Finite Group Databasebeta

← #11803151

Subgroups — #11803151

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C211yesmaximal, characteristic
2#10592363C211yesmaximal, characteristic, complemented
3C3×#4664C211yesmaximal, characteristic, complemented
4C3×#4648C211yesmaximal, characteristic, complemented
5#10591383C212yesmaximal
6#10591355C211yesmaximal, characteristic, complemented
7#10591327C212yesmaximal, complemented
8#10591295C211yesmaximal, characteristic, complemented
9#10591282C212yesmaximal, complemented
10#10591259C212yesmaximal, complemented
11#10591242C211yesmaximal, characteristic, complemented
12#74055—31nomaximal
13#73415—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626C2211yescharacteristic
17C2×#3752C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×#3724C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic3⋊Dic3C2211yescharacteristic
25C2×#3722C2212yes—
26C2×#3722C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×Dic32C2212yes—
30C4×#626C418yescomplemented
31C32×#95C2211yescharacteristic
32#63658C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C2×C4×#67—31no—
39C2×C4×D12—31no—
40C3×#381—31no—
41C3×#376—31no—
42#5212—31no—
43#4957—32no—
44#4945—32no—
45#4939—32no—
46C4×C4⋊Dic3—31no—
47#4928—32no—
48#4670—32no—
49#4669—32no—
50#4669—32no—
51#4667—31no—
52#4667—31no—
53#4667—31no—
54#4664—31no—
55#4664—31no—
56#4664—61no—
57#4664D311yescharacteristic, complemented
58#4649—31no—
59#4648D311yescharacteristic, complemented
60#4647—32no—
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×C414yes—
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—24no—
77C2×#626C2×C414yes—
78#3752—42no—
79C3×(C2×D3)⋊C4—42no—
80C3×C4×Dic3—24no—
81C3×C4×Dic3C2×C414yes—
82#3724—42no—
83Dic3⋊Dic3—24no—
84Dic3⋊Dic3—42no—
85Dic3⋊Dic3C2×C414yes—
86#3722—42no—
87#3722C2×C414yes—
88(C2×D3)⋊Dic3—42no—
89(C2×D3)⋊Dic3C2×C414yes—
90Dic32—42no—
91#2319—91noSylow
92C23×C3×C4—31no—
93C22×#67—31no—
94C22×D12—31no—
95C22×C4×D3—31no—
96C22×C4×D3—31no—
97C22×C4×D3—61no—
98C22×C4×D3C2×D311yescharacteristic
99C2×C3×C22⋊C4—32no—
100C2×C3×C42—31no—
101C2×C3×C42—32no—
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×(C2×D3)⋊C4C2×D312yes—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3C2×D312yes—
126C2×C4×Dic3C2×D311yescharacteristic
127C4×D12—38no—
128C3×#95—21no—
129C3×#95—32no—
130C3×#95—31no—
131C3×#95—31no—
132C3×#95—32no—
133C3×#95C2×D311yescharacteristic
134C3×#95C2×D311yescharacteristic
135C3⋊#95—32no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—61no—
140C3⋊#95—62no—
141C3⋊#95C2×D311yescharacteristic
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3C22×C412yes—
151C22×C3×D3—22no—
152C22×C3×D3—21no—
153C22×C3×D3—22no—
154C22×C3×D3—21no—
155C22×C3×D3C22×C412yes—
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—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3#4114yes—
180C3×C4×D3—44no—
181#626—28no—
182C2×C4×D4—91no—
183#390—92no—
184#389—92no—
185#388—92no—
186#388—92no—
187#381—31no—
188#381—91no—
189#380—91no—
190#380—91no—
191C4×C4⋊C4—91no—
192#376—31no—
193C24×C3—31no—
194C23×D3—31no—
195C23×D3—31no—
196C23×D3—61no—
197C23×D3C22×D311yescharacteristic
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—34no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—122no—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—34no—
212C2×#67—64no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218C22×Dic3—62no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C2×D12—34no—
225C2×D12—64no—
226C2×C4×D3—34no—
227C2×C4×D3—34no—
228C2×C4×D3—42no—
229C2×C4×D3—64no—
230C2×C4×D3—122no—
231C2×C4×D3—122no—
232C2×C4×D3—124no—
233C2×C4×D3C4×D314yes—
234C3×C22⋊C4—122no—
235C3×C42—34no—
236C3×C42—64no—
237#217—34no—
238#217—122no—
239(C2×D3)⋊C4—34no—
240(C2×D3)⋊C4—34no—
241(C2×D3)⋊C4—34no—
242(C2×D3)⋊C4—42no—
243(C2×D3)⋊C4—122no—
244(C2×D3)⋊C4—122no—
245(C2×D3)⋊C4—122no—
246(C2×D3)⋊C4—122no—
247(C2×D3)⋊C4—122no—
248(C2×D3)⋊C4—124no—
249C4⋊Dic3—34no—
250C4⋊Dic3—64no—
251C4⋊Dic3—122no—
252Dic3⋊C4—34no—
253Dic3⋊C4—64no—
254Dic3⋊C4—122no—
255Dic3⋊C4—122no—
256Dic3⋊C4—122no—
257C4×Dic3—24no—
258C4×Dic3—122no—
259C4×Dic3—122no—
260C4×Dic3C4×D314yes—
261C22×C32C23×C411yescharacteristic
262C22×C32C2×#4112yes—
263C22×C32H(5,𝔽2)12yes—
264C22×C32H(5,𝔽2)11yescharacteristic
265C22×C322−1+411yescharacteristic
266C2×C3⋊D3—22no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3—22no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C32×C4—22no—
277C32×C4—42no—
278C3⋊Dic3—22no—
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—42no—
283C3×Dic3—42no—
284C3×Dic3#11714yes—
285C22×D4—91no—
286C23×C4—31no—
287C23×C4—91no—
288C4×D4—98no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—92no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—92no—
293C2×C22⋊C4—32no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C42—31no—
300C2×C42—32no—
301C2×C42—92no—
302#95—31no—
303#95—32no—
304#95—31no—
305#95—32no—
306#95—91no—
307#95—92no—
308#95D3211yescharacteristic
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—62no—
312C23×C3—61no—
313C23×C3—62no—
314C23×C3—61no—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—21no—
320C22×D3—21no—
321C22×D3—32no—
322C22×D3—32no—
323C22×D3—62no—
324C22×D3—64no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—62no—
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—122no—
334C22×D3—121no—
335C22×D3—121no—
336C22×D3C2×C4×D312yes—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
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—32no—
347C2×C3×C4—34no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—61no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—124no—
364C2×C3×C4C2×C4×D312yes—
365C2×C3×C4C2×C4×D312yes—
366#67—68no—
367C2×Dic3—22no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390C2×Dic3—122no—
391C2×Dic3C2×C4×D312yes—
392C2×Dic3C2×C4×D312yes—
393C2×Dic3C2×C4×D312yes—
394C2×Dic3#23514yes—
395D12—68no—
396C4×D3—44no—
397C4×D3—124no—
398C4×D3—124no—
399C4×D3—128no—
400C2×C32C2×#11711yescharacteristic
401C2×C32#51811yescharacteristic
402C2×C32#52011yescharacteristic
403C2×C32#54012yes—
404C2×C32#54212yes—
405C3⋊D3—42no—
406C3×D3—42no—
407C24—31no—
408C24—91no—
409C2×D4—94no—
410C2×D4—184no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—34no—
415C22×C4—32no—
416C22×C4—32no—
417C22×C4—91no—
418C22×C4—94no—
419C22×C4—92no—
420C22×C4—122no—
421C22×C4—362no—
422C22×C4C2×D3212yes—
423C22×C4C2×D3211yescharacteristic
424C4⋊C4—94no—
425C4⋊C4—184no—
426C4⋊C4—362no—
427C4⋊C4—362no—
428C22⋊C4—94no—
429C22⋊C4—94no—
430C22⋊C4—122no—
431C22⋊C4—362no—
432C22⋊C4—362no—
433C22⋊C4—362no—
434C42—34no—
435C42—64no—
436C42—362no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—62no—
443C22×C3—62no—
444C22×C3—62no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3C22×C4×D311yescharacteristic
448C22×C3C22×C4×D311yescharacteristic
449C22×C3C2×#23512yes—
450C22×C3#100412yes—
451C22×C3D3×#4112yes—
452C22×C3#100912yes—
453C22×C3#100911yescharacteristic
454C22×C3#100911yescharacteristic
455C22×C3#101011yescharacteristic
456C22×C3#101011yescharacteristic
457C2×D3—22no—
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—64no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—124no—
472C2×D3—124no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—122no—
477C3×C4—22no—
478C3×C4—22no—
479C3×C4—34no—
480C3×C4—42no—
481C3×C4—42no—
482C3×C4—42no—
483C3×C4—62no—
484C3×C4—62no—
485C3×C4—82no—
486C3×C4—122no—
487C3×C4—122no—
488Dic3—22no—
489Dic3—22no—
490Dic3—42no—
491Dic3—42no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495Dic3—122no—
496Dic3—122no—
497Dic3—242no—
498Dic3#87214yes—
499C32#231911yescharacteristic, complemented, Sylow
500C23—32no—
501C23—62no—
502C23—61no—
503C23—62no—
504C23—61no—
505C23—92no—
506C23—182no—
507C23—181no—
508C23—182no—
509C23—181no—
510C23C22×D3211yescharacteristic
511D4—188no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—32no—
517C2×C4—34no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—61no—
521C2×C4—62no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—92no—
530C2×C4—124no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—364no—
536C2×C4C4×D3212yes—
537C2×C3—21no—
538C2×C3—22no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—22no—
542C2×C3—122no—
543C2×C3C2×#87211yescharacteristic
544C2×C3#548611yescharacteristic
545C2×C3D3×#11711yescharacteristic
546C2×C3#552111yescharacteristic
547C2×C3#552311yescharacteristic
548C2×C3#552311yescharacteristic
549C2×C3#553412yes—
550C2×C3#553512yes—
551C2×C3#566212yes—
552C2×C3#566312yes—
553D3—42no—
554D3—124no—
555D3—122no—
556D3—122no—
557C22—62no—
558C22—62no—
559C22—62no—
560C22—122no—
561C22—122no—
562C22—182no—
563C22—182no—
564C22—182no—
565C22—362no—
566C22—362no—
567C22C2×C4×D3211yescharacteristic
568C22D3×#23512yes—
569C22#6430911yescharacteristic
570C22#6431412yes—
571C22#6432011yescharacteristic
572C4—22no—
573C4—34no—
574C4—42no—
575C4—62no—
576C4—62no—
577C4—122no—
578C4—122no—
579C4—182no—
580C4—362no—
581C3—21no—
582C3#7341511yescharacteristic, complemented
583C3#7405511yescharacteristic, complemented
584C2—122no—
585C2—362no—
586C2D3×#87211yescharacteristic
587C2#1059418211yescharacteristic
588C2#1059420512yes—
589C2#1059451111yescharacteristic
590C2#1059454612yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2319
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592363C2semidirect
3. C3×#4664C2semidirect
4. C3×#4648C2semidirect
6. #10591355C2semidirect
7. #10591327C2semidirect
8. #10591295C2semidirect
9. #10591282C2semidirect
10. #10591259C2semidirect
11. #10591242C2semidirect
30. C4×#626C4semidirect
57. #4664D3semidirect
59. #4648D3semidirect
499. C32#2319semidirect
582. C3#73415semidirect
583. C3#74055semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
#105923632
C3×#46642
C3×#46482
#105913832
#105913552
#105913272
#105912952
#105912822
#105912592
#105912422
#740553
#734153