Finite Group Databasebeta

← #11803070

Subgroups — #11803070

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic, complemented
3C3×D3×#95C211yesmaximal, characteristic, complemented
4C3×#4651C211yesmaximal, characteristic, complemented
5#10591382C212yesmaximal
6#10591278C212yesmaximal, complemented
7#10591259C212yesmaximal, complemented
8#10591251C212yesmaximal, complemented
9#10591237C211yesmaximal, characteristic, complemented
10#10591219C211yesmaximal, characteristic, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#74295—31nomaximal
13#73367—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626C2211yescharacteristic
18C2×#3752C2212yes—
19C2×#3750C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×Dic3⋊Dic3C2212yes—
22C2×Dic3⋊Dic3C2211yescharacteristic
23C2×#3722C2212yes—
24C2×#3722C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2211yescharacteristic
27C2×Dic32C2212yes—
28C4×#626C418yescomplemented
29C32×#95C2211yescharacteristic
30#63658C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×D12—31no—
40C3×#383—31no—
41C2×C3×#95—31no—
42#5213—32no—
43#5210—32no—
44C4×#217—31no—
45#4936—31no—
46#4670—32no—
47#4669—32no—
48#4668—32no—
49#4667—31no—
50#4667—31no—
51#4667—61no—
52#4666—31no—
53#4665—32no—
54#4664—31no—
55#4664—31no—
56D3×#95D311yescharacteristic, complemented
57#4654—32no—
58#4652—32no—
59#4651D311yescharacteristic, complemented
60#4650—31no—
61C23×C3⋊D3C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
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—24no—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3—42no—
77C2×C3×C4×D3—42no—
78C2×C3×C4×D3C2×C414yes—
79C2×#626—24no—
80C2×#626C2×C414yes—
81#3752—42no—
82#3750—42no—
83C3×C4×Dic3C2×C414yescomplemented
84Dic3⋊Dic3—42no—
85Dic3⋊Dic3C2×C414yescomplemented
86#3722—42no—
87#3722C2×C414yescomplemented
88(C2×D3)⋊Dic3—24no—
89(C2×D3)⋊Dic3C2×C414yes—
90Dic32—42no—
91#2318—91noSylow
92C23×C3×C4—31no—
93C23×C3×C4—32no—
94C22×#67—31no—
95C22×D12—31no—
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—61no—
99C22×C4×D3C2×D312yes—
100C22×C4×D3C2×D311yescharacteristic
101C2×C3×C42—31no—
102C2×#217—31no—
103C2×#217—32no—
104C4×#67—38no—
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
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—62no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—32no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—62no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3C2×D311yescharacteristic
124C4×D12—38no—
125C3×#95—21no—
126C3×#95—31no—
127C3×#95—32no—
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—61no—
140C3⋊#95C2×D312yes—
141C3⋊#95C2×D311yescharacteristic
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D311yescharacteristic
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3C22×C412yes—
151C22×C3×D3—22no—
152C22×C3×D3—21no—
153C22×C3×D3—21no—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4114yes—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C22×C412yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3C22×C412yes—
166C4×C3⋊D3—44no—
167C2×C3×Dic3—22no—
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×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C3×C4×D3—44no—
181C3×C4×D3—48no—
182#626—28no—
183C2×C4×D4—91no—
184#388—92no—
185#387—92no—
186#386—92no—
187#385—92no—
188#383—31no—
189#382—91no—
190#381—91no—
191#380—91no—
192C4×C22⋊C4—91no—
193C2×#95—31no—
194C24×C3—31no—
195C23×D3—31no—
196C23×D3—31no—
197C23×D3—61no—
198C23×D3C22×D311yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—34no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—64no—
208C22×C3×C4—122no—
209C22×C3×C4—122no—
210C22×C3×C4—122no—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—34no—
216C2×#67—64no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—61no—
222C22×Dic3—62no—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D311yescharacteristic
227C22×Dic3C22×D311yescharacteristic
228C2×D12—34no—
229C2×D12—64no—
230C2×C4×D3—24no—
231C2×C4×D3—34no—
232C2×C4×D3—34no—
233C2×C4×D3—42no—
234C2×C4×D3—42no—
235C2×C4×D3—42no—
236C2×C4×D3—64no—
237C2×C4×D3—122no—
238C2×C4×D3—122no—
239C2×C4×D3—124no—
240C2×C4×D3C4×D314yes—
241C3×C42—34no—
242#217—34no—
243#217—64no—
244(C2×D3)⋊C4—34no—
245(C2×D3)⋊C4—34no—
246(C2×D3)⋊C4—34no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—122no—
249(C2×D3)⋊C4—122no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4—122no—
252(C2×D3)⋊C4—124no—
253C4⋊Dic3—34no—
254C4⋊Dic3—122no—
255Dic3⋊C4—34no—
256Dic3⋊C4—122no—
257Dic3⋊C4—122no—
258Dic3⋊C4—122no—
259Dic3⋊C4—124no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C4×Dic3C4×D314yescomplemented
263C22×C32C23×C411yescharacteristic
264C22×C32C2×#4112yes—
265C22×C32H(5,𝔽2)12yes—
266C22×C32H(5,𝔽2)11yescharacteristic
267C22×C322−1+411yescharacteristic
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3×D3—22no—
274C2×C3×D3—22no—
275C2×C3×D3—24no—
276C2×C3×D3—24no—
277C2×C3×D3#11714yes—
278C32×C4—22no—
279C32×C4—42no—
280C3⋊Dic3—22no—
281C3⋊Dic3—42no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C22×D4—91no—
288C23×C4—31no—
289C23×C4—32no—
290C23×C4—91no—
291C4×D4—98no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C42—31no—
301C2×C42—92no—
302#95—31no—
303#95—32no—
304#95—31no—
305#95—32no—
306#95—32no—
307#95—92no—
308#95—92no—
309#95—91no—
310#95D3211yescharacteristic
311C23×C3—21no—
312C23×C3—32no—
313C23×C3—34no—
314C23×C3—61no—
315C23×C3—62no—
316C23×C3—61no—
317C23×C3C23×D311yescharacteristic
318C23×C3C23×D311yescharacteristic
319C22×D3—22no—
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—32no—
323C22×D3—32no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—61no—
329C22×D3—62no—
330C22×D3—61no—
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—62no—
334C22×D3—61no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3C2×C4×D312yes—
338C22×D3#23514yes—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
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—124no—
366C2×C3×C4—128no—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4C2×C4×D312yes—
369#67—68no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—32no—
381C2×Dic3—32no—
382C2×Dic3—62no—
383C2×Dic3—64no—
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—122no—
395C2×Dic3C2×C4×D312yes—
396C2×Dic3C2×C4×D312yes—
397C2×Dic3C2×C4×D312yes—
398D12—68no—
399C4×D3—44no—
400C4×D3—48no—
401C4×D3—124no—
402C4×D3—124no—
403C4×D3—128no—
404C2×C32C2×#11711yescharacteristic
405C2×C32#51811yescharacteristic
406C2×C32#52011yescharacteristic
407C2×C32#53812yes—
408C2×C32#53912yes—
409C3⋊D3—42no—
410C3×D3—24no—
411C24—31no—
412C24—91no—
413C2×D4—94no—
414C2×D4—184no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—34no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—64no—
422C22×C4—91no—
423C22×C4—94no—
424C22×C4—92no—
425C22×C4—122no—
426C22×C4—122no—
427C22×C4—122no—
428C22×C4—362no—
429C22×C4C2×D3212yes—
430C22×C4C2×D3211yescharacteristic
431C4⋊C4—94no—
432C4⋊C4—362no—
433C4⋊C4—362no—
434C22⋊C4—94no—
435C22⋊C4—94no—
436C22⋊C4—184no—
437C22⋊C4—362no—
438C22⋊C4—362no—
439C42—34no—
440C42—362no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—34no—
447C22×C3—64no—
448C22×C3—64no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C22×C4×D311yescharacteristic
453C22×C3C2×#23512yes—
454C22×C3#100412yes—
455C22×C3#100411yescharacteristic
456C22×C3#100711yescharacteristic
457C22×C3D3×#4112yes—
458C22×C3#100911yescharacteristic
459C22×C3#100912yes—
460C22×C3#101011yescharacteristic
461C2×D3—22no—
462C2×D3—24no—
463C2×D3—22no—
464C2×D3—24no—
465C2×D3—64no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—124no—
475C2×D3—124no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3#87214yes—
481C3×C4—22no—
482C3×C4—22no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—62no—
487C3×C4—62no—
488C3×C4—62no—
489C3×C4—82no—
490C3×C4—122no—
491C3×C4—122no—
492Dic3—22no—
493Dic3—22no—
494Dic3—22no—
495Dic3—42no—
496Dic3—42no—
497Dic3—64no—
498Dic3—62no—
499Dic3—62no—
500Dic3—122no—
501Dic3—122no—
502Dic3—242no—
503C32#231811yescharacteristic, complemented, Sylow
504C23—32no—
505C23—34no—
506C23—62no—
507C23—61no—
508C23—61no—
509C23—92no—
510C23—182no—
511C23—181no—
512C23—182no—
513C23—181no—
514C23C22×D3211yescharacteristic
515D4—188no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—32no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—92no—
534C2×C4—124no—
535C2×C4—128no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—364no—
541C2×C4C4×D3212yes—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—22no—
547C2×C3—64no—
548C2×C3C2×#87211yescharacteristic
549C2×C3#548611yescharacteristic
550C2×C3#549412yes—
551C2×C3#550411yescharacteristic
552C2×C3#551512yes—
553C2×C3D3×#11711yescharacteristic
554C2×C3#552111yescharacteristic
555C2×C3#552311yescharacteristic
556C2×C3#570412yes—
557C2×C3#570712yes—
558D3—24no—
559D3—124no—
560D3—122no—
561D3—122no—
562C22—34no—
563C22—62no—
564C22—64no—
565C22—62no—
566C22—64no—
567C22—182no—
568C22—182no—
569C22—182no—
570C22—362no—
571C22—362no—
572C22C2×C4×D3211yescharacteristic
573C22D3×#23512yes—
574C22#6431412yes—
575C22#6431411yescharacteristic
576C22#6431511yescharacteristic
577C4—22no—
578C4—42no—
579C4—62no—
580C4—62no—
581C4—62no—
582C4—122no—
583C4—122no—
584C4—182no—
585C4—362no—
586C3—21no—
587C3#7336711yescharacteristic, complemented
588C3#7429511yescharacteristic, complemented
589C2—64no—
590C2—362no—
591C2D3×#87211yescharacteristic
592C2#1059418211yescharacteristic
593C2#1059419912yes—
594C2#1059451011yescharacteristic
595C2#1059454112yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592366C2semidirect
3. C3×D3×#95C2semidirect
4. C3×#4651C2semidirect
6. #10591278C2semidirect
7. #10591259C2semidirect
8. #10591251C2semidirect
9. #10591237C2semidirect
10. #10591219C2semidirect
11. #10591206C2semidirect
28. C4×#626C4semidirect
56. D3×#95D3semidirect
59. #4651D3semidirect
68. C2×C4×C3⋊D3C2×C4semidirect
83. C3×C4×Dic3C2×C4semidirect
85. Dic3⋊Dic3C2×C4semidirect
87. #3722C2×C4semidirect
262. C4×Dic3C4×D3semidirect
503. C32#2318semidirect
587. C3#73367semidirect
588. C3#74295semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
#105923662
C3×D3×#952
C3×#46512
#105913822
#105912782
#105912592
#105912512
#105912372
#105912192
#105912062
#742953
#733673