Finite Group Databasebeta

← #11773367

Subgroups — #11773367

Order 1152.

1337 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C2×C3×C3⋊#95C212yesmaximal
4C2×#63579C212yesmaximal
5C2×#63579C211yesmaximal, characteristic
6#69409—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C2×#3750—22no—
13C2×#3750—22no—
14C2×#3750C414yescomplemented
15C2×#3724—22no—
16C2×#3724—24no—
17C3×C3⋊#95—24no—
18#63579—22no—
19#63579—24no—
20C22×Dic3⋊C4—32no—
21C22×Dic3⋊C4—32no—
22C22×Dic3⋊C4—61no—
23C2×C3×#95—32no—
24C2×C3⋊#95—32no—
25C2×C3⋊#95—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95D312yes—
28C24×C32C2311yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4—21no—
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C412yes—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3C2×C412yes—
42C22×C3⋊Dic3D412yes—
43C22×C3⋊Dic3D412yes—
44C22×C3⋊Dic3D412yes—
45C22×C3⋊Dic3Q812yes—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3D414yes—
59C22×C3×Dic3Q814yes—
60#3750—28no—
61#3724—28no—
62#1441—91noSylow
63C23×C3×C4—21no—
64C23×C3×C4—32no—
65C23×C3×C4—32no—
66C23×C3×C4C2×D312yes—
67C23×Dic3—32no—
68C23×Dic3—32no—
69C23×Dic3—61no—
70C23×Dic3—61no—
71C23×Dic3C2×D312yes—
72C23×Dic3C2×D312yes—
73C2×Dic3⋊C4—38no—
74C2×Dic3⋊C4—64no—
75C2×Dic3⋊C4—64no—
76C2×Dic3⋊C4—64no—
77C2×Dic3⋊C4—64no—
78C2×Dic3⋊C4—64no—
79C2×Dic3⋊C4—64no—
80C2×Dic3⋊C4—64no—
81C2×Dic3⋊C4—64no—
82C3×#95—64no—
83C3⋊#95—24no—
84C3⋊#95—64no—
85C3⋊#95—64no—
86C3⋊#95—64no—
87C23×C32C22×C411yescharacteristic
88C23×C32C2×D411yescharacteristic
89C23×C32C2×D411yescharacteristic
90C23×C32C2×D411yescharacteristic
91C23×C32C2×D412yes—
92C23×C32C2×Q812yes—
93C23×C32C2×Q811yescharacteristic
94C23×C32#4111yescharacteristic
95C23×C32#4111yescharacteristic
96C23×C32#4112yes—
97C23×C32#4112yes—
98C2×C32×C4—22no—
99C2×C32×C4—24no—
100C2×C32×C4—41no—
101C2×C32×C4—42no—
102C2×C32×C4—41no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3C22⋊C414yes—
114C2×C3⋊Dic3C4⋊C414yescomplemented
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C2×C3×Dic3—42no—
129C22×C4⋊C4—91no—
130C22×C4⋊C4—91no—
131C2×#95—32no—
132C2×#95—92no—
133C2×#95—91no—
134C24×C3—21no—
135C24×C3C22×D312yes—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—34no—
146C22×C3×C4—34no—
147C22×C3×C4—42no—
148C22×C3×C4—42no—
149C22×C3×C4—62no—
150C22×C3×C4—62no—
151C22×C3×C4—62no—
152C22×C3×C4—62no—
153C22×C3×C4—62no—
154C22×C3×C4—62no—
155C22×C3×C4—62no—
156C22×C3×C4—62no—
157C22×C3×C4—62no—
158C22×C3×C4—62no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C22×C3×C4C4×D314yes—
162C22×Dic3—22no—
163C22×Dic3—22no—
164C22×Dic3—22no—
165C22×Dic3—22no—
166C22×Dic3—22no—
167C22×Dic3—22no—
168C22×Dic3—22no—
169C22×Dic3—22no—
170C22×Dic3—22no—
171C22×Dic3—22no—
172C22×Dic3—22no—
173C22×Dic3—22no—
174C22×Dic3—34no—
175C22×Dic3—34no—
176C22×Dic3—34no—
177C22×Dic3—34no—
178C22×Dic3—34no—
179C22×Dic3—34no—
180C22×Dic3—62no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3—62no—
189C22×Dic3—62no—
190C22×Dic3—62no—
191C22×Dic3—62no—
192C22×Dic3—62no—
193C22×Dic3—62no—
194C22×Dic3—62no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197C22×Dic3—62no—
198C22×Dic3—122no—
199C22×Dic3—122no—
200C22×Dic3Dic614yes—
201C22×Dic3#6714yes—
202Dic3⋊C4—616no—
203Dic3⋊C4—616no—
204Dic3⋊C4—616no—
205C22×C32C2×C22⋊C411yescharacteristic
206C22×C32C2×C4⋊C411yescharacteristic
207C22×C32#11711yescharacteristic
208C22×C32C4×D412yes—
209C22×C32C4×Q812yes—
210C22×C32#12011yescharacteristic
211C22×C32#12111yescharacteristic
212C22×C32#12111yescharacteristic
213C22×C32#12112yes—
214C22×C32#12112yes—
215C22×C32C22⋊Q812yes—
216C22×C32C22⋊Q812yes—
217C22×C32C22⋊Q811yescharacteristic
218C22×C32C22⋊Q811yescharacteristic
219C22×C32C22⋊Q812yes—
220C22×C32#12311yescharacteristic
221C22×C32#12312yes—
222C22×C32#12411yescharacteristic
223C22×C32#12512yes—
224C22×C32#12512yes—
225C22×C32#12612yes—
226C22×C32C4⋊Q811yescharacteristic
227C22×C32C4⋊Q812yes—
228C32×C4—42no—
229C3⋊Dic3—24no—
230C3⋊Dic3—24no—
231C3×Dic3—44no—
232C3×Dic3—44no—
233C23×C4—32no—
234C23×C4—32no—
235C23×C4—91no—
236C23×C4—91no—
237C23×C4D3211yescharacteristic
238C2×C4⋊C4—94no—
239C2×C4⋊C4—182no—
240C2×C4⋊C4—182no—
241C2×C4⋊C4—184no—
242C2×C4⋊C4—182no—
243#95—64no—
244#95—184no—
245#95—182no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—22no—
253C23×C3—21no—
254C23×C3—22no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3C2×Dic612yes—
258C23×C3C2×C4×D312yes—
259C23×C3#23512yes—
260C23×C3#23512yes—
261C23×C3#23512yes—
262C23×C3#23512yes—
263C23×C3D3×D412yes—
264C23×C3D3×D412yes—
265C23×C3D3×D412yes—
266C23×C3D3×D412yes—
267C23×C3#23712yes—
268C23×C3#23712yes—
269C23×C3D3×Q812yes—
270C23×C3D3×Q812yes—
271C23×C3C2×#6712yes—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—24no—
275C2×C3×C4—24no—
276C2×C3×C4—44no—
277C2×C3×C4—44no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—64no—
285C2×C3×C4—64no—
286C2×C3×C4—64no—
287C2×C3×C4—64no—
288C2×C3×C4—64no—
289C2×C3×C4—64no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×C3×C4—122no—
293C2×C3×C4—122no—
294C2×C3×C4—122no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297C2×C3×C4—122no—
298C2×Dic3—24no—
299C2×Dic3—24no—
300C2×Dic3—24no—
301C2×Dic3—24no—
302C2×Dic3—24no—
303C2×Dic3—24no—
304C2×Dic3—38no—
305C2×Dic3—38no—
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C2×Dic3—42no—
314C2×Dic3—64no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320C2×Dic3—64no—
321C2×Dic3—64no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—64no—
325C2×Dic3—64no—
326C2×Dic3—64no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332C2×Dic3—64no—
333C2×Dic3—64no—
334C2×Dic3—124no—
335C2×Dic3—124no—
336C2×Dic3—122no—
337C2×Dic3—122no—
338C2×C32#38011yescharacteristic
339C2×C32#38611yescharacteristic
340C2×C32#38712yes—
341C2×C32#38912yes—
342C2×C32#39111yescharacteristic
343C2×C32#39411yescharacteristic
344C2×C32#39511yescharacteristic
345C2×C32#39612yes—
346C2×C32#39811yescharacteristic
347C2×C32#39812yes—
348C2×C32#40011yescharacteristic
349C24C2×D3211yescharacteristic
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—34no—
355C22×C4—34no—
356C22×C4—62no—
357C22×C4—62no—
358C22×C4—62no—
359C22×C4—62no—
360C22×C4—62no—
361C22×C4—62no—
362C22×C4—62no—
363C22×C4—62no—
364C22×C4—62no—
365C22×C4—62no—
366C22×C4—62no—
367C22×C4—62no—
368C22×C4—92no—
369C22×C4—92no—
370C22×C4—92no—
371C22×C4—92no—
372C22×C4—92no—
373C22×C4—92no—
374C22×C4—181no—
375C22×C4—181no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4#62412yes—
381C4⋊C4—188no—
382C4⋊C4—188no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3C4×Dic612yes—
407C22×C3#87012yes—
408C22×C3#87212yes—
409C22×C3#87612yes—
410C22×C3#87812yes—
411C22×C3#87812yes—
412C22×C3#87912yes—
413C22×C3D3×C22⋊C412yes—
414C22×C3#67⋊C412yes—
415C22×C3#88312yes—
416C22×C3#88312yes—
417C22×C3#88412yes—
418C22×C3#88412yes—
419C22×C3#88412yes—
420C22×C3#88412yes—
421C22×C3#88512yes—
422C22×C3#88712yes—
423C22×C3#88812yes—
424C22×C3#88812yes—
425C22×C3#88912yes—
426C22×C3#88912yes—
427C22×C3#88912yes—
428C22×C3D3×C4⋊C412yes—
429C22×C3#89612yes—
430C22×C3#89612yes—
431C22×C3#89612yes—
432C22×C3#89612yes—
433C22×C3#89612yes—
434C22×C3#92412yes—
435C22×C3C4×#6712yes—
436C22×C3#92912yes—
437C22×C3#93712yes—
438C22×C3#93812yes—
439C22×C3#93912yes—
440C22×C3#94412yes—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4—124no—
444C3×C4—124no—
445Dic3—44no—
446Dic3—44no—
447Dic3—68no—
448Dic3—68no—
449Dic3—68no—
450Dic3—124no—
451C32#144111yescharacteristic, complemented, Sylow
452C23D3×Dic612yes—
453C23#379512yes—
454C23#379711yescharacteristic
455C23#379811yescharacteristic
456C23#379811yescharacteristic
457C23#380211yescharacteristic
458C23#380412yes—
459C23C2×#62411yescharacteristic
460C23D3×#6712yes—
461C23#381111yescharacteristic
462C23#381111yescharacteristic
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—64no—
469C2×C4—64no—
470C2×C4—64no—
471C2×C4—64no—
472C2×C4—64no—
473C2×C4—64no—
474C2×C4—94no—
475C2×C4—94no—
476C2×C4—122no—
477C2×C4—122no—
478C2×C4—122no—
479C2×C4—122no—
480C2×C4—122no—
481C2×C4—122no—
482C2×C4—122no—
483C2×C4—122no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4—184no—
490C2×C4—184no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C3—22no—
495C2×C3—21no—
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—22no—
502C2×C3—22no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3#464612yes—
506C2×C3#464712yes—
507C2×C3#465212yes—
508C2×C3#465712yes—
509C2×C3#465712yes—
510C2×C3#465812yes—
511C2×C3#466712yes—
512C2×C3#467612yes—
513C2×C3#493312yes—
514C2×C3#494812yes—
515C2×C3#495612yes—
516C2×C3#495912yes—
517C2×C3#497612yes—
518C2×C3#497912yes—
519C2×C3#498312yes—
520C22#6383912yes—
521C22#6384011yescharacteristic
522C22#6384412yes—
523C22#6384712yes—
524C22#6385112yes—
525C22#6385912yes—
526C22#6386511yescharacteristic
527C22#6386511yescharacteristic
528C22#6386712yes—
529C22#6387411yescharacteristic
530C22#6388512yes—
531C22#6389612yes—
532C22#6389912yes—
533C22#6390011yescharacteristic
534C22#6390512yes—
535C22#6391211yescharacteristic
536C22#6391211yescharacteristic
537C22#6391311yescharacteristic
538C22#6395212yes—
539C22#6395812yes—
540C22#6397411yescharacteristic
541C22#6397511yescharacteristic
542C22#6398311yescharacteristic
543C4—42no—
544C4—124no—
545C4—124no—
546C4—184no—
547C4—184no—
548C3—21no—
549C3#6940912yescomplemented
550C2#1059119511yescharacteristic
551C2#1059119712yes—
552C2#1059119812yes—
553C2#1059121711yescharacteristic
554C2#1059126412yes—
555C2#1059127311yescharacteristic
556C2#1059130912yes—
557C2#1059135511yescharacteristic
558C2#1059135611yescharacteristic
559C2#1059138811yescharacteristic
560C2#1059172211yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1441
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
14. C2×#3750C4semidirect
114. C2×C3⋊Dic3C4⋊C4semidirect
451. C32#1441semidirect
549. C3#69409semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C22×#37242
C2×C3×C3⋊#952
C2×#635792
#694093