Finite Group Databasebeta

← #11792599

Subgroups — #11792599

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×#3754C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71729—31nomaximal
9#70215—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3754—22no—
14C2×#3754—22no—
15C2×#3754—22no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#217—22no—
18C3×#936—22no—
19C3×#936—22no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3719—22no—
24C2×#3719—22no—
25C2×#3719—22no—
26C3×#832—22no—
27#63579—22no—
28#63565—22no—
29C2×C3×#124—31no—
30C22×#216—31no—
31C2×#936D311yescharacteristic
32C22×#214—31no—
33C22×#214—31no—
34C22×#214—61no—
35C22×Dic12—31no—
36C2×C3×#102—31no—
37C2×#835—31no—
38C2×#832D311yescharacteristic
39#4973—31no—
40C2×#810—31no—
41#4929—31no—
42#4550—31no—
43#4524—31no—
44C24×C32—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4D412yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634D412yes—
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#3754—28no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)D412yes—
72C3×#217—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#3719—28no—
81#2015—91noSylow
82C22×C3×Q8—31no—
83C22×C3×D4—21no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C22×Dic6C2×D311yescharacteristic
90C22×C3×C8—31no—
91C3×#124—62no—
92C3×#124—62no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—62no—
95C2×C3×C42—31no—
96C2×#217—22no—
97C2×#216—62no—
98C2×#216—62no—
99C2×#216—62no—
100#936—22no—
101#936—22no—
102C2×#214—62no—
103C2×#214—62no—
104C2×#214—62no—
105C2×#214—62no—
106C2×#214—64no—
107C2×#214—64no—
108C2×#214—64no—
109C2×#214—62no—
110C2×#214—62no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3C2×D311yescharacteristic
113C22×C3⋊C8—31no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117C2×Dic12—62no—
118C2×Dic12—62no—
119C2×Dic12—62no—
120C3×#102—62no—
121#835—62no—
122#832—22no—
123C3⋊#95—62no—
124C3⋊#95—62no—
125#810—62no—
126C23×C32—22no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32—42no—
130C23×C32—42no—
131C23×C32C2×D411yescharacteristic
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145#634—22no—
146#634—22no—
147#634—41no—
148#634—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—91no—
164C22×SD16—91no—
165C2×#124—31no—
166C2×#103—91no—
167C2×#102—31no—
168#391—91no—
169#336—91no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—41no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—41no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4D1212yes—
196C2×C3×D4#6712yes—
197C22×C3×C4—21no—
198C22×C3×C4—32no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—121no—
208C22×Dic3#6712yes—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—32no—
215C2×Dic6—32no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×Dic6—121no—
230C2×Dic6—121no—
231C2×Dic6—121no—
232C2×Dic6#6712yes—
233C2×C3×C8—32no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C22⋊C4—68no—
239C3×C42—61no—
240C3×C42—61no—
241#217—28no—
242#216—68no—
243#214—616no—
244#214—68no—
245#214—68no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8#6712yes—
262Dic12—68no—
263C22×C32—42no—
264C22×C32—44no—
265C22×C32—82no—
266C22×C32—81no—
267C22×C32—81no—
268C22×C32#12011yescharacteristic
269C22×C32#12111yescharacteristic
270C22×C32#12711yescharacteristic
271C22×C32#13512yes—
272C22×C32#13712yes—
273C32×C4#12011yescharacteristic
274C32×C4#12011yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12111yescharacteristic
277C3⋊Dic3—42no—
278C3×Dic3—42no—
279C3×Dic3—42no—
280C3×Dic3—81no—
281C22×Q8—31no—
282C22×Q8—91no—
283C22×D4D3211yescharacteristic
284C2×Q16—182no—
285C2×Q16—182no—
286C2×Q16—182no—
287C2×SD16—182no—
288C2×SD16—182no—
289C2×SD16—182no—
290C22×C8—31no—
291C22×C8—91no—
292#124—62no—
293#124—62no—
294C2×C4⋊C4—31no—
295C2×C22⋊C4—62no—
296C2×C42—31no—
297#103—182no—
298#102—62no—
299#95—182no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—41no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—41no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—82no—
315C23×C3—82no—
316C23×C3D3×D411yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C3×D4—24no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—41no—
331C3×D4—41no—
332C3×D4—41no—
333C3×D4—41no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4—122no—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—42no—
367C2×Dic3—41no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377Dic6—22no—
378Dic6—22no—
379Dic6—41no—
380Dic6—41no—
381Dic6—64no—
382Dic6—62no—
383Dic6—62no—
384Dic6—62no—
385Dic6—62no—
386Dic6—122no—
387Dic6—122no—
388Dic6—122no—
389Dic6—121no—
390Dic6—121no—
391Dic6—121no—
392Dic6—121no—
393C3×C8—62no—
394C3⋊C8—22no—
395C3⋊C8—64no—
396C3⋊C8—62no—
397C3⋊C8—62no—
398C2×C32—82no—
399C2×C32#39211yescharacteristic
400C2×C32#45212yes—
401C2×C32#46412yes—
402C2×C32#49511yescharacteristic
403C2×C32#49711yescharacteristic
404C24—21no—
405C2×Q8—32no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—92no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×Q8—181no—
416C2×Q8—181no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4#62612yes—
423C22×C4—32no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—188no—
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—68no—
439C42—61no—
440C42—61no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—44no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—44no—
450C22×C3—44no—
451C22×C3—84no—
452C22×C3—82no—
453C22×C3—84no—
454C22×C3—82no—
455C22×C3—81no—
456C22×C3—81no—
457C22×C3—82no—
458C22×C3—82no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3#88211yescharacteristic
462C22×C3#88411yescharacteristic
463C22×C3#91212yes—
464C22×C3#91512yes—
465C22×C3#93811yescharacteristic
466C22×C3#94011yescharacteristic
467C22×C3#94011yescharacteristic
468C22×C3#95012yes—
469C22×C3#95112yes—
470C22×C3#95311yescharacteristic
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—122no—
476C3×C4—122no—
477C3×C4—241no—
478C3×C4#88211yescharacteristic
479C3×C4#88411yescharacteristic
480C3×C4#93011yescharacteristic
481C3×C4#93711yescharacteristic
482C3×C4#93711yescharacteristic
483C3×C4#93711yescharacteristic
484C3×C4#93911yescharacteristic
485C3×C4#93911yescharacteristic
486Dic3—42no—
487Dic3—42no—
488Dic3—81no—
489Dic3—124no—
490Dic3—122no—
491Dic3—122no—
492C32#201511yescharacteristic, complemented, Sylow
493C23—22no—
494C23—42no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23D3×#6711yescharacteristic
499Q8—62no—
500Q8—62no—
501Q8—121no—
502Q8—121no—
503Q8—182no—
504Q8—182no—
505Q8—361no—
506Q8—361no—
507D4—22no—
508D4—22no—
509D4—41no—
510D4—41no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—121no—
516C2×C4—121no—
517C2×C4—122no—
518C2×C4—121no—
519C2×C4—182no—
520C2×C4—361no—
521C2×C4—361no—
522C2×C4#380411yescharacteristic
523C2×C4C2×#62611yescharacteristic
524C2×C4D3×#6711yescharacteristic
525C2×C4D3×#6711yescharacteristic
526C2×C4#381111yescharacteristic
527C2×C4#381111yescharacteristic
528C8—62no—
529C8—182no—
530C2×C3—21no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—84no—
536C2×C3—82no—
537C2×C3—82no—
538C2×C3#476712yes—
539C2×C3#478312yes—
540C2×C3#496011yescharacteristic
541C2×C3#505412yes—
542C2×C3#505911yescharacteristic
543C2×C3#506011yescharacteristic
544C2×C3#515511yescharacteristic
545C2×C3#516711yescharacteristic
546C2×C3#522311yescharacteristic
547C2×C3#523912yes—
548C22—44no—
549C22—42no—
550C22—81no—
551C22—82no—
552C22—81no—
553C22#6392912yes—
554C22#6393312yes—
555C22#6395811yescharacteristic
556C22#6397711yescharacteristic
557C22#6397911yescharacteristic
558C4—122no—
559C4—122no—
560C4—241no—
561C4—362no—
562C4#6397111yescharacteristic
563C4#6397811yescharacteristic
564C4#6398111yescharacteristic
565C4#6398311yescharacteristic
566C3—21no—
567C3#7021511yescharacteristic, complemented
568C3#7172911yescharacteristic, complemented
569C2—82no—
570C2#1059144112yes—
571C2#1059146312yes—
572C2#1059147011yescharacteristic
573C2#1059149111yescharacteristic
574C2#1059172411yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C22×#3719C2semidirect
5. #10591213C2semidirect
6. C2×#63565C2semidirect
7. #10589155C2semidirect
492. C32#2015semidirect
567. C3#70215semidirect
568. C3#71729semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×#9362
C22×#37192
C2×C3×#8322
#105912132
C2×#635652
#105891552
#717293
#702153