Finite Group Databasebeta

← #11792598

Subgroups — #11792598

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#947C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5#10591220C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589155C211yesmaximal, characteristic, complemented
8#72072—31nomaximal
9#71729—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#947—22no—
16C3×#947—22no—
17C2×C3×#216—22no—
18C2×C3×#216—22no—
19C2×C3×#216—22no—
20C2×C3×(C2×D3)⋊C4—22no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3715—22no—
24C2×#3715—22no—
25C2×#3715—22no—
26#63662—22no—
27#63579—22no—
28#63563—22no—
29C22×C3×Q16—31no—
30C2×C3×#124—31no—
31C2×#947D311yescharacteristic
32C22×#216D311yescharacteristic, complemented
33C22×#215—31no—
34C22×#214—31no—
35#5229—31no—
36C2×#835—31no—
37C2×#835—31no—
38C2×#835—61no—
39C2×#832—31no—
40C2×#821—31no—
41#4929—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—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)D412yes—
73C3×#216—28no—
74C3×(C2×D3)⋊C4—28no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D412yes—
80#3715—28no—
81#2015—91noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—31no—
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×Q8C2×D311yescharacteristic
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C2×C3×Q16—62no—
90C2×C3×Q16—62no—
91C2×C3×Q16—62no—
92C22×C3×C8—31no—
93C3×#124—62no—
94C3×#124—62no—
95C2×C3×C22⋊C4—62no—
96C2×C3×C42—31no—
97#947—22no—
98#947—22no—
99C2×#216—22no—
100C2×#216—22no—
101C2×#216—22no—
102C2×#215—62no—
103C2×#215—62no—
104C2×#215—62no—
105C2×#214—62no—
106C2×#214—62no—
107C2×#214—62no—
108C2×(C2×D3)⋊C4—22no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—61no—
112C2×C4×Dic3C2×D311yescharacteristic
113C22×C3⋊C8—31no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117#835—62no—
118#835—62no—
119#835—64no—
120#832—62no—
121C3⋊#95—62no—
122C3⋊#95—62no—
123#821—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C32×Q8—22no—
131C32×Q8—22no—
132C32×Q8—41no—
133C32×Q8—41no—
134C2×C32×C4—22no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—42no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—22no—
161C22×Q16—31no—
162C22×SD16—91no—
163C2×#124—31no—
164C2×#103—91no—
165C2×#102—91no—
166#391—91no—
167#336—91no—
168C24×C3—61no—
169C23×D3—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
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—22no—
183C2×C3×Q8—32no—
184C2×C3×Q8—41no—
185C2×C3×Q8—41no—
186C2×C3×Q8—41no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8#6712yes—
193C2×C3×Q8#6712yes—
194C2×C3×D4—32no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—32no—
204C22×C3×C4—41no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×Dic3—21no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—121no—
212C22×Dic3#6712yes—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12#6712yes—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6#6712yes—
225C3×Q16—68no—
226C2×C3×C8—32no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C3×C22⋊C4—68no—
230C3×C42—61no—
231C3×C42—61no—
232#216—28no—
233#215—68no—
234#214—68no—
235(C2×D3)⋊C4—28no—
236C4⋊Dic3—62no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—121no—
242C4×Dic3—21no—
243C4×Dic3—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—121no—
254C2×C3⋊C8—121no—
255C2×C3⋊C8#6712yes—
256C22×C32#12011yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12711yescharacteristic
259C22×C32#13512yes—
260C22×C32#13712yes—
261C2×C3×D3—42no—
262C2×C3×D3—44no—
263C2×C3×D3—82no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C32×C4—42no—
267C32×C4#12011yescharacteristic
268C32×C4#12011yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12111yescharacteristic
271C3⋊Dic3—81no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×Q8D3211yescharacteristic
276C22×D4—31no—
277C2×Q16—62no—
278C2×Q16—62no—
279C2×Q16—62no—
280C2×SD16—182no—
281C2×SD16—182no—
282C2×SD16—182no—
283C22×C8—31no—
284C22×C8—91no—
285#124—62no—
286#124—62no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—62no—
289C2×C42—31no—
290#103—182no—
291#102—182no—
292#95—182no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—122no—
296C23×C3—122no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—22no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—42no—
305C22×D3—42no—
306C3×Q8—24no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—42no—
312C3×Q8—42no—
313C3×Q8—42no—
314C3×Q8—41no—
315C3×Q8—41no—
316C3×Q8—41no—
317C3×Q8—41no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
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×C4#23711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—122no—
370C2×Dic3—242no—
371D12—22no—
372D12—22no—
373D12—41no—
374D12—41no—
375Dic6—22no—
376Dic6—22no—
377Dic6—41no—
378Dic6—41no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—62no—
382C3⋊C8—62no—
383C3⋊C8—122no—
384C2×C32#39211yescharacteristic
385C2×C32#45212yes—
386C2×C32#46412yes—
387C2×C32#49511yescharacteristic
388C2×C32#49711yescharacteristic
389C3×D3—82no—
390C24—61no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—32no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8#62512yes—
403C2×D4—32no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C22×C4—21no—
410C22×C4—32no—
411C22×C4—61no—
412C22×C4—181no—
413C22×C4C2×D3211yescharacteristic
414Q16—68no—
415SD16—188no—
416C2×C8—32no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—92no—
420C2×C8—181no—
421C2×C8—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C22⋊C4—68no—
425C42—61no—
426C42—61no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—124no—
433C22×C3—122no—
434C22×C3—242no—
435C22×C3—241no—
436C22×C3—241no—
437C22×C3#91812yes—
438C22×C3#91912yes—
439C22×C3#93711yescharacteristic
440C22×C3#93811yescharacteristic
441C22×C3#93911yescharacteristic
442C22×C3#94011yescharacteristic
443C22×C3#94011yescharacteristic
444C22×C3#95012yes—
445C22×C3#95112yes—
446C22×C3#95311yescharacteristic
447C2×D3—42no—
448C2×D3—44no—
449C2×D3—82no—
450C2×D3—81no—
451C2×D3—81no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—44no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—122no—
460C3×C4—122no—
461C3×C4#93711yescharacteristic
462C3×C4#93711yescharacteristic
463C3×C4#93711yescharacteristic
464C3×C4#93811yescharacteristic
465C3×C4#93911yescharacteristic
466C3×C4#93911yescharacteristic
467C3×C4#93911yescharacteristic
468C3×C4#95311yescharacteristic
469Dic3—42no—
470Dic3—42no—
471Dic3—242no—
472Dic3—241no—
473Dic3—241no—
474C32#201511yescharacteristic, complemented, Sylow
475C23—62no—
476C23—122no—
477C23—122no—
478C23—121no—
479C23—121no—
480C23D3×#6711yescharacteristic
481Q8—22no—
482Q8—22no—
483Q8—41no—
484Q8—41no—
485Q8—62no—
486Q8—62no—
487Q8—121no—
488Q8—121no—
489D4—62no—
490D4—62no—
491D4—121no—
492D4—121no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—362no—
503C2×C4—361no—
504C2×C4#380511yescharacteristic
505C2×C4C2×#62511yescharacteristic
506C2×C4D3×#6711yescharacteristic
507C2×C4D3×#6711yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C2×C4#381111yescharacteristic
510C8—62no—
511C8—182no—
512C2×C3—22no—
513C2×C3—22no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—242no—
518C2×C3#505412yes—
519C2×C3#505911yescharacteristic
520C2×C3#506011yescharacteristic
521C2×C3#518512yes—
522C2×C3#518712yes—
523C2×C3#519011yescharacteristic
524C2×C3#519111yescharacteristic
525C2×C3#522311yescharacteristic
526C2×C3#522311yescharacteristic
527C2×C3#523912yes—
528D3—82no—
529C22—124no—
530C22—122no—
531C22—242no—
532C22—241no—
533C22—241no—
534C22#6394312yes—
535C22#6394912yes—
536C22#6397011yescharacteristic
537C22#6397611yescharacteristic
538C22#6397911yescharacteristic
539C4—42no—
540C4—122no—
541C4—122no—
542C4—721no—
543C4#6397011yescharacteristic
544C4#6397611yescharacteristic
545C4#6398011yescharacteristic
546C4#6398311yescharacteristic
547C3—21no—
548C3#7172911yescharacteristic, complemented
549C3#7207211yescharacteristic, complemented
550C2—242no—
551C2#1059157812yes—
552C2#1059159712yes—
553C2#1059160911yescharacteristic
554C2#1059162711yescharacteristic
555C2#1059172311yescharacteristic
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
2. C22×C3×#216C2semidirect
4. C2×#63662C2semidirect
5. #10591220C2semidirect
7. #10589155C2semidirect
32. C22×#216D3semidirect
474. C32#2015semidirect
548. C3#71729semidirect
549. C3#72072semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C22×C3×#2162
C22×#37152
C2×#636622
#105912202
C2×#635632
#105891552
#720723
#717293