Finite Group Databasebeta

← C2×#82693 #11430273

Subgroups — C2×#82693 #11430273

Order 768.

3542 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C22×#886C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5221C211yesmaximal, characteristic, complemented
7C2×#5220C211yesmaximal, characteristic, complemented
8C2×#5220C211yesmaximal, characteristic, complemented
9C2×#5213C211yesmaximal, characteristic, complemented
10C2×#5212C211yesmaximal, characteristic, complemented
11#82693C2116yesmaximal, direct product factor
12C2×#4986C211yesmaximal, characteristic, complemented
13C2×#4990C211yesmaximal, characteristic, complemented
14C2×#4953C211yesmaximal, characteristic, complemented
15C2×#4961C211yesmaximal, characteristic, complemented
16C2×#4951C211yesmaximal, characteristic, complemented
17C2×#2703—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C24×Dic3C2211yescharacteristic
26C2×C3×#121—28no—
27C2×C3×#121C2218yescomplemented
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×C4⋊Dic3C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C22×C4⋊Dic3C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#886—28no—
48C2×#886C2218yescomplemented
49#5223C2218yescomplemented
50#5223C2218yescomplemented
51#5223C2218yescomplemented
52#5221C2218yescomplemented
53#5220C2218yescomplemented
54#5220C2218yescomplemented
55#5213C2218yescomplemented
56#5212C2218yescomplemented
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63C2×C3⋊#95C2211yescharacteristic
64C2×C3⋊#95C2211yescharacteristic
65#4990C2218yescomplemented
66#4986C2218yescomplemented
67#4961C2218yescomplemented
68#4953C2218yescomplemented
69#4951C2218yescomplemented
70C22×#123—31no—
71C22×#121D311yescharacteristic, complemented
72#2703—316no—
73C2×#400—31no—
74C2×#397—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#380—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—24no—
95C22×C3×D4—24no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4—42no—
99C22×C3×D4C2314yes—
100C22×C3×D4C2314yes—
101C22×C3×D4C2314yes—
102C23×C3×C4—24no—
103C23×C3×C4—24no—
104C23×C3×C4—42no—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2314yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C22×#67—24no—
111C22×#67—24no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67—42no—
116C22×#67—42no—
117C22×#67—42no—
118C22×#67—42no—
119C22×#67C2314yes—
120C22×#67C2314yes—
121C22×#67C2314yes—
122C23×Dic3—24no—
123C23×Dic3—42no—
124C23×Dic3—42no—
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2311yescharacteristic
131C23×Dic3C2311yescharacteristic
132C23×Dic3C2314yes—
133C3×#121—232no—
134C2×C3×C4⋊C4—24no—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4D418yescomplemented
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2314yes—
140C2×#217—42no—
141C2×#217—42no—
142C2×#217—42no—
143C2×#217—42no—
144C2×#217—42no—
145C2×#217—42no—
146C2×#217—42no—
147C2×#217—42no—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2314yes—
156C2×(C2×D3)⋊C4—24no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—42no—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×C4⋊Dic3—24no—
165C2×C4⋊Dic3—24no—
166C2×C4⋊Dic3—42no—
167C2×C4⋊Dic3C2314yes—
168C2×C4⋊Dic3C2314yes—
169C2×C4⋊Dic3C2314yes—
170C2×C4×Dic3—42no—
171C2×C4×Dic3C2314yes—
172#886—232no—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4C2×D311yescharacteristic
185C23×D4C2×D311yescharacteristic
186C23×D4C2×D311yescharacteristic
187C24×C4—31no—
188C24×C4C2×D311yescharacteristic
189C2×#123—38no—
190C2×#123—68no—
191C2×#121—28no—
192C2×#121C2×D318yescomplemented
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4C2×D311yescharacteristic
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×C42—31no—
212#400—38no—
213#397—38no—
214#394—38no—
215#392—38no—
216#392—38no—
217#392—38no—
218#390—38no—
219#388—38no—
220#388—38no—
221#386—38no—
222#386—38no—
223#386—38no—
224#380—38no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
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—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3C2×D414yes—
253C24×C3#4114yes—
254C24×C3C2412yes—
255C24×C3C2412yes—
256C24×C3C2412yes—
257C24×C3C2411yescharacteristic
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3—22no—
265C23×D3C2412yes—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
270C2×C3×D4—28no—
271C2×C3×D4—28no—
272C2×C3×D4—44no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—416no—
276C2×C3×D4—416no—
277C2×C3×D4—416no—
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—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—28no—
288C22×C3×C4—28no—
289C22×C3×C4—44no—
290C22×C3×C4—416no—
291C22×C3×C4C2×D414yes—
292C22×C3×C4C2×D414yes—
293C22×C3×C4#4114yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C2×#67—28no—
299C2×#67—28no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—416no—
308C2×#67—416no—
309C2×#67—416no—
310C22×Dic3—28no—
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×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—22no—
332C22×Dic3—44no—
333C22×Dic3—44no—
334C22×Dic3—416no—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C22×Dic3C2412yes—
338C22×Dic3C2412yes—
339C22×Dic3C2412yes—
340C22×Dic3C2412yes—
341C22×Dic3C2412yes—
342C3×C4⋊C4—28no—
343C3×C22⋊C4—28no—
344C3×C22⋊C4C2×D4116yescomplemented
345#217—44no—
346#217—44no—
347#217—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351#217—44no—
352#217—44no—
353(C2×D3)⋊C4—28no—
354(C2×D3)⋊C4—28no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—28no—
358C4⋊Dic3—28no—
359C4⋊Dic3—44no—
360C4×Dic3—44no—
361C25—31no—
362C25C22×D311yescharacteristic
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—34no—
372C22×D4—34no—
373C22×D4—34no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4C22×D314yes—
387C22×D4C22×D314yes—
388C22×D4C22×D314yes—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—34no—
399C23×C4—42no—
400C23×C4—64no—
401C23×C4—122no—
402C23×C4—122no—
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D314yes—
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408#123—632no—
409#121—232no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—64no—
416C2×C4⋊C4—122no—
417C2×C4⋊C4C22×D314yes—
418C2×C22⋊C4—24no—
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—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—122no—
435C2×C22⋊C4—122no—
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⋊C4—122no—
443C2×C22⋊C4#6718yescomplemented
444C2×C22⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C42—34no—
447C2×C42—122no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95—34no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—28no—
461C23×C3—28no—
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—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3—44no—
485C23×C3—44no—
486C23×C3—44no—
487C23×C3—44no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—44no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
496C23×C3C22×D414yes—
497C23×C3C22×D412yes—
498C23×C3C2×#4114yes—
499C23×C3C2×#4112yes—
500C23×C3C2×#4112yes—
501C23×C3H(5,𝔽2)12yes—
502C23×C3H(5,𝔽2)12yes—
503C23×C3H(5,𝔽2)12yes—
504C23×C3H(5,𝔽2)12yes—
505C23×C3C2511yescharacteristic
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C22×D3—44no—
520C3×D4—416no—
521C3×D4—416no—
522C3×D4—416no—
523C2×C3×C4—28no—
524C2×C3×C4—28no—
525C2×C3×C4—28no—
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×C4C22×D414yes—
538C2×C3×C4C22×D414yes—
539C2×C3×C4C2×#4114yes—
540#67—416no—
541#67—416no—
542#67—416no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
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—22no—
564C2×Dic3—416no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3—44no—
569C2×Dic3—44no—
570C2×Dic3—44no—
571C2×Dic3—44no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—32no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24#23714yes—
600C24C2×#6714yes—
601C24C23×D312yes—
602C24C23×D312yes—
603C24C23×D312yes—
604C24C23×D311yescharacteristic
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—416no—
616C2×D4—416no—
617C2×D4—68no—
618C2×D4—68no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—124no—
625C2×D4—124no—
626C2×D4—1216no—
627C2×D4—1216no—
628C2×D4—1216no—
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—28no—
639C22×C4—28no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—44no—
648C22×C4—416no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
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×C4—62no—
670C22×C4—68no—
671C22×C4—124no—
672C22×C4—124no—
673C22×C4—1216no—
674C22×C4#23714yes—
675C22×C4C2×#6714yes—
676C22×C4C2×#6714yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—28no—
682C4⋊C4—68no—
683C4⋊C4—68no—
684C4⋊C4—124no—
685C22⋊C4—28no—
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—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4C2×#67116yescomplemented
699C42—124no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—416no—
712C22×C3—416no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—88no—
724C22×C3#53514yes—
725C22×C3#53814yes—
726C22×C3#54014yes—
727C22×C3#54614yes—
728C22×C3#54614yes—
729C22×C3#55314yes—
730C22×C3#56014yes—
731C22×C3C23×D411yescharacteristic
732C22×C3C22×#4111yescharacteristic
733C22×C3C22×#4111yescharacteristic
734C22×C3C2×H(5,𝔽2)11yescharacteristic
735C22×C3C2×H(5,𝔽2)11yescharacteristic
736C22×C3C2×H(5,𝔽2)11yescharacteristic
737C22×C3C2×H(5,𝔽2)11yescharacteristic
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—88no—
746C3×C4—24no—
747C3×C4—24no—
748C3×C4—24no—
749C3×C4—42no—
750Dic3—42no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—28no—
770C23—28no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—28no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23C2×#23714yes—
812C23C2×#23712yes—
813C23C2×#23712yes—
814C23#100412yes—
815C23#100412yes—
816C23#100912yes—
817C23#100912yes—
818C23C22×#6714yes—
819C23C22×#6712yes—
820C23C24×D311yescharacteristic
821D4—416no—
822D4—416no—
823D4—416no—
824D4—1216no—
825D4—1216no—
826D4—1216no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—416no—
840C2×C4—44no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—1216no—
863C2×C4—124no—
864C2×C4—124no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—124no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4C2×#23714yes—
871C2×C4C22×#6714yes—
872C2×C4C22×#6714yes—
873C2×C3—44no—
874C2×C3—44no—
875C2×C3—82no—
876C2×C3#270318yescomplemented
877C2×C3C2×#53511yescharacteristic
878C2×C3C2×#53811yescharacteristic
879C2×C3C2×#54011yescharacteristic
880C2×C3C2×#54611yescharacteristic
881C2×C3C2×#54611yescharacteristic
882C2×C3C2×#55311yescharacteristic
883C2×C3C2×#56011yescharacteristic
884D3—82no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—416no—
892C22—416no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—88no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—248no—
917C22#561714yes—
918C22#561814yes—
919C22#561914yes—
920C22#562014yes—
921C22#580614yes—
922C22#580614yes—
923C22#583014yes—
924C22C22×#23711yescharacteristic
925C22C22×#23711yescharacteristic
926C22C2×#100411yescharacteristic
927C22C2×#100411yescharacteristic
928C22C2×#100911yescharacteristic
929C22C2×#100911yescharacteristic
930C22C23×#6711yescharacteristic
931C4—24no—
932C4—24no—
933C4—24no—
934C4—42no—
935C4—122no—
936C4—122no—
937C4—122no—
938C4—122no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#270311yescharacteristic, complemented, Sylow
943C2—44no—
944C2—44no—
945C2—82no—
946C2—242no—
947C2#8269318yesdirect product factor
948C2C2×#561911yescharacteristic
949C2C2×#561811yescharacteristic
950C2C2×#561711yescharacteristic
951C2C2×#562011yescharacteristic
952C2C2×#580611yescharacteristic
953C2C2×#580611yescharacteristic
954C2C2×#583011yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#121C2
socleC24×C3C24
hypercenterC22×#121D3
hypocenterC3C2×#2703
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C22×#886C2semidirect
3. C2×#5223C2semidirect
4. C2×#5223C2semidirect
5. C2×#5223C2semidirect
6. C2×#5221C2semidirect
7. C2×#5220C2semidirect
8. C2×#5220C2semidirect
9. C2×#5213C2semidirect
10. C2×#5212C2semidirect
11. #82693C2direct (N × H)
12. C2×#4986C2semidirect
13. C2×#4990C2semidirect
14. C2×#4953C2semidirect
15. C2×#4961C2semidirect
16. C2×#4951C2semidirect
27. C2×C3×#121C22semidirect
48. C2×#886C22semidirect
49. #5223C22semidirect
50. #5223C22semidirect
51. #5223C22semidirect
52. #5221C22semidirect
53. #5220C22semidirect
54. #5220C22semidirect
55. #5213C22semidirect
56. #5212C22semidirect
65. #4990C22semidirect
66. #4986C22semidirect
67. #4961C22semidirect
68. #4953C22semidirect
69. #4951C22semidirect
71. C22×#121D3semidirect
137. C2×C3×C22⋊C4D4semidirect
192. C2×#121C2×D3semidirect
344. C3×C22⋊C4C2×D4semidirect
443. C2×C22⋊C4#67semidirect
698. C22⋊C4C2×#67semidirect
876. C2×C3#2703semidirect
942. C3C2×#2703semidirect
947. C2#82693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#8862
C2×#52232
C2×#52212
C2×#52202
C2×#52132
C2×#52122
#826932
C2×#49862
C2×#49902
C2×#49532
C2×#49612
C2×#49512
C2×#27033