Finite Group Databasebeta

← #11810308

Subgroups — #11810308

Order 1152.

2400 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64162C211yesmaximal, characteristic
2C22×#3757C211yesmaximal, characteristic, complemented
3C2×#64092C211yesmaximal, characteristic, complemented
4C2×#64090C211yesmaximal, characteristic, complemented
5C32×#379C211yesmaximal, characteristic, complemented
6#10592660C211yesmaximal, characteristic, complemented
7#10592658C211yesmaximal, characteristic, complemented
8#10592657C211yesmaximal, characteristic, complemented
9#10592655C211yesmaximal, characteristic, complemented
10#10592651C211yesmaximal, characteristic, complemented
11#10592650C211yesmaximal, characteristic, complemented
12#10592649C211yesmaximal, characteristic, complemented
13#10592648C211yesmaximal, characteristic, complemented
14#10592644C211yesmaximal, characteristic, complemented
15#10592641C211yesmaximal, characteristic, complemented
16#73826—34nomaximal
17C25×C32C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30#64162—24no—
31C2×#3757—24no—
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37C2×#3757C2211yescharacteristic
38C2×#3757C2211yescharacteristic
39C2×#3752C2211yescharacteristic, complemented
40C2×#3752C2211yescharacteristic, complemented
41C2×#3752C2211yescharacteristic, complemented
42C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
48#64092—24no—
49#64090—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C2×#953—34no—
57C22×#217—34no—
58C2×#883—34no—
59C2×#67⋊C4—34no—
60C3×#379D314yescomplemented
61#4961—34no—
62#4959—34no—
63#4958—34no—
64#4956—34no—
65#4952—34no—
66#4951—34no—
67#4950—34no—
68#4949—34no—
69#4945—34no—
70#4942—34no—
71C24×C32—22no—
72C24×C32—22no—
73C24×C32—22no—
74C24×C32—22no—
75C24×C32—22no—
76C24×C32—41no—
77C24×C32—41no—
78C24×C32C2311yescharacteristic
79C24×C32C2311yescharacteristic
80C24×C32C2311yescharacteristic
81C23×C3⋊D3C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C2×#638—22no—
87C2×#638—22no—
88C2×#638—22no—
89C2×#638—22no—
90C2×#638—22no—
91C2×#638—22no—
92C2×#638—41no—
93C2×#638—41no—
94C2×#638D414yes—
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3—22no—
99C22×C3⋊Dic3—41no—
100C22×C3⋊Dic3—41no—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—41no—
111C32×C22⋊C4—22no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4—22no—
115C32×C22⋊C4—41no—
116C32×C22⋊C4—41no—
117#3757—22no—
118#3757—22no—
119#3757—22no—
120#3757—22no—
121#3757—22no—
122#3757—22no—
123#3757D414yescomplemented
124#3752—22no—
125#3752—22no—
126#3752—41no—
127C4⋊(C3⋊Dic3)—22no—
128C4⋊(C3⋊Dic3)—41no—
129#3750—22no—
130#3750—22no—
131#3750—41no—
132C4×C3⋊Dic3—22no—
133#2418—91noSylow
134C25×C3C2×D314yes—
135C22×#67—34no—
136C22×#67—34no—
137C22×#67—34no—
138C23×Dic3—34no—
139C23×Dic3—34no—
140C22×C4×D3—34no—
141C2×C3×C22⋊C4C2×D314yes—
142C2×C3×C22⋊C4C2×D314yes—
143C2×C3×C22⋊C4C2×D314yes—
144C2×C3×C22⋊C4C2×D314yes—
145C2×C3×C22⋊C4C2×D314yes—
146C2×C3×C22⋊C4C2×D314yes—
147#953—616no—
148C2×#217—34no—
149C2×#217—34no—
150C2×#217—34no—
151C2×#217—34no—
152C2×#217—34no—
153C2×#217—34no—
154C2×#217—34no—
155C2×#217—616no—
156C2×(C2×D3)⋊C4—34no—
157C2×(C2×D3)⋊C4—34no—
158C2×(C2×D3)⋊C4—34no—
159C2×C4⋊Dic3—34no—
160C2×C4⋊Dic3—34no—
161C2×Dic3⋊C4—34no—
162C2×Dic3⋊C4—34no—
163C2×Dic3⋊C4—34no—
164C2×C4×Dic3—34no—
165#883—616no—
166#67⋊C4—616no—
167C3⋊#95—34no—
168C3⋊#95—34no—
169C3⋊#95—34no—
170C3⋊#95—34no—
171C3⋊#95—34no—
172C3⋊#95—34no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—28no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—21no—
189C23×C32—21no—
190C23×C32—44no—
191C23×C32—44no—
192C23×C32—44no—
193C23×C32—44no—
194C23×C32—44no—
195C23×C32—44no—
196C23×C32C2×D412yes—
197C23×C32C2×D412yes—
198C23×C32#4112yes—
199C23×C32#4112yes—
200C23×C32#4112yes—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3C2×D412yes—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221#638—28no—
222#638—44no—
223#638—44no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—44no—
243C2×C3⋊Dic3—44no—
244C2×C3⋊Dic3C2×D412yes—
245C2×C3⋊Dic3C2×D412yes—
246C2×C3⋊Dic3C2×D412yes—
247C4×C3⋊D3—44no—
248C2×#123—91no—
249C2×#120—91no—
250C2×C4×D4—91no—
251C22×C22⋊C4—91no—
252#399—91no—
253#397—91no—
254#394—91no—
255#394—91no—
256#388—91no—
257#388—91no—
258#386—91no—
259#386—91no—
260#385—91no—
261#380—91no—
262#379C3⋊D311yescharacteristic, complemented
263C24×C3—28no—
264C24×C3—28no—
265C24×C3—28no—
266C24×C3—28no—
267C24×C3—28no—
268C24×C3—44no—
269C24×C3—44no—
270C24×C3C22×D314yes—
271C24×C3C22×D314yes—
272C24×C3C22×D314yes—
273C23×D3—34no—
274C22×C3×C4C22×D314yes—
275C22×C3×C4C22×D314yes—
276C22×C3×C4C22×D314yes—
277C22×C3×C4C22×D314yes—
278C2×#67—316no—
279C2×#67—68no—
280C2×#67—68no—
281C2×#67—68no—
282C2×#67—68no—
283C2×#67—68no—
284C2×#67—68no—
285C2×#67—124no—
286C2×#67—124no—
287C22×Dic3—34no—
288C22×Dic3—34no—
289C22×Dic3—34no—
290C22×Dic3—34no—
291C22×Dic3—34no—
292C22×Dic3—34no—
293C22×Dic3—34no—
294C22×Dic3—68no—
295C22×Dic3—68no—
296C22×Dic3—68no—
297C22×Dic3—68no—
298C22×Dic3—124no—
299C22×Dic3—124no—
300C2×C4×D3—68no—
301C2×C4×D3—68no—
302C2×C4×D3—124no—
303C3×C22⋊C4—28no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—28no—
306C3×C22⋊C4—28no—
307C3×C22⋊C4—44no—
308C3×C22⋊C4—44no—
309#217—316no—
310#217—68no—
311#217—68no—
312#217—68no—
313#217—68no—
314#217—68no—
315#217—68no—
316(C2×D3)⋊C4—68no—
317(C2×D3)⋊C4—68no—
318(C2×D3)⋊C4—124no—
319C4⋊Dic3—68no—
320C4⋊Dic3—124no—
321Dic3⋊C4—68no—
322Dic3⋊C4—68no—
323Dic3⋊C4—124no—
324C4×Dic3—68no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—416no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32#12314yescomplemented
347C22×C32C22×D411yescharacteristic
348C22×C32C22×D411yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32H(5,𝔽2)11yescharacteristic
353C22×C32H(5,𝔽2)11yescharacteristic
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—41no—
358C2×C3⋊D3—41no—
359C2×C3⋊D3—41no—
360C2×C3⋊D3—41no—
361C32×C4—41no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C3⋊Dic3—22no—
366C3⋊Dic3—22no—
367C3⋊Dic3—22no—
368C3⋊Dic3—41no—
369C3⋊Dic3—41no—
370C3⋊Dic3—41no—
371C3⋊Dic3—41no—
372C25C2×C3⋊D311yescharacteristic
373C22×D4—91no—
374C22×D4—91no—
375C22×D4—91no—
376C23×C4—91no—
377C23×C4—91no—
378C23×C4—91no—
379#123—184no—
380#120—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—91no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—91no—
392C2×C22⋊C4—91no—
393C2×C22⋊C4—91no—
394C2×C22⋊C4—91no—
395C2×C22⋊C4—91no—
396C2×C22⋊C4—91no—
397C2×C22⋊C4—184no—
398C2×C22⋊C4C2×C3⋊D311yescharacteristic
399C2×C22⋊C4C2×C3⋊D311yescharacteristic
400C2×C22⋊C4C2×C3⋊D311yescharacteristic
401C2×C22⋊C4C2×C3⋊D311yescharacteristic
402C2×C22⋊C4C2×C3⋊D311yescharacteristic
403C2×C22⋊C4C2×C3⋊D311yescharacteristic
404C2×C42—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—232no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—416no—
429C23×C3—416no—
430C23×C3—416no—
431C23×C3—416no—
432C23×C3—416no—
433C23×C3—416no—
434C23×C3#23518yes—
435C23×C3D3×D418yes—
436C23×C3D3×D418yes—
437C23×C3#23718yes—
438C23×C3#23718yes—
439C23×C3C23×D314yes—
440C22×D3—38no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—64no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459#67—632no—
460#67—1216no—
461#67—1216no—
462C2×Dic3—38no—
463C2×Dic3—38no—
464C2×Dic3—38no—
465C2×Dic3—64no—
466C2×Dic3—64no—
467C2×Dic3—64no—
468C2×Dic3—64no—
469C2×Dic3—64no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—64no—
473C2×Dic3—64no—
474C2×Dic3—64no—
475C2×Dic3—64no—
476C2×Dic3—64no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—64no—
481C2×Dic3—64no—
482C2×Dic3—64no—
483C2×Dic3—1216no—
484C2×Dic3—1216no—
485C4×D3—1216no—
486C2×C32—24no—
487C2×C32—42no—
488C2×C32—42no—
489C2×C32C2×#12311yescharacteristic
490C2×C32#52511yescharacteristic
491C2×C32#53811yescharacteristic
492C2×C32D4211yescharacteristic
493C2×C32#54611yescharacteristic
494C2×C32#54611yescharacteristic
495C2×C32#55111yescharacteristic
496C3⋊D3—42no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—41no—
503C24—41no—
504C24—91no—
505C24C22×C3⋊D311yescharacteristic
506C24C22×C3⋊D311yescharacteristic
507C24C22×C3⋊D311yescharacteristic
508C2×D4—94no—
509C2×D4—182no—
510C2×D4—182no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—361no—
516C2×D4—361no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—182no—
525C22×C4—182no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—182no—
529C22×C4—182no—
530C22×C4—361no—
531C22×C4—361no—
532C22×C4—361no—
533C22×C4C22×C3⋊D311yescharacteristic
534C22×C4C22×C3⋊D311yescharacteristic
535C22×C4C22×C3⋊D311yescharacteristic
536C22×C4C22×C3⋊D311yescharacteristic
537C4⋊C4—182no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—94no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—182no—
552C22⋊C4—182no—
553C22⋊C4—182no—
554C22⋊C4—182no—
555C22⋊C4—182no—
556C22⋊C4—182no—
557C22⋊C4—361no—
558C42—182no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—28no—
565C22×C3—28no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—28no—
571C22×C3—464no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3#883116yescomplemented
581C22×C3C2×#23514yes—
582C22×C3C2×D3×D414yes—
583C22×C3C2×D3×D414yes—
584C22×C3C2×#23714yes—
585C22×C3C2×#23714yes—
586C22×C3#100414yes—
587C22×C3#100414yes—
588C2×D3—68no—
589C2×D3—68no—
590C2×D3—68no—
591C2×D3—124no—
592C2×D3—124no—
593C2×D3—124no—
594C2×D3—124no—
595C3×C4—44no—
596C3×C4—44no—
597C3×C4—44no—
598C3×C4—44no—
599Dic3—68no—
600Dic3—68no—
601Dic3—68no—
602Dic3—124no—
603Dic3—124no—
604Dic3—124no—
605Dic3—124no—
606C32#241811yescharacteristic, complemented, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—28no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—92no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—181no—
635C23—181no—
636C23—181no—
637C23#382812yes—
638C23D4×C3⋊D312yes—
639C23D4×C3⋊D312yes—
640C23#383012yes—
641C23#383012yes—
642C23C23×C3⋊D311yescharacteristic
643D4—188no—
644D4—364no—
645D4—364no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—92no—
659C2×C4—92no—
660C2×C4—92no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—364no—
680C2×C4—364no—
681C2×C4—364no—
682C2×C3—216no—
683C2×C3—48no—
684C2×C3—48no—
685C2×C3C2×#88314yes—
686C2×C3#549014yes—
687C2×C3#549514yes—
688C2×C3#558614yes—
689C2×C3#559014yes—
690C2×C3#559114yes—
691C2×C3#559314yes—
692D3—128no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—416no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—182no—
715C22—182no—
716C22—182no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22#6409214yescomplemented
722C22C2×#382811yescharacteristic
723C22C2×D4×C3⋊D311yescharacteristic
724C22C2×D4×C3⋊D311yescharacteristic
725C22C2×#383011yescharacteristic
726C22C2×#383011yescharacteristic
727C22#6436111yescharacteristic
728C22#6436111yescharacteristic
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—182no—
734C4—182no—
735C4—182no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#7382614yescomplemented
741C2—24no—
742C2—42no—
743C2—42no—
744C2—362no—
745C2C2×#6409211yescharacteristic
746C2#1059596111yescharacteristic
747C2#1059596611yescharacteristic
748C2#1059605711yescharacteristic
749C2#1059606111yescharacteristic
750C2#1059606211yescharacteristic
751C2#1059606411yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#379C2
prime radicalC2×#64162C2
hypercenter#379C3⋊D3
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C22×#3757C2semidirect
3. C2×#64092C2semidirect
4. C2×#64090C2semidirect
5. C32×#379C2semidirect
6. #10592660C2semidirect
7. #10592658C2semidirect
8. #10592657C2semidirect
9. #10592655C2semidirect
10. #10592651C2semidirect
11. #10592650C2semidirect
12. #10592649C2semidirect
13. #10592648C2semidirect
14. #10592644C2semidirect
15. #10592641C2semidirect
23. C22×C4×C3⋊D3C22semidirect
39. C2×#3752C22semidirect
40. C2×#3752C22semidirect
41. C2×#3752C22semidirect
42. C2×C4⋊(C3⋊Dic3)C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C2×#3750C22semidirect
45. C2×#3750C22semidirect
46. C2×#3750C22semidirect
47. C2×C4×C3⋊Dic3C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
60. C3×#379D3semidirect
123. #3757D4semidirect
262. #379C3⋊D3semidirect
346. C22×C32#123semidirect
580. C22×C3#883semidirect
606. C32#2418semidirect
721. C22#64092semidirect
740. C3#73826semidirect

Maximal subgroups

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

subgroupindex
C2×#641622
C22×#37572
C2×#640922
C2×#640902
C32×#3792
#105926602
#105926582
#105926572
#105926552
#105926512
#105926502
#105926492
#105926482
#105926442
#105926412
#738263