Finite Group Databasebeta

← #11792600

Subgroups — #11792600

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×#64145C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic
5#10591221C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72058—31nomaximal
9#70215—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3757—22no—
14#64145—22no—
15#64145—22no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×#214—22no—
18C2×C3×#214—22no—
19C2×C3×#214—22no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3719—22no—
24C2×#3719—22no—
25C2×#3719—22no—
26C3×#832—22no—
27#63579—22no—
28#63567—22no—
29C22×C3×SD16—31no—
30C22×#216—31no—
31C2×#936—31no—
32C2×#936—31no—
33C2×#936—61no—
34C22×#214D311yescharacteristic
35C22×Dic12—31no—
36C2×C3×#102—31no—
37#5229—31no—
38C2×#832D311yescharacteristic
39C2×#816—31no—
40#4973—31no—
41C2×#810—31no—
42#4550—31no—
43#4550—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—
53C22×C3⋊Dic3D412yes—
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—
68#3757—28no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3—21no—
71C3×#214—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8D412yes—
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
90C2×C3×SD16—62no—
91C2×C3×SD16—62no—
92C2×C3×SD16—62no—
93C22×C3×C8—31no—
94C22×C3×C8—31no—
95C2×C3×C4⋊C4—31no—
96C2×#217—62no—
97C2×#217—62no—
98C2×#217—64no—
99C2×#216—62no—
100C2×#216—62no—
101C2×#216—62no—
102#936—62no—
103#936—62no—
104#936—64no—
105#936—64no—
106#936—62no—
107#936—62no—
108C2×#214—22no—
109C2×#214—22no—
110C2×#214—22no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117C2×Dic12—62no—
118C2×Dic12—62no—
119C2×Dic12—62no—
120C3×#102—62no—
121#832—22no—
122C3⋊#95—62no—
123C3⋊#95—62no—
124#816—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—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—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—31no—
165C2×#124—91no—
166C2×#103—91no—
167C2×#102—31no—
168#391—91no—
169#336—91no—
170C24×C3—22no—
171C24×C3—21no—
172C24×C3—21no—
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—21no—
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—22no—
191C2×C3×D4—41no—
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—61no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—62no—
207C22×Dic3—62no—
208C22×Dic3—61no—
209C22×Dic3—61no—
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×Dic6#6712yes—
234C3×SD16—68no—
235C2×C3×C8—32no—
236C2×C3×C8—32no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C2×C3×C8—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243#217—616no—
244#217—68no—
245#217—68no—
246#216—68no—
247#214—28no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4×Dic3—62no—
251C4×Dic3—62no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8#6712yes—
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—62no—
288C2×SD16—62no—
289C2×SD16—62no—
290C22×C8—31no—
291C22×C8—31no—
292#124—182no—
293#124—182no—
294C2×C4⋊C4—31no—
295C2×C22⋊C4—182no—
296C2×C42—91no—
297#103—182no—
298#102—62no—
299#95—182no—
300C23×C3—24no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—21no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—44no—
307C23×C3—44no—
308C23×C3—41no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3D3×D411yescharacteristic
317C23×C3D3×D411yescharacteristic
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—42no—
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—121no—
342C2×C3×C4—121no—
343C2×C3×C4—122no—
344C2×C3×C4—121no—
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4#23511yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—42no—
361C2×Dic3—41no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—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—82no—
401C2×C32#39211yescharacteristic
402C2×C32#45212yes—
403C2×C32#46412yes—
404C2×C32#49511yescharacteristic
405C2×C32#49711yescharacteristic
406C24—21no—
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—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4#62612yes—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4—92no—
428C22×C4—181no—
429C22×C4C2×D3211yescharacteristic
430Q16—188no—
431SD16—68no—
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—181no—
442C42—181no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—44no—
449C22×C3—48no—
450C22×C3—44no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—44no—
454C22×C3—82no—
455C22×C3—84no—
456C22×C3—82no—
457C22×C3—81no—
458C22×C3—82no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—82no—
463C22×C3#88211yescharacteristic
464C22×C3#88411yescharacteristic
465C22×C3#91212yes—
466C22×C3#91512yes—
467C22×C3#91512yes—
468C22×C3#91612yes—
469C22×C3#93711yescharacteristic
470C22×C3#93911yescharacteristic
471C22×C3#94011yescharacteristic
472C22×C3#94011yescharacteristic
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—122no—
478C3×C4—241no—
479C3×C4#88211yescharacteristic
480C3×C4#88411yescharacteristic
481C3×C4#93011yescharacteristic
482C3×C4#93711yescharacteristic
483C3×C4#93711yescharacteristic
484C3×C4#93811yescharacteristic
485C3×C4#93911yescharacteristic
486C3×C4#95311yescharacteristic
487Dic3—42no—
488Dic3—81no—
489Dic3—124no—
490Dic3—124no—
491Dic3—122no—
492Dic3—122no—
493Dic3—122no—
494Dic3—122no—
495C32#201511yescharacteristic, complemented, Sylow
496C23—22no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23#381111yescharacteristic
502Q8—62no—
503Q8—62no—
504Q8—121no—
505Q8—121no—
506Q8—182no—
507Q8—182no—
508Q8—361no—
509Q8—361no—
510D4—22no—
511D4—22no—
512D4—41no—
513D4—41no—
514C2×C4—62no—
515C2×C4—121no—
516C2×C4—121no—
517C2×C4—122no—
518C2×C4—121no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4#380411yescharacteristic
526C2×C4C2×#62611yescharacteristic
527C2×C4D3×#6711yescharacteristic
528C2×C4D3×#6711yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4#381111yescharacteristic
531C8—62no—
532C8—62no—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—84no—
539C2×C3—82no—
540C2×C3—82no—
541C2×C3#476712yes—
542C2×C3#478312yes—
543C2×C3#496011yescharacteristic
544C2×C3#515511yescharacteristic
545C2×C3#516612yes—
546C2×C3#516711yescharacteristic
547C2×C3#516711yescharacteristic
548C2×C3#516811yescharacteristic
549C2×C3#517312yes—
550C2×C3#522311yescharacteristic
551C22—44no—
552C22—42no—
553C22—81no—
554C22—82no—
555C22—81no—
556C22#6393112yes—
557C22#6393612yes—
558C22#6397111yescharacteristic
559C22#6397911yescharacteristic
560C22#6398111yescharacteristic
561C4—122no—
562C4—241no—
563C4—362no—
564C4—362no—
565C4#6395811yescharacteristic
566C4#6397711yescharacteristic
567C4#6397811yescharacteristic
568C4#6398311yescharacteristic
569C3—21no—
570C3#7021511yescharacteristic, complemented
571C3#7205811yescharacteristic, complemented
572C2—82no—
573C2#1059144312yes—
574C2#1059146612yes—
575C2#1059147411yescharacteristic
576C2#1059149311yescharacteristic
577C2#1059172411yescharacteristic
subgroupG/H
centerC23#3811
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. #10591221C2semidirect
6. C2×#63567C2semidirect
7. #10589156C2semidirect
495. C32#2015semidirect
570. C3#70215semidirect
571. C3#72058semidirect

Maximal subgroups

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

subgroupindex
C2×#641452
C22×C3×#2142
C22×#37192
C2×C3×#8322
#105912212
C2×#635672
#105891562
#720583
#702153