Finite Group Databasebeta

← #11805919

Subgroups — #11805919

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4#10591359C211yesmaximal, characteristic
5#10591274C211yesmaximal, characteristic
6#10591274C211yesmaximal, characteristic
7#10591273C212yesmaximal
8#10591271C212yesmaximal
9#10591243C212yesmaximal
10#10591230C211yesmaximal, characteristic
11#10591197C212yesmaximal
12#74158—31nomaximal
13#73642—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C4×#634C418yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×#3724C2212yes—
28C2×#3724C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×Dic6—31no—
39C2×C4×Dic6—31no—
40C2×C4×Dic6—61no—
41C3×#382—31no—
42C3×C4×C4⋊C4—31no—
43#4977—31no—
44#4977—31no—
45#4975—31no—
46#4975—31no—
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4—31no—
49Dic3×C4⋊C4—31no—
50Dic3×C4⋊C4—31no—
51#4936D311yescharacteristic
52C4×C4⋊Dic3D311yescharacteristic
53#4933—32no—
54C4×Dic3⋊C4—32no—
55#4654—32no—
56#4653—32no—
57#4652—32no—
58#4649—32no—
59#4646—32no—
60#4646—32no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×#634—22no—
69C2×#634—22no—
70C2×#634C2×C414yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C32×C42C2×C414yes—
76C4⋊(C3⋊Dic3)C2×C414yes—
77#3750C2×C414yes—
78#3750C2×C414yes—
79C4×C3⋊Dic3C2×C414yes—
80C4×C3⋊Dic3C2×C414yes—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3Q814yescomplemented
85C3×C4×Dic3—42no—
86#3724—24no—
87#3724—42no—
88Dic32—24no—
89Dic32—42no—
90#2355—91noSylow
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C42—21no—
99C2×C3×C42—32no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—31no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—61no—
118C2×Dic3⋊C4—61no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—61no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3C2×D312yes—
130C4×Dic6—38no—
131C4×Dic6—38no—
132C4×Dic6—68no—
133C3×#95—32no—
134C3×#95—32no—
135C3×#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D312yes—
146C3⋊#95C2×D312yes—
147C23×C32C2411yescharacteristic
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C2×Q812yes—
156C2×C32×C4#4112yes—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C22×C412yes—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3⋊Dic3C22×C412yes—
167C2×C3⋊Dic3#4112yes—
168C2×C3⋊Dic3#4112yes—
169#634—28no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×Q814yes—
182C2×C4×Q8—91no—
183#391—92no—
184#387—92no—
185#387—92no—
186#384—91no—
187#382—31no—
188#382—91no—
189C4×C4⋊C4—31no—
190C4×C4⋊C4—92no—
191C4×C4⋊C4—91no—
192C4×C4⋊C4—91no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C2×Dic6—34no—
223C2×Dic6—34no—
224C2×Dic6—64no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—64no—
230C2×Dic6—64no—
231C3×C4⋊C4—34no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C42—24no—
236C3×C42—122no—
237C3×C42C4×D314yes—
238C3×C42C4×D314yes—
239C4⋊Dic3—22no—
240C4⋊Dic3—22no—
241C4⋊Dic3—22no—
242C4⋊Dic3—34no—
243C4⋊Dic3—34no—
244C4⋊Dic3—64no—
245C4⋊Dic3Dic614yescomplemented
246Dic3⋊C4—34no—
247Dic3⋊C4—34no—
248Dic3⋊C4—34no—
249Dic3⋊C4—34no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—122no—
255Dic3⋊C4—122no—
256C4×Dic3—34no—
257C4×Dic3—34no—
258C4×Dic3—34no—
259C4×Dic3—34no—
260C4×Dic3—42no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C4×Dic3—122no—
266C4×Dic3—122no—
267C22×C32C23×C411yescharacteristic
268C22×C32C22×Q811yescharacteristic
269C22×C32C2×#4111yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32H(5,𝔽2)11yescharacteristic
273C22×C322−1+411yescharacteristic
274C32×C4—22no—
275C32×C4—22no—
276C32×C4C4×Q814yes—
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C3⋊Dic3—22no—
280C3⋊Dic3#11714yes—
281C3×Dic3—24no—
282C3×Dic3—42no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C22×Q8—91no—
286C4×Q8—98no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—91no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C42—32no—
297C2×C42—91no—
298C2×C42—91no—
299C2×C42—92no—
300C2×C42—92no—
301C2×C42D3211yescharacteristic
302#95—32no—
303#95—32no—
304#95—32no—
305#95—92no—
306#95—92no—
307#95—92no—
308#95—92no—
309C23×C3—21no—
310C23×C3C23×D311yescharacteristic
311C23×C3C23×D311yescharacteristic
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—34no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4C2×Dic612yes—
342C2×C3×C4C2×C4×D312yes—
343C2×C3×C4C2×C4×D312yes—
344C2×C3×C4C2×C4×D312yes—
345C2×C3×C4C2×C4×D312yes—
346C2×C3×C4C2×C4×D312yes—
347C2×C3×C4C2×C4×D312yes—
348C2×C3×C4#23512yes—
349C2×C3×C4#23712yes—
350C2×C3×C4D3×Q812yes—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—121no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3C2×Dic614yes—
399Dic6—68no—
400Dic6—68no—
401Dic6—616no—
402C2×C32C2×#11711yescharacteristic
403C2×C32C2×C4×Q811yescharacteristic
404C2×C32#52011yescharacteristic
405C2×C32#55411yescharacteristic
406C2×C32#55611yescharacteristic
407C2×C32#55711yescharacteristic
408C2×C32#55911yescharacteristic
409C2×Q8—94no—
410C2×Q8—182no—
411C2×Q8—182no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4C2×D3211yescharacteristic
421C22×C4C2×D3211yescharacteristic
422C22×C4C2×D3211yescharacteristic
423C4⋊C4—34no—
424C4⋊C4—62no—
425C4⋊C4—62no—
426C4⋊C4—62no—
427C4⋊C4—94no—
428C4⋊C4—94no—
429C4⋊C4—94no—
430C4⋊C4—184no—
431C4⋊C4—362no—
432C42—94no—
433C42—94no—
434C42—122no—
435C42—184no—
436C42—362no—
437C42#62414yes—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3C22×Dic611yescharacteristic
446C22×C3C22×C4×D311yescharacteristic
447C22×C3C22×C4×D311yescharacteristic
448C22×C3C2×#23511yescharacteristic
449C22×C3C2×#23711yescharacteristic
450C22×C3#100411yescharacteristic
451C22×C3C2×D3×Q811yescharacteristic
452C22×C3#100711yescharacteristic
453C22×C3D3×#4111yescharacteristic
454C22×C3D3×#4111yescharacteristic
455C22×C3D3×#4111yescharacteristic
456C22×C3D3×#4111yescharacteristic
457C22×C3#100911yescharacteristic
458C22×C3#101011yescharacteristic
459C3×C4—24no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—24no—
465C3×C4—42no—
466C3×C4—64no—
467C3×C4—122no—
468C3×C4—122no—
469C3×C4—122no—
470C3×C4C4×Dic614yes—
471C3×C4#88714yes—
472Dic3—24no—
473Dic3—34no—
474Dic3—34no—
475Dic3—42no—
476Dic3—42no—
477Dic3—42no—
478Dic3—64no—
479Dic3—64no—
480Dic3—62no—
481Dic3—62no—
482Dic3—62no—
483Dic3—62no—
484Dic3—62no—
485Dic3—62no—
486Dic3—122no—
487Dic3—122no—
488C32#235511yescharacteristic, complemented, Sylow
489C23C22×D3211yescharacteristic
490Q8—188no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—34no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—92no—
508C2×C4—92no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—92no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4D3×Dic612yes—
520C2×C4#379512yes—
521C2×C4C2×#62412yes—
522C2×C4C2×#62412yes—
523C2×C4C2×#62412yes—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3C2×C4×Dic611yescharacteristic
532C2×C3C2×#88711yescharacteristic
533C2×C3#550411yescharacteristic
534C2×C3D3×#11711yescharacteristic
535C2×C3D3×#11711yescharacteristic
536C2×C3#552311yescharacteristic
537C2×C3#553911yescharacteristic
538C2×C3#555911yescharacteristic
539C2×C3#556811yescharacteristic
540C2×C3#556911yescharacteristic
541C2×C3#567111yescharacteristic
542C2×C3#568111yescharacteristic
543C2×C3#568511yescharacteristic
544C2×C3#569011yescharacteristic
545C22C2×D3×Dic611yescharacteristic
546C22C2×#379511yescharacteristic
547C22#6429711yescharacteristic
548C22#6430611yescharacteristic
549C22#6430611yescharacteristic
550C22#6430711yescharacteristic
551C22C22×#62411yescharacteristic
552C4—22no—
553C4—22no—
554C4—64no—
555C4—94no—
556C4—122no—
557C4—122no—
558C4—122no—
559C4—182no—
560C4—182no—
561C4—182no—
562C4#6384414yes—
563C3—21no—
564C3#7364211yescharacteristic, complemented
565C3#7415811yescharacteristic, complemented
566C2#1059385311yescharacteristic
567C2#1059394111yescharacteristic
568C2#1059394211yescharacteristic
569C2#1059398111yescharacteristic
570C2C2×#6384411yescharacteristic
571C2#1059496911yescharacteristic
572C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
21. C4×#634C4semidirect
84. C3×C4⋊Dic3Q8semidirect
245. C4⋊Dic3Dic6semidirect
488. C32#2355semidirect
564. C3#73642semidirect
565. C3#74158semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×#49362
C3×C4×C4⋊Dic32
#105913592
#105912742
#105912732
#105912712
#105912432
#105912302
#105911972
#741583
#736423