Finite Group Databasebeta

← #11806049

Subgroups — #11806049

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 596 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×#4649C211yesmaximal, characteristic, complemented
5#10591383C212yesmaximal
6#10591285C212yesmaximal, complemented
7#10591260C211yesmaximal, characteristic, complemented
8#10591258C212yesmaximal, complemented
9#10591242C212yesmaximal, complemented
10#10591237C211yesmaximal, characteristic, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#74061—31nomaximal
13#73645—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626C2211yescharacteristic
17C2×#3752C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2211yescharacteristic
24C2×#3722C2212yes—
25C2×#3722C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30C4×#626C418yescomplemented
31C32×#95C2211yescharacteristic
32#63658C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×D12—31no—
40C3×#381—31no—
41C3×C4×C4⋊C4—31no—
42C4×#217—31no—
43#4990—32no—
44#4990—32no—
45#4957—32no—
46#4944—32no—
47#4939—32no—
48#4936—31no—
49C4×C4⋊Dic3—32no—
50#4669—32no—
51#4666—31no—
52#4666—31no—
53#4666—31no—
54#4664—31no—
55#4664—31no—
56#4664—61no—
57#4664D311yescharacteristic, complemented
58#4650—31no—
59#4649—32no—
60#4649D311yescharacteristic, complemented
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×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×C4×D3—42no—
75C2×C3×C4×D3C2×C414yes—
76C2×#626—22no—
77C2×#626—22no—
78C2×#626C2×C414yes—
79#3752—42no—
80C3×(C2×D3)⋊C4—42no—
81C3×Dic3⋊C4—24no—
82C3×C4×Dic3—24no—
83C3×C4×Dic3C2×C414yes—
84Dic3⋊Dic3—24no—
85Dic3⋊Dic3C2×C414yes—
86#3722—24no—
87#3722C2×C414yes—
88(C2×D3)⋊Dic3—24no—
89(C2×D3)⋊Dic3C2×C414yes—
90Dic32—42no—
91Dic32—42no—
92#2357—91noSylow
93C23×C3×C4—31no—
94C22×#67—31no—
95C22×D12—31no—
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—61no—
99C22×C4×D3C2×D311yescharacteristic
100C2×C3×C4⋊C4—32no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C42—31no—
103C2×C3×C42—32no—
104C2×#217—31no—
105C2×#217—32no—
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—32no—
115C2×(C2×D3)⋊C4—62no—
116C2×(C2×D3)⋊C4C2×D312yes—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—32no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4C2×D312yes—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3C2×D312yes—
127C2×C4×Dic3C2×D311yescharacteristic
128C4×D12—38no—
129C3×#95—21no—
130C3×#95—32no—
131C3×#95—31no—
132C3×#95—31no—
133C3×#95C2×D311yescharacteristic
134C3×#95C2×D311yescharacteristic
135C3⋊#95—32no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—61no—
142C3⋊#95—62no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D312yes—
146C23×C32C2411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3C22×C412yes—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—22no—
156C22×C3×D3C22×C412yes—
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⋊Dic3—22no—
166C2×C3⋊Dic3C22×C412yes—
167C4×C3⋊D3—44no—
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×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3#4114yes—
179C2×C3×Dic3#4112yes—
180C2×C3×Dic3#4112yes—
181C3×C4×D3—44no—
182#626—28no—
183C2×C4×D4—91no—
184#390—92no—
185#388—92no—
186#388—92no—
187#382—91no—
188#381—31no—
189#381—91no—
190C4×C4⋊C4—31no—
191C4×C4⋊C4—92no—
192C4×C22⋊C4—91no—
193C4×C22⋊C4—91no—
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—32no—
205C22×C3×C4—34no—
206C22×C3×C4—32no—
207C22×C3×C4—122no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—34no—
213C2×#67—62no—
214C2×#67—62no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—61no—
220C22×Dic3—62no—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D311yescharacteristic
226C2×D12—34no—
227C2×D12—62no—
228C2×D12—62no—
229C2×C4×D3—34no—
230C2×C4×D3—34no—
231C2×C4×D3—42no—
232C2×C4×D3—64no—
233C2×C4×D3—122no—
234C2×C4×D3—122no—
235C2×C4×D3—124no—
236C2×C4×D3C4×D314yes—
237C3×C4⋊C4—64no—
238C3×C22⋊C4—122no—
239C3×C42—34no—
240C3×C42—64no—
241#217—34no—
242#217—64no—
243(C2×D3)⋊C4—34no—
244(C2×D3)⋊C4—34no—
245(C2×D3)⋊C4—34no—
246(C2×D3)⋊C4—42no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4—122no—
252(C2×D3)⋊C4—124no—
253C4⋊Dic3—34no—
254C4⋊Dic3—64no—
255Dic3⋊C4—24no—
256Dic3⋊C4—34no—
257Dic3⋊C4—64no—
258C4×Dic3—24no—
259C4×Dic3—122no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C4×Dic3—122no—
263C4×Dic3C4×D314yes—
264C22×C32C23×C411yescharacteristic
265C22×C32C2×#4112yes—
266C22×C32C2×#4111yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C22×C32H(5,𝔽2)12yes—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—22no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C32×C4—22no—
280C32×C4—42no—
281C3⋊Dic3—22no—
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—24no—
286C3×Dic3—42no—
287C3×Dic3#11714yes—
288C22×D4—91no—
289C23×C4—31no—
290C23×C4—91no—
291C4×D4—98no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—91no—
294C2×C4⋊C4—92no—
295C2×C22⋊C4—32no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C22⋊C4—92no—
301C2×C42—31no—
302C2×C42—32no—
303C2×C42—92no—
304C2×C42—92no—
305#95—31no—
306#95—31no—
307#95—32no—
308#95—92no—
309#95—91no—
310#95—92no—
311#95D3211yescharacteristic
312C23×C3—21no—
313C23×C3—32no—
314C23×C3—62no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3—62no—
318C23×C3C23×D311yescharacteristic
319C23×C3C23×D311yescharacteristic
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—21no—
323C22×D3—21no—
324C22×D3—32no—
325C22×D3—32no—
326C22×D3—62no—
327C22×D3—64no—
328C22×D3—62no—
329C22×D3—61no—
330C22×D3—62no—
331C22×D3—61no—
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—
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—22no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—34no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
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×C4—124no—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4C2×C4×D312yes—
369#67—68no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—32no—
378C2×Dic3—32no—
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—62no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392C2×Dic3C2×C4×D312yes—
393C2×Dic3C2×C4×D312yes—
394C2×Dic3C2×C4×D312yes—
395C2×Dic3#23514yes—
396C2×Dic3#23712yes—
397C2×Dic3#23912yes—
398D12—68no—
399C4×D3—44no—
400C4×D3—124no—
401C4×D3—124no—
402C4×D3—128no—
403C2×C32C2×#11711yescharacteristic
404C2×C32C4×#4111yescharacteristic
405C2×C32#51811yescharacteristic
406C2×C32#55312yes—
407C2×C32#55912yes—
408C3⋊D3—42no—
409C3×D3—42no—
410C24—31no—
411C24—91no—
412C2×D4—94no—
413C2×D4—182no—
414C2×D4—182no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—32no—
418C22×C4—31no—
419C22×C4—34no—
420C22×C4—32no—
421C22×C4—91no—
422C22×C4—94no—
423C22×C4—92no—
424C22×C4—122no—
425C22×C4—362no—
426C22×C4C2×D3212yes—
427C22×C4C2×D3211yescharacteristic
428C4⋊C4—64no—
429C4⋊C4—94no—
430C4⋊C4—184no—
431C22⋊C4—94no—
432C22⋊C4—94no—
433C22⋊C4—122no—
434C22⋊C4—184no—
435C22⋊C4—184no—
436C22⋊C4—362no—
437C42—34no—
438C42—64no—
439C42—362no—
440C42—362no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—62no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C22×C4×D311yescharacteristic
453C22×C3C2×#23512yes—
454C22×C3C2×#23711yescharacteristic
455C22×C3#100412yes—
456C22×C3C2×#23911yescharacteristic
457C22×C3D3×#4112yes—
458C22×C3D3×#4111yescharacteristic
459C22×C3D3×#4111yescharacteristic
460C22×C3#100912yes—
461C2×D3—22no—
462C2×D3—22no—
463C2×D3—22no—
464C2×D3—42no—
465C2×D3—42no—
466C2×D3—64no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—124no—
476C2×D3—124no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C3×C4—22no—
482C3×C4—22no—
483C3×C4—34no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—64no—
488C3×C4—62no—
489C3×C4—62no—
490C3×C4—82no—
491C3×C4—122no—
492Dic3—22no—
493Dic3—22no—
494Dic3—24no—
495Dic3—42no—
496Dic3—62no—
497Dic3—62no—
498Dic3—122no—
499Dic3—122no—
500Dic3—122no—
501Dic3—242no—
502Dic3#89214yes—
503C32#235711yescharacteristic, complemented, Sylow
504C23—32no—
505C23—62no—
506C23—61no—
507C23—62no—
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—32no—
524C2×C4—32no—
525C2×C4—34no—
526C2×C4—62no—
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—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—364no—
540C2×C4C4×D3212yes—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—22no—
546C2×C3—122no—
547C2×C3C4×#23511yescharacteristic
548C2×C3#548611yescharacteristic
549C2×C3C2×#89211yescharacteristic
550C2×C3D3×#11711yescharacteristic
551C2×C3#552111yescharacteristic
552C2×C3#552211yescharacteristic
553C2×C3#556512yes—
554C2×C3#558512yes—
555C2×C3#566112yes—
556C2×C3#566412yes—
557D3—42no—
558D3—124no—
559D3—122no—
560D3—122no—
561C22—62no—
562C22—62no—
563C22—62no—
564C22—122no—
565C22—122no—
566C22—182no—
567C22—182no—
568C22—182no—
569C22—362no—
570C22—362no—
571C22C2×C4×D3211yescharacteristic
572C22D3×#23512yes—
573C22D3×#23711yescharacteristic
574C22#6431412yes—
575C22D3×#23911yescharacteristic
576C4—22no—
577C4—34no—
578C4—42no—
579C4—62no—
580C4—64no—
581C4—62no—
582C4—122no—
583C4—182no—
584C4—362no—
585C3—21no—
586C3#7364511yescharacteristic, complemented
587C3#7406111yescharacteristic, complemented
588C2—122no—
589C2—362no—
590C2#1059396511yescharacteristic
591C2#1059418211yescharacteristic
592C2#1059419712yes—
593C2#1059454912yes—
594C2D3×#89211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2357
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×#4649C2semidirect
6. #10591285C2semidirect
7. #10591260C2semidirect
8. #10591258C2semidirect
9. #10591242C2semidirect
10. #10591237C2semidirect
11. #10591206C2semidirect
30. C4×#626C4semidirect
57. #4664D3semidirect
60. #4649D3semidirect
503. C32#2357semidirect
586. C3#73645semidirect
587. C3#74061semidirect

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×#46492
#105913832
#105912852
#105912602
#105912582
#105912422
#105912372
#105912062
#740613
#736453