Finite Group Databasebeta

← #11878918

Subgroups — #11878918

Order 1152.

842 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic
3#10592927C211yesmaximal, characteristic
4C3×#5228C211yesmaximal, characteristic
5#10591626C212yesmaximal, complemented
6#10591623C212yesmaximal, complemented
7#10591575C212yesmaximal, complemented
8#10591574C212yesmaximal, complemented
9#10591186C211yesmaximal, characteristic
10#10591185C211yesmaximal, characteristic
11#10591053C211yesmaximal, characteristic
12#83222—31nomaximal
13#80178—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×#3756C2212yes—
17#64133C2211yescharacteristic
18C3×#944—21no—
19C3×#944—21no—
20C3×#944C2212yes—
21C3×#944C2212yes—
22C2×C3×#216C2212yes—
23C3×#924C2211yescharacteristic
24C2×C3×Dic3⋊C4—21no—
25C2×C3×Dic3⋊C4—21no—
26C2×C3×C4×Dic3C2211yescharacteristic
27#63964—21no—
28#63955—21no—
29#63918C2211yescharacteristic
30#63867—21no—
31#63866C2211yescharacteristic
32#63844C2211yescharacteristic
33Dic3×Dic6C2211yescharacteristic
34#63837—21no—
35C2×#3719C2212yes—
36C2×#3718C2212yes—
37#63662C2212yes—
38#63657C2211yescharacteristic
39C3×#835C2212yes—
40C3×#830C2211yescharacteristic
41Dic3⋊(C3⋊C8)C2212yes—
42#63566C2212yes—
43#63565C2212yes—
44Dic3×C3⋊C8C2212yes—
45C2×C3×C4⋊Q8—31no—
46C2×#944D311yescharacteristic
47#5622—31no—
48#5470—31no—
49C3×#451—31no—
50#5228—31no—
51#5228—31no—
52#5228—31no—
53#5228—31no—
54#5228—61no—
55#5228D311yescharacteristic
56#5183—32no—
57#5182—32no—
58#5092—32no—
59#5090—32no—
60#5090—32no—
61#5079—32no—
62#5050—31no—
63#4925—31no—
64#4795—32no—
65#4792—32no—
66#4739—31no—
67#4718—31no—
68C2×C32×Q8—21no—
69C2×C32×Q8—42no—
70C2×C32×Q8C2312yes—
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×#634C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3D411yescharacteristic
76C22×C3×Dic3D411yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—42no—
79C2×C3×Dic6C2311yescharacteristic
80C2×C3×Dic6C2312yes—
81C2×#627—21no—
82#3757—21no—
83#3756—42no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—21no—
88C3×#216—42no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic32—21no—
106Dic32—21no—
107#3719—42no—
108#3718—42no—
109#3209—91noSylow
110C22×C3×Q8—21no—
111C22×C3×Q8—31no—
112C22×C3×Q8C2×D311yescharacteristic
113C22×C3×Q8C2×D311yescharacteristic
114C22×Dic6C2×D311yescharacteristic
115C2×C3×Q16—32no—
116C3×C4⋊Q8—32no—
117C3×C4⋊Q8—32no—
118C3×C4⋊Q8—61no—
119C3×C4⋊Q8—61no—
120C3×C22⋊Q8—31no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C4⋊C4—61no—
123C2×C3×C42—31no—
124Q8×Dic3—31no—
125#944—21no—
126#944—21no—
127#944—31no—
128#944C2×D312yes—
129#944C2×D312yes—
130C2×#216—32no—
131C2×#216—32no—
132C2×#216—32no—
133C2×#216—32no—
134C2×#216—32no—
135C2×#216—62no—
136C2×#216C2×D312yes—
137#926—61no—
138#924—31no—
139#924—31no—
140#924—61no—
141#924—61no—
142#924C2×D311yescharacteristic
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×C4×Dic3C2×D311yescharacteristic
146C2×Dic12—32no—
147#889—61no—
148#888—31no—
149#887—31no—
150#887—61no—
151#878—61no—
152#877—61no—
153#870—61no—
154#869—31no—
155#869—31no—
156C4×Dic6—31no—
157C4×Dic6—31no—
158C4×Dic6—61no—
159C3×#103—32no—
160C3×C22⋊C8—31no—
161#835—32no—
162#835—32no—
163#835—32no—
164#835—32no—
165#835—62no—
166#835C2×D312yes—
167#830—31no—
168#830—31no—
169#830—61no—
170#830C2×D311yescharacteristic
171#816—32no—
172Dic3⋊C8—32no—
173C8×Dic3—32no—
174#810—32no—
175C4⋊(C3⋊C8)—32no—
176C4×C3⋊C8—32no—
177C23×C32C2×D411yescharacteristic
178C32×Q8—22no—
179C32×Q8—22no—
180C32×Q8—42no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188#634—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3Q1614yescomplemented
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×Dic6—22no—
200C3×Dic6—22no—
201C3×Dic6—22no—
202C3×Dic6—42no—
203#627—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207C2×C4⋊Q8—31no—
208#494—92no—
209#487—92no—
210#462—92no—
211#462—92no—
212#451—31no—
213#451—91no—
214#451—91no—
215#451—91no—
216#431—91no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—22no—
220C2×C3×Q8—32no—
221C2×C3×Q8—31no—
222C2×C3×Q8—41no—
223C2×C3×Q8—42no—
224C2×C3×Q8—42no—
225C2×C3×Q8—44no—
226C2×C3×Q8—61no—
227C2×C3×Q8—122no—
228C2×C3×Q8C22×D312yes—
229C2×C3×Q8C22×D312yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—41no—
236C22×C3×C4—61no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×Dic3—21no—
240C22×Dic3#6711yescharacteristic
241C22×Dic3#6711yescharacteristic
242C2×Dic6—21no—
243C2×Dic6—31no—
244C2×Dic6—31no—
245C2×Dic6—42no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C2×Dic6—61no—
249C2×Dic6C22×D312yes—
250C2×Dic6C22×D311yescharacteristic
251C3×Q16—122no—
252C2×C3×C8—32no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4—61no—
259C3×C22⋊C4—61no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—31no—
263C3×C42—31no—
264#217—21no—
265#217—61no—
266#217—61no—
267#217—121no—
268#216—42no—
269#216—122no—
270#216—122no—
271#216—122no—
272#216—122no—
273#216—122no—
274#216—124no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3C22×D311yescharacteristic
283Dic3⋊C4—21no—
284Dic3⋊C4—22no—
285Dic3⋊C4—22no—
286Dic3⋊C4—22no—
287Dic3⋊C4—22no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296Dic3⋊C4—121no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3#6711yescharacteristic
302C4×Dic3#6711yescharacteristic
303C4×Dic3C22×D311yescharacteristic
304C4×Dic3C22×D311yescharacteristic
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8C22×D312yes—
309Dic12—122no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32C2×Q1612yes—
313C22×C32C22×D411yescharacteristic
314C32×C4—21no—
315C32×C4—42no—
316C32×C4H(5,𝔽2)12yes—
317C3⋊Dic3—41no—
318C3⋊Dic3—41no—
319C3×Dic3—21no—
320C3×Dic3—42no—
321C3×Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3C2×Q1612yes—
324C3×Dic3C2×Q1612yes—
325C3×Dic3#13712yes—
326C22×Q8—31no—
327C22×Q8D3211yescharacteristic
328C2×Q16—32no—
329C2×Q16—92no—
330C2×Q16—92no—
331C2×Q16—92no—
332C4⋊Q8—32no—
333C4⋊Q8—32no—
334C4⋊Q8—61no—
335C4⋊Q8—61no—
336C4⋊Q8—91no—
337C4⋊Q8—91no—
338#125—181no—
339C22⋊Q8—31no—
340C22⋊Q8—91no—
341C22⋊Q8—181no—
342C4×Q8—91no—
343C4×Q8—91no—
344C4×Q8—181no—
345#117—181no—
346C2×C4⋊C4—61no—
347C2×C4⋊C4—61no—
348C2×C42—31no—
349C4⋊C8—92no—
350#103—32no—
351#103—92no—
352#103—92no—
353#103—92no—
354C22⋊C8—31no—
355C22⋊C8—91no—
356C4×C8—92no—
357C23×C3—21no—
358C23×C3D3×D411yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C3×Q8—24no—
361C3×Q8—22no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—22no—
365C3×Q8—42no—
366C3×Q8—42no—
367C3×Q8—42no—
368C3×Q8—44no—
369C3×Q8—62no—
370C3×Q8—62no—
371C3×Q8—62no—
372C3×Q8—122no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—34no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—44no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—122no—
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398C2×Dic3—22no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—42no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3#21614yescomplemented
410C2×Dic3C2×#6711yescharacteristic
411C2×Dic3C2×#6711yescharacteristic
412C2×Dic3C2×#6711yescharacteristic
413C2×Dic3C2×#6711yescharacteristic
414Dic6—22no—
415Dic6—22no—
416Dic6—22no—
417Dic6—42no—
418Dic6—62no—
419Dic6—62no—
420Dic6—122no—
421Dic6—122no—
422Dic6—122no—
423C3×C8—62no—
424C3⋊C8—22no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
428C2×C32—22no—
429C2×C32#53511yescharacteristic
430C2×C32C22×Q1611yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C2×Q8—21no—
433C2×Q8—32no—
434C2×Q8—31no—
435C2×Q8—42no—
436C2×Q8—61no—
437C2×Q8—91no—
438C2×Q8—122no—
439C2×Q8—181no—
440C2×Q8C2×D3212yes—
441C22×C4—21no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—61no—
445C22×C4C2×D3211yescharacteristic
446Q16—122no—
447Q16—362no—
448Q16—362no—
449Q16—362no—
450C2×C8—32no—
451C2×C8—92no—
452C4⋊C4—31no—
453C4⋊C4—62no—
454C4⋊C4—62no—
455C4⋊C4—62no—
456C4⋊C4—62no—
457C4⋊C4—61no—
458C4⋊C4—91no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C22⋊C4—61no—
466C22⋊C4—181no—
467C42—31no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—181no—
472C42—181no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3D3×Q1612yes—
482C22×C3C2×#21612yes—
483C22×C3C2×D3×D411yescharacteristic
484C22×C3C22×#6711yescharacteristic
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—32no—
489C3×C4—32no—
490C3×C4—32no—
491C3×C4—41no—
492C3×C4—44no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—61no—
496C3×C4—121no—
497C3×C4—121no—
498C3×C4—122no—
499C3×C4#100412yes—
500C3×C4#100412yes—
501Dic3—21no—
502Dic3—41no—
503Dic3—42no—
504Dic3—41no—
505Dic3—121no—
506Dic3—121no—
507Dic3—121no—
508Dic3—121no—
509Dic3—241no—
510Dic3—241no—
511Dic3#94212yes—
512Dic3C2×#21612yes—
513Dic3C2×#21612yes—
514C32#320911yescharacteristic, complemented, Sylow
515C23D3×#6711yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—42no—
519Q8—62no—
520Q8—62no—
521Q8—62no—
522Q8—122no—
523Q8—182no—
524Q8—362no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—31no—
528C2×C4—31no—
529C2×C4—31no—
530C2×C4—34no—
531C2×C4—31no—
532C2×C4—42no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—62no—
537C2×C4—122no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4D3×#6711yescharacteristic
541C2×C4C22×D3211yescharacteristic
542C8—62no—
543C8—182no—
544C2×C3—22no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—42no—
550C2×C3#559211yescharacteristic
551C2×C3C2×D3×Q1611yescharacteristic
552C2×C3D3×#13711yescharacteristic
553C2×C3#580511yescharacteristic
554C2×C3C2×#94211yescharacteristic
555C2×C3C22×#21611yescharacteristic
556C22—21no—
557C22—21no—
558C22D3×#21612yes—
559C22C2×D3×#6711yescharacteristic
560C4—21no—
561C4—32no—
562C4—32no—
563C4—32no—
564C4—42no—
565C4—61no—
566C4—122no—
567C4—121no—
568C4—121no—
569C4—361no—
570C4—361no—
571C4#6433012yes—
572C3—21no—
573C3#8017811yescharacteristic, complemented
574C3#8322211yescharacteristic, complemented
575C2—22no—
576C2D3×#94211yescharacteristic
577C2C2×D3×#21611yescharacteristic
578C2#1059551311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
5. #10591626C2semidirect
6. #10591623C2semidirect
7. #10591575C2semidirect
8. #10591574C2semidirect
194. C2×C3×Dic3Q16semidirect
409. C2×Dic3#216semidirect
514. C32#3209semidirect
573. C3#80178semidirect
574. C3#83222semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9442
#105948082
#105929272
C3×#52282
#105916262
#105916232
#105915752
#105915742
#105911862
#105911852
#105910532
#832223
#801783