Finite Group Databasebeta

← #11812958

Subgroups — #11812958

Order 1152.

1830 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64148C211yesmaximal, characteristic
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×#386C211yesmaximal, characteristic, complemented
4#10592912C211yesmaximal, characteristic, complemented
5C2×#63658C211yesmaximal, characteristic, complemented
6#10592660C211yesmaximal, characteristic, complemented
7#10592657C211yesmaximal, characteristic, complemented
8#10592657C211yesmaximal, characteristic, complemented
9#10592652C211yesmaximal, characteristic, complemented
10#10592649C211yesmaximal, characteristic, complemented
11#10592642C211yesmaximal, characteristic, complemented
12#10592373C211yesmaximal, characteristic, complemented
13#10592369C211yesmaximal, characteristic, complemented
14#10592358C211yesmaximal, characteristic, complemented
15#10592352C211yesmaximal, characteristic, complemented
16#74706—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C23×C3⋊Dic3C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30#64148—24no—
31D4×C3⋊Dic3—24no—
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
38C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
39C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
40C2×#3750C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42C32×#95C2211yescharacteristic
43C32×#95C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C2×#939—34no—
55C2×D4×Dic3—34no—
56C3×#386D314yescomplemented
57#5213—34no—
58C2×C3⋊#95—34no—
59#4961—34no—
60#4958—34no—
61#4958—34no—
62#4953—34no—
63#4950—34no—
64#4943—34no—
65#4674—34no—
66#4670—34no—
67#4659—34no—
68#4653—34no—
69C24×C32C2311yescharacteristic
70C24×C32C2311yescharacteristic
71C23×C3⋊D3C2311yescharacteristic
72C2×C32×D4—22no—
73C2×C32×D4—22no—
74C2×C32×D4D414yes—
75C22×C32×C4—22no—
76C22×C32×C4—41no—
77C22×C32×C4—41no—
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C2×#638—22no—
84C2×#638—22no—
85C2×#638—22no—
86C2×#638—22no—
87C2×#638—22no—
88C2×#638—41no—
89C22×C3⋊Dic3—22no—
90C22×C3⋊Dic3—22no—
91C22×C3⋊Dic3—22no—
92C22×C3⋊Dic3—22no—
93C22×C3⋊Dic3—22no—
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—41no—
96C22×C3⋊Dic3—41no—
97C22×C3⋊Dic3—41no—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C32×C22⋊C4—22no—
106C32×C22⋊C4—41no—
107C32×C22⋊C4—41no—
108#3757—22no—
109#3757—22no—
110#3757—22no—
111#3752—22no—
112#3752—22no—
113#3752—41no—
114#3752—41no—
115#3752—41no—
116C4⋊(C3⋊Dic3)—22no—
117C4⋊(C3⋊Dic3)—22no—
118C4⋊(C3⋊Dic3)—41no—
119#3750—22no—
120C4×C3⋊Dic3—22no—
121#2444—91noSylow
122C22×C3×D4C2×D314yes—
123C23×C3×C4C2×D314yes—
124C22×#67—34no—
125C22×#67—34no—
126C23×Dic3—34no—
127C23×Dic3—34no—
128C23×Dic3—34no—
129C2×C3×C22⋊C4C2×D314yes—
130C2×C3×C22⋊C4C2×D314yes—
131C2×C3×C22⋊C4C2×D314yes—
132C2×#217—34no—
133C2×#217—34no—
134C2×#217—34no—
135#939—616no—
136D4×Dic3—616no—
137C2×(C2×D3)⋊C4—34no—
138C2×(C2×D3)⋊C4—34no—
139C2×(C2×D3)⋊C4—34no—
140C2×(C2×D3)⋊C4—34no—
141C2×(C2×D3)⋊C4—34no—
142C2×C4⋊Dic3—34no—
143C2×C4⋊Dic3—34no—
144C2×C4⋊Dic3—34no—
145C2×Dic3⋊C4—34no—
146C2×C4×Dic3—34no—
147C3×#95C2×D314yes—
148C3×#95C2×D314yes—
149C3⋊#95—34no—
150C3⋊#95—34no—
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×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32C2×D412yes—
170C23×C32C2×D412yes—
171C23×C32#4112yes—
172C23×C32#4112yes—
173C23×C32C2411yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—21no—
179C22×C3⋊D3—21no—
180C22×C3⋊D3—21no—
181C32×D4—28no—
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×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—44no—
197C2×C32×C4C2×D412yes—
198#638—44no—
199#638—44no—
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—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—44no—
220C2×C3⋊Dic3—44no—
221C2×C3⋊Dic3—44no—
222C2×C3⋊Dic3#4112yes—
223C2×C3⋊Dic3#4112yes—
224C2×#121—91no—
225C2×C4×D4—91no—
226#400—91no—
227#397—91no—
228#397—91no—
229#394—91no—
230#388—91no—
231#387—91no—
232#386—91no—
233#386—91no—
234#386—91no—
235#386C3⋊D311yescharacteristic, complemented
236#385—91no—
237#381—91no—
238C2×#95—91no—
239C24×C3C22×D314yes—
240C24×C3C22×D314yes—
241C23×D3—34no—
242C2×C3×D4—28no—
243C2×C3×D4—28no—
244C2×C3×D4D12116yes—
245C22×C3×C4—28no—
246C22×C3×C4—44no—
247C22×C3×C4—44no—
248C22×C3×C4C22×D314yes—
249C22×C3×C4C22×D314yes—
250C22×C3×C4C22×D314yes—
251C22×C3×C4C22×D314yes—
252C22×C3×C4C22×D314yes—
253C2×#67—68no—
254C2×#67—68no—
255C2×#67—68no—
256C2×#67—68no—
257C2×#67—68no—
258C2×#67—124no—
259C22×Dic3—34no—
260C22×Dic3—34no—
261C22×Dic3—34no—
262C22×Dic3—34no—
263C22×Dic3—34no—
264C22×Dic3—34no—
265C22×Dic3—34no—
266C22×Dic3—68no—
267C22×Dic3—68no—
268C22×Dic3—68no—
269C22×Dic3—68no—
270C22×Dic3—68no—
271C22×Dic3—68no—
272C22×Dic3—124no—
273C22×Dic3—124no—
274C22×Dic3—124no—
275C3×C22⋊C4—28no—
276C3×C22⋊C4—44no—
277C3×C22⋊C4—44no—
278#217—68no—
279#217—68no—
280#217—68no—
281(C2×D3)⋊C4—68no—
282(C2×D3)⋊C4—68no—
283(C2×D3)⋊C4—124no—
284(C2×D3)⋊C4—124no—
285(C2×D3)⋊C4—124no—
286C4⋊Dic3—68no—
287C4⋊Dic3—68no—
288C4⋊Dic3—124no—
289Dic3⋊C4—68no—
290C4×Dic3—68no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32#12314yes—
305C22×C32C22×D411yescharacteristic
306C22×C32C2×#4111yescharacteristic
307C22×C32C2×#4111yescharacteristic
308C22×C32C2×#4111yescharacteristic
309C22×C32C2×#4111yescharacteristic
310C22×C32H(5,𝔽2)11yescharacteristic
311C22×C32H(5,𝔽2)11yescharacteristic
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C32×C4—22no—
320C32×C4—41no—
321C32×C4—41no—
322C32×C4—41no—
323C32×C4—41no—
324C3⋊Dic3—22no—
325C3⋊Dic3—22no—
326C3⋊Dic3—41no—
327C3⋊Dic3—41no—
328C3⋊Dic3—41no—
329C3⋊Dic3—41no—
330C3⋊Dic3—41no—
331C22×D4—91no—
332C22×D4—91no—
333C22×D4C2×C3⋊D311yescharacteristic
334C23×C4—91no—
335C23×C4—91no—
336C23×C4—91no—
337C23×C4C2×C3⋊D311yescharacteristic
338#121—184no—
339C4×D4—184no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—91no—
344C2×C22⋊C4—91no—
345C2×C22⋊C4—91no—
346C2×C22⋊C4—91no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—91no—
351C2×C22⋊C4—91no—
352C2×C22⋊C4C2×C3⋊D311yescharacteristic
353C2×C22⋊C4C2×C3⋊D311yescharacteristic
354C2×C22⋊C4C2×C3⋊D311yescharacteristic
355C2×C42—91no—
356#95—91no—
357#95—91no—
358#95—91no—
359#95—91no—
360#95—91no—
361#95—91no—
362#95—91no—
363#95—91no—
364#95—91no—
365#95—91no—
366#95C2×C3⋊D311yescharacteristic
367#95C2×C3⋊D311yescharacteristic
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3C2×D1218yes—
379C23×C3C2×D1218yes—
380C23×C3#23718yes—
381C23×C3#23718yes—
382C23×C3C23×D314yes—
383C22×D3—64no—
384C22×D3—64no—
385C22×D3—64no—
386C22×D3—64no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—64no—
390C3×D4—232no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—416no—
406C2×C3×C4C2×D1218yes—
407#67—1216no—
408#67—1216no—
409C2×Dic3—38no—
410C2×Dic3—38no—
411C2×Dic3—64no—
412C2×Dic3—64no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—1216no—
431C2×Dic3—1216no—
432C2×Dic3—1216no—
433C2×C32—24no—
434C2×C32—42no—
435C2×C32C2×#12311yescharacteristic
436C2×C32#52911yescharacteristic
437C2×C32#53811yescharacteristic
438C2×C32#54611yescharacteristic
439C2×C32#54611yescharacteristic
440C2×C32#55311yescharacteristic
441C2×C32#55311yescharacteristic
442C3⋊D3—81no—
443C24—91no—
444C24C22×C3⋊D311yescharacteristic
445C24C22×C3⋊D311yescharacteristic
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—182no—
449C2×D4—182no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4—182no—
453C2×D4—361no—
454C2×D4C4⋊(C3⋊D3)14yes—
455C22×C4—22no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—182no—
466C22×C4—182no—
467C22×C4—182no—
468C22×C4—182no—
469C22×C4—182no—
470C22×C4—182no—
471C22×C4—361no—
472C22×C4—361no—
473C22×C4—361no—
474C22×C4C22×C3⋊D311yescharacteristic
475C22×C4C22×C3⋊D311yescharacteristic
476C22×C4C22×C3⋊D311yescharacteristic
477C22×C4C22×C3⋊D311yescharacteristic
478C22×C4C22×C3⋊D311yescharacteristic
479C4⋊C4—182no—
480C4⋊C4—182no—
481C4⋊C4—182no—
482C4⋊C4—361no—
483C22⋊C4—22no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—182no—
487C22⋊C4—182no—
488C22⋊C4—182no—
489C22⋊C4—182no—
490C22⋊C4—182no—
491C22⋊C4—361no—
492C22⋊C4—361no—
493C22⋊C4—361no—
494C42—182no—
495C22×C3—28no—
496C22×C3—28no—
497C22×C3—28no—
498C22×C3—28no—
499C22×C3—28no—
500C22×C3—28no—
501C22×C3—28no—
502C22×C3—28no—
503C22×C3—28no—
504C22×C3—44no—
505C22×C3—44no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3#886116yes—
509C22×C3C22×D1214yes—
510C22×C3C2×#23714yes—
511C22×C3C2×#23714yes—
512C22×C3#100414yes—
513C22×C3#100414yes—
514C22×C3D3×#4114yes—
515C22×C3D3×#4114yes—
516C2×D3—124no—
517C2×D3—124no—
518C2×D3—124no—
519C2×D3—124no—
520C2×D3—124no—
521C2×D3—124no—
522C2×D3—124no—
523C3×C4—28no—
524C3×C4—44no—
525C3×C4—44no—
526C3×C4—44no—
527C3×C4—44no—
528Dic3—68no—
529Dic3—68no—
530Dic3—124no—
531Dic3—124no—
532Dic3—124no—
533Dic3—124no—
534Dic3—124no—
535C32#244411yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—181no—
547C23—181no—
548C23—181no—
549C23—181no—
550C23—181no—
551C23—181no—
552C23—181no—
553C23C2×C4⋊(C3⋊D3)12yes—
554C23C2×C4⋊(C3⋊D3)12yes—
555C23#383012yes—
556C23#383012yes—
557C23C23×C3⋊D311yescharacteristic
558D4—28no—
559D4—364no—
560D4—364no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—44no—
576C2×C4—92no—
577C2×C4—92no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—181no—
596C2×C4—181no—
597C2×C4—364no—
598C2×C4—364no—
599C2×C4—364no—
600C2×C4C2×C4⋊(C3⋊D3)12yes—
601C2×C3—216no—
602C2×C3—48no—
603C2×C3C2×#88614yes—
604C2×C3#555414yes—
605C2×C3#555414yes—
606C2×C3#559314yes—
607C2×C3#560114yes—
608C2×C3#560114yes—
609C2×C3#564914yes—
610D3—244no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—361no—
625C22—361no—
626C22—361no—
627C22—361no—
628C22—361no—
629C22—361no—
630C22—361no—
631C22#6409514yes—
632C22C22×C4⋊(C3⋊D3)11yescharacteristic
633C22C2×#383011yescharacteristic
634C22C2×#383011yescharacteristic
635C22#6436111yescharacteristic
636C22#6436111yescharacteristic
637C22#41×C3⋊D311yescharacteristic
638C22#41×C3⋊D311yescharacteristic
639C4—22no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—182no—
645C4—182no—
646C4—361no—
647C4—361no—
648C4—361no—
649C4—361no—
650C4—361no—
651C3#7470614yescomplemented
652C2—24no—
653C2—42no—
654C2—721no—
655C2C2×#6409511yescharacteristic
656C2#1059602511yescharacteristic
657C2#1059602511yescharacteristic
658C2#1059606411yescharacteristic
659C2#1059607211yescharacteristic
660C2#1059607211yescharacteristic
661C2#1059612011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#386C2
prime radicalC2×#64148C2
hypercenter#386C3⋊D3
hypocenterC32#2444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×C3⋊Dic3C2semidirect
3. C32×#386C2semidirect
4. #10592912C2semidirect
5. C2×#63658C2semidirect
6. #10592660C2semidirect
7. #10592657C2semidirect
8. #10592657C2semidirect
9. #10592652C2semidirect
10. #10592649C2semidirect
11. #10592642C2semidirect
12. #10592373C2semidirect
13. #10592369C2semidirect
14. #10592358C2semidirect
15. #10592352C2semidirect
56. C3×#386D3semidirect
235. #386C3⋊D3semidirect
535. C32#2444semidirect
651. C3#74706semidirect

Maximal subgroups

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

subgroupindex
C2×#641482
C2×D4×C3⋊Dic32
C32×#3862
#105929122
C2×#636582
#105926602
#105926572
#105926522
#105926492
#105926422
#105923732
#105923692
#105923582
#105923522
#747063