Finite Group Databasebeta

← #11792603

Subgroups — #11792603

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C211yesmaximal, characteristic, complemented
2C2×#63864C211yesmaximal, characteristic
3C22×#3717C211yesmaximal, characteristic
4C2×#63648C211yesmaximal, characteristic
5#10591220C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#72072—31nomaximal
9#68677—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×C3×Dic12—22no—
18C2×C3×Dic12—22no—
19C2×C3×Dic12—22no—
20C2×#3722—22no—
21#63864—22no—
22#63864—22no—
23C2×#3717—22no—
24C2×#3717—22no—
25C2×#3717—22no—
26#63648—22no—
27#63579—22no—
28#63566—22no—
29C22×C3×Q16—31no—
30C2×#947—31no—
31C22×#215—31no—
32C22×Dic12D311yescharacteristic, complemented
33C22×#204—31no—
34C2×#875—31no—
35#5229—31no—
36C2×#835—31no—
37C2×#821—31no—
38C2×#821—31no—
39C2×#821—61no—
40C2×#816—31no—
41#4929—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)D412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D412yes—
67C2×C3×Dic6D412yes—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8D412yes—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yes—
78C3×Dic12—28no—
79#3722—28no—
80#3717—28no—
81#2015—91noSylow
82C22×C3×Q8—31no—
83C22×C3×Q8—31no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×Dic6C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C2×C3×Q16—62no—
90C2×C3×Q16—62no—
91C2×C3×Q16—62no—
92C22×C3×C8—21no—
93C22×C3×C8—31no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C2×D311yescharacteristic
96C2×C3×C42—31no—
97#947—62no—
98#947—62no—
99C2×#215—62no—
100C2×#215—62no—
101C2×#215—62no—
102C2×(C2×D3)⋊C4—62no—
103C2×(C2×D3)⋊C4—62no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C2×C4×Dic3C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C2×Dic12—22no—
110C2×Dic12—22no—
111C2×Dic12—22no—
112C2×#204—62no—
113C2×#204—62no—
114C2×#204—62no—
115#875—62no—
116#875—62no—
117#835—62no—
118C3⋊#95—62no—
119C3⋊#95—62no—
120#821—64no—
121#821—62no—
122#821—62no—
123#816—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—42no—
129C22×C3⋊D3—42no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—42no—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—41no—
141C4⋊(C3⋊D3)—41no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C32×C8—22no—
160C3×C3⋊C8—22no—
161C22×Q16—31no—
162C22×SD16—91no—
163C2×#124—91no—
164C2×#103—91no—
165C2×#102—91no—
166#391—91no—
167#336—31no—
168C23×D3—61no—
169C23×D3—61no—
170C23×D3—121no—
171C2×C3×Q8—32no—
172C2×C3×Q8—32no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C22×C3×C4—21no—
184C22×C3×C4—32no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194C22×Dic3D1212yes—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×D12—62no—
199C2×D12—62no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—121no—
211C2×D12—121no—
212C2×D12—121no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6#6712yes—
224C2×Dic6#6712yes—
225C3×Q16—68no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—22no—
231C2×C3×C8—32no—
232C2×C3×C8—41no—
233C2×C3×C8—41no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8D1212yes—
237C2×C3×C8#6712yes—
238C3×C42—61no—
239C3×C42—61no—
240#215—68no—
241(C2×D3)⋊C4—68no—
242(C2×D3)⋊C4—68no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—121no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8D1212yes—
254Dic12—28no—
255#204—68no—
256C22×C32#12011yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12711yescharacteristic
259C22×C32#13512yes—
260C22×C32#13712yes—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—44no—
263C2×C3⋊D3—82no—
264C2×C3⋊D3—81no—
265C2×C3⋊D3—81no—
266C32×C4#12011yescharacteristic
267C32×C4#12011yescharacteristic
268C32×C4#12111yescharacteristic
269C32×C4#12111yescharacteristic
270C3⋊Dic3—81no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×Q8—31no—
276C22×D4—91no—
277C2×Q16—62no—
278C2×Q16—62no—
279C2×Q16—62no—
280C2×SD16—182no—
281C2×SD16—182no—
282C2×SD16—182no—
283C22×C8—31no—
284C22×C8D3211yescharacteristic
285#124—182no—
286#124—182no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—182no—
289C2×C42—31no—
290#103—182no—
291#102—182no—
292#95—182no—
293C23×C3—21no—
294C23×C3C2×D1211yescharacteristic
295C23×C3D3×D411yescharacteristic
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—122no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—121no—
308C22×D3—121no—
309C22×D3—242no—
310C22×D3—242no—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×Q8—62no—
315C3×Q8—121no—
316C3×Q8—121no—
317C3×Q8—121no—
318C3×Q8—121no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4#23911yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—122no—
356C2×Dic3—121no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—121no—
360C2×Dic3—242no—
361D12—64no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—62no—
366D12—122no—
367D12—122no—
368D12—122no—
369D12—121no—
370D12—121no—
371D12—121no—
372D12—121no—
373Dic6—22no—
374Dic6—22no—
375Dic6—22no—
376Dic6—22no—
377Dic6—41no—
378Dic6—41no—
379Dic6—41no—
380Dic6—41no—
381C3×C8—22no—
382C3×C8—22no—
383C3×C8—42no—
384C3×C8—62no—
385C3⋊C8—22no—
386C2×C32#39211yescharacteristic
387C2×C32#45212yes—
388C2×C32#46412yes—
389C2×C32#49511yescharacteristic
390C2×C32#49711yescharacteristic
391C3⋊D3—82no—
392C24—181no—
393C2×Q8—32no—
394C2×Q8—32no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×D4—92no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4—181no—
409C2×D4—181no—
410C2×D4—181no—
411C22×C4—32no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—181no—
415C22×C4C2×D3211yescharacteristic
416Q16—68no—
417SD16—188no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—32no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8#62612yes—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C22⋊C4—188no—
427C42—61no—
428C42—61no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3#87411yescharacteristic
435C22×C3#88211yescharacteristic
436C22×C3#89511yescharacteristic
437C22×C3#90412yes—
438C22×C3#90912yes—
439C22×C3#91812yes—
440C22×C3#91912yes—
441C22×C3#93711yescharacteristic
442C22×C3#93911yescharacteristic
443C22×C3#94011yescharacteristic
444C2×D3—124no—
445C2×D3—122no—
446C2×D3—124no—
447C2×D3—122no—
448C2×D3—124no—
449C2×D3—244no—
450C2×D3—244no—
451C2×D3—242no—
452C2×D3—242no—
453C2×D3—242no—
454C2×D3—241no—
455C2×D3—241no—
456C2×D3—241no—
457C2×D3—241no—
458C2×D3—242no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—122no—
464C3×C4—122no—
465C3×C4—122no—
466C3×C4#88211yescharacteristic
467C3×C4#88211yescharacteristic
468C3×C4#89511yescharacteristic
469C3×C4#89511yescharacteristic
470C3×C4#93711yescharacteristic
471C3×C4#93811yescharacteristic
472C3×C4#93911yescharacteristic
473C3×C4#95311yescharacteristic
474Dic3—42no—
475Dic3—42no—
476Dic3—42no—
477Dic3—242no—
478Dic3—241no—
479Dic3—241no—
480C32#201511yescharacteristic, complemented, Sylow
481C23—182no—
482C23—362no—
483C23—362no—
484C23—361no—
485C23—361no—
486C23D3×D1211yescharacteristic
487Q8—62no—
488Q8—62no—
489Q8—62no—
490Q8—62no—
491Q8—121no—
492Q8—121no—
493Q8—121no—
494Q8—121no—
495D4—182no—
496D4—182no—
497D4—361no—
498D4—361no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—362no—
509C2×C4—361no—
510C2×C4#379611yescharacteristic
511C2×C4D3×D1211yescharacteristic
512C2×C4#380211yescharacteristic
513C2×C4C2×#62611yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C8—22no—
517C8—62no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3#467111yescharacteristic
524C2×C3#469611yescharacteristic
525C2×C3#471511yescharacteristic
526C2×C3#473312yes—
527C2×C3#484512yes—
528C2×C3#518512yes—
529C2×C3#518712yes—
530C2×C3#519011yescharacteristic
531C2×C3#519111yescharacteristic
532C2×C3#522311yescharacteristic
533D3—244no—
534D3—242no—
535D3—242no—
536C22—362no—
537C22—364no—
538C22—722no—
539C22—721no—
540C22—721no—
541C22#6380112yes—
542C22#6380812yes—
543C22#6388611yescharacteristic
544C22#6391111yescharacteristic
545C22#6392211yescharacteristic
546C4—122no—
547C4—122no—
548C4—122no—
549C4—721no—
550C4#6388611yescharacteristic
551C4#6391611yescharacteristic
552C4#6392211yescharacteristic
553C4#6397711yescharacteristic
554C3—21no—
555C3#6867711yescharacteristic, complemented
556C3#7207211yescharacteristic, complemented
557C2—722no—
558C2#1059080112yes—
559C2#1059086511yescharacteristic
560C2#1059089911yescharacteristic
561C2#1059096612yes—
562C2#1059139111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic12C2semidirect
5. #10591220C2semidirect
6. C2×#63566C2semidirect
7. C3×#4550C2semidirect
32. C22×Dic12D3semidirect
43. #4550D3semidirect
480. C32#2015semidirect
555. C3#68677semidirect
556. C3#72072semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C2×#638642
C22×#37172
C2×#636482
#105912202
C2×#635662
C3×#45502
#720723
#686773