Finite Group Databasebeta

← #11792602

Subgroups — #11792602

Order 1152.

909 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3746C211yesmaximal, characteristic, complemented
2C2×#63860C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic
4C2×C3×#821C211yesmaximal, characteristic
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#70215—31nomaximal
9#68677—31nomaximal
10C22×#634C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×#3746—22no—
15C2×#3746—22no—
16C2×#3746—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—22no—
21#63860—22no—
22#63860—22no—
23C2×#3716—22no—
24C2×#3716—22no—
25C2×#3716—22no—
26C3×#821—22no—
27#63579—22no—
28#63567—22no—
29C2×#936—31no—
30C22×#214—31no—
31C22×Dic12—31no—
32C22×Dic12—31no—
33C22×Dic12—61no—
34C22×#204—31no—
35C2×#875—31no—
36C2×C3×#102—31no—
37C2×#821D311yescharacteristic
38C2×#816—31no—
39#4973—31no—
40C2×#810—31no—
41#4929—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634D412yes—
59C2×#634D412yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D412yes—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12D412yes—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8D412yes—
71#3746—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8D412yes—
79(C2×D3)⋊Dic3—28no—
80#3716—28no—
81#2015—91noSylow
82C22×C3×D4—31no—
83C22×D12C2×D311yescharacteristic
84C22×Dic6—31no—
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C22×Dic6—61no—
90C22×C3×C8—21no—
91C22×C3×C8—31no—
92C22×C3×C8C2×D311yescharacteristic
93C22×C3×C8C2×D311yescharacteristic
94C2×C3×C4⋊C4—31no—
95C2×C3×C42—31no—
96C2×#217—62no—
97#936—62no—
98#936—62no—
99C2×#214—62no—
100C2×#214—62no—
101C2×#214—62no—
102C2×(C2×D3)⋊C4—62no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C2×Dic12—62no—
107C2×Dic12—62no—
108C2×Dic12—62no—
109C2×Dic12—62no—
110C2×Dic12—64no—
111C2×Dic12—64no—
112C2×Dic12—64no—
113C2×Dic12—62no—
114C2×Dic12—62no—
115C2×#204—62no—
116C2×#204—62no—
117C2×#204—62no—
118#875—62no—
119#875—62no—
120C3×#102—62no—
121C3⋊#95—62no—
122C3⋊#95—62no—
123#821—22no—
124#816—62no—
125#810—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×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144#634—22no—
145#634—22no—
146#634—22no—
147#634—22no—
148#634—41no—
149#634—41no—
150#634—41no—
151#634—41no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—42no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—41no—
160C3×D12—41no—
161C32×C8—22no—
162C3×C3⋊C8—22no—
163C22×Q16—91no—
164C22×SD16—91no—
165C2×#124—91no—
166C2×#103—91no—
167C2×#102—31no—
168#391—91no—
169#336—31no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×D4—32no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—121no—
189C22×Dic3—121no—
190C22×Dic3D1212yes—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12D1212yes—
197C2×Dic6—32no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—62no—
202C2×Dic6—62no—
203C2×Dic6—62no—
204C2×Dic6—62no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
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—61no—
227C2×Dic6—121no—
228C2×Dic6—121no—
229C2×Dic6—121no—
230C2×Dic6—121no—
231C2×Dic6—121no—
232C2×Dic6—121no—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—22no—
240C2×C3×C8—32no—
241C2×C3×C8—61no—
242C2×C3×C8—61no—
243C2×C3×C8D1212yes—
244C2×C3×C8#6712yes—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C42—61no—
248C3×C42—61no—
249#217—68no—
250#214—68no—
251(C2×D3)⋊C4—68no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4×Dic3—21no—
255C4×Dic3—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8D1212yes—
259Dic12—616no—
260Dic12—68no—
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#12011yescharacteristic
274C32×C4#12011yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12111yescharacteristic
277C3⋊Dic3—42no—
278C3⋊Dic3—42no—
279C3×Dic3—42no—
280C3×Dic3—81no—
281C22×Q8—91no—
282C22×Q8—91no—
283C22×D4—31no—
284C2×Q16—182no—
285C2×Q16—182no—
286C2×Q16—182no—
287C2×SD16—182no—
288C2×SD16—182no—
289C2×SD16—182no—
290C22×C8—31no—
291C22×C8D3211yescharacteristic
292#124—182no—
293#124—182no—
294C2×C4⋊C4—31no—
295C2×C22⋊C4—182no—
296C2×C42—31no—
297#103—182no—
298#102—62no—
299#95—182no—
300C23×C3—21no—
301C23×C3—62no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3—122no—
305C23×C3—122no—
306C23×C3C2×D1211yescharacteristic
307C23×C3D3×D411yescharacteristic
308C22×D3—22no—
309C22×D3—41no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3—41no—
313C3×D4—62no—
314C3×D4—62no—
315C3×D4—121no—
316C3×D4—121no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—121no—
327C2×C3×C4—122no—
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23911yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—42no—
344C2×Dic3—41no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363D12—22no—
364D12—22no—
365D12—41no—
366D12—41no—
367Dic6—64no—
368Dic6—64no—
369Dic6—62no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—62no—
374Dic6—62no—
375Dic6—62no—
376Dic6—62no—
377Dic6—122no—
378Dic6—122no—
379Dic6—122no—
380Dic6—122no—
381Dic6—122no—
382Dic6—122no—
383Dic6—121no—
384Dic6—121no—
385Dic6—121no—
386Dic6—121no—
387Dic6—121no—
388Dic6—121no—
389Dic6—121no—
390Dic6—121no—
391C3×C8—24no—
392C3×C8—22no—
393C3×C8—22no—
394C3×C8—62no—
395C3⋊C8—22no—
396C2×C32#39211yescharacteristic
397C2×C32#45212yes—
398C2×C32#46412yes—
399C2×C32#49511yescharacteristic
400C2×C32#49711yescharacteristic
401C3×D3—82no—
402C24—61no—
403C2×Q8—92no—
404C2×Q8—92no—
405C2×Q8—181no—
406C2×Q8—181no—
407C2×Q8—181no—
408C2×Q8—181no—
409C2×Q8—181no—
410C2×Q8—181no—
411C2×Q8—181no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×D4—32no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C22×C4—32no—
422C22×C4—61no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C2×D3211yescharacteristic
426Q16—188no—
427SD16—188no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—32no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8#62612yes—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C22⋊C4—188no—
437C42—61no—
438C42—61no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—122no—
445C22×C3—124no—
446C22×C3—241no—
447C22×C3—241no—
448C22×C3—242no—
449C22×C3#87411yescharacteristic
450C22×C3#88211yescharacteristic
451C22×C3#88211yescharacteristic
452C22×C3#88411yescharacteristic
453C22×C3#89511yescharacteristic
454C22×C3#90412yes—
455C22×C3#90912yes—
456C22×C3#91212yes—
457C22×C3#91512yes—
458C22×C3#94011yescharacteristic
459C2×D3—42no—
460C2×D3—44no—
461C2×D3—81no—
462C2×D3—81no—
463C2×D3—82no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—122no—
469C3×C4—241no—
470C3×C4#88211yescharacteristic
471C3×C4#88211yescharacteristic
472C3×C4#88211yescharacteristic
473C3×C4#88411yescharacteristic
474C3×C4#89511yescharacteristic
475C3×C4#89511yescharacteristic
476C3×C4#93011yescharacteristic
477C3×C4#93711yescharacteristic
478Dic3—42no—
479Dic3—81no—
480Dic3—124no—
481Dic3—124no—
482Dic3—122no—
483Dic3—122no—
484Dic3—122no—
485Dic3—122no—
486C32#201511yescharacteristic, complemented, Sylow
487C23—62no—
488C23—122no—
489C23—122no—
490C23—121no—
491C23—121no—
492C23D3×D1211yescharacteristic
493Q8—182no—
494Q8—182no—
495Q8—182no—
496Q8—182no—
497Q8—361no—
498Q8—361no—
499Q8—361no—
500Q8—361no—
501D4—62no—
502D4—62no—
503D4—121no—
504D4—121no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—122no—
509C2×C4—121no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—361no—
513C2×C4—361no—
514C2×C4—361no—
515C2×C4—361no—
516C2×C4#379911yescharacteristic
517C2×C4D3×D1211yescharacteristic
518C2×C4D3×D1211yescharacteristic
519C2×C4C2×#62611yescharacteristic
520C2×C4#381111yescharacteristic
521C2×C4#381111yescharacteristic
522C8—22no—
523C8—62no—
524C2×C3—22no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—22no—
529C2×C3—242no—
530C2×C3#467111yescharacteristic
531C2×C3#469611yescharacteristic
532C2×C3#471511yescharacteristic
533C2×C3#473312yes—
534C2×C3#476712yes—
535C2×C3#478312yes—
536C2×C3#484512yes—
537C2×C3#496011yescharacteristic
538C2×C3#515511yescharacteristic
539C2×C3#516711yescharacteristic
540D3—82no—
541C22—122no—
542C22—124no—
543C22—242no—
544C22—241no—
545C22—241no—
546C22#6380012yes—
547C22#6380712yes—
548C22#6391011yescharacteristic
549C22#6391111yescharacteristic
550C22#6392311yescharacteristic
551C4—122no—
552C4—241no—
553C4—362no—
554C4—362no—
555C4#6390911yescharacteristic
556C4#6391011yescharacteristic
557C4#6392311yescharacteristic
558C4#6398111yescharacteristic
559C3—21no—
560C3#6867711yescharacteristic, complemented
561C3#7021511yescharacteristic, complemented
562C2—242no—
563C2#1059086112yes—
564C2#1059086411yescharacteristic
565C2#1059089711yescharacteristic
566C2#1059096912yes—
567C2#1059139511yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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×#3746C2semidirect
5. #10591213C2semidirect
6. C2×#63567C2semidirect
7. C3×#4550C2semidirect
43. #4550D3semidirect
486. C32#2015semidirect
560. C3#68677semidirect
561. C3#70215semidirect

Maximal subgroups

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

subgroupindex
C22×#37462
C2×#638602
C22×#37162
C2×C3×#8212
#105912132
C2×#635672
C3×#45502
#702153
#686773