Finite Group Databasebeta

← #11792609

Subgroups — #11792609

Order 1152.

945 conjugacy classes of subgroups.

The subgroup lattice has 579 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic
2C22×#3719C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic
4C3×#4929C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic, complemented
8#69689—31nomaximal
9#68677—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3752—22no—
15#64084—22no—
16#64084—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3719—22no—
21C2×#3719—22no—
22C2×#3719—22no—
23C2×#3717—22no—
24C2×#3717—22no—
25C2×#3717—22no—
26C3×C3⋊#95—22no—
27#63567—22no—
28#63564—22no—
29C22×#216—31no—
30C22×#215—31no—
31C22×Dic12—31no—
32C22×#204—31no—
33C2×#875—31no—
34C2×#875—31no—
35C2×#875—61no—
36C3×#391—31no—
37C2×#821—31no—
38C2×#816—31no—
39C2×#810—31no—
40C2×#809—31no—
41#4929D311yescharacteristic, complemented
42C3×#336—31no—
43#4524D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C22×C32×C4D412yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—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)—21no—
53C2×C4⋊(C3⋊D3)D412yes—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634D412yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C32×C42—21no—
69C32×C42—21no—
70#3752—28no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yes—
78C2×C3×C3⋊C8D412yes—
79#3719—28no—
80#3717—28no—
81#2015—91noSylow
82C22×C3×Q8—31no—
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—61no—
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C22×Dic6C2×D311yescharacteristic
90C22×C3×C8—31no—
91C22×C3×C8—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C42—21no—
94C2×C3×C42C2×D311yescharacteristic
95C2×C3×C42C2×D311yescharacteristic
96C2×#216—62no—
97C2×#216—62no—
98C2×#216—62no—
99C2×#215—62no—
100C2×#215—62no—
101C2×#215—62no—
102C2×(C2×D3)⋊C4—64no—
103C2×(C2×D3)⋊C4—62no—
104C2×(C2×D3)⋊C4—62no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C22×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×Dic12—62no—
109C2×Dic12—62no—
110C2×Dic12—62no—
111C2×#204—62no—
112C2×#204—62no—
113C2×#204—62no—
114#875—62no—
115#875—62no—
116#875—62no—
117#875—62no—
118#875—64no—
119#875—64no—
120C3×#95—62no—
121C3⋊#95—22no—
122#821—62no—
123#816—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—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—41no—
147C4⋊(C3⋊D3)—41no—
148#634—22no—
149#634—22no—
150#634—41no—
151#634—41no—
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—91no—
164C22×SD16—91no—
165C2×#124—91no—
166C2×#103—91no—
167C2×#102—91no—
168#391—31no—
169#336—31no—
170C23×D3—62no—
171C23×D3—61no—
172C23×D3—61no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4D1212yes—
184C22×C3×C4#6712yes—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—62no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C2×D12—32no—
193C2×D12—32no—
194C2×D12—62no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—62no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—121no—
207C2×D12—121no—
208C2×D12—121no—
209C2×D12—121no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—32no—
216C2×Dic6—32no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—62no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×Dic6—121no—
230C2×Dic6—121no—
231C2×Dic6—121no—
232C2×Dic6—121no—
233C2×Dic6D1212yes—
234C2×C3×C8—32no—
235C2×C3×C8—32no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C42—22no—
243C3×C42—22no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248#216—68no—
249#215—68no—
250(C2×D3)⋊C4—616no—
251(C2×D3)⋊C4—68no—
252(C2×D3)⋊C4—68no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8D1212yes—
260C2×C3⋊C8D1212yes—
261Dic12—68no—
262#204—68no—
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×Q8—91no—
283C22×D4—91no—
284C2×Q16—182no—
285C2×Q16—182no—
286C2×Q16—182no—
287C2×SD16—182no—
288C2×SD16—182no—
289C2×SD16—182no—
290C22×C8—31no—
291C22×C8—31no—
292#124—182no—
293#124—182no—
294C2×C4⋊C4—31no—
295C2×C22⋊C4—182no—
296C2×C42D3211yescharacteristic
297#103—182no—
298#102—182no—
299#95—62no—
300C23×C3—21no—
301C23×C3C2×D1211yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—64no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—124no—
309C22×D3—124no—
310C22×D3—121no—
311C22×D3—121no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—121no—
315C22×D3—121no—
316C22×D3—122no—
317C22×D3—122no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C2×C3×C4—24no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—62no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—122no—
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4#23911yescharacteristic
354C2×Dic3—22no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—42no—
359C2×Dic3—64no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368D12—62no—
369D12—62no—
370D12—62no—
371D12—62no—
372D12—122no—
373D12—122no—
374D12—122no—
375D12—122no—
376D12—121no—
377D12—121no—
378D12—121no—
379D12—121no—
380Dic6—22no—
381Dic6—22no—
382Dic6—41no—
383Dic6—41no—
384Dic6—62no—
385Dic6—62no—
386Dic6—62no—
387Dic6—62no—
388Dic6—122no—
389Dic6—122no—
390Dic6—122no—
391Dic6—122no—
392Dic6—121no—
393Dic6—121no—
394Dic6—121no—
395Dic6—121no—
396C3×C8—62no—
397C3×C8—62no—
398C3⋊C8—22no—
399C3⋊C8—22no—
400C2×C32#39211yescharacteristic
401C2×C32#45212yes—
402C2×C32#46412yes—
403C2×C32#49511yescharacteristic
404C2×C32#49711yescharacteristic
405C3⋊D3—82no—
406C24—181no—
407C2×Q8—32no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—92no—
414C2×Q8—181no—
415C2×Q8—181no—
416C2×Q8—181no—
417C2×Q8—181no—
418C2×Q8—181no—
419C2×D4—92no—
420C2×D4—181no—
421C2×D4—181no—
422C2×D4—181no—
423C2×D4—181no—
424C2×D4—181no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4—181no—
428C22×C4#62612yes—
429C22×C4C2×D3211yescharacteristic
430Q16—188no—
431SD16—188no—
432C2×C8—32no—
433C2×C8—32no—
434C2×C8—61no—
435C2×C8—61no—
436C2×C8—61no—
437C2×C8—61no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C22⋊C4—188no—
441C42—21no—
442C42—21no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3#87411yescharacteristic
449C22×C3#88211yescharacteristic
450C22×C3#89511yescharacteristic
451C22×C3#90412yes—
452C22×C3#90912yes—
453C22×C3#93011yescharacteristic
454C22×C3#93711yescharacteristic
455C22×C3#94011yescharacteristic
456C22×C3#94212yes—
457C22×C3#95012yes—
458C2×D3—124no—
459C2×D3—128no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—124no—
463C2×D3—124no—
464C2×D3—244no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—241no—
468C2×D3—241no—
469C2×D3—242no—
470C2×D3—241no—
471C2×D3—241no—
472C2×D3—242no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—44no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—122no—
481C3×C4—241no—
482C3×C4#88211yescharacteristic
483C3×C4#88211yescharacteristic
484C3×C4#88211yescharacteristic
485C3×C4#88211yescharacteristic
486C3×C4#88411yescharacteristic
487C3×C4#88411yescharacteristic
488C3×C4#89511yescharacteristic
489C3×C4#89511yescharacteristic
490Dic3—42no—
491Dic3—81no—
492Dic3—124no—
493Dic3—122no—
494Dic3—122no—
495C32#201511yescharacteristic, complemented, Sylow
496C23—182no—
497C23—362no—
498C23—362no—
499C23—361no—
500C23—361no—
501C23C2×#62611yescharacteristic
502Q8—62no—
503Q8—62no—
504Q8—121no—
505Q8—121no—
506Q8—182no—
507Q8—182no—
508Q8—361no—
509Q8—361no—
510D4—182no—
511D4—182no—
512D4—361no—
513D4—361no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—62no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—122no—
521C2×C4—121no—
522C2×C4—182no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4#379911yescharacteristic
526C2×C4D3×D1211yescharacteristic
527C2×C4D3×D1211yescharacteristic
528C2×C4D3×D1211yescharacteristic
529C2×C4#381111yescharacteristic
530C2×C4#381111yescharacteristic
531C8—62no—
532C8—62no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3#467111yescharacteristic
539C2×C3#469611yescharacteristic
540C2×C3#471511yescharacteristic
541C2×C3#473312yes—
542C2×C3#484512yes—
543C2×C3#496011yescharacteristic
544C2×C3#502812yes—
545C2×C3#504712yes—
546C2×C3#505911yescharacteristic
547C2×C3#508611yescharacteristic
548D3—244no—
549D3—242no—
550D3—242no—
551C22—362no—
552C22—364no—
553C22—722no—
554C22—721no—
555C22—721no—
556C22#6382912yes—
557C22#6383312yes—
558C22#6390911yescharacteristic
559C22#6391111yescharacteristic
560C22#6398111yescharacteristic
561C4—42no—
562C4—122no—
563C4—241no—
564C4—362no—
565C4#6391011yescharacteristic
566C4#6391011yescharacteristic
567C4#6392311yescharacteristic
568C4#6392311yescharacteristic
569C3—21no—
570C3#6867711yescharacteristic, complemented
571C3#6968911yescharacteristic, complemented
572C2—722no—
573C2#1059036812yes—
574C2#1059037011yescharacteristic
575C2#1059037411yescharacteristic
576C2#1059118412yes—
577C2#1059139511yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C22×#3719C2semidirect
4. C3×#4929C2semidirect
5. C2×#63567C2semidirect
7. C3×#4524C2semidirect
41. #4929D3semidirect
43. #4524D3semidirect
495. C32#2015semidirect
570. C3#68677semidirect
571. C3#69689semidirect

Maximal subgroups

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

subgroupindex
C2×#640842
C22×#37192
C22×#37172
C3×#49292
C2×#635672
C2×#635642
C3×#45242
#696893
#686773