Finite Group Databasebeta

← C2×#77151 #11430397

Subgroups — C2×#77151 #11430397

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×#940C211yesmaximal, characteristic
2C22×#883C211yesmaximal, characteristic, complemented
3C2×C3×#394C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#4991C211yesmaximal, characteristic, complemented
6C2×#4980C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4956C211yesmaximal, characteristic, complemented
9C2×#4961C211yesmaximal, characteristic, complemented
10C2×#4961C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic, complemented
12C2×#4958C211yesmaximal, characteristic, complemented
13C2×#4958C211yesmaximal, characteristic, complemented
14#77151C2116yesmaximal, direct product factor
15C2×#4665C211yesmaximal, characteristic, complemented
16C2×#4654C211yesmaximal, characteristic, complemented
17C2×#2709—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C24×Dic3C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C2×#940—28no—
35C2×#940C2218yes—
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×(C2×D3)⋊C4C2211yescharacteristic
43C22×C4⋊Dic3C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#883—28no—
48C2×#883C2218yescomplemented
49C3×#394C2218yescomplemented
50C2×C3×#95C2211yescharacteristic
51#5220C2218yescomplemented
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4991C2218yescomplemented
60#4980C2218yescomplemented
61#4961C2218yescomplemented
62#4961C2218yescomplemented
63#4961C2218yescomplemented
64#4959C2218yescomplemented
65#4958C2218yescomplemented
66#4958C2218yescomplemented
67#4956C2218yescomplemented
68#4665C2218yescomplemented
69#4654C2218yescomplemented
70C22×#127—31no—
71C22×#123—31no—
72#2709—316no—
73C2×#394—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#394—31no—
78C2×#394D311yescharacteristic, complemented
79C2×#387—31no—
80C2×#387—31no—
81C2×#386—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#386—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—42no—
93C22×C3×D4C2314yes—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C22×#67—24no—
100C22×#67—24no—
101C22×#67—24no—
102C22×#67—24no—
103C22×#67—24no—
104C22×#67—42no—
105C22×#67—42no—
106C22×#67—42no—
107C22×#67—42no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67D418yes—
111C22×#67C2314yes—
112C22×#67C2314yes—
113C22×#67C2314yes—
114C22×#67C2314yes—
115C23×Dic3—42no—
116C23×Dic3—42no—
117C23×Dic3—42no—
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2314yes—
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×C4⋊C4—24no—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—42no—
137C2×C3×C22⋊C4—42no—
138C2×C3×C22⋊C4—42no—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×#217—24no—
144C2×#217—42no—
145C2×#217—42no—
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2314yes—
149#940—232no—
150C2×(C2×D3)⋊C4—24no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4—42no—
154C2×(C2×D3)⋊C4—42no—
155C2×(C2×D3)⋊C4—42no—
156C2×(C2×D3)⋊C4—42no—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
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⋊Dic3C2314yes—
167C2×C4⋊Dic3C2314yes—
168C2×Dic3⋊C4—24no—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3—24no—
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×C4—31no—
189C2×#127—38no—
190C2×#127—68no—
191C2×#123—38no—
192C2×#123—68no—
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⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#394—38no—
213#394—38no—
214#394—38no—
215#394—38no—
216#394—38no—
217#394C2×D318yescomplemented
218#387—38no—
219#387—38no—
220#386—38no—
221#386—38no—
222#386—38no—
223#386—38no—
224#386—38no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
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×C3C2×D414yes—
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—28no—
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#4114yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—28no—
293C2×#67—28no—
294C2×#67—28no—
295C2×#67—416no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—416no—
303C2×#67—416no—
304C2×#67—416no—
305C2×#67C2×D4116yes—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
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—44no—
323C22×Dic3—44no—
324C22×Dic3—44no—
325C22×Dic3—416no—
326C22×Dic3C2×D414yes—
327C22×Dic3#4114yes—
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×C4⋊C4—28no—
343C3×C22⋊C4—28no—
344C3×C22⋊C4—44no—
345C3×C22⋊C4—44no—
346C3×C22⋊C4—44no—
347#217—28no—
348#217—44no—
349#217—44no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—28no—
358C4⋊Dic3—28no—
359Dic3⋊C4—28no—
360C4×Dic3—28no—
361C25—31no—
362C25—31no—
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—38no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—34no—
372C22×D4—34no—
373C22×D4—42no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—64no—
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—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—34no—
396C23×C4—34no—
397C23×C4—64no—
398C23×C4—122no—
399C23×C4—122no—
400C23×C4—122no—
401C23×C4—122no—
402C23×C4—122no—
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408#127—632no—
409#123—632no—
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—64no—
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—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
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⋊C4C22×D314yes—
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C42—34no—
447C2×C42—64no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
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×D414yes—
484C23×C3C22×D412yes—
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—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—22no—
536C2×C3×C4—44no—
537C2×C3×C4—44no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4C2×#4114yes—
541#67—416no—
542#67—416no—
543#67—416no—
544#67—416no—
545C2×Dic3—28no—
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—416no—
564C2×Dic3—44no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3C22×D414yes—
569C2×Dic3C2×#4114yes—
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—
601C24D3×D414yes—
602C24C23×D312yes—
603C24C23×D312yes—
604C24C23×D311yescharacteristic
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—316no—
608C2×D4—44no—
609C2×D4—416no—
610C2×D4—68no—
611C2×D4—68no—
612C2×D4—68no—
613C2×D4—68no—
614C2×D4—68no—
615C2×D4—68no—
616C2×D4—68no—
617C2×D4—124no—
618C2×D4—1216no—
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—22no—
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—68no—
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—124no—
669C22×C4—124no—
670C22×C4—1216no—
671C22×C4—124no—
672C22×C4—124no—
673C22×C4—124no—
674C22×C4—1216no—
675C22×C4#23714yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—28no—
682C4⋊C4—68no—
683C4⋊C4—68no—
684C4⋊C4—68no—
685C22⋊C4—28no—
686C22⋊C4—44no—
687C22⋊C4—44no—
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—68no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—416no—
706C22×C3—42no—
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#53414yes—
717C22×C3#54014yes—
718C22×C3#54014yes—
719C22×C3#54614yes—
720C22×C3#54614yes—
721C22×C3#55914yes—
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—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751Dic3—24no—
752Dic3—24no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—28no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
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—68no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
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×D3×D414yes—
813C23C2×D3×D412yes—
814C23C2×#23712yes—
815C23#100412yes—
816C23#100412yes—
817C23D3×#4112yes—
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—28no—
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—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—34no—
843C2×C4—34no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—68no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—68no—
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—62no—
866C2×C4—1216no—
867C2×C4—1216no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4—124no—
872C2×C4C2×#23714yes—
873C2×C3—44no—
874C2×C3—82no—
875C2×C3#270918yescomplemented
876C2×C3C2×#53411yescharacteristic
877C2×C3C2×#54011yescharacteristic
878C2×C3C2×#54011yescharacteristic
879C2×C3C2×#54611yescharacteristic
880C2×C3C2×#54611yescharacteristic
881C2×C3C2×#55911yescharacteristic
882C2×C3C2×#56011yescharacteristic
883D3—44no—
884D3—82no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—42no—
889C22—416no—
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—122no—
905C22—1216no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—248no—
917C22#559114yes—
918C22#560514yes—
919C22#561514yes—
920C22#561914yes—
921C22#565414yes—
922C22#566614yes—
923C22#568114yes—
924C22C22×D3×D411yescharacteristic
925C22C22×#23711yescharacteristic
926C22C2×#100411yescharacteristic
927C22C2×#100411yescharacteristic
928C22C2×D3×#4111yescharacteristic
929C22C2×#100911yescharacteristic
930C22C2×#100911yescharacteristic
931C4—24no—
932C4—42no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—64no—
937C4—64no—
938C4—122no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#270911yescharacteristic, complemented, Sylow
943C2—44no—
944C2—82no—
945C2—124no—
946C2—242no—
947C2#7715118yesdirect product factor
948C2C2×#559111yescharacteristic
949C2C2×#561911yescharacteristic
950C2C2×#561511yescharacteristic
951C2C2×#560511yescharacteristic
952C2C2×#565411yescharacteristic
953C2C2×#566611yescharacteristic
954C2C2×#568111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#394C2
socleC24×C3C24
prime radicalC22×#940C2
hypercenterC2×#394D3
hypocenterC3C2×#2709
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#883C2semidirect
3. C2×C3×#394C2semidirect
4. C2×#5220C2semidirect
5. C2×#4991C2semidirect
6. C2×#4980C2semidirect
7. C2×#4959C2semidirect
8. C2×#4956C2semidirect
9. C2×#4961C2semidirect
10. C2×#4961C2semidirect
11. C2×#4961C2semidirect
12. C2×#4958C2semidirect
13. C2×#4958C2semidirect
14. #77151C2direct (N × H)
15. C2×#4665C2semidirect
16. C2×#4654C2semidirect
48. C2×#883C22semidirect
49. C3×#394C22semidirect
51. #5220C22semidirect
59. #4991C22semidirect
60. #4980C22semidirect
61. #4961C22semidirect
62. #4961C22semidirect
63. #4961C22semidirect
64. #4959C22semidirect
65. #4958C22semidirect
66. #4958C22semidirect
67. #4956C22semidirect
68. #4665C22semidirect
69. #4654C22semidirect
78. C2×#394D3semidirect
217. #394C2×D3semidirect
875. C2×C3#2709semidirect
942. C3C2×#2709semidirect
947. C2#77151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9402
C22×#8832
C2×C3×#3942
C2×#52202
C2×#49912
C2×#49802
C2×#49592
C2×#49562
C2×#49612
C2×#49582
#771512
C2×#46652
C2×#46542
C2×#27093