Finite Group Databasebeta

← #11805767

Subgroups — #11805767

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic
2#10592365C211yesmaximal, characteristic, complemented
3C3×#4667C211yesmaximal, characteristic, complemented
4C3×#4651C211yesmaximal, characteristic, complemented
5#10591368C212yesmaximal, complemented
6#10591364C212yesmaximal
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591334C212yesmaximal, complemented
9#10591258C212yesmaximal, complemented
10#10591239C211yesmaximal, characteristic, complemented
11#10591219C211yesmaximal, characteristic, complemented
12#74297—31nomaximal
13#73884—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3752C2212yes—
19C2×C4×C3⋊Dic3C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×Dic3⋊Dic3C2211yescharacteristic
24C2×#3722C2212yes—
25C2×#3722C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2211yescharacteristic
27C2×Dic32C2212yes—
28C4×#626C418yescomplemented
29C32×#95C2211yescharacteristic
30#63658C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×D12—31no—
40C3×#383—31no—
41C3×#380—31no—
42C2×C3⋊#95—31no—
43#4990—32no—
44#4978—32no—
45#4958—32no—
46Dic3×C22⋊C4—32no—
47#4932—31no—
48#4669—32no—
49#4667D311yescharacteristic, complemented
50#4666—32no—
51#4666—31no—
52#4666—31no—
53#4666—61no—
54#4665—32no—
55#4664—31no—
56#4664—31no—
57D3×#95—31no—
58#4653—32no—
59#4651D311yescharacteristic, complemented
60#4648—31no—
61C23×C3⋊D3C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C2×C4×C3⋊D3—42no—
68C2×C4×C3⋊D3C2×C414yescomplemented
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×C4×D3—42no—
75C2×C3×C4×D3C2×C414yes—
76C2×#626—22no—
77C2×#626—22no—
78C2×#626C2×C414yes—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—42no—
82#3752—24no—
83C4×C3⋊Dic3—42no—
84C3×(C2×D3)⋊C4—24no—
85C3×Dic3⋊C4—42no—
86C3×C4×Dic3C2×C414yescomplemented
87Dic3⋊Dic3C2×C414yescomplemented
88#3722—42no—
89#3722C2×C414yescomplemented
90(C2×D3)⋊Dic3C2×C414yes—
91Dic32—24no—
92#2353—91noSylow
93C23×C3×C4—31no—
94C22×#67—31no—
95C23×Dic3—32no—
96C22×D12—31no—
97C22×C4×D3—31no—
98C22×C4×D3—31no—
99C22×C4×D3—32no—
100C22×C4×D3—61no—
101C22×C4×D3C2×D311yescharacteristic
102C2×C3×C4⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C42—31no—
105C2×#217—31no—
106C4×#67—38no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—62no—
115C2×(C2×D3)⋊C4C2×D312yes—
116C2×C4⋊Dic3—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4C2×D312yes—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—62no—
124C2×C4×Dic3C2×D311yescharacteristic
125C4×D12—38no—
126C3×#95—21no—
127C3×#95—31no—
128C3×#95—32no—
129C3×#95—31no—
130C3×#95—32no—
131C3×#95C2×D311yescharacteristic
132C3×#95C2×D311yescharacteristic
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—61no—
142C3⋊#95C2×D311yescharacteristic
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D311yescharacteristic
146C23×C32C2411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3C22×C412yes—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4112yes—
156C22×C3×D3#4112yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C22×C412yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3⋊Dic3#4114yes—
167C4×C3⋊D3—44no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C3×C4×D3—44no—
182#626—28no—
183D3×Dic3—48no—
184C2×C4×D4—91no—
185#388—92no—
186#387—92no—
187#386—92no—
188#383—31no—
189#381—91no—
190#380—31no—
191C4×C22⋊C4—92no—
192C4×C22⋊C4—91no—
193#376—91no—
194C2×#95—91no—
195C24×C3—31no—
196C23×D3—31no—
197C23×D3—31no—
198C23×D3—61no—
199C23×D3C22×D311yescharacteristic
200C22×C3×C4—21no—
201C22×C3×C4—22no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—34no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—122no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—34no—
214C2×#67—62no—
215C2×#67—62no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—61no—
221C22×Dic3—62no—
222C22×Dic3—64no—
223C22×Dic3—64no—
224C22×Dic3—122no—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C2×D12—34no—
231C2×D12—62no—
232C2×D12—62no—
233C2×C4×D3—34no—
234C2×C4×D3—34no—
235C2×C4×D3—42no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—122no—
240C2×C4×D3—122no—
241C2×C4×D3—124no—
242C2×C4×D3—122no—
243C2×C4×D3C4×D314yes—
244C3×C4⋊C4—122no—
245C3×C22⋊C4—64no—
246C3×C42—34no—
247#217—34no—
248(C2×D3)⋊C4—24no—
249(C2×D3)⋊C4—34no—
250(C2×D3)⋊C4—34no—
251(C2×D3)⋊C4—34no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—68no—
255(C2×D3)⋊C4—122no—
256(C2×D3)⋊C4—122no—
257C4⋊Dic3—34no—
258Dic3⋊C4—34no—
259Dic3⋊C4—42no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—122no—
263C4×Dic3—122no—
264C4×Dic3—124no—
265C4×Dic3C4×D314yescomplemented
266C22×C32C23×C411yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C22×C32C2×#4111yescharacteristic
269C22×C32C2×#4112yes—
270C22×C32H(5,𝔽2)12yes—
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—24no—
279C2×C3×D3—24no—
280C2×C3×D3#11714yes—
281C32×C4—22no—
282C32×C4—42no—
283C3⋊Dic3—22no—
284C3⋊Dic3—24no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—42no—
289C3×Dic3—42no—
290C22×D4—91no—
291C23×C4—31no—
292C23×C4—92no—
293C23×C4—91no—
294C4×D4—98no—
295C2×C4⋊C4—32no—
296C2×C4⋊C4—91no—
297C2×C22⋊C4—32no—
298C2×C22⋊C4—91no—
299C2×C22⋊C4—91no—
300C2×C22⋊C4—92no—
301C2×C22⋊C4—92no—
302C2×C42—31no—
303C2×C42—92no—
304C2×C42—92no—
305#95—31no—
306#95—31no—
307#95—32no—
308#95—32no—
309#95—92no—
310#95—92no—
311#95—92no—
312#95—91no—
313#95D3211yescharacteristic
314C23×C3—21no—
315C23×C3—32no—
316C23×C3—32no—
317C23×C3—32no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3C23×D311yescharacteristic
321C23×C3C23×D311yescharacteristic
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—32no—
325C22×D3—32no—
326C22×D3—62no—
327C22×D3—64no—
328C22×D3—61no—
329C22×D3—62no—
330C22×D3—61no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—62no—
336C22×D3—122no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3C2×C4×D312yes—
340C22×D3#23712yes—
341C22×D3#23912yes—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—24no—
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—32no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
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×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—124no—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4C2×C4×D312yes—
371#67—68no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—34no—
385C2×Dic3—34no—
386C2×Dic3—62no—
387C2×Dic3—64no—
388C2×Dic3—64no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—128no—
398C2×Dic3C2×C4×D312yes—
399C2×Dic3C2×C4×D312yes—
400C2×Dic3C2×C4×D312yes—
401D12—68no—
402C4×D3—44no—
403C4×D3—124no—
404C4×D3—124no—
405C4×D3—128no—
406C4×D3—128no—
407C2×C32C2×#11711yescharacteristic
408C2×C32C4×#4111yescharacteristic
409C2×C32#51811yescharacteristic
410C2×C32#55112yes—
411C2×C32#55312yes—
412C3⋊D3—42no—
413C3×D3—24no—
414C24—31no—
415C24—91no—
416C2×D4—94no—
417C2×D4—182no—
418C2×D4—182no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—34no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—92no—
426C22×C4—91no—
427C22×C4—94no—
428C22×C4—122no—
429C22×C4—184no—
430C22×C4—184no—
431C22×C4—362no—
432C22×C4—362no—
433C22×C4C2×D3212yes—
434C22×C4C2×D3211yescharacteristic
435C4⋊C4—94no—
436C4⋊C4—122no—
437C22⋊C4—64no—
438C22⋊C4—94no—
439C22⋊C4—94no—
440C22⋊C4—184no—
441C22⋊C4—362no—
442C42—34no—
443C42—184no—
444C42—362no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—34no—
451C22×C3—64no—
452C22×C3—64no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3C22×C4×D311yescharacteristic
456C22×C3C22×C4×D311yescharacteristic
457C22×C3C2×#23711yescharacteristic
458C22×C3#100412yes—
459C22×C3C2×#23911yescharacteristic
460C22×C3D3×#4112yes—
461C22×C3D3×#4112yes—
462C22×C3D3×#4111yescharacteristic
463C22×C3D3×#4111yescharacteristic
464C22×C3#100912yes—
465C2×D3—24no—
466C2×D3—22no—
467C2×D3—22no—
468C2×D3—24no—
469C2×D3—64no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—62no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—124no—
479C2×D3—124no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3#89214yes—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—42no—
488C3×C4—44no—
489C3×C4—42no—
490C3×C4—42no—
491C3×C4—62no—
492C3×C4—62no—
493C3×C4—62no—
494C3×C4—122no—
495C3×C4—122no—
496Dic3—22no—
497Dic3—22no—
498Dic3—22no—
499Dic3—42no—
500Dic3—42no—
501Dic3—64no—
502Dic3—64no—
503Dic3—64no—
504Dic3—62no—
505Dic3—62no—
506Dic3—124no—
507C32#235311yescharacteristic, complemented, Sylow
508C23—32no—
509C23—32no—
510C23—32no—
511C23—62no—
512C23—62no—
513C23—92no—
514C23—182no—
515C23—181no—
516C23—182no—
517C23—181no—
518C23C22×D3211yescharacteristic
519D4—188no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—92no—
538C2×C4—94no—
539C2×C4—124no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—364no—
544C2×C4—368no—
545C2×C4C4×D3212yes—
546C2×C3—21no—
547C2×C3—22no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—64no—
552C2×C3#548611yescharacteristic
553C2×C3C2×#89211yescharacteristic
554C2×C3D3×#11711yescharacteristic
555C2×C3#552111yescharacteristic
556C2×C3#552211yescharacteristic
557C2×C3#552211yescharacteristic
558C2×C3#560112yes—
559C2×C3#563712yes—
560C2×C3#570512yes—
561C2×C3#570912yes—
562D3—24no—
563D3—124no—
564D3—122no—
565D3—122no—
566C22—34no—
567C22—64no—
568C22—64no—
569C22—62no—
570C22—62no—
571C22—182no—
572C22—182no—
573C22—182no—
574C22—362no—
575C22—362no—
576C22C2×C4×D3211yescharacteristic
577C22#6430612yes—
578C22D3×#23711yescharacteristic
579C22#6431412yes—
580C22D3×#23911yescharacteristic
581C4—22no—
582C4—42no—
583C4—62no—
584C4—62no—
585C4—62no—
586C4—122no—
587C4—122no—
588C4—184no—
589C4—182no—
590C3—21no—
591C3#7388411yescharacteristic, complemented
592C3#7429711yescharacteristic, complemented
593C2—64no—
594C2—362no—
595C2#1059396611yescharacteristic
596C2#1059412412yes—
597C2#1059418211yescharacteristic
598C2D3×#89211yescharacteristic
599C2#1059465512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592365C2semidirect
3. C3×#4667C2semidirect
4. C3×#4651C2semidirect
5. #10591368C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591334C2semidirect
9. #10591258C2semidirect
10. #10591239C2semidirect
11. #10591219C2semidirect
28. C4×#626C4semidirect
49. #4667D3semidirect
59. #4651D3semidirect
68. C2×C4×C3⋊D3C2×C4semidirect
86. C3×C4×Dic3C2×C4semidirect
87. Dic3⋊Dic3C2×C4semidirect
89. #3722C2×C4semidirect
265. C4×Dic3C4×D3semidirect
507. C32#2353semidirect
591. C3#73884semidirect
592. C3#74297semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
#105923652
C3×#46672
C3×#46512
#105913682
#105913642
D3×C3⋊#952
#105913342
#105912582
#105912392
#105912192
#742973
#738843