Finite Group Databasebeta

← C2×#74813 #11430281

Subgroups — C2×#74813 #11430281

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×#930C211yesmaximal, characteristic, complemented
2C22×#883C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5212C211yesmaximal, characteristic, complemented
7C2×#4960C211yesmaximal, characteristic, complemented
8C2×#4956C211yesmaximal, characteristic, complemented
9C2×#4961C211yesmaximal, characteristic, complemented
10C2×#4957C211yesmaximal, characteristic, complemented
11C2×#4951C211yesmaximal, characteristic, complemented
12#74813C2116yesmaximal, direct product factor
13C2×#4665C211yesmaximal, characteristic, complemented
14C2×#4660C211yesmaximal, characteristic, complemented
15C2×#4674C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2703—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C2×#930—28no—
34C2×#930C2218yescomplemented
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×C4⋊Dic3C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#883—28no—
48C2×#883C2218yescomplemented
49C3×#386C2218yescomplemented
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52#5223C2218yescomplemented
53#5223C2218yescomplemented
54#5212C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4961C2218yescomplemented
62#4960C2218yescomplemented
63#4957C2218yescomplemented
64#4956C2218yescomplemented
65#4951C2218yescomplemented
66#4674C2218yescomplemented
67#4670C2218yescomplemented
68#4665C2218yescomplemented
69#4660C2218yescomplemented
70C22×#123—31no—
71C22×#121—31no—
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×#386D311yescharacteristic, complemented
85C2×#380—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—24no—
96C23×C3×C4—42no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2314yes—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
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—24no—
127C22×D12—42no—
128C22×D12C2314yes—
129C22×C4×D3—24no—
130C22×C4×D3—42no—
131C22×C4×D3—42no—
132C22×C4×D3C2314yes—
133C2×C3×C22⋊C4—24no—
134C2×C3×C22⋊C4—24no—
135C2×C3×C22⋊C4—42no—
136C2×C3×C22⋊C4C2314yes—
137C2×C3×C22⋊C4C2314yes—
138C2×C3×C22⋊C4C2314yes—
139C2×#217—24no—
140C2×#217—42no—
141C2×#217—42no—
142C2×#217—42no—
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147#930—232no—
148C2×(C2×D3)⋊C4—24no—
149C2×(C2×D3)⋊C4—42no—
150C2×(C2×D3)⋊C4—42no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4—42no—
154C2×(C2×D3)⋊C4D418yescomplemented
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×C4⋊Dic3—24no—
163C2×C4⋊Dic3—24no—
164C2×C4⋊Dic3—42no—
165C2×C4⋊Dic3C2314yes—
166C2×C4⋊Dic3C2314yes—
167C2×C4⋊Dic3C2314yes—
168C2×Dic3⋊C4—24no—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3—42no—
171C2×C4×Dic3C2314yes—
172#883—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×D4—31no—
185C23×D4—31no—
186C23×D4C2×D311yescharacteristic
187C24×C4—31no—
188C24×C4C2×D311yescharacteristic
189C2×#123—38no—
190C2×#123—68no—
191C2×#121—38no—
192C2×#121—68no—
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⋊C4C2×D311yescharacteristic
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#386C2×D318yescomplemented
224#380—38no—
225C2×#95—31no—
226C2×#95—31no—
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×D3C2×D414yes—
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—28no—
284C22×C3×C4—28no—
285C22×C3×C4—44no—
286C22×C3×C4—416no—
287C22×C3×C4C2×D414yes—
288C22×C3×C4#4114yes—
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×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3C2×D414yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C2×D12—28no—
335C2×D12—28no—
336C2×D12—44no—
337C2×D12—416no—
338C2×C4×D3—28no—
339C2×C4×D3—44no—
340C2×C4×D3—44no—
341C2×C4×D3—416no—
342C3×C22⋊C4—28no—
343C3×C22⋊C4—28no—
344C3×C22⋊C4—44no—
345#217—28no—
346#217—44no—
347#217—44no—
348#217—44no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4C2×D4116yescomplemented
356C4⋊Dic3—28no—
357C4⋊Dic3—28no—
358C4⋊Dic3—44no—
359Dic3⋊C4—28no—
360C4×Dic3—44no—
361C25—31no—
362C25—31no—
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—24no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C22×D4—122no—
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—34no—
398C23×C4—42no—
399C23×C4—64no—
400C23×C4—122no—
401C23×C4—122no—
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D314yes—
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408#123—632no—
409#121—632no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—64no—
416C2×C4⋊C4—64no—
417C2×C4⋊C4—122no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—38no—
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—34no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
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⋊C4C22×D314yes—
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#95C22×D314yes—
455#95C22×D314yes—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
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—22no—
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×C3—44no—
483C23×C3C22×D412yes—
484C23×C3C2×#4114yes—
485C23×C3C2×#4112yes—
486C23×C3C2×#4112yes—
487C23×C3H(5,𝔽2)12yes—
488C23×C3H(5,𝔽2)12yes—
489C23×C3H(5,𝔽2)12yes—
490C23×C3H(5,𝔽2)12yes—
491C23×C3C2511yescharacteristic
492C22×D3—28no—
493C22×D3—28no—
494C22×D3—28no—
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—22no—
506C22×D3—22no—
507C22×D3—22no—
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—
519C22×D3C22×D414yes—
520C3×D4—416no—
521C2×C3×C4—28no—
522C2×C3×C4—28no—
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—22no—
536C2×C3×C4—416no—
537C2×C3×C4—44no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4C22×D414yes—
541C2×C3×C4C2×#4114yes—
542#67—416no—
543#67—416no—
544#67—416no—
545#67—416no—
546C2×Dic3—28no—
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—44no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3—44no—
569C2×Dic3C22×D414yes—
570D12—416no—
571C4×D3—416no—
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—34no—
586C24—32no—
587C24—32no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—62no—
601C24#23514yes—
602C24C23×D312yes—
603C24C23×D312yes—
604C24C23×D311yescharacteristic
605C2×D4—28no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—416no—
609C2×D4—68no—
610C2×D4—68no—
611C2×D4—68no—
612C2×D4—68no—
613C2×D4—68no—
614C2×D4—68no—
615C2×D4—68no—
616C2×D4—124no—
617C2×D4—1216no—
618C2×D4—124no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—124no—
625C2×D4—1216no—
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—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—28no—
643C22×C4—28no—
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—416no—
653C22×C4—68no—
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—62no—
671C22×C4—124no—
672C22×C4—124no—
673C22×C4—1216no—
674C22×C4D3×D414yes—
675C22×C4#23714yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—68no—
682C4⋊C4—68no—
683C4⋊C4—68no—
684C4⋊C4—124no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—316no—
688C22⋊C4—44no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C42—124no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—416no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—88no—
716C22×C3#53514yes—
717C22×C3#53814yes—
718C22×C3#54014yes—
719C22×C3#54614yes—
720C22×C3#54614yes—
721C22×C3#55314yes—
722C22×C3#56014yes—
723C22×C3C23×D411yescharacteristic
724C22×C3C22×#4111yescharacteristic
725C22×C3C22×#4111yescharacteristic
726C22×C3C2×H(5,𝔽2)11yescharacteristic
727C22×C3C2×H(5,𝔽2)11yescharacteristic
728C22×C3C2×H(5,𝔽2)11yescharacteristic
729C22×C3C2×H(5,𝔽2)11yescharacteristic
730C2×D3—24no—
731C2×D3—24no—
732C2×D3—24no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—416no—
736C2×D3—42no—
737C2×D3—42no—
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—42no—
749C3×C4—42no—
750C3×C4—42no—
751Dic3—24no—
752Dic3—42no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—28no—
764C23—28no—
765C23—28no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—34no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—68no—
792C23—68no—
793C23—68no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—124no—
802C23—124no—
803C23—124no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23—124no—
812C23C2×#23514yes—
813C23C2×#23512yes—
814C23C2×D3×D412yes—
815C23C2×#23712yes—
816C23#100412yes—
817C23#100412yes—
818C23#100912yes—
819C23#100912yes—
820C23C24×D311yescharacteristic
821D4—416no—
822D4—1216no—
823D4—1216no—
824D4—1216no—
825D4—1216no—
826D4—1216no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—34no—
843C2×C4—416no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—68no—
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—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—1216no—
866C2×C4—124no—
867C2×C4—124no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4C2×D3×D414yes—
872C2×C4C2×#23714yes—
873C2×C3—44no—
874C2×C3—82no—
875C2×C3#270318yescomplemented
876C2×C3C2×#53511yescharacteristic
877C2×C3C2×#53811yescharacteristic
878C2×C3C2×#54011yescharacteristic
879C2×C3C2×#54611yescharacteristic
880C2×C3C2×#54611yescharacteristic
881C2×C3C2×#55311yescharacteristic
882C2×C3C2×#56011yescharacteristic
883D3—44no—
884D3—82no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—416no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—64no—
901C22—64no—
902C22—64no—
903C22—88no—
904C22—1216no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—248no—
917C22#549414yes—
918C22#555014yes—
919C22#556514yes—
920C22#559114yes—
921C22#560714yes—
922C22#561914yes—
923C22#566614yes—
924C22C22×#23511yescharacteristic
925C22C22×D3×D411yescharacteristic
926C22C22×#23711yescharacteristic
927C22C2×#100411yescharacteristic
928C22C2×#100411yescharacteristic
929C22C2×#100911yescharacteristic
930C22C2×#100911yescharacteristic
931C4—24no—
932C4—24no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—64no—
937C4—122no—
938C4—122no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#270311yescharacteristic, complemented, Sylow
943C2—44no—
944C2—82no—
945C2—124no—
946C2—242no—
947C2#7481318yesdirect product factor
948C2C2×#549411yescharacteristic
949C2C2×#556511yescharacteristic
950C2C2×#555011yescharacteristic
951C2C2×#559111yescharacteristic
952C2C2×#561911yescharacteristic
953C2C2×#560711yescharacteristic
954C2C2×#566611yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
hypercenterC2×#386D3
hypocenterC3C2×#2703
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×#883C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5223C2semidirect
5. C2×#5223C2semidirect
6. C2×#5212C2semidirect
7. C2×#4960C2semidirect
8. C2×#4956C2semidirect
9. C2×#4961C2semidirect
10. C2×#4957C2semidirect
11. C2×#4951C2semidirect
12. #74813C2direct (N × H)
13. C2×#4665C2semidirect
14. C2×#4660C2semidirect
15. C2×#4674C2semidirect
16. C2×#4670C2semidirect
34. C2×#930C22semidirect
48. C2×#883C22semidirect
49. C3×#386C22semidirect
52. #5223C22semidirect
53. #5223C22semidirect
54. #5212C22semidirect
61. #4961C22semidirect
62. #4960C22semidirect
63. #4957C22semidirect
64. #4956C22semidirect
65. #4951C22semidirect
66. #4674C22semidirect
67. #4670C22semidirect
68. #4665C22semidirect
69. #4660C22semidirect
84. C2×#386D3semidirect
154. C2×(C2×D3)⋊C4D4semidirect
223. #386C2×D3semidirect
355. (C2×D3)⋊C4C2×D4semidirect
875. C2×C3#2703semidirect
942. C3C2×#2703semidirect
947. C2#74813direct (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×#8832
C2×C3×#3862
C2×#52232
C2×#52122
C2×#49602
C2×#49562
C2×#49612
C2×#49572
C2×#49512
#748132
C2×#46652
C2×#46602
C2×#46742
C2×#46702
C2×#27033