Finite Group Databasebeta

← C2×#74823 #11430475

Subgroups — C2×#74823 #11430475

Order 768.

3434 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#930C211yesmaximal, characteristic, complemented
2C22×#879C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5210C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4960C211yesmaximal, characteristic, complemented
9C2×#4957C211yesmaximal, characteristic, complemented
10C2×#4957C211yesmaximal, characteristic, complemented
11C2×#4957C211yesmaximal, characteristic, complemented
12#74823C2116yesmaximal, direct product factor
13C2×#4675C211yesmaximal, characteristic, complemented
14C2×#4672C211yesmaximal, characteristic, complemented
15C2×#4669C211yesmaximal, characteristic, complemented
16C2×#4653C211yesmaximal, characteristic, complemented
17C2×#2714—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C2×#930—28no—
33C2×#930C2218yescomplemented
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×(C2×D3)⋊C4C2211yescharacteristic
42C22×C4⋊Dic3C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×C4×Dic3C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#879—28no—
50C2×#879C2218yescomplemented
51C3×#386C2218yescomplemented
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54#5223C2218yescomplemented
55#5223C2218yescomplemented
56#5210C2218yescomplemented
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4960C2218yescomplemented
62#4959C2218yescomplemented
63#4957C2218yescomplemented
64#4957C2218yescomplemented
65#4957C2218yescomplemented
66#4675C2218yescomplemented
67#4672C2218yescomplemented
68#4669C2218yescomplemented
69#4653C2218yescomplemented
70C22×#126—31no—
71C22×#121—31no—
72#2714—316no—
73C2×#397—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#390—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#387—31no—
84C2×#386D311yescharacteristic, complemented
85C2×#385—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—42no—
92C22×C3×D4—42no—
93C22×C3×D4C2314yes—
94C23×C3×C4—24no—
95C23×C3×C4—42no—
96C23×C3×C4—42no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2314yes—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67C2314yes—
116C22×#67C2314yes—
117C22×#67C2314yes—
118C22×#67C2314yes—
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C22×D12—24no—
126C22×D12—42no—
127C22×D12—42no—
128C22×D12C2314yes—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4—42no—
131C2×C3×C22⋊C4—42no—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yes—
135C2×#217—24no—
136C2×#217—24no—
137C2×#217—24no—
138C2×#217—42no—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143#930—232no—
144C2×(C2×D3)⋊C4—24no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—42no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4—42no—
150C2×(C2×D3)⋊C4—42no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×C4⋊Dic3D418yescomplemented
161C2×C4⋊Dic3C2314yes—
162C2×Dic3⋊C4—24no—
163C2×Dic3⋊C4—24no—
164C2×Dic3⋊C4—42no—
165C2×Dic3⋊C4—42no—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3—24no—
171C2×C4×Dic3—42no—
172C2×C4×Dic3C2314yes—
173C2×C4×Dic3C2314yes—
174#879—232no—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4—31no—
186C23×D4C2×D311yescharacteristic
187C24×C4C2×D311yescharacteristic
188C2×#126—38no—
189C2×#126—68no—
190C2×#121—38no—
191C2×#121—68no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C42—31no—
213C22×C42—31no—
214#397—38no—
215#394—38no—
216#394—38no—
217#392—38no—
218#392—38no—
219#392—38no—
220#390—38no—
221#390—38no—
222#390—38no—
223#388—38no—
224#387—38no—
225#386C2×D318yescomplemented
226#385—38no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95C2×D311yescharacteristic
232C2×#95C2×D311yescharacteristic
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3#4114yes—
247C24×C3C2412yes—
248C24×C3C2412yes—
249C24×C3C2411yescharacteristic
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3C2412yes—
265C23×D3C2412yes—
266C2×C3×D4—28no—
267C2×C3×D4—44no—
268C2×C3×D4—44no—
269C2×C3×D4—416no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—28no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—416no—
288C22×C3×C4C2×D414yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
294C2×#67—28no—
295C2×#67—28no—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—28no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—416no—
307C2×#67—416no—
308C2×#67—416no—
309C2×#67—416no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3C2×D414yes—
326C22×Dic3C2×D414yes—
327C22×Dic3#4114yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C2×D12—28no—
335C2×D12—44no—
336C2×D12—44no—
337C2×D12—416no—
338C3×C22⋊C4—28no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341#217—28no—
342#217—28no—
343#217—28no—
344#217—44no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353C4⋊Dic3C2×D4116yescomplemented
354Dic3⋊C4—28no—
355Dic3⋊C4—28no—
356Dic3⋊C4—44no—
357Dic3⋊C4—44no—
358C4×Dic3—28no—
359C4×Dic3—44no—
360C25—31no—
361C25—31no—
362C25C22×D311yescharacteristic
363C25C22×D311yescharacteristic
364C22×D4—24no—
365C22×D4—34no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—64no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—122no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C22×D4C22×D314yes—
388C23×C4—24no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D314yes—
403#126—632no—
404#121—632no—
405C2×C4⋊C4—38no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—64no—
412C2×C4⋊C4—64no—
413C2×C4⋊C4—122no—
414C2×C4⋊C4—122no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—122no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4C22×D314yes—
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D314yes—
445C2×C42—34no—
446C2×C42—34no—
447C2×C42—64no—
448C2×C42—122no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95C22×D314yes—
454#95C22×D314yes—
455C23×C3—28no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—44no—
472C23×C3—44no—
473C23×C3—44no—
474C23×C3—44no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3—44no—
478C23×C3—44no—
479C23×C3—44no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3C22×D412yes—
483C23×C3C2×#4114yes—
484C23×C3C2×#4112yes—
485C23×C3C2×#4112yes—
486C23×C3H(5,𝔽2)12yes—
487C23×C3H(5,𝔽2)12yes—
488C23×C3H(5,𝔽2)12yes—
489C23×C3H(5,𝔽2)12yes—
490C23×C3C2511yescharacteristic
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—44no—
506C22×D3—44no—
507C22×D3—44no—
508C22×D3—44no—
509C22×D3—44no—
510C22×D3—44no—
511C22×D3—44no—
512C22×D3—44no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C3×D4—416no—
520C2×C3×C4—28no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—416no—
536C2×C3×C4—44no—
537C2×C3×C4—44no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4C22×D414yes—
541#67—416no—
542#67—416no—
543#67—416no—
544#67—416no—
545C2×Dic3—28no—
546C2×Dic3—28no—
547C2×Dic3—28no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—44no—
564C2×Dic3—44no—
565C2×Dic3—44no—
566C2×Dic3C22×D414yes—
567C2×Dic3C22×D414yes—
568C2×Dic3C2×#4114yes—
569D12—416no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—32no—
584C24—32no—
585C24—62no—
586C24—62no—
587C24—62no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24#23514yes—
600C24C23×D312yes—
601C24C23×D312yes—
602C24C23×D311yescharacteristic
603C2×D4—28no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—416no—
607C2×D4—68no—
608C2×D4—68no—
609C2×D4—68no—
610C2×D4—68no—
611C2×D4—68no—
612C2×D4—68no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—1216no—
616C2×D4—124no—
617C2×D4—124no—
618C2×D4—124no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—1216no—
624C2×D4—1216no—
625C2×D4—1216no—
626C2×D4—1216no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—28no—
642C22×C4—34no—
643C22×C4—34no—
644C22×C4—34no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—416no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4D3×D414yes—
670C22×C4C23×D312yes—
671C22×C4C23×D312yes—
672C22×C4C23×D312yes—
673C22×C4C23×D312yes—
674C22×C4C23×D312yes—
675C4⋊C4—316no—
676C4⋊C4—68no—
677C4⋊C4—68no—
678C4⋊C4—124no—
679C4⋊C4—124no—
680C22⋊C4—28no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—68no—
684C22⋊C4—68no—
685C22⋊C4—68no—
686C22⋊C4—68no—
687C22⋊C4—68no—
688C22⋊C4—68no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C42—68no—
696C42—124no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—416no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—88no—
713C22×C3#53514yes—
714C22×C3#53814yes—
715C22×C3#53814yes—
716C22×C3#54614yes—
717C22×C3#55014yes—
718C22×C3#55314yes—
719C22×C3#56014yes—
720C22×C3C23×D411yescharacteristic
721C22×C3C22×#4111yescharacteristic
722C22×C3C22×#4111yescharacteristic
723C22×C3C2×H(5,𝔽2)11yescharacteristic
724C22×C3C2×H(5,𝔽2)11yescharacteristic
725C22×C3C2×H(5,𝔽2)11yescharacteristic
726C22×C3C2×H(5,𝔽2)11yescharacteristic
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—88no—
742C2×D3—88no—
743C3×C4—24no—
744C3×C4—42no—
745C3×C4—42no—
746C3×C4—42no—
747C3×C4—42no—
748Dic3—24no—
749Dic3—24no—
750Dic3—24no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—28no—
761C23—28no—
762C23—28no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—124no—
796C23—124no—
797C23—124no—
798C23—124no—
799C23—124no—
800C23—124no—
801C23—124no—
802C23—124no—
803C23—124no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23C2×#23514yes—
810C23C2×#23512yes—
811C23C2×D3×D412yes—
812C23#100412yes—
813C23#100412yes—
814C23#100412yes—
815C23D3×#4112yes—
816C23#100912yes—
817C23C24×D311yescharacteristic
818D4—416no—
819D4—1216no—
820D4—1216no—
821D4—1216no—
822D4—1216no—
823D4—1216no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—34no—
840C2×C4—34no—
841C2×C4—34no—
842C2×C4—416no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—68no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—68no—
855C2×C4—68no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—124no—
868C2×C4C2×D3×D414yes—
869C2×C3—44no—
870C2×C3—82no—
871C2×C3#271418yescomplemented
872C2×C3C2×#53511yescharacteristic
873C2×C3C2×#53811yescharacteristic
874C2×C3C2×#53811yescharacteristic
875C2×C3C2×#54611yescharacteristic
876C2×C3C2×#55011yescharacteristic
877C2×C3C2×#55311yescharacteristic
878C2×C3C2×#56011yescharacteristic
879D3—82no—
880D3—82no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—416no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—88no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—248no—
912C22—248no—
913C22#549414yes—
914C22#554014yes—
915C22#555014yes—
916C22#559214yes—
917C22#559914yes—
918C22#562014yes—
919C22#565714yes—
920C22C22×#23511yescharacteristic
921C22C22×D3×D411yescharacteristic
922C22C2×#100411yescharacteristic
923C22C2×#100411yescharacteristic
924C22C2×#100411yescharacteristic
925C22C2×D3×#4111yescharacteristic
926C22C2×#100911yescharacteristic
927C4—24no—
928C4—42no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—64no—
933C4—64no—
934C4—64no—
935C4—122no—
936C4—122no—
937C4—122no—
938C3C2×#271411yescharacteristic, complemented, Sylow
939C2—44no—
940C2—82no—
941C2—242no—
942C2—242no—
943C2#7482318yesdirect product factor
944C2C2×#549411yescharacteristic
945C2C2×#554011yescharacteristic
946C2C2×#555011yescharacteristic
947C2C2×#559211yescharacteristic
948C2C2×#559911yescharacteristic
949C2C2×#562011yescharacteristic
950C2C2×#565711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
hypercenterC2×#386D3
hypocenterC3C2×#2714
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#930C2semidirect
2. C22×#879C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5223C2semidirect
5. C2×#5223C2semidirect
6. C2×#5210C2semidirect
7. C2×#4959C2semidirect
8. C2×#4960C2semidirect
9. C2×#4957C2semidirect
10. C2×#4957C2semidirect
11. C2×#4957C2semidirect
12. #74823C2direct (N × H)
13. C2×#4675C2semidirect
14. C2×#4672C2semidirect
15. C2×#4669C2semidirect
16. C2×#4653C2semidirect
33. C2×#930C22semidirect
50. C2×#879C22semidirect
51. C3×#386C22semidirect
54. #5223C22semidirect
55. #5223C22semidirect
56. #5210C22semidirect
61. #4960C22semidirect
62. #4959C22semidirect
63. #4957C22semidirect
64. #4957C22semidirect
65. #4957C22semidirect
66. #4675C22semidirect
67. #4672C22semidirect
68. #4669C22semidirect
69. #4653C22semidirect
84. C2×#386D3semidirect
160. C2×C4⋊Dic3D4semidirect
225. #386C2×D3semidirect
353. C4⋊Dic3C2×D4semidirect
871. C2×C3#2714semidirect
938. C3C2×#2714semidirect
943. C2#74823direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9302
C22×#8792
C2×C3×#3862
C2×#52232
C2×#52102
C2×#49592
C2×#49602
C2×#49572
#748232
C2×#46752
C2×#46722
C2×#46692
C2×#46532
C2×#27143