#52912yes—
404C2×C32#53211yescharacteristic
405C3⋊D3—42no—
406C3×D3—44no—
407C24—32no—
408C24—91no—
409C2×D4—184no—
410C2×D4—184no—
411C2×D4—184no—
412C2×D4—182no—
413C2×D4—184no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—32no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—94no—
420C22×C4—91no—
421C22×C4—182no—
422C22×C4—182no—
423C22×C4—184no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4C2×D3211yescharacteristic
427C22×C4C2×D3211yescharacteristic
428C22×C4C2×D3211yescharacteristic
429C4⋊C4—22no—
430C4⋊C4—64no—
431C4⋊C4—64no—
432C4⋊C4—182no—
433C4⋊C4—182no—
434C22⋊C4—64no—
435C22⋊C4—64no—
436C22⋊C4—64no—
437C22⋊C4—182no—
438C22⋊C4—184no—
439C22⋊C4—184no—
440C22⋊C4—182no—
441C42—94no—
442C42—182no—
443C42—184no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—64no—
450C22×C3—64no—
451C22×C3—64no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—122no—
455C22×C3—122no—
456C22×C3C2×D3×D412yes—
457C22×C3C2×D3×D412yes—
458C22×C3C2×#23712yes—
459C22×C3C2×#23912yes—
460C22×C3D3×#4112yes—
461C22×C3D3×#4112yes—
462C22×C3D3×#4112yes—
463C2×D3—24no—
464C2×D3—24no—
465C2×D3—24no—
466C2×D3—42no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—64no—
471C2×D3—64no—
472C2×D3—64no—
473C2×D3—64no—
474C2×D3—124no—
475C2×D3—122no—
476C2×D3—122no—
477C2×D3—124no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—122no—
482C3×C4—24no—
483C3×C4—24no—
484C3×C4—24no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—42no—
488C3×C4—64no—
489C3×C4—122no—
490C3×C4—122no—
491Dic3—24no—
492Dic3—38no—
493Dic3—42no—
494Dic3—42no—
495Dic3—64no—
496Dic3—64no—
497Dic3—122no—
498Dic3—122no—
499Dic3—122no—
500C32#239211yescharacteristic, complemented, Sylow
501C23—34no—
502C23—62no—
503C23—62no—
504C23—62no—
505C23—62no—
506C23—62no—
507C23—62no—
508C23—92no—
509C23—181no—
510C23—182no—
511C23—182no—
512C23—181no—
513C23C22×D3211yescharacteristic
514D4—1816no—
515D4—188no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—34no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—92no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—92no—
534C2×C4—188no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—181no—
538C2×C4—368no—
539C2×C4#380212yes—
540C2×C4#381112yes—
541C2×C3—21no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—22no—
546C2×C3—124no—
547C2×C3#559612yes—
548C2×C3D3×#12112yes—
549C2×C3#560612yes—
550C2×C3#562412yes—
551C2×C3#562712yes—
552C2×C3#562712yes—
553C2×C3#570612yes—
554D3—44no—
555D3—124no—
556D3—124no—
557C22—64no—
558C22—64no—
559C22—64no—
560C22—122no—
561C22—122no—
562C22—122no—
563C22—122no—
564C22—182no—
565C22—184no—
566C22—361no—
567C22—361no—
568C22—362no—
569C22C2×#380211yescharacteristic
570C22#6430611yescharacteristic
571C22D3×#23712yes—
572C22D3×#23912yes—
573C22C2×#381111yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—64no—
578C4—94no—
579C4—122no—
580C4—122no—
581C4—182no—
582C4—361no—
583C3—21no—
584C3#7728112yescomplemented
585C2—124no—
586C2—362no—
587C2#1059444212yes—
588C2#1059463212yes—
589C2#1059508111yescharacteristic
590C2#1059516511yescharacteristic
591C2#1059543011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radical#10591393C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64101C2semidirect
2. C2×#63902C2semidirect
3. C2×#63881C2semidirect
4. C3×#4994C2semidirect
5. #10591394C2semidirect
7. #10591392C2semidirect
8. #10591368C2semidirect
9. #10591274C2semidirect
10. #10591216C2semidirect
11. #10591215C2semidirect
45. #4994D3semidirect
65. C2×C4×C3⋊D3D4semidirect
82. C4×C3⋊Dic3D4semidirect
500. C32#2392semidirect
584. C3#77281semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#639022
C2×#638812
C3×#49942
#105913942
#105913932
#105913922
#105913682
#105912742
#105912162
#105912152
#772813