Finite Group Databasebeta

← #11878914

Subgroups — #11878914

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
1C3×#5622C211yesmaximal, characteristic
2C2×#63866C211yesmaximal, characteristic
3#10592749C211yesmaximal, characteristic
4C3×#5050C211yesmaximal, characteristic
5#10591626C212yesmaximal, complemented
6#10591625C212yesmaximal, complemented
7#10591190C211yesmaximal, characteristic
8#10591185C211yesmaximal, characteristic
9#10591053C211yesmaximal, characteristic
10#10590561C212yesmaximal, complemented
11#10590560C212yesmaximal, complemented
12#83370—31nomaximal
13#80178—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×C22⋊Q8C2211yescharacteristic
17C2×#3756C2212yes—
18C3×Q8×Dic3C2211yescharacteristic
19C3×#944C2211yescharacteristic
20C2×C3×#216C2212yes—
21C3×#924C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C3×#889—21no—
24C3×#888C2211yescharacteristic
25C3×#887—21no—
26C3×#887C2211yescharacteristic
27C3×#878—21no—
28C3×#877—21no—
29C2×Dic3⋊Dic3—21no—
30C2×Dic3⋊Dic3—21no—
31#63866—21no—
32#63866—21no—
33#63866C2212yes—
34#63866C2212yes—
35C2×#3719C2212yes—
36C2×#3718C2212yes—
37#63657C2211yescharacteristic
38#63637C2212yes—
39C3×#830C2211yescharacteristic
40C3×#810C2212yes—
41Dic3⋊(C3⋊C8)C2212yes—
42#63567C2212yes—
43#63565C2212yes—
44Dic3×C3⋊C8C2212yes—
45C3×#533—31no—
46C2×#944—31no—
47#5622D311yescharacteristic
48C2×#869—31no—
49C3×#451—31no—
50#5228—31no—
51#5183—32no—
52#5182—32no—
53#5093—32no—
54#5092—32no—
55#5050—31no—
56#5050—31no—
57#5050—31no—
58#5050—31no—
59#5050—61no—
60#5050D311yescharacteristic
61#5031—32no—
62#5031—32no—
63#4925—31no—
64#4795—32no—
65#4792—32no—
66#4739—31no—
67#4718—31no—
68C2×C32×Q8C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×#634—21no—
72C2×#634—42no—
73C2×#634C2312yes—
74C22×C3×Dic3—21no—
75C22×C3×Dic3D411yescharacteristic
76C22×C3×Dic3D411yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6—42no—
80C2×C3×Dic6C2311yescharacteristic
81C2×C3×Dic6C2312yes—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85#3756—42no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—21no—
88C3×#216—42no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106Dic3⋊Dic3—22no—
107#3719—42no—
108#3718—42no—
109#3209—91noSylow
110C22×C3×Q8—31no—
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×Dic6C2×D311yescharacteristic
115C2×C3×Q16—32no—
116C3×C4⋊Q8—31no—
117C3×C4⋊Q8—31no—
118C3×#125—61no—
119C3×C22⋊Q8—21no—
120C3×C22⋊Q8—31no—
121C3×C22⋊Q8—61no—
122C3×C22⋊Q8C2×D311yescharacteristic
123C3×C22⋊Q8C2×D311yescharacteristic
124C3×C4×Q8—31no—
125C3×C4×Q8—31no—
126C3×C4×Q8—61no—
127C3×#117—61no—
128C2×C3×C42—31no—
129Q8×Dic3C2×D311yescharacteristic
130#944—32no—
131#944—32no—
132#944—61no—
133#944—61no—
134#944C2×D311yescharacteristic
135C2×#216—32no—
136C2×#216—32no—
137C2×#216—32no—
138C2×#216—32no—
139C2×#216—32no—
140C2×#216—62no—
141C2×#216C2×D312yes—
142C2×C4⋊Dic3—61no—
143C2×C4⋊Dic3—61no—
144#924C2×D311yescharacteristic
145C2×Dic3⋊C4—61no—
146C2×Dic3⋊C4—61no—
147C2×C4×Dic3C2×D311yescharacteristic
148C2×Dic12—32no—
149#889—21no—
150#888C2×D311yescharacteristic
151#887—21no—
152#887C2×D311yescharacteristic
153#878—21no—
154#877—21no—
155#869—32no—
156#869—32no—
157#869—61no—
158#869—61no—
159C3×#103—32no—
160C3×C22⋊C8—31no—
161#835—32no—
162#830—31no—
163#830—31no—
164#830—61no—
165#830C2×D311yescharacteristic
166#816—32no—
167Dic3⋊C8—32no—
168C8×Dic3—32no—
169#810—32no—
170#810—32no—
171#810—32no—
172#810—32no—
173#810—62no—
174#810C2×D312yes—
175C4⋊(C3⋊C8)—32no—
176C4×C3⋊C8—32no—
177C23×C32C2×D411yescharacteristic
178C32×Q8—22no—
179C2×C32×C4—22no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—42no—
186#634—22no—
187#634—22no—
188#634—42no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
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—
203C3×Dic6—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—31no—
207C2×C4⋊Q8—91no—
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—32no—
219C2×C3×Q8—31no—
220C2×C3×Q8—61no—
221C2×C3×Q8—61no—
222C2×C3×Q8—122no—
223C2×C3×Q8C22×D311yescharacteristic
224C2×C3×Q8C22×D311yescharacteristic
225C22×C3×C4—21no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—61no—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×Dic3—21no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—121no—
235C22×Dic3#6711yescharacteristic
236C22×Dic3#6711yescharacteristic
237C2×Dic6—21no—
238C2×Dic6—21no—
239C2×Dic6—32no—
240C2×Dic6—32no—
241C2×Dic6—42no—
242C2×Dic6—62no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—121no—
246C2×Dic6—122no—
247C2×Dic6—122no—
248C2×Dic6—124no—
249C2×Dic6C22×D312yes—
250C2×Dic6C22×D311yescharacteristic
251C3×Q16—122no—
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—41no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C22×D311yescharacteristic
266C3×C22⋊C4—21no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—41no—
269C3×C22⋊C4—61no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—61no—
275C3×C42—61no—
276#217—21no—
277#216—42no—
278#216—122no—
279#216—122no—
280#216—122no—
281#216—122no—
282#216—122no—
283#216—124no—
284C4⋊Dic3—21no—
285C4⋊Dic3—62no—
286C4⋊Dic3—62no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295Dic3⋊C4—62no—
296Dic3⋊C4—62no—
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299C4×Dic3—21no—
300C4×Dic3—21no—
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—41no—
316C32×C4—41no—
317C32×C4H(5,𝔽2)12yes—
318C3⋊Dic3—42no—
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×Q8—91no—
328C2×Q16—32no—
329C2×Q16—92no—
330C2×Q16—92no—
331C2×Q16—92no—
332C4⋊Q8—31no—
333C4⋊Q8—31no—
334C4⋊Q8—92no—
335C4⋊Q8—92no—
336C4⋊Q8—181no—
337C4⋊Q8—181no—
338#125—61no—
339C22⋊Q8—31no—
340C22⋊Q8—61no—
341C22⋊Q8D3211yescharacteristic
342C4×Q8—31no—
343C4×Q8—31no—
344C4×Q8—61no—
345#117—61no—
346C2×C4⋊C4—181no—
347C2×C4⋊C4—181no—
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—22no—
361C3×Q8—22no—
362C3×Q8—42no—
363C3×Q8—62no—
364C3×Q8—62no—
365C3×Q8—62no—
366C3×Q8—122no—
367C3×Q8—122no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—34no—
377C2×C3×C4—31no—
378C2×C3×C4—31no—
379C2×C3×C4—31no—
380C2×C3×C4—31no—
381C2×C3×C4—42no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—122no—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—42no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—122no—
403C2×Dic3—124no—
404C2×Dic3#21614yescomplemented
405C2×Dic3C2×#6711yescharacteristic
406C2×Dic3C2×#6711yescharacteristic
407C2×Dic3C2×#6711yescharacteristic
408C2×Dic3C2×#6711yescharacteristic
409Dic6—22no—
410Dic6—22no—
411Dic6—22no—
412Dic6—42no—
413Dic6—42no—
414Dic6—64no—
415Dic6—62no—
416Dic6—62no—
417Dic6—62no—
418Dic6—62no—
419Dic6—122no—
420Dic6—122no—
421Dic6—122no—
422Dic6—124no—
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—32no—
433C2×Q8—31no—
434C2×Q8—61no—
435C2×Q8—61no—
436C2×Q8—92no—
437C2×Q8—122no—
438C2×Q8—181no—
439C2×Q8—362no—
440C2×Q8C2×D3211yescharacteristic
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—61no—
444C22×C4—181no—
445C22×C4C2×D3211yescharacteristic
446Q16—122no—
447Q16—362no—
448Q16—362no—
449Q16—362no—
450C2×C8—32no—
451C2×C8—92no—
452C4⋊C4—21no—
453C4⋊C4—31no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C4⋊C4—182no—
463C4⋊C4—182no—
464C4⋊C4C2×D3211yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—61no—
467C42—31no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—61no—
472C42—61no—
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—41no—
493C3×C4—41no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—61no—
497C3×C4—81no—
498C3×C4—81no—
499C3×C4—121no—
500C3×C4—122no—
501C3×C4—121no—
502C3×C4#100412yes—
503C3×C4#100912yes—
504Dic3—21no—
505Dic3—41no—
506Dic3—41no—
507Dic3—42no—
508Dic3—124no—
509Dic3—122no—
510Dic3—122no—
511Dic3C2×#21612yes—
512Dic3C2×#21612yes—
513Dic3#95112yes—
514C32#320911yescharacteristic, complemented, Sylow
515C23D3×#6711yescharacteristic
516Q8—22no—
517Q8—62no—
518Q8—62no—
519Q8—62no—
520Q8—122no—
521Q8—122no—
522Q8—182no—
523Q8—182no—
524Q8—362no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—31no—
529C2×C4—31no—
530C2×C4—31no—
531C2×C4—34no—
532C2×C4—31no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—62no—
537C2×C4—122no—
538C2×C4—182no—
539C2×C4—362no—
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×C3C22×#21611yescharacteristic
554C2×C3C2×#95111yescharacteristic
555C2×C3#583011yescharacteristic
556C22—21no—
557C22—21no—
558C22D3×#21612yes—
559C22C2×D3×#6711yescharacteristic
560C4—21no—
561C4—32no—
562C4—32no—
563C4—32no—
564C4—41no—
565C4—41no—
566C4—61no—
567C4—121no—
568C4—122no—
569C4—121no—
570C4—362no—
571C4#6431412yes—
572C3—21no—
573C3#8017811yescharacteristic, complemented
574C3#8337011yescharacteristic, complemented
575C2—22no—
576C2#1059523811yescharacteristic
577C2C2×D3×#21611yescharacteristic
578C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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. #10591625C2semidirect
10. #10590561C2semidirect
11. #10590560C2semidirect
194. C2×C3×Dic3Q16semidirect
404. C2×Dic3#216semidirect
514. C32#3209semidirect
573. C3#80178semidirect
574. C3#83370semidirect

Maximal subgroups

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

subgroupindex
C3×#56222
C2×#638662
#105927492
C3×#50502
#105916262
#105916252
#105911902
#105911852
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