Finite Group Databasebeta

← #11811914

Subgroups — #11811914

Order 1152.

1801 conjugacy classes of subgroups.

The subgroup lattice has 605 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×C3×#875C211yesmaximal, characteristic, complemented
3C2×#63873C211yesmaximal, characteristic, complemented
4C2×#63871C211yesmaximal, characteristic, complemented
5C4×#3752C211yesmaximal, characteristic, complemented
6C3×#4929C211yesmaximal, characteristic, complemented
7#10591373C214yesmaximal, complemented
8#10591323C211yesmaximal, characteristic, complemented
9#10591292C214yesmaximal, complemented
10#82959—31nomaximal
11#76498—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626C2212yes—
17C22×D3×Dic3C2212yes—
18C2×#3796—24no—
19C2×#3796—24no—
20C2×#3796—24no—
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C3×#875—24no—
27C2×#3724C2214yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×#3722C2212yes—
30C2×(C2×D3)⋊Dic3C2214yes—
31#63873—24no—
32#63871—24no—
33#63658C2212yes—
34C3×C3⋊#95C2214yes—
35C22×#239—31no—
36C22×#237—31no—
37C2×C3×#124—31no—
38C2×#946—31no—
39C2×#944—31no—
40C2×#944—31no—
41C2×#897—31no—
42C2×#875D311yescharacteristic, complemented
43C3×#391—31no—
44#5221—31no—
45#4988—31no—
46#4959—34no—
47#4946—34no—
48C4×(C2×D3)⋊C4—31no—
49C4×(C2×D3)⋊C4—31no—
50C4×(C2×D3)⋊C4—61no—
51#4929D311yescharacteristic, complemented
52#4672—34no—
53#4668—34no—
54C23×C3⋊D3C2311yescharacteristic
55C23×C3×D3C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3D414yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12D414yes—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6D414yes—
75C2×#626—24no—
76C2×#626—24no—
77C2×#626—24no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81#3796—232no—
82C32×C42—22no—
83#3752—24no—
84C4×C3⋊Dic3—22no—
85C3×(C2×D3)⋊C4—28no—
86C3×C4⋊Dic3—22no—
87#3724—28no—
88Dic3⋊Dic3—24no—
89#3722—24no—
90(C2×D3)⋊Dic3—28no—
91#2432—91noSylow
92C22×C3×Q8—31no—
93C22×C3×Q8—31no—
94C22×C3×D4—31no—
95C22×#67—32no—
96C23×Dic3—32no—
97C2×#239—64no—
98C2×#239—64no—
99C2×#239—64no—
100C2×#237—64no—
101C2×#237—64no—
102C2×#237—64no—
103C22×D12—32no—
104C22×D12C2×D311yescharacteristic
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C22×C4×D3—32no—
108C22×C4×D3—61no—
109C22×Dic6C2×D311yescharacteristic
110C22×Dic6C2×D311yescharacteristic
111C3×#124—64no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—34no—
114C2×C3×C42—21no—
115C2×C3×C42C2×D311yescharacteristic
116C2×C3×C42C2×D311yescharacteristic
117C2×#217—34no—
118#946—64no—
119#944—64no—
120#944—64no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—62no—
127C2×(C2×D3)⋊C4C2×D314yes—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×Dic3⋊C4—34no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—34no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—61no—
136#897—64no—
137#875—24no—
138C3×#95—34no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—62no—
142C3⋊#95C2×D314yes—
143C23×C32C2411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3C2×D412yes—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—24no—
152C22×C3×D3—24no—
153C22×C3×D3C2×D414yes—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C2×D412yes—
165C2×C3⋊Dic3#4114yescomplemented
166C4×C3⋊D3—28no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—24no—
174C2×C3×Dic3C2×D414yes—
175C3×D12—28no—
176C3×Dic6—28no—
177C3×Dic6—44no—
178#626—216no—
179D3×Dic3—216no—
180C22×#41—91no—
181C2×C4⋊Q8—91no—
182C2×#124—31no—
183C2×C22⋊Q8—91no—
184#394—94no—
185#391—31no—
186#390—91no—
187#385—94no—
188C4×C22⋊C4—91no—
189C24×C3—32no—
190C23×D3—31no—
191C23×D3—31no—
192C23×D3—61no—
193C23×D3C22×D312yes—
194C2×C3×Q8—34no—
195C2×C3×Q8—62no—
196C2×C3×Q8—62no—
197C2×C3×Q8—62no—
198C2×C3×Q8—62no—
199C2×C3×Q8—62no—
200C2×C3×D4—34no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—64no—
213C2×#67—64no—
214C2×#67—64no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—61no—
220C22×Dic3—62no—
221C22×Dic3—64no—
222C22×Dic3—64no—
223C22×Dic3—64no—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227#239—632no—
228#237—632no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—64no—
232C2×D12—64no—
233C2×D12—64no—
234C2×D12#6714yes—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—122no—
246C2×C4×D3—122no—
247C2×Dic6—22no—
248C2×Dic6—22no—
249C2×Dic6—22no—
250C2×Dic6—22no—
251C2×Dic6—22no—
252C2×Dic6D1214yes—
253C3×C4⋊C4—62no—
254C3×C22⋊C4—68no—
255C3×C42—22no—
256C3×C42—22no—
257C3×C42—42no—
258#217—68no—
259(C2×D3)⋊C4—28no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—68no—
265(C2×D3)⋊C4—68no—
266C4⋊Dic3—22no—
267C4⋊Dic3—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—68no—
270Dic3⋊C4—68no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—122no—
274C22×C32C22×D411yescharacteristic
275C22×C32C22×D411yescharacteristic
276C22×C32C22×D411yescharacteristic
277C22×C32C2×#4112yes—
278C22×C322−1+412yes—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—22no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3×D3—24no—
285C2×C3×D3—28no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—44no—
289C32×C4—42no—
290C32×C4#12014yes—
291C3⋊Dic3—22no—
292C3⋊Dic3—24no—
293C3×Dic3—24no—
294C3×Dic3—42no—
295C3×Dic3—42no—
296C2×#41—184no—
297C2×#41—184no—
298C2×#41—184no—
299C22×Q8—31no—
300C22×Q8—31no—
301C22×D4—31no—
302C22×D4—92no—
303C23×C4—92no—
304C23×C4—91no—
305C4⋊Q8—184no—
306#124—64no—
307C22⋊Q8—184no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—94no—
311C2×C22⋊C4—34no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—94no—
314C2×C22⋊C4—92no—
315C2×C42—91no—
316C2×C42D3211yescharacteristic
317#95—34no—
318#95—92no—
319C23×C3—21no—
320C23×C3—34no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3—64no—
324C23×C3—64no—
325C23×C3C23×D311yescharacteristic
326C23×C3C23×D311yescharacteristic
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—24no—
330C22×D3—24no—
331C22×D3—32no—
332C22×D3—32no—
333C22×D3—62no—
334C22×D3—64no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—61no—
343C22×D3—121no—
344C22×D3—121no—
345C22×D3—122no—
346C22×D3C2×#6714yes—
347C3×Q8—68no—
348C3×Q8—124no—
349C3×D4—68no—
350C2×C3×C4—24no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—34no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—64no—
370C2×C3×C4C2×D1212yes—
371C2×C3×C4D3×D412yes—
372C2×C3×C4D3×D412yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4D3×D412yes—
375C2×C3×C4C2×#6712yes—
376#67—616no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—24no—
383C2×Dic3—22no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—62no—
389C2×Dic3—64no—
390C2×Dic3—616no—
391C2×Dic3—62no—
392C2×Dic3—61no—
393C2×Dic3—62no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—61no—
399C2×Dic3—122no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3C2×D1214yes—
404D12—28no—
405D12—616no—
406C4×D3—616no—
407C4×D3—68no—
408C4×D3—68no—
409C4×D3—128no—
410Dic6—28no—
411Dic6—44no—
412C2×C32C2×#12011yescharacteristic
413C2×C32#53211yescharacteristic
414C2×C32#53611yescharacteristic
415C2×C32#54712yes—
416C2×C32#54812yes—
417C3⋊D3—42no—
418C3×D3—44no—
419C24—32no—
420C24—91no—
421#41—1832no—
422C2×Q8—34no—
423C2×Q8—62no—
424C2×Q8—62no—
425C2×Q8—62no—
426C2×Q8—62no—
427C2×Q8—62no—
428C2×D4—34no—
429C2×D4—62no—
430C2×D4—62no—
431C2×D4—184no—
432C2×D4—184no—
433C2×D4—184no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—91no—
438C22×C4—92no—
439C22×C4—94no—
440C22×C4—184no—
441C22×C4—184no—
442C22×C4—184no—
443C22×C4—182no—
444C22×C4—182no—
445C22×C4C2×D3212yes—
446C22×C4C2×D3211yescharacteristic
447C4⋊C4—62no—
448C4⋊C4—188no—
449C4⋊C4—184no—
450C22⋊C4—68no—
451C22⋊C4—184no—
452C22⋊C4—184no—
453C22⋊C4—188no—
454C42—22no—
455C42—182no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—64no—
462C22×C3—68no—
463C22×C3—122no—
464C22×C3—122no—
465C22×C3—124no—
466C22×C3C22×D1211yescharacteristic
467C22×C3C2×D3×D411yescharacteristic
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
470C22×C3C2×D3×D411yescharacteristic
471C22×C3#100712yes—
472C22×C3D3×#4112yes—
473C22×C3D3×#4112yes—
474C22×C3#101012yes—
475C22×C3C22×#6711yescharacteristic
476C2×D3—24no—
477C2×D3—28no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—44no—
481C2×D3—64no—
482C2×D3—62no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—124no—
491C2×D3—124no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C3×C4—24no—
497C3×C4—44no—
498C3×C4—42no—
499C3×C4—42no—
500C3×C4—64no—
501C3×C4—122no—
502C3×C4—122no—
503C3×C4#88214yes—
504C3×C4#93714yes—
505Dic3—24no—
506Dic3—42no—
507Dic3—42no—
508Dic3—64no—
509Dic3—62no—
510Dic3—62no—
511Dic3—64no—
512Dic3—122no—
513Dic3—124no—
514C32#243211yescharacteristic, complemented, Sylow
515C23—34no—
516C23—64no—
517C23—62no—
518C23—62no—
519C23—64no—
520C23—92no—
521C23—182no—
522C23—181no—
523C23—182no—
524C23—181no—
525C23C22×D3211yescharacteristic
526Q8—68no—
527Q8—124no—
528D4—68no—
529D4—1816no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—34no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—64no—
540C2×C4—62no—
541C2×C4—92no—
542C2×C4—94no—
543C2×C4—1816no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—188no—
549C2×C4D3×D1212yes—
550C2×C4#380212yes—
551C2×C4D3×#6712yes—
552C2×C3—22no—
553C2×C3—22no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—124no—
558C2×C3C2×#88211yescharacteristic
559C2×C3#557612yes—
560C2×C3#563112yes—
561C2×C3#566811yescharacteristic
562C2×C3#566811yescharacteristic
563C2×C3#567511yescharacteristic
564C2×C3#567712yes—
565C2×C3#572411yescharacteristic
566C2×C3C2×#93711yescharacteristic
567C2×C3#582412yes—
568D3—44no—
569D3—124no—
570D3—122no—
571D3—122no—
572C22—68no—
573C22—64no—
574C22—124no—
575C22—122no—
576C22—122no—
577C22—182no—
578C22—182no—
579C22—182no—
580C22—362no—
581C22—362no—
582C22#6429712yes—
583C22C2×D3×D1211yescharacteristic
584C22C2×#380211yescharacteristic
585C22#6430612yes—
586C22C2×D3×#6711yescharacteristic
587C4—42no—
588C4—64no—
589C4—122no—
590C4—122no—
591C4—184no—
592C4—182no—
593C4#6392214yes—
594C3—21no—
595C3#7649811yescharacteristic, complemented
596C3#8295911yescharacteristic, complemented
597C2—124no—
598C2—362no—
599C2#1059390112yes—
600C2#1059390811yescharacteristic
601C2#1059397111yescharacteristic
602C2#1059489012yes—
603C2C2×#6392211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC22×#3796C2
hypercenterC2×C42D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#875C2semidirect
3. C2×#63873C2semidirect
4. C2×#63871C2semidirect
5. C4×#3752C2semidirect
6. C3×#4929C2semidirect
7. #10591373C2semidirect
8. #10591323C2semidirect
9. #10591292C2semidirect
42. C2×#875D3semidirect
51. #4929D3semidirect
165. C2×C3⋊Dic3#41semidirect
514. C32#2432semidirect
595. C3#76498semidirect
596. C3#82959semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C3×#8752
C2×#638732
C2×#638712
C4×#37522
C3×#49292
#105913732
#105913232
#105912922
#829593
#764983