Finite Group Databasebeta

← #11836014

Subgroups — #11836014

Order 1152.

2796 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×#64149C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×#64146C211yesmaximal, characteristic, complemented
5C2×#64139C211yesmaximal, characteristic, complemented
6C2×#64091C211yesmaximal, characteristic, complemented
7#10592922C211yesmaximal, characteristic, complemented
8#10592922C211yesmaximal, characteristic, complemented
9#10592922C211yesmaximal, characteristic, complemented
10#10592912C211yesmaximal, characteristic, complemented
11#10592690C211yesmaximal, characteristic, complemented
12#10592689C211yesmaximal, characteristic, complemented
13#10592660C211yesmaximal, characteristic, complemented
14#10592659C211yesmaximal, characteristic, complemented
15#10592650C211yesmaximal, characteristic, complemented
16#82714—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic, complemented
21C23×C32×C4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic
24C22×#638C2211yescharacteristic
25C22×#638C2211yescharacteristic
26C22×#638C2211yescharacteristic
27C22×#638C2211yescharacteristic, complemented
28C22×#638C2211yescharacteristic, complemented
29C22×C4⋊(C3⋊D3)C2211yescharacteristic
30C22×C4⋊(C3⋊D3)C2211yescharacteristic
31C32×#121—24no—
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic, complemented
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37C2×#3757C2211yescharacteristic, complemented
38C2×#3757C2211yescharacteristic, complemented
39#64149—24no—
40#64146—24no—
41#64146—24no—
42#64139—24no—
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3752C2211yescharacteristic
46C2×#3752C2211yescharacteristic
47C2×#3752C2211yescharacteristic
48C2×#3752C2211yescharacteristic
49C2×#3752C2211yescharacteristic, complemented
50C2×#3752C2211yescharacteristic, complemented
51C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
53#64091—24no—
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56#63658C2211yescharacteristic, complemented
57#63658C2211yescharacteristic, complemented
58C2×C3×#121D314yescomplemented
59C2×#940—34no—
60C2×#937—34no—
61C2×#937—34no—
62C2×#930—34no—
63C2×#882—34no—
64#5223—34no—
65#5223—34no—
66#5223—34no—
67#5213—34no—
68#4991—34no—
69#4990—34no—
70#4961—34no—
71#4960—34no—
72#4951—34no—
73C24×C32C2311yescharacteristic
74C24×C32C2311yescharacteristic
75C24×C32C2311yescharacteristic
76C23×C3⋊D3—22no—
77C23×C3⋊D3—22no—
78C23×C3⋊D3—22no—
79C23×C3⋊D3—41no—
80C23×C3⋊D3—41no—
81C23×C3⋊D3—41no—
82C23×C3⋊D3—41no—
83C23×C3⋊D3C2311yescharacteristic
84C23×C3⋊D3C2311yescharacteristic
85C23×C3⋊D3C2311yescharacteristic
86C2×C32×D4—22no—
87C2×C32×D4—22no—
88C2×C32×D4—22no—
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4—22no—
92C2×C32×D4—41no—
93C2×C32×D4—41no—
94C2×C32×D4—41no—
95C22×C32×C4—22no—
96C22×C32×C4—22no—
97C22×C32×C4—41no—
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×#638—22no—
103C2×#638—22no—
104C2×#638—22no—
105C2×#638—22no—
106C2×#638—22no—
107C2×#638—22no—
108C2×#638—22no—
109C2×#638—22no—
110C2×#638—22no—
111C2×#638—41no—
112C2×#638—41no—
113C2×#638—41no—
114C2×#638—41no—
115C2×#638—41no—
116C2×#638—41no—
117C2×#638—41no—
118C2×#638—41no—
119C2×#638—41no—
120C2×#638—41no—
121C2×#638—41no—
122C2×#638D414yescomplemented
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2311yescharacteristic
128C2×C4⋊(C3⋊D3)—22no—
129C2×C4⋊(C3⋊D3)—22no—
130C2×C4⋊(C3⋊D3)—22no—
131C2×C4⋊(C3⋊D3)—22no—
132C2×C4⋊(C3⋊D3)—41no—
133C2×C4⋊(C3⋊D3)—41no—
134C32×C4⋊C4—22no—
135C32×C22⋊C4—22no—
136C32×C22⋊C4D414yescomplemented
137#3757—22no—
138#3757—22no—
139#3757—41no—
140#3757—41no—
141#3752—22no—
142#3752—22no—
143#3752—22no—
144#3752—22no—
145#3752—22no—
146#3752—22no—
147#3752—41no—
148#3752D414yescomplemented
149C4⋊(C3⋊Dic3)—22no—
150C4×C3⋊Dic3—22no—
151#2669—91noSylow
152C24×D3—34no—
153C22×C3×D4C2×D314yes—
154C22×C3×D4C2×D314yes—
155C22×C3×D4C2×D314yescomplemented
156C23×C3×C4C2×D314yescomplemented
157C22×#67—34no—
158C22×#67—34no—
159C22×#67—34no—
160C22×#67—34no—
161C22×#67—34no—
162C22×#67—34no—
163C22×#67—34no—
164C22×D12—34no—
165C22×D12—34no—
166C3×#121—216no—
167C2×C3×C4⋊C4C2×D314yescomplemented
168C2×C3×C22⋊C4C2×D314yes—
169C2×C3×C22⋊C4C2×D314yescomplemented
170C2×#217—34no—
171C2×#217—34no—
172C2×#217—34no—
173C2×#217—34no—
174#940—616no—
175#937—616no—
176#937—616no—
177#930—616no—
178C2×(C2×D3)⋊C4—34no—
179C2×(C2×D3)⋊C4—34no—
180C2×(C2×D3)⋊C4—34no—
181C2×(C2×D3)⋊C4—34no—
182C2×(C2×D3)⋊C4—34no—
183C2×(C2×D3)⋊C4—34no—
184C2×(C2×D3)⋊C4—34no—
185C2×(C2×D3)⋊C4—34no—
186C2×C4⋊Dic3—34no—
187C2×C4×Dic3—34no—
188#882—616no—
189C3⋊#95—34no—
190C3⋊#95—34no—
191C3⋊#95—34no—
192C3⋊#95—34no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32C2×D412yes—
213C23×C32C2×D412yes—
214C23×C32C2411yescharacteristic
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—44no—
235C22×C3⋊D3—44no—
236C22×C3⋊D3—44no—
237C22×C3⋊D3—44no—
238C22×C3⋊D3—44no—
239C22×C3⋊D3—44no—
240C22×C3⋊D3—44no—
241C22×C3⋊D3C2×D412yes—
242C22×C3⋊D3C2×D412yes—
243C32×D4—44no—
244C32×D4—44no—
245C32×D4—44no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—44no—
256C2×C32×C4C2×D412yes—
257C2×C32×C4C2×D412yes—
258C2×C32×C4C2×D412yes—
259#638—44no—
260#638—44no—
261#638—44no—
262#638—44no—
263#638—44no—
264#638—44no—
265#638—44no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3C2×D412yes—
280C2×C3⋊Dic3C2×D412yes—
281C4⋊(C3⋊D3)—44no—
282C4⋊(C3⋊D3)—44no—
283C2×#127—91no—
284C2×#121—91no—
285C2×#121C3⋊D311yescharacteristic, complemented
286C2×#120—91no—
287C2×#120—91no—
288C2×#120—91no—
289#394—91no—
290#394—91no—
291#392—91no—
292#392—91no—
293#392—91no—
294#392—91no—
295#388—91no—
296#388—91no—
297#386—91no—
298C24×C3C22×D314yes—
299C24×C3C22×D314yes—
300C24×C3C22×D314yes—
301C23×D3—34no—
302C23×D3—34no—
303C23×D3—34no—
304C23×D3—68no—
305C23×D3—68no—
306C23×D3—68no—
307C23×D3—124no—
308C23×D3—124no—
309C23×D3—124no—
310C23×D3—124no—
311C2×C3×D4—28no—
312C2×C3×D4—28no—
313C2×C3×D4—28no—
314C2×C3×D4—28no—
315C2×C3×D4—28no—
316C2×C3×D4—28no—
317C2×C3×D4—44no—
318C2×C3×D4—44no—
319C2×C3×D4—44no—
320C22×C3×C4—28no—
321C22×C3×C4—28no—
322C22×C3×C4—44no—
323C22×C3×C4C22×D314yes—
324C22×C3×C4C22×D314yes—
325C22×C3×C4C22×D314yes—
326C22×C3×C4C22×D314yes—
327C2×#67—316no—
328C2×#67—68no—
329C2×#67—68no—
330C2×#67—68no—
331C2×#67—68no—
332C2×#67—68no—
333C2×#67—68no—
334C2×#67—68no—
335C2×#67—68no—
336C2×#67—68no—
337C2×#67—124no—
338C2×#67—124no—
339C2×#67—124no—
340C2×#67—124no—
341C2×#67—124no—
342C2×#67—124no—
343C2×#67—124no—
344C2×#67—124no—
345C2×#67—124no—
346C2×#67—124no—
347C2×#67—124no—
348C22×Dic3—34no—
349C22×Dic3—34no—
350C22×Dic3—34no—
351C22×Dic3—34no—
352C22×Dic3—34no—
353C2×D12—68no—
354C2×D12—68no—
355C2×D12—68no—
356C2×D12—68no—
357C2×D12—124no—
358C2×D12—124no—
359C3×C4⋊C4—28no—
360C3×C22⋊C4—28no—
361C3×C22⋊C4#67116yescomplemented
362#217—68no—
363#217—68no—
364#217—124no—
365#217—124no—
366(C2×D3)⋊C4—316no—
367(C2×D3)⋊C4—68no—
368(C2×D3)⋊C4—68no—
369(C2×D3)⋊C4—68no—
370(C2×D3)⋊C4—68no—
371(C2×D3)⋊C4—68no—
372(C2×D3)⋊C4—68no—
373(C2×D3)⋊C4—124no—
374C4⋊Dic3—68no—
375C4×Dic3—68no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—22no—
379C22×C32—22no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C22×C32C22×D411yescharacteristic
399C22×C32C22×D411yescharacteristic
400C22×C32H(5,𝔽2)11yescharacteristic
401C22×C32H(5,𝔽2)11yescharacteristic
402C22×C32H(5,𝔽2)11yescharacteristic
403C22×C32H(5,𝔽2)11yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—22no—
408C2×C3⋊D3—22no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—416no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C32×C4—22no—
427C32×C4—22no—
428C32×C4—22no—
429C32×C4—41no—
430C3⋊Dic3—22no—
431C3⋊Dic3—22no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C25—91no—
436C22×D4—91no—
437C22×D4—91no—
438C22×D4—91no—
439C22×D4—91no—
440C22×D4—91no—
441C22×D4—91no—
442C22×D4—91no—
443C22×D4—91no—
444C22×D4—91no—
445C22×D4C2×C3⋊D311yescharacteristic
446C22×D4C2×C3⋊D311yescharacteristic
447C22×D4C2×C3⋊D311yescharacteristic, complemented
448C23×C4C2×C3⋊D311yescharacteristic, complemented
449#127—184no—
450#121—24no—
451#121—184no—
452#120—184no—
453#120—184no—
454#120—184no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4—91no—
469C2×C22⋊C4C2×C3⋊D311yescharacteristic
470C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
471C2×C42—91no—
472#95—91no—
473#95—91no—
474#95—91no—
475#95—91no—
476C23×C3—24no—
477C23×C3—24no—
478C23×C3—24no—
479C23×C3—24no—
480C23×C3—24no—
481C23×C3—24no—
482C23×C3—24no—
483C23×C3—24no—
484C23×C3—24no—
485C23×C3—24no—
486C23×C3—24no—
487C23×C3—24no—
488C23×C3—24no—
489C23×C3—24no—
490C23×C3—24no—
491C23×C3—24no—
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—24no—
495C23×C3D3×D418yes—
496C23×C3C2×#6718yes—
497C23×C3C23×D314yes—
498C22×D3—38no—
499C22×D3—38no—
500C22×D3—64no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—64no—
504C22×D3—64no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—64no—
509C22×D3—64no—
510C22×D3—64no—
511C22×D3—64no—
512C22×D3—64no—
513C22×D3—64no—
514C22×D3—64no—
515C22×D3—64no—
516C22×D3—64no—
517C22×D3—64no—
518C22×D3—64no—
519C22×D3—1216no—
520C22×D3—1216no—
521C22×D3—1216no—
522C22×D3—1216no—
523C22×D3—1216no—
524C22×D3—1216no—
525C22×D3—1216no—
526C3×D4—416no—
527C3×D4—416no—
528C3×D4—416no—
529C2×C3×C4—24no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—24no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—24no—
537C2×C3×C4—24no—
538C2×C3×C4—416no—
539C2×C3×C4D3×D418yes—
540C2×C3×C4C2×#6718yes—
541C2×C3×C4C2×#6718yes—
542#67—1216no—
543#67—1216no—
544#67—1216no—
545#67—1216no—
546#67—1216no—
547#67—1216no—
548#67—1216no—
549C2×Dic3—38no—
550C2×Dic3—38no—
551C2×Dic3—64no—
552C2×Dic3—64no—
553C2×Dic3—64no—
554C2×Dic3—64no—
555C2×Dic3—64no—
556C2×Dic3—64no—
557C2×Dic3—64no—
558C2×Dic3—64no—
559C2×Dic3—64no—
560C2×Dic3—64no—
561C2×Dic3—64no—
562C2×Dic3—64no—
563C2×Dic3—64no—
564D12—1216no—
565D12—1216no—
566C2×C32—42no—
567C2×C32—42no—
568C2×C32—81no—
569C2×C32#53411yescharacteristic
570C2×C32#53511yescharacteristic
571C2×C32#53511yescharacteristic
572C2×C32D4211yescharacteristic
573C2×C32D4211yescharacteristic
574C2×C32D4211yescharacteristic
575C2×C32#56011yescharacteristic
576C3⋊D3—42no—
577C3⋊D3—42no—
578C3⋊D3—81no—
579C24—91no—
580C24—91no—
581C24—91no—
582C24—182no—
583C24—182no—
584C24—182no—
585C24—361no—
586C24—361no—
587C24—361no—
588C24—361no—
589C24C22×C3⋊D311yescharacteristic
590C24C22×C3⋊D311yescharacteristic
591C24C22×C3⋊D311yescharacteristic
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—94no—
602C2×D4—182no—
603C2×D4—182no—
604C2×D4—182no—
605C2×D4—182no—
606C2×D4—182no—
607C2×D4—182no—
608C2×D4—182no—
609C2×D4—182no—
610C2×D4—182no—
611C2×D4—182no—
612C2×D4—182no—
613C2×D4—182no—
614C2×D4—182no—
615C2×D4—361no—
616C2×D4—361no—
617C2×D4—361no—
618C2×D4—361no—
619C2×D4—361no—
620C2×D4—361no—
621C2×D4—361no—
622C2×D4—361no—
623C2×D4—361no—
624C2×D4—361no—
625C2×D4—361no—
626C2×D4—361no—
627C2×D4—361no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—41no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4C22×C3⋊D311yescharacteristic
637C22×C4C22×C3⋊D311yescharacteristic
638C22×C4C22×C3⋊D311yescharacteristic
639C22×C4C22×C3⋊D311yescharacteristic
640C4⋊C4—22no—
641C4⋊C4—182no—
642C22⋊C4—22no—
643C22⋊C4—94no—
644C22⋊C4—182no—
645C22⋊C4—182no—
646C22⋊C4—182no—
647C22⋊C4—182no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—361no—
653C22⋊C4—361no—
654C22⋊C4—361no—
655C22⋊C4#63814yescomplemented
656C42—182no—
657C22×C3—28no—
658C22×C3—28no—
659C22×C3—28no—
660C22×C3—28no—
661C22×C3—28no—
662C22×C3—28no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—44no—
672C22×C3—44no—
673C22×C3—44no—
674C22×C3—44no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—44no—
678C22×C3C2×D3×D414yes—
679C22×C3C2×D3×D414yes—
680C22×C3#100414yes—
681C22×C3#100414yes—
682C22×C3#100914yes—
683C22×C3#100914yes—
684C22×C3C22×#6714yes—
685C2×D3—68no—
686C2×D3—68no—
687C2×D3—68no—
688C2×D3—68no—
689C2×D3—68no—
690C2×D3—68no—
691C2×D3—1264no—
692C2×D3—124no—
693C2×D3—124no—
694C2×D3—124no—
695C2×D3—124no—
696C2×D3—124no—
697C2×D3—124no—
698C2×D3—124no—
699C2×D3—124no—
700C2×D3—124no—
701C2×D3—124no—
702C2×D3—124no—
703C2×D3—124no—
704C2×D3—124no—
705C2×D3—124no—
706C2×D3—124no—
707C3×C4—28no—
708C3×C4—28no—
709C3×C4—28no—
710C3×C4—44no—
711Dic3—68no—
712Dic3—68no—
713Dic3—124no—
714Dic3—124no—
715Dic3—124no—
716C32#266911yescharacteristic, complemented, Sylow
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—92no—
737C23—92no—
738C23—181no—
739C23—181no—
740C23—181no—
741C23—181no—
742C23—181no—
743C23—181no—
744C23—181no—
745C23—181no—
746C23—181no—
747C23—181no—
748C23—181no—
749C23—181no—
750C23—181no—
751C23—181no—
752C23—181no—
753C23—181no—
754C23—181no—
755C23—181no—
756C23—181no—
757C23—364no—
758C23—364no—
759C23—364no—
760C23—364no—
761C23—364no—
762C23—364no—
763C23—364no—
764C23D4×C3⋊D312yes—
765C23C2×#63812yes—
766C23C23×C3⋊D311yescharacteristic
767D4—44no—
768D4—44no—
769D4—44no—
770D4—364no—
771D4—364no—
772D4—364no—
773D4—364no—
774D4—364no—
775D4—364no—
776D4—364no—
777D4—364no—
778D4—364no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—44no—
789C2×C4—92no—
790C2×C4—92no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4D4×C3⋊D312yes—
805C2×C4C2×#63812yes—
806C2×C4C2×#63812yes—
807C2×C3—48no—
808C2×C3—48no—
809C2×C3—84no—
810C2×C3#560514yes—
811C2×C3#560714yes—
812C2×C3#560914yes—
813C2×C3#562014yes—
814C2×C3D4×#6714yes—
815C2×C3D4×#6714yes—
816C2×C3#583014yes—
817D3—128no—
818D3—128no—
819D3—244no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—182no—
842C22—182no—
843C22—182no—
844C22—182no—
845C22—182no—
846C22—182no—
847C22—3616no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22C2×D4×C3⋊D311yescharacteristic
864C22C2×D4×C3⋊D311yescharacteristic
865C22#6436111yescharacteristic
866C22#6436111yescharacteristic
867C22#6436611yescharacteristic
868C22#6436611yescharacteristic
869C22C22×#63811yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—41no—
874C4—182no—
875C4—182no—
876C4—361no—
877C4—361no—
878C4—361no—
879C3#8271414yescomplemented
880C2—42no—
881C2—42no—
882C2—81no—
883C2—362no—
884C2—362no—
885C2—721no—
886C2#1059607611yescharacteristic
887C2#1059607811yescharacteristic
888C2#1059608011yescharacteristic
889C2#1059609111yescharacteristic
890C2D4×#63811yescharacteristic
891C2D4×#63811yescharacteristic
892C2#1059630111yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×#121C2
hypercenterC2×#121C3⋊D3
hypocenterC32#2669
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×#64149C2semidirect
3. C2×#64146C2semidirect
4. C2×#64146C2semidirect
5. C2×#64139C2semidirect
6. C2×#64091C2semidirect
7. #10592922C2semidirect
8. #10592922C2semidirect
9. #10592922C2semidirect
10. #10592912C2semidirect
11. #10592690C2semidirect
12. #10592689C2semidirect
13. #10592660C2semidirect
14. #10592659C2semidirect
15. #10592650C2semidirect
20. C22×C32×D4C22semidirect
21. C23×C32×C4C22semidirect
27. C22×#638C22semidirect
28. C22×#638C22semidirect
32. C2×C32×C4⋊C4C22semidirect
34. C2×C32×C22⋊C4C22semidirect
37. C2×#3757C22semidirect
38. C2×#3757C22semidirect
49. C2×#3752C22semidirect
50. C2×#3752C22semidirect
51. C2×C4⋊(C3⋊Dic3)C22semidirect
52. C2×C4×C3⋊Dic3C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. #63658C22semidirect
57. #63658C22semidirect
58. C2×C3×#121D3semidirect
122. C2×#638D4semidirect
136. C32×C22⋊C4D4semidirect
148. #3752D4semidirect
155. C22×C3×D4C2×D3semidirect
156. C23×C3×C4C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
169. C2×C3×C22⋊C4C2×D3semidirect
285. C2×#121C3⋊D3semidirect
361. C3×C22⋊C4#67semidirect
447. C22×D4C2×C3⋊D3semidirect
448. C23×C4C2×C3⋊D3semidirect
456. C2×C4⋊C4C2×C3⋊D3semidirect
470. C2×C22⋊C4C2×C3⋊D3semidirect
655. C22⋊C4#638semidirect
716. C32#2669semidirect
879. C3#82714semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×#641492
C2×#641462
C2×#641392
C2×#640912
#105929222
#105929122
#105926902
#105926892
#105926602
#105926592
#105926502
#827143