Finite Group Databasebeta

← #11792593

Subgroups — #11792593

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×#3756C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×#63860C211yesmaximal, characteristic
4C3×#5229C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7#10589155C211yesmaximal, characteristic, complemented
8#72058—31nomaximal
9#69689—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C2×#3756—22no—
14C2×#3756—22no—
15C2×#3756—22no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#215—22no—
18C2×C3×#215—22no—
19C2×C3×#215—22no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—22no—
24#63860—22no—
25#63860—22no—
26C3×C3⋊#95—22no—
27#63567—22no—
28#63562—22no—
29C22×C3×SD16—31no—
30C22×#216—31no—
31C22×#216—31no—
32C22×#216—61no—
33C22×#215D311yescharacteristic
34C2×#936—31no—
35C2×#875—31no—
36C3×#391—31no—
37#5229D311yescharacteristic, complemented
38C2×#832—31no—
39C2×#816—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
53C22×C3⋊Dic3—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
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—
68#3756—28no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)D412yes—
72C3×#215—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(C2×D3)⋊Dic3—28no—
81#2015—91noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8C2×D311yescharacteristic
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C2×C3×SD16—62no—
91C2×C3×SD16—62no—
92C2×C3×SD16—62no—
93C22×C3×C8—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C42—31no—
96C2×#217—62no—
97C2×#216—62no—
98C2×#216—62no—
99C2×#216—62no—
100C2×#216—62no—
101C2×#216—64no—
102C2×#216—64no—
103C2×#216—64no—
104C2×#216—62no—
105C2×#216—62no—
106C2×#215—22no—
107C2×#215—22no—
108C2×#215—22no—
109#936—62no—
110#936—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#832—62no—
122C3⋊#95—22no—
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—
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
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—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—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C22×Q16—91no—
164C22×SD16—31no—
165C2×#124—91no—
166C2×#103—91no—
167C2×#102—91no—
168#391—31no—
169#336—91no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—21no—
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—22no—
185C2×C3×Q8—41no—
186C2×C3×Q8—41no—
187C2×C3×Q8—41no—
188C2×C3×Q8D1212yes—
189C2×C3×Q8#6712yes—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—32no—
200C22×C3×C4—41no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—21no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—121no—
208C22×Dic3#6712yes—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12#6712yes—
215C2×Dic6—32no—
216C2×Dic6—32no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
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—61no—
230C2×Dic6—121no—
231C2×Dic6—121no—
232C2×Dic6—121no—
233C3×SD16—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#217—68no—
242#216—616no—
243#216—68no—
244#216—68no—
245#215—28no—
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—91no—
282C22×Q8D3211yescharacteristic
283C22×D4—31no—
284C2×Q16—182no—
285C2×Q16—182no—
286C2×Q16—182no—
287C2×SD16—62no—
288C2×SD16—62no—
289C2×SD16—62no—
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×C3—62no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3—122no—
305C23×C3—122no—
306C23×C3D3×D411yescharacteristic
307C23×C3C2×#6711yescharacteristic
308C22×D3—22no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3—41no—
312C22×D3—41no—
313C3×Q8—24no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—42no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—41no—
322C3×Q8—41no—
323C3×Q8—41no—
324C3×Q8—41no—
325C3×D4—62no—
326C3×D4—62no—
327C3×D4—121no—
328C3×D4—121no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4—121no—
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—41no—
365C2×Dic3—42no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375D12—22no—
376D12—22no—
377D12—41no—
378D12—41no—
379Dic6—64no—
380Dic6—62no—
381Dic6—62no—
382Dic6—62no—
383Dic6—62no—
384Dic6—122no—
385Dic6—122no—
386Dic6—122no—
387Dic6—121no—
388Dic6—121no—
389Dic6—121no—
390Dic6—121no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8—64no—
394C3⋊C8—62no—
395C3⋊C8—62no—
396C2×C32#39211yescharacteristic
397C2×C32#45212yes—
398C2×C32#46412yes—
399C2×C32#49511yescharacteristic
400C2×C32#49711yescharacteristic
401C3×D3—82no—
402C24—61no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—92no—
409C2×Q8—181no—
410C2×Q8—181no—
411C2×Q8—181no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8#62612yes—
415C2×D4—32no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C22×C4—21no—
422C22×C4—32no—
423C22×C4—61no—
424C22×C4—181no—
425C22×C4C2×D3211yescharacteristic
426Q16—188no—
427SD16—68no—
428C2×C8—32no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—92no—
432C2×C8—181no—
433C2×C8—181no—
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—242no—
447C22×C3—241no—
448C22×C3—241no—
449C22×C3#91512yes—
450C22×C3#91612yes—
451C22×C3#93011yescharacteristic
452C22×C3#93711yescharacteristic
453C22×C3#93711yescharacteristic
454C22×C3#93911yescharacteristic
455C22×C3#94011yescharacteristic
456C22×C3#94011yescharacteristic
457C22×C3#94212yes—
458C22×C3#95012yes—
459C2×D3—44no—
460C2×D3—42no—
461C2×D3—82no—
462C2×D3—81no—
463C2×D3—81no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—44no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—122no—
472C3×C4—241no—
473C3×C4#88211yescharacteristic
474C3×C4#88211yescharacteristic
475C3×C4#88411yescharacteristic
476C3×C4#88411yescharacteristic
477C3×C4#93711yescharacteristic
478C3×C4#93811yescharacteristic
479C3×C4#93911yescharacteristic
480C3×C4#95311yescharacteristic
481Dic3—42no—
482Dic3—81no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486C32#201511yescharacteristic, complemented, Sylow
487C23—62no—
488C23—122no—
489C23—122no—
490C23—121no—
491C23—121no—
492C23D3×#6711yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497Q8—182no—
498Q8—182no—
499Q8—361no—
500Q8—361no—
501D4—62no—
502D4—62no—
503D4—121no—
504D4—121no—
505C2×C4—22no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—122no—
512C2×C4—121no—
513C2×C4—182no—
514C2×C4—361no—
515C2×C4—361no—
516C2×C4#380411yescharacteristic
517C2×C4C2×#62611yescharacteristic
518C2×C4D3×#6711yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4#381111yescharacteristic
521C2×C4#381111yescharacteristic
522C8—62no—
523C8—182no—
524C2×C3—22no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—242no—
530C2×C3#496011yescharacteristic
531C2×C3#502812yes—
532C2×C3#504712yes—
533C2×C3#505911yescharacteristic
534C2×C3#508611yescharacteristic
535C2×C3#516612yes—
536C2×C3#516711yescharacteristic
537C2×C3#516811yescharacteristic
538C2×C3#517312yes—
539C2×C3#522311yescharacteristic
540D3—82no—
541C22—124no—
542C22—122no—
543C22—242no—
544C22—241no—
545C22—241no—
546C22#6394612yes—
547C22#6394712yes—
548C22#6397811yescharacteristic
549C22#6397911yescharacteristic
550C22#6398311yescharacteristic
551C4—42no—
552C4—122no—
553C4—241no—
554C4—362no—
555C4#6395811yescharacteristic
556C4#6397111yescharacteristic
557C4#6397711yescharacteristic
558C4#6398111yescharacteristic
559C3—21no—
560C3#6968911yescharacteristic, complemented
561C3#7205811yescharacteristic, complemented
562C2—242no—
563C2#1059160412yes—
564C2#1059160511yescharacteristic
565C2#1059160611yescharacteristic
566C2#1059165512yes—
567C2#1059172411yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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
1. C22×#3756C2semidirect
4. C3×#5229C2semidirect
5. C2×#63567C2semidirect
7. #10589155C2semidirect
37. #5229D3semidirect
486. C32#2015semidirect
560. C3#69689semidirect
561. C3#72058semidirect

Maximal subgroups

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

subgroupindex
C22×#37562
C22×C3×#2152
C2×#638602
C3×#52292
C2×#635672
C2×#635622
#105891552
#720583
#696893