Finite Group Databasebeta

← C2×#77094 #11001535

Subgroups — C2×#77094 #11001535

Order 768.

2822 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4985C211yesmaximal, characteristic, complemented
6C2×#4959C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4960C211yesmaximal, characteristic, complemented
9C2×#4960C211yesmaximal, characteristic, complemented
10C2×#4953C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4945C211yesmaximal, characteristic, complemented
14#77094C2116yesmaximal, direct product factor
15C2×#4675C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2828—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×C4⋊Dic3C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C3×#394C2218yescomplemented
46C2×C3×#95C2211yescharacteristic
47#5223C2218yescomplemented
48#5223C2218yescomplemented
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4991C2218yescomplemented
57#4985C2218yescomplemented
58#4961C2218yescomplemented
59#4960C2218yescomplemented
60#4960C2218yescomplemented
61#4959C2218yescomplemented
62#4959C2218yescomplemented
63#4957C2218yescomplemented
64#4953C2218yescomplemented
65#4945C2218yescomplemented
66#4675C2218yescomplemented
67#4670C2218yescomplemented
68#2828—316no—
69C2×#400—31no—
70C2×#397—31no—
71C2×#397—31no—
72C2×#394—31no—
73C2×#394—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#394D311yescharacteristic, complemented
77C2×#392—31no—
78C2×#392—31no—
79C2×#392—31no—
80C2×#392—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#388—31no—
84C25×C3C2311yescharacteristic
85C25×C3C2311yescharacteristic
86C24×D3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C22×C3×D4—42no—
89C22×C3×D4—42no—
90C22×C3×D4—42no—
91C22×C3×D4C2314yes—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—24no—
98C22×#67—42no—
99C22×#67—42no—
100C22×#67—42no—
101C22×#67—42no—
102C22×#67—42no—
103C22×#67—42no—
104C22×#67—42no—
105C22×#67—42no—
106C22×#67—42no—
107C22×#67—42no—
108C22×#67—42no—
109C22×#67C2314yes—
110C22×#67C2314yes—
111C22×#67C2314yes—
112C22×#67C2314yes—
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C22×D12—42no—
120C22×D12—42no—
121C22×D12—42no—
122C22×D12C2314yes—
123C2×C3×C4⋊C4—42no—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C22⋊C4—42no—
126C2×C3×C22⋊C4—42no—
127C2×C3×C22⋊C4—42no—
128C2×C3×C22⋊C4—42no—
129C2×C3×C22⋊C4C2314yes—
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133C2×#217—24no—
134C2×#217—42no—
135C2×#217—42no—
136C2×#217—42no—
137C2×#217C2314yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—42no—
143C2×(C2×D3)⋊C4—42no—
144C2×(C2×D3)⋊C4—42no—
145C2×(C2×D3)⋊C4—42no—
146C2×(C2×D3)⋊C4—42no—
147C2×(C2×D3)⋊C4—42no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×C4⋊Dic3—42no—
158C2×C4⋊Dic3C2314yes—
159C2×Dic3⋊C4—42no—
160C2×Dic3⋊C4—42no—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3—42no—
164C2×C4×Dic3C2314yes—
165C3×#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C23×D4—31no—
174C23×D4—31no—
175C23×D4—31no—
176C23×D4—31no—
177C23×D4—31no—
178C23×D4C2×D311yescharacteristic
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4C2×D311yescharacteristic
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4C2×D311yescharacteristic
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C42—31no—
200#400—38no—
201#397—38no—
202#397—38no—
203#394—38no—
204#394—38no—
205#394—38no—
206#394—38no—
207#394C2×D318yescomplemented
208#392—38no—
209#392—38no—
210#392—38no—
211#392—38no—
212#390—38no—
213#388—38no—
214#388—38no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95C2×D311yescharacteristic
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3C2412yes—
238C24×C3C2412yes—
239C24×C3C2411yescharacteristic
240C23×D3—22no—
241C23×D3—22no—
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3C2412yes—
255C23×D3C2412yes—
256C2×C3×D4—44no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—416no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C2×#67—28no—
281C2×#67—44no—
282C2×#67—44no—
283C2×#67—44no—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—416no—
293C2×#67—416no—
294C2×#67—416no—
295C2×#67—416no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3#4114yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C22×Dic3C2412yes—
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C2×D12—44no—
321C2×D12—44no—
322C2×D12—44no—
323C2×D12—416no—
324C3×C4⋊C4—44no—
325C3×C22⋊C4—44no—
326C3×C22⋊C4—44no—
327C3×C22⋊C4—44no—
328C3×C22⋊C4—44no—
329#217—28no—
330#217—44no—
331#217—44no—
332#217—44no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341C4⋊Dic3—44no—
342Dic3⋊C4—44no—
343Dic3⋊C4—44no—
344C4×Dic3—44no—
345C25—31no—
346C25—31no—
347C25C22×D311yescharacteristic
348C25C22×D311yescharacteristic
349C22×D4—34no—
350C22×D4—34no—
351C22×D4—34no—
352C22×D4—34no—
353C22×D4—34no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—64no—
358C22×D4—122no—
359C22×D4—122no—
360C22×D4—122no—
361C22×D4—122no—
362C22×D4—122no—
363C22×D4—122no—
364C22×D4—122no—
365C22×D4—122no—
366C22×D4—122no—
367C22×D4—122no—
368C22×D4—122no—
369C22×D4—122no—
370C22×D4—122no—
371C22×D4—122no—
372C22×D4C22×D314yes—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D311yescharacteristic
383C23×C4C22×D311yescharacteristic
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—122no—
389C2×C4⋊C4—122no—
390C2×C4⋊C4—122no—
391C2×C4⋊C4C22×D314yes—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—122no—
411C2×C22⋊C4—122no—
412C2×C22⋊C4—122no—
413C2×C22⋊C4—122no—
414C2×C22⋊C4—122no—
415C2×C22⋊C4—122no—
416C2×C22⋊C4—122no—
417C2×C22⋊C4—122no—
418C2×C22⋊C4—122no—
419C2×C22⋊C4—122no—
420C2×C22⋊C4C22×D314yes—
421C2×C22⋊C4C22×D314yes—
422C2×C22⋊C4C22×D314yes—
423C2×C22⋊C4C22×D314yes—
424C2×C42—34no—
425C2×C42—122no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95C22×D314yes—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—44no—
449C23×C3—44no—
450C23×C3—44no—
451C23×C3—44no—
452C23×C3—44no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3—44no—
459C23×C3—44no—
460C23×C3—44no—
461C23×C3—44no—
462C23×C3C2×#4112yes—
463C23×C3H(5,𝔽2)12yes—
464C23×C3H(5,𝔽2)12yes—
465C23×C3H(5,𝔽2)12yes—
466C23×C3H(5,𝔽2)12yes—
467C23×C3H(5,𝔽2)12yes—
468C23×C3H(5,𝔽2)12yes—
469C23×C3C2511yescharacteristic
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—44no—
485C22×D3—44no—
486C22×D3—44no—
487C22×D3—44no—
488C22×D3—44no—
489C22×D3—44no—
490C22×D3—44no—
491C22×D3—44no—
492C22×D3—44no—
493C22×D3—44no—
494C22×D3—44no—
495C22×D3—44no—
496C22×D3—44no—
497C22×D3—44no—
498C3×D4—416no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—44no—
515C2×C3×C4—44no—
516C2×C3×C4—44no—
517C2×C3×C4—44no—
518C2×C3×C4—44no—
519#67—416no—
520#67—416no—
521#67—416no—
522#67—416no—
523C2×Dic3—28no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—44no—
542C2×Dic3—44no—
543C2×Dic3—44no—
544C2×Dic3—44no—
545C2×Dic3—44no—
546C2×Dic3C2×#4114yes—
547D12—416no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—32no—
563C24—32no—
564C24—62no—
565C24—62no—
566C24—62no—
567C24—62no—
568C24—62no—
569C24—62no—
570C24—62no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—62no—
575C24—62no—
576C24—62no—
577C24—62no—
578C24C23×D312yes—
579C24C23×D312yes—
580C24C23×D311yescharacteristic
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—416no—
585C2×D4—68no—
586C2×D4—124no—
587C2×D4—124no—
588C2×D4—124no—
589C2×D4—1216no—
590C2×D4—124no—
591C2×D4—124no—
592C2×D4—124no—
593C2×D4—124no—
594C2×D4—124no—
595C2×D4—124no—
596C2×D4—124no—
597C2×D4—124no—
598C2×D4—124no—
599C2×D4—124no—
600C2×D4—124no—
601C2×D4—1216no—
602C2×D4—1216no—
603C2×D4—1216no—
604C2×D4—1216no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—34no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—32no—
625C22×C4—32no—
626C22×C4—32no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4C23×D312yes—
645C22×C4C23×D312yes—
646C22×C4C23×D312yes—
647C22×C4C23×D312yes—
648C22×C4C23×D312yes—
649C4⋊C4—44no—
650C4⋊C4—124no—
651C4⋊C4—124no—
652C4⋊C4—124no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—68no—
658C22⋊C4—68no—
659C22⋊C4—124no—
660C22⋊C4—124no—
661C22⋊C4—124no—
662C22⋊C4—124no—
663C22⋊C4—124no—
664C22⋊C4—124no—
665C22⋊C4—124no—
666C22⋊C4—124no—
667C22⋊C4—124no—
668C22⋊C4—124no—
669C42—124no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—88no—
685C22×C3—88no—
686C22×C3#53814yes—
687C22×C3#54014yes—
688C22×C3#54014yes—
689C22×C3#56014yes—
690C22×C3#56014yes—
691C22×C3#56014yes—
692C22×C3H(3,𝔽4)14yes—
693C22×C3C22×#4111yescharacteristic
694C22×C3C2×H(5,𝔽2)11yescharacteristic
695C22×C3C2×H(5,𝔽2)11yescharacteristic
696C22×C3C2×H(5,𝔽2)11yescharacteristic
697C22×C3C2×H(5,𝔽2)11yescharacteristic
698C22×C3C2×H(5,𝔽2)11yescharacteristic
699C22×C3C2×H(5,𝔽2)11yescharacteristic
700C2×D3—42no—
701C2×D3—42no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—88no—
715C2×D3—88no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721Dic3—24no—
722Dic3—42no—
723Dic3—42no—
724Dic3—42no—
725Dic3—42no—
726Dic3—42no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—62no—
766C23—62no—
767C23—62no—
768C23—62no—
769C23—124no—
770C23—124no—
771C23—124no—
772C23—124no—
773C23—124no—
774C23—124no—
775C23—124no—
776C23—124no—
777C23—124no—
778C23—124no—
779C23—124no—
780C23—124no—
781C23—124no—
782C23—124no—
783C23#100412yes—
784C23#100412yes—
785C23#100412yes—
786C23#100412yes—
787C23D3×#4112yes—
788C23#100912yes—
789C23#100912yes—
790C23C24×D311yescharacteristic
791D4—416no—
792D4—1216no—
793D4—1216no—
794D4—1216no—
795D4—1216no—
796D4—1216no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—34no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—68no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—124no—
837C2×C4—124no—
838C2×C4—124no—
839C2×C4—124no—
840C2×C4—124no—
841C2×C3—82no—
842C2×C3—82no—
843C2×C3#282818yescomplemented
844C2×C3C2×#53811yescharacteristic
845C2×C3C2×#54011yescharacteristic
846C2×C3C2×#54011yescharacteristic
847C2×C3C2×#56011yescharacteristic
848C2×C3C2×#56011yescharacteristic
849C2×C3C2×#56011yescharacteristic
850C2×C3C2×H(3,𝔽4)11yescharacteristic
851D3—82no—
852D3—82no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—88no—
868C22—88no—
869C22—122no—
870C22—122no—
871C22—122no—
872C22—122no—
873C22—122no—
874C22—122no—
875C22—122no—
876C22—122no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—122no—
882C22—122no—
883C22—248no—
884C22—248no—
885C22#559414yes—
886C22#561514yes—
887C22#562014yes—
888C22#562014yes—
889C22#566314yes—
890C22#566614yes—
891C22#567814yes—
892C22C2×#100411yescharacteristic
893C22C2×#100411yescharacteristic
894C22C2×#100411yescharacteristic
895C22C2×#100411yescharacteristic
896C22C2×D3×#4111yescharacteristic
897C22C2×#100911yescharacteristic
898C22C2×#100911yescharacteristic
899C4—42no—
900C4—42no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—64no—
905C4—122no—
906C4—122no—
907C4—122no—
908C4—122no—
909C4—122no—
910C3C2×#282811yescharacteristic, complemented, Sylow
911C2—82no—
912C2—82no—
913C2—242no—
914C2—242no—
915C2#7709418yesdirect product factor
916C2C2×#559411yescharacteristic
917C2C2×#561511yescharacteristic
918C2C2×#562011yescharacteristic
919C2C2×#562011yescharacteristic
920C2C2×#566311yescharacteristic
921C2C2×#566611yescharacteristic
922C2C2×#567811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#394C2
socleC24×C3C24
hypercenterC2×#394D3
hypocenterC3C2×#2828
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×C3×#394C2semidirect
2. C2×#5223C2semidirect
3. C2×#5223C2semidirect
4. C2×#4991C2semidirect
5. C2×#4985C2semidirect
6. C2×#4959C2semidirect
7. C2×#4959C2semidirect
8. C2×#4960C2semidirect
9. C2×#4960C2semidirect
10. C2×#4953C2semidirect
11. C2×#4961C2semidirect
12. C2×#4957C2semidirect
13. C2×#4945C2semidirect
14. #77094C2direct (N × H)
15. C2×#4675C2semidirect
16. C2×#4670C2semidirect
45. C3×#394C22semidirect
47. #5223C22semidirect
48. #5223C22semidirect
56. #4991C22semidirect
57. #4985C22semidirect
58. #4961C22semidirect
59. #4960C22semidirect
60. #4960C22semidirect
61. #4959C22semidirect
62. #4959C22semidirect
63. #4957C22semidirect
64. #4953C22semidirect
65. #4945C22semidirect
66. #4675C22semidirect
67. #4670C22semidirect
76. C2×#394D3semidirect
207. #394C2×D3semidirect
843. C2×C3#2828semidirect
910. C3C2×#2828semidirect
915. C2#77094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×#52232
C2×#49912
C2×#49852
C2×#49592
C2×#49602
C2×#49532
C2×#49612
C2×#49572
C2×#49452
#770942
C2×#46752
C2×#46702
C2×#28283