Finite Group Databasebeta

← #11792594

Subgroups — #11792594

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63864C211yesmaximal, characteristic
4C3×#5229C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7#10589155C211yesmaximal, characteristic, complemented
8#72072—31nomaximal
9#69689—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3755—22no—
14C2×#3755—22no—
15C2×#3755—22no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#216—22no—
18C2×C3×#216—22no—
19C2×C3×#216—22no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3722—22no—
24#63864—22no—
25#63864—22no—
26C3×C3⋊#95—22no—
27#63565—22no—
28#63564—22no—
29C22×C3×Q16—31no—
30C2×#947—31no—
31C22×#216D311yescharacteristic, complemented
32C22×#215—31no—
33C22×#215—31no—
34C22×#215—61no—
35C2×#875—31no—
36C3×#391—31no—
37#5229D311yescharacteristic, complemented
38C2×#835—31no—
39C2×#821—31no—
40C2×#810—31no—
41C2×#809—31no—
42#4550—31no—
43#4524—31no—
44C23×C3⋊D3—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8D412yes—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)D412yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68#3755—28no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)D412yes—
72C3×#216—28no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D412yes—
80#3722—28no—
81#2015—91noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—31no—
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×Q8C2×D311yescharacteristic
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×Dic6C2×D311yescharacteristic
90C2×C3×Q16—62no—
91C2×C3×Q16—62no—
92C2×C3×Q16—62no—
93C22×C3×C8—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C42—31no—
96#947—62no—
97#947—62no—
98C2×#216—22no—
99C2×#216—22no—
100C2×#216—22no—
101C2×#215—62no—
102C2×#215—62no—
103C2×#215—62no—
104C2×#215—62no—
105C2×#215—64no—
106C2×#215—64no—
107C2×#215—64no—
108C2×#215—62no—
109C2×#215—62no—
110C2×(C2×D3)⋊C4—62no—
111C2×(C2×D3)⋊C4—62no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×C4×Dic3C2×D311yescharacteristic
114C22×C3⋊C8—31no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—61no—
117C22×C3⋊C8C2×D311yescharacteristic
118#875—62no—
119#875—62no—
120C3×#95—62no—
121#835—62no—
122C3⋊#95—22no—
123#821—62no—
124#810—62no—
125#809—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C32×Q8—22no—
133C32×Q8—22no—
134C32×Q8—41no—
135C32×Q8—41no—
136C2×C32×C4—22no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—41no—
148C4⋊(C3⋊D3)—41no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—42no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—41no—
160C3×Dic6—41no—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C22×Q16—31no—
164C22×SD16—91no—
165C2×#124—91no—
166C2×#103—91no—
167C2×#102—91no—
168#391—31no—
169#336—91no—
170C23×D3—61no—
171C23×D3—61no—
172C23×D3—121no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—22no—
186C2×C3×Q8—32no—
187C2×C3×Q8—41no—
188C2×C3×Q8—41no—
189C2×C3×Q8—41no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8—61no—
193C2×C3×Q8—61no—
194C2×C3×Q8—61no—
195C2×C3×Q8D1212yes—
196C2×C3×Q8#6712yes—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—32no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3#6712yes—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—121no—
225C2×D12—121no—
226C2×D12—121no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6#6712yes—
233C3×Q16—68no—
234C2×C3×C8—32no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C42—61no—
240C3×C42—61no—
241#216—28no—
242#215—616no—
243#215—68no—
244#215—68no—
245(C2×D3)⋊C4—68no—
246(C2×D3)⋊C4—68no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8#6712yes—
263C22×C32#12011yescharacteristic
264C22×C32#12111yescharacteristic
265C22×C32#12711yescharacteristic
266C22×C32#13512yes—
267C22×C32#13712yes—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—44no—
270C2×C3⋊D3—82no—
271C2×C3⋊D3—81no—
272C2×C3⋊D3—81no—
273C32×C4—42no—
274C32×C4#12011yescharacteristic
275C32×C4#12011yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12111yescharacteristic
278C3×Dic3—42no—
279C3×Dic3—42no—
280C3×Dic3—81no—
281C22×Q8—31no—
282C22×Q8D3211yescharacteristic
283C22×D4—91no—
284C2×Q16—62no—
285C2×Q16—62no—
286C2×Q16—62no—
287C2×SD16—182no—
288C2×SD16—182no—
289C2×SD16—182no—
290C22×C8—31no—
291C22×C8—91no—
292#124—182no—
293#124—182no—
294C2×C4⋊C4—31no—
295C2×C22⋊C4—182no—
296C2×C42—31no—
297#103—182no—
298#102—182no—
299#95—62no—
300C23×C3—21no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—121no—
311C22×D3—121no—
312C22×D3—121no—
313C22×D3—121no—
314C22×D3—122no—
315C22×D3—122no—
316C22×D3—242no—
317C22×D3—242no—
318C3×Q8—24no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—42no—
324C3×Q8—42no—
325C3×Q8—42no—
326C3×Q8—41no—
327C3×Q8—41no—
328C3×Q8—41no—
329C3×Q8—41no—
330C3×Q8—62no—
331C3×Q8—62no—
332C3×Q8—121no—
333C3×Q8—121no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—122no—
356C2×C3×C4—121no—
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4#23511yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4#23711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3—42no—
377D12—64no—
378D12—62no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—122no—
383D12—122no—
384D12—122no—
385D12—121no—
386D12—121no—
387D12—121no—
388D12—121no—
389Dic6—22no—
390Dic6—22no—
391Dic6—41no—
392Dic6—41no—
393C3×C8—62no—
394C3⋊C8—22no—
395C3⋊C8—64no—
396C3⋊C8—62no—
397C3⋊C8—62no—
398C2×C32#39211yescharacteristic
399C2×C32#45212yes—
400C2×C32#46412yes—
401C2×C32#49511yescharacteristic
402C2×C32#49711yescharacteristic
403C3⋊D3—82no—
404C24—181no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—32no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×Q8#62612yes—
417C2×D4—92no—
418C2×D4—181no—
419C2×D4—181no—
420C2×D4—181no—
421C2×D4—181no—
422C2×D4—181no—
423C22×C4—21no—
424C22×C4—32no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4C2×D3211yescharacteristic
428Q16—68no—
429SD16—188no—
430C2×C8—32no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—92no—
434C2×C8—181no—
435C2×C8—181no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C22⋊C4—188no—
439C42—61no—
440C42—61no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#91812yes—
447C22×C3#91912yes—
448C22×C3#93011yescharacteristic
449C22×C3#93711yescharacteristic
450C22×C3#93711yescharacteristic
451C22×C3#93911yescharacteristic
452C22×C3#94011yescharacteristic
453C22×C3#94011yescharacteristic
454C22×C3#94212yes—
455C22×C3#95012yes—
456C2×D3—124no—
457C2×D3—124no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—124no—
461C2×D3—244no—
462C2×D3—244no—
463C2×D3—242no—
464C2×D3—242no—
465C2×D3—242no—
466C2×D3—241no—
467C2×D3—241no—
468C2×D3—242no—
469C2×D3—241no—
470C2×D3—241no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—44no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—122no—
479C3×C4—122no—
480C3×C4—241no—
481C3×C4#88211yescharacteristic
482C3×C4#88211yescharacteristic
483C3×C4#88411yescharacteristic
484C3×C4#88411yescharacteristic
485C3×C4#93711yescharacteristic
486C3×C4#93811yescharacteristic
487C3×C4#93911yescharacteristic
488C3×C4#95311yescharacteristic
489Dic3—42no—
490Dic3—42no—
491Dic3—81no—
492C32#201511yescharacteristic, complemented, Sylow
493C23—182no—
494C23—362no—
495C23—362no—
496C23—361no—
497C23—361no—
498C23D3×#6711yescharacteristic
499Q8—22no—
500Q8—22no—
501Q8—41no—
502Q8—41no—
503Q8—62no—
504Q8—62no—
505Q8—121no—
506Q8—121no—
507D4—182no—
508D4—182no—
509D4—361no—
510D4—361no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—122no—
521C2×C4—121no—
522C2×C4#380411yescharacteristic
523C2×C4C2×#62611yescharacteristic
524C2×C4D3×#6711yescharacteristic
525C2×C4D3×#6711yescharacteristic
526C2×C4#381111yescharacteristic
527C2×C4#381111yescharacteristic
528C8—62no—
529C8—182no—
530C2×C3—22no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3#496011yescharacteristic
536C2×C3#502812yes—
537C2×C3#504712yes—
538C2×C3#505911yescharacteristic
539C2×C3#508611yescharacteristic
540C2×C3#518512yes—
541C2×C3#518712yes—
542C2×C3#519011yescharacteristic
543C2×C3#519111yescharacteristic
544C2×C3#522311yescharacteristic
545D3—244no—
546D3—242no—
547D3—242no—
548C22—364no—
549C22—362no—
550C22—722no—
551C22—721no—
552C22—721no—
553C22#6394812yes—
554C22#6394912yes—
555C22#6397811yescharacteristic
556C22#6397911yescharacteristic
557C22#6398311yescharacteristic
558C4—42no—
559C4—122no—
560C4—122no—
561C4—241no—
562C4#6395811yescharacteristic
563C4#6397111yescharacteristic
564C4#6397711yescharacteristic
565C4#6398111yescharacteristic
566C3—21no—
567C3#6968911yescharacteristic, complemented
568C3#7207211yescharacteristic, complemented
569C2—722no—
570C2#1059160712yes—
571C2#1059160811yescharacteristic
572C2#1059160911yescharacteristic
573C2#1059165712yes—
574C2#1059172411yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
4. C3×#5229C2semidirect
5. C2×#63565C2semidirect
7. #10589155C2semidirect
31. C22×#216D3semidirect
37. #5229D3semidirect
492. C32#2015semidirect
567. C3#69689semidirect
568. C3#72072semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C22×C3×#2162
C2×#638642
C3×#52292
C2×#635652
C2×#635642
#105891552
#720723
#696893