Finite Group Databasebeta

← #11803351

Subgroups — #11803351

Order 1152.

1896 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64092C211yesmaximal, characteristic
3C2×#64090C211yesmaximal, characteristic
4C32×#388C211yesmaximal, characteristic, complemented
5#10592675C211yesmaximal, characteristic, complemented
6#10592655C211yesmaximal, characteristic
7#10592649C211yesmaximal, characteristic, complemented
8#10592645C211yesmaximal, characteristic, complemented
9#10592644C211yesmaximal, characteristic, complemented
10C4×#3752C211yesmaximal, characteristic, complemented
11#10592627C211yesmaximal, characteristic, complemented
12#10592367C211yesmaximal, characteristic, complemented
13#10592363C211yesmaximal, characteristic, complemented
14#10592354C211yesmaximal, characteristic, complemented
15#10592353C211yesmaximal, characteristic, complemented
16#75828—34nomaximal
17C22×#638C2211yescharacteristic
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×#3750C2211yescharacteristic
38C2×#3750C2211yescharacteristic
39C2×#3750C2211yescharacteristic
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42C4⋊C4×C3⋊D3—24no—
43#64092C418yescomplemented
44#64090—24no—
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55C2×D3×C4⋊C4—34no—
56C2×#883—34no—
57C2×#67⋊C4—34no—
58C3×#388D314yescomplemented
59#4976—34no—
60#4956—34no—
61#4950—34no—
62#4946—34no—
63#4945—34no—
64C4×(C2×D3)⋊C4—34no—
65#4928—34no—
66#4668—34no—
67#4664—34no—
68#4655—34no—
69#4654—34no—
70C24×C32C2311yescharacteristic
71C23×C3⋊D3C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—22no—
79C2×#638—22no—
80C2×#638C2×C414yes—
81C22×C3⋊Dic3—22no—
82C22×C3⋊Dic3—41no—
83C22×C3⋊Dic3—41no—
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3—22no—
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—41no—
95C2×C4×C3⋊D3—41no—
96C2×C4×C3⋊D3—41no—
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3C2×C414yescomplemented
99C2×C4×C3⋊D3D414yes—
100C32×C4⋊C4—22no—
101C32×C22⋊C4—22no—
102C32×C22⋊C4—41no—
103C32×C22⋊C4C2×C414yescomplemented
104C32×C42—41no—
105#3757—41no—
106#3757C2×C414yescomplemented
107#3752—22no—
108#3752—22no—
109#3752C2×C414yescomplemented
110C4⋊(C3⋊Dic3)—22no—
111C4⋊(C3⋊Dic3)—41no—
112C4⋊(C3⋊Dic3)C2×C414yescomplemented
113#3750—22no—
114#3750—22no—
115#3750—22no—
116#3750—41no—
117#3750C2×C414yescomplemented
118C4×C3⋊Dic3—22no—
119C4×C3⋊Dic3—41no—
120#2322—91noSylow
121C22×#67—34no—
122C23×Dic3—34no—
123C22×C4×D3—34no—
124C22×C4×D3—34no—
125C22×C4×D3—34no—
126C2×C3×C4⋊C4C2×D314yes—
127C2×C3×C22⋊C4C2×D314yes—
128C2×C3×C22⋊C4C2×D314yes—
129C2×C3×C22⋊C4C2×D314yes—
130C2×C3×C42C2×D314yes—
131C2×#217—34no—
132C2×#217—34no—
133C2×(C2×D3)⋊C4—34no—
134C2×(C2×D3)⋊C4—34no—
135C2×(C2×D3)⋊C4—34no—
136C2×C4⋊Dic3—34no—
137C2×C4⋊Dic3—34no—
138C2×C4⋊Dic3—34no—
139C2×Dic3⋊C4—34no—
140C2×Dic3⋊C4—34no—
141C2×Dic3⋊C4—34no—
142C2×Dic3⋊C4—34no—
143C2×Dic3⋊C4—34no—
144C2×C4×Dic3—34no—
145C2×C4×Dic3—34no—
146D3×C4⋊C4—616no—
147#883—332no—
148#67⋊C4—616no—
149C3×#95C2×D314yes—
150C3×#95C2×D314yes—
151C3⋊#95—34no—
152C3⋊#95—34no—
153C3⋊#95—34no—
154C3⋊#95—34no—
155C3⋊#95—34no—
156C3⋊#95—34no—
157C3⋊#95—34no—
158C3⋊#95—34no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32C22×C412yes—
166C23×C32C2411yescharacteristic
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3C22×C412yes—
172C22×C3⋊D3C2×D412yes—
173C22×C3⋊D3#4112yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C2×D412yes—
192#638—28no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—44no—
211C2×C3⋊Dic3C22×C412yes—
212C2×C3⋊Dic3C22×C412yes—
213C2×C3⋊Dic3C22×C412yes—
214C2×C3⋊Dic3C2×D412yes—
215C4×C3⋊D3—28no—
216C4×C3⋊D3—44no—
217C4×C3⋊D3—44no—
218C2×#123—91no—
219C2×C4×D4—91no—
220C22×C4⋊C4—91no—
221#389—91no—
222#389—91no—
223#388—91no—
224#388C3⋊D311yescharacteristic, complemented
225#387—91no—
226#387—91no—
227#386—91no—
228#385—91no—
229#385—91no—
230#385—91no—
231#381—91no—
232C4×C22⋊C4—91no—
233C24×C3C22×D314yes—
234C23×D3—34no—
235C22×C3×C4C22×D314yes—
236C22×C3×C4C22×D314yes—
237C22×C3×C4C22×D314yes—
238C22×C3×C4C22×D314yes—
239C22×C3×C4C22×D314yes—
240C22×C3×C4C22×D314yes—
241C2×#67—316no—
242C2×#67—68no—
243C2×#67—68no—
244C22×Dic3—34no—
245C22×Dic3—34no—
246C22×Dic3—34no—
247C22×Dic3—34no—
248C22×Dic3—34no—
249C22×Dic3—34no—
250C22×Dic3—34no—
251C22×Dic3—68no—
252C22×Dic3—124no—
253C22×Dic3—124no—
254C2×C4×D3—316no—
255C2×C4×D3—316no—
256C2×C4×D3—68no—
257C2×C4×D3—68no—
258C2×C4×D3—68no—
259C2×C4×D3—124no—
260C2×C4×D3—124no—
261C2×C4×D3—124no—
262C2×C4×D3—124no—
263C3×C4⋊C4—28no—
264C3×C22⋊C4—28no—
265C3×C22⋊C4—44no—
266C3×C22⋊C4C4×D3116yescomplemented
267C3×C42—44no—
268#217—316no—
269#217—124no—
270(C2×D3)⋊C4—316no—
271(C2×D3)⋊C4—68no—
272(C2×D3)⋊C4—68no—
273C4⋊Dic3—316no—
274C4⋊Dic3—68no—
275C4⋊Dic3—124no—
276Dic3⋊C4—316no—
277Dic3⋊C4—68no—
278Dic3⋊C4—68no—
279Dic3⋊C4—68no—
280Dic3⋊C4—124no—
281C4×Dic3—68no—
282C4×Dic3—124no—
283C22×C32—22no—
284C22×C32—22no—
285C22×C32—22no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32C23×C411yescharacteristic
291C22×C32C22×D411yescharacteristic
292C22×C32C2×#4111yescharacteristic
293C22×C32H(5,𝔽2)11yescharacteristic
294C22×C32H(5,𝔽2)11yescharacteristic
295C22×C322−1+411yescharacteristic
296C22×C322−1+411yescharacteristic
297C2×C3⋊D3—22no—
298C2×C3⋊D3—22no—
299C2×C3⋊D3—22no—
300C2×C3⋊D3—22no—
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3C4×D414yes—
304C32×C4—22no—
305C32×C4—22no—
306C32×C4—22no—
307C32×C4—41no—
308C32×C4—41no—
309C32×C4—41no—
310C3⋊Dic3—22no—
311C3⋊Dic3—22no—
312C3⋊Dic3—22no—
313C3⋊Dic3—22no—
314C3⋊Dic3—41no—
315C3⋊Dic3—41no—
316C3⋊Dic3—41no—
317C22×D4—91no—
318C23×C4—91no—
319C23×C4—91no—
320C23×C4—91no—
321C23×C4—91no—
322#123—98no—
323C4×D4—184no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4—91no—
330C2×C4⋊C4—91no—
331C2×C4⋊C4—91no—
332C2×C4⋊C4—184no—
333C2×C4⋊C4C2×C3⋊D311yescharacteristic
334C2×C22⋊C4—91no—
335C2×C22⋊C4—91no—
336C2×C22⋊C4—91no—
337C2×C22⋊C4—91no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4C2×C3⋊D311yescharacteristic
340C2×C22⋊C4C2×C3⋊D311yescharacteristic
341C2×C22⋊C4C2×C3⋊D311yescharacteristic
342C2×C42—91no—
343C2×C42—91no—
344C2×C42C2×C3⋊D311yescharacteristic
345#95—91no—
346#95—91no—
347#95—91no—
348#95—91no—
349#95—91no—
350#95—91no—
351#95—91no—
352#95—91no—
353#95C2×C3⋊D311yescharacteristic
354#95C2×C3⋊D311yescharacteristic
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3C2×C4×D318yes—
362C23×C3C23×D314yes—
363C22×D3—38no—
364C22×D3—38no—
365C22×D3—38no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—64no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4C2×C4×D318yes—
386C2×C3×C4C2×C4×D318yes—
387C2×C3×C4D3×D418yes—
388#67—632no—
389C2×Dic3—38no—
390C2×Dic3—38no—
391C2×Dic3—38no—
392C2×Dic3—38no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—64no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—64no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—1216no—
411C4×D3—632no—
412C4×D3—1216no—
413C4×D3—1216no—
414C2×C32—42no—
415C2×C32C2×C4×D411yescharacteristic
416C2×C32#52011yescharacteristic
417C2×C32#52011yescharacteristic
418C2×C32#53411yescharacteristic
419C2×C32#53611yescharacteristic
420C2×C32#53911yescharacteristic
421C2×C32#53911yescharacteristic
422C3⋊D3—24no—
423C24—91no—
424C24C22×C3⋊D311yescharacteristic
425C2×D4—94no—
426C2×D4—182no—
427C2×D4—182no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—94no—
433C22×C4—94no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—91no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4—182no—
440C22×C4—182no—
441C22×C4—361no—
442C22×C4—361no—
443C22×C4—361no—
444C22×C4—361no—
445C22×C4—361no—
446C22×C4—361no—
447C22×C4C22×C3⋊D311yescharacteristic
448C22×C4C22×C3⋊D311yescharacteristic
449C22×C4C22×C3⋊D311yescharacteristic
450C22×C4C22×C3⋊D311yescharacteristic
451C22×C4C22×C3⋊D311yescharacteristic
452C22×C4C22×C3⋊D311yescharacteristic
453C4⋊C4—22no—
454C4⋊C4—94no—
455C4⋊C4—94no—
456C4⋊C4—182no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—182no—
460C4⋊C4—361no—
461C4⋊C4—361no—
462C22⋊C4—22no—
463C22⋊C4—41no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C22⋊C4—361no—
469C22⋊C4C4×C3⋊D314yescomplemented
470C42—41no—
471C42—182no—
472C42—361no—
473C22×C3—28no—
474C22×C3—28no—
475C22×C3—28no—
476C22×C3—44no—
477C22×C3—44no—
478C22×C3—44no—
479C22×C3—44no—
480C22×C3C22×C4×D314yes—
481C22×C3C2×D3×D414yes—
482C22×C3#100414yes—
483C22×C3D3×#4114yes—
484C22×C3#100914yes—
485C22×C3#101014yes—
486C22×C3#101014yes—
487C2×D3—316no—
488C2×D3—68no—
489C2×D3—68no—
490C2×D3—68no—
491C2×D3—68no—
492C2×D3—68no—
493C2×D3—68no—
494C3×C4—28no—
495C3×C4—28no—
496C3×C4—28no—
497C3×C4—44no—
498C3×C4—44no—
499C3×C4—44no—
500Dic3—68no—
501Dic3—68no—
502Dic3—68no—
503Dic3—68no—
504Dic3—124no—
505Dic3—124no—
506Dic3—124no—
507C32#232211yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—92no—
515C23—92no—
516C23—92no—
517C23—181no—
518C23—181no—
519C23—181no—
520C23—181no—
521C23C2×C4×C3⋊D312yes—
522C23C23×C3⋊D311yescharacteristic
523D4—188no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—92no—
540C2×C4—92no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—188no—
544C2×C4—181no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—364no—
562C2×C4—364no—
563C2×C4—364no—
564C2×C4C2×C4×C3⋊D312yes—
565C2×C4C2×C4×C3⋊D312yes—
566C2×C4D4×C3⋊D312yes—
567C2×C3—48no—
568C2×C3#552314yes—
569C2×C3C4×D3×D414yes—
570C2×C3#554614yes—
571C2×C3#560514yes—
572C2×C3#566014yes—
573C2×C3#567514yes—
574C2×C3#570714yes—
575D3—616no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—94no—
584C22—182no—
585C22—182no—
586C22—182no—
587C22—182no—
588C22—182no—
589C22—182no—
590C22C22×C4×C3⋊D311yescharacteristic
591C22C2×D4×C3⋊D311yescharacteristic
592C22#6436111yescharacteristic
593C22#41×C3⋊D311yescharacteristic
594C22#6436611yescharacteristic
595C22#6436711yescharacteristic
596C22#6436711yescharacteristic
597C4—22no—
598C4—22no—
599C4—22no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—182no—
604C4—182no—
605C4—182no—
606C4—182no—
607C4—361no—
608C4—361no—
609C4—361no—
610C3#7582814yescomplemented
611C2—42no—
612C2—184no—
613C2#1059599411yescharacteristic
614C2C4×D4×C3⋊D311yescharacteristic
615C2#1059601711yescharacteristic
616C2#1059607611yescharacteristic
617C2#1059613111yescharacteristic
618C2#1059614611yescharacteristic
619C2#1059617811yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#388C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenter#388C3⋊D3
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
4. C32×#388C2semidirect
5. #10592675C2semidirect
7. #10592649C2semidirect
8. #10592645C2semidirect
9. #10592644C2semidirect
10. C4×#3752C2semidirect
11. #10592627C2semidirect
12. #10592367C2semidirect
13. #10592363C2semidirect
14. #10592354C2semidirect
15. #10592353C2semidirect
43. #64092C4semidirect
58. C3×#388D3semidirect
98. C2×C4×C3⋊D3C2×C4semidirect
103. C32×C22⋊C4C2×C4semidirect
106. #3757C2×C4semidirect
109. #3752C2×C4semidirect
112. C4⋊(C3⋊Dic3)C2×C4semidirect
117. #3750C2×C4semidirect
224. #388C3⋊D3semidirect
266. C3×C22⋊C4C4×D3semidirect
469. C22⋊C4C4×C3⋊D3semidirect
507. C32#2322semidirect
610. C3#75828semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#640922
C2×#640902
C32×#3882
#105926752
#105926552
#105926492
#105926452
#105926442
C4×#37522
#105926272
#105923672
#105923632
#105923542
#105923532
#758283