Finite Group Databasebeta

← C2×#74530 #11430473

Subgroups — C2×#74530 #11430473

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×#898C211yesmaximal, characteristic, complemented
3C2×C3×#385C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C2×#4991C211yesmaximal, characteristic, complemented
6C2×#4988C211yesmaximal, characteristic, complemented
7C2×#4990C211yesmaximal, characteristic, complemented
8C2×#4960C211yesmaximal, characteristic, complemented
9C2×#4960C211yesmaximal, characteristic, complemented
10C2×#4957C211yesmaximal, characteristic, complemented
11C2×#4957C211yesmaximal, characteristic, complemented
12#74530C2116yesmaximal, direct product factor
13C2×#4675C211yesmaximal, characteristic, complemented
14C2×#4671C211yesmaximal, characteristic, complemented
15C2×#4672C211yesmaximal, characteristic, complemented
16C2×#4654C211yesmaximal, characteristic, complemented
17C2×#2714—31nomaximal, Sylow
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C2×#930—28no—
31C2×#930C2218yescomplemented
32C22×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×C4×Dic3C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#898—28no—
50C2×#898C2218yescomplemented
51C3×#385C2218yescomplemented
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54#5213C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4991C2218yescomplemented
60#4990C2218yescomplemented
61#4988C2218yescomplemented
62#4960C2218yescomplemented
63#4960C2218yescomplemented
64#4957C2218yescomplemented
65#4957C2218yescomplemented
66#4675C2218yescomplemented
67#4672C2218yescomplemented
68#4671C2218yescomplemented
69#4654C2218yescomplemented
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×#386—31no—
85C2×#385D311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C23×C3×C4—24no—
91C23×C3×C4—42no—
92C23×C3×C4—42no—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2314yes—
100C22×#67—24no—
101C22×#67—24no—
102C22×#67—24no—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—42no—
106C22×#67—42no—
107C22×#67—42no—
108C22×#67—42no—
109C22×#67C2314yes—
110C22×#67C2314yes—
111C22×#67C2314yes—
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C22×D12—24no—
118C22×D12—24no—
119C22×D12—42no—
120C22×D12—42no—
121C22×D12—42no—
122C22×D12—42no—
123C22×D12—42no—
124C22×D12—42no—
125C22×D12—42no—
126C22×D12C2314yes—
127C22×D12C2314yes—
128C22×D12C2314yes—
129C2×C3×C4⋊C4—24no—
130C2×C3×C4⋊C4—42no—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C22⋊C4—24no—
134C2×C3×C22⋊C4—42no—
135C2×C3×C22⋊C4C2314yes—
136C2×C3×C22⋊C4C2314yes—
137C2×#217—42no—
138C2×#217C2314yes—
139#930—232no—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4—24no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—42no—
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×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×C4⋊Dic3D418yescomplemented
165C2×C4⋊Dic3C2314yes—
166C2×Dic3⋊C4—24no—
167C2×Dic3⋊C4—42no—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3—24no—
171C2×C4×Dic3—42no—
172C2×C4×Dic3C2314yes—
173C2×C4×Dic3C2314yes—
174#898—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×D4—31no—
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⋊C4C2×D311yescharacteristic
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⋊C4—31no—
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#386—38no—
226#385C2×D318yescomplemented
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#4114yes—
240C24×C3C2412yes—
241C24×C3C2411yescharacteristic
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×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×D3C2412yes—
264C23×D3C2412yes—
265C23×D3C2412yes—
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×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—28no—
283C22×C3×C4—44no—
284C22×C3×C4—44no—
285C22×C3×C4—416no—
286C22×C3×C4C2×D414yes—
287C22×C3×C4#4114yes—
288C22×C3×C4C2412yes—
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—416no—
304C2×#67—416no—
305C2×#67—416no—
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×Dic3C2×D414yes—
320C22×Dic3C2×D414yes—
321C22×Dic3C2412yes—
322C22×Dic3C2412yes—
323C22×Dic3C2412yes—
324C22×Dic3C2412yes—
325C22×Dic3C2412yes—
326C2×D12—28no—
327C2×D12—28no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×D12—44no—
332C2×D12—44no—
333C2×D12—44no—
334C2×D12—44no—
335C2×D12—416no—
336C2×D12—416no—
337C2×D12—416no—
338C3×C4⋊C4—28no—
339C3×C4⋊C4—44no—
340C3×C22⋊C4—28no—
341C3×C22⋊C4—44no—
342#217—44no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
349(C2×D3)⋊C4—44no—
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—
355C4⋊Dic3C2×D4116yescomplemented
356Dic3⋊C4—28no—
357Dic3⋊C4—44no—
358C4×Dic3—28no—
359C4×Dic3—44no—
360C25—31no—
361C25—31no—
362C25—31no—
363C25C22×D311yescharacteristic
364C22×D4—34no—
365C22×D4—34no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—64no—
371C22×D4—64no—
372C22×D4—64no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—122no—
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×D4—122no—
388C23×C4—24no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4C22×D311yescharacteristic
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—24no—
406C2×C4⋊C4—38no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—64no—
412C2×C4⋊C4—122no—
413C2×C4⋊C4C22×D314yes—
414C2×C4⋊C4C22×D314yes—
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—34no—
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⋊C4—122no—
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—44no—
465C23×C3—44no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3C22×D412yes—
469C23×C3C2×#4112yes—
470C23×C3C2×#4114yes—
471C23×C3C2×#4112yes—
472C23×C3H(5,𝔽2)12yes—
473C23×C3H(5,𝔽2)12yes—
474C23×C3H(5,𝔽2)12yes—
475C23×C3H(5,𝔽2)12yes—
476C23×C3C2511yescharacteristic
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—44no—
499C22×D3—44no—
500C22×D3—44no—
501C22×D3—44no—
502C22×D3—44no—
503C22×D3—44no—
504C22×D3—44no—
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—
519C2×C3×C4—28no—
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—22no—
536C2×C3×C4—22no—
537C2×C3×C4—416no—
538C2×C3×C4—44no—
539C2×C3×C4—44no—
540C2×C3×C4—44no—
541C2×C3×C4—44no—
542C2×C3×C4C22×D414yes—
543C2×C3×C4C2×#4114yes—
544#67—416no—
545#67—416no—
546#67—416no—
547C2×Dic3—28no—
548C2×Dic3—28no—
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—44no—
563C2×Dic3—44no—
564C2×Dic3—44no—
565C2×Dic3C22×D414yes—
566C2×Dic3C22×D414yes—
567D12—416no—
568D12—416no—
569D12—416no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—32no—
577C24—32no—
578C24—32no—
579C24—62no—
580C24—62no—
581C24—62no—
582C24—62no—
583C24—62no—
584C24—62no—
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—62no—
600C24#23914yes—
601C24C23×D312yes—
602C24C23×D311yescharacteristic
603C2×D4—68no—
604C2×D4—68no—
605C2×D4—68no—
606C2×D4—68no—
607C2×D4—68no—
608C2×D4—68no—
609C2×D4—68no—
610C2×D4—124no—
611C2×D4—124no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—124no—
616C2×D4—124no—
617C2×D4—1216no—
618C2×D4—1216no—
619C2×D4—1216no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
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—22no—
642C22×C4—22no—
643C22×C4—28no—
644C22×C4—34no—
645C22×C4—34no—
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#23514yes—
668C22×C4D3×D414yes—
669C22×C4C23×D312yes—
670C22×C4C23×D312yes—
671C22×C4C23×D312yes—
672C22×C4C23×D312yes—
673C22×C4C23×D312yes—
674C22×C4C23×D312yes—
675C4⋊C4—28no—
676C4⋊C4—316no—
677C4⋊C4—44no—
678C4⋊C4—68no—
679C4⋊C4—124no—
680C22⋊C4—28no—
681C22⋊C4—44no—
682C22⋊C4—68no—
683C22⋊C4—68no—
684C22⋊C4—68no—
685C22⋊C4—68no—
686C22⋊C4—68no—
687C22⋊C4—68no—
688C22⋊C4—124no—
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#53514yes—
706C22×C3#53814yes—
707C22×C3#53814yes—
708C22×C3#54614yes—
709C22×C3#55014yes—
710C22×C3#55314yes—
711C22×C3#56014yes—
712C22×C3C23×D411yescharacteristic
713C22×C3C22×#4111yescharacteristic
714C22×C3C22×#4111yescharacteristic
715C22×C3C2×H(5,𝔽2)11yescharacteristic
716C22×C3C2×H(5,𝔽2)11yescharacteristic
717C22×C3C2×H(5,𝔽2)11yescharacteristic
718C22×C3C2×H(5,𝔽2)11yescharacteristic
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
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—88no—
741C2×D3—88no—
742C2×D3—88no—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—42no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—42no—
749Dic3—24no—
750Dic3—24no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754C23—28no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—28no—
762C23—28no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—124no—
789C23—124no—
790C23—124no—
791C23—124no—
792C23—124no—
793C23—124no—
794C23—124no—
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×#23512yes—
810C23C2×D3×D412yes—
811C23#100412yes—
812C23#100412yes—
813C23C2×#23914yes—
814C23C2×#23912yes—
815C23#100912yes—
816C23#100912yes—
817C23C24×D311yescharacteristic
818D4—1216no—
819D4—1216no—
820D4—1216no—
821D4—1216no—
822D4—1216no—
823D4—1216no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—28no—
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—416no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—68no—
854C2×C4—68no—
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—124no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4C2×#23514yes—
868C2×C4C2×D3×D414yes—
869C2×C3—44no—
870C2×C3#271418yescomplemented
871C2×C3C2×#53511yescharacteristic
872C2×C3C2×#53811yescharacteristic
873C2×C3C2×#53811yescharacteristic
874C2×C3C2×#54611yescharacteristic
875C2×C3C2×#55011yescharacteristic
876C2×C3C2×#55311yescharacteristic
877C2×C3C2×#56011yescharacteristic
878D3—82no—
879D3—82no—
880D3—82no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—42no—
885C22—416no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—122no—
890C22—122no—
891C22—122no—
892C22—122no—
893C22—122no—
894C22—122no—
895C22—122no—
896C22—122no—
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—248no—
911C22—248no—
912C22—248no—
913C22#551414yes—
914C22#555314yes—
915C22#556014yes—
916C22#559214yes—
917C22#563014yes—
918C22#564414yes—
919C22#566614yes—
920C22C22×#23511yescharacteristic
921C22C22×D3×D411yescharacteristic
922C22C2×#100411yescharacteristic
923C22C2×#100411yescharacteristic
924C22C22×#23911yescharacteristic
925C22C2×#100911yescharacteristic
926C22C2×#100911yescharacteristic
927C4—24no—
928C4—24no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—64no—
934C4—64no—
935C4—122no—
936C4—122no—
937C4—122no—
938C3C2×#271411yescharacteristic, complemented, Sylow
939C2—44no—
940C2—242no—
941C2—242no—
942C2—242no—
943C2#7453018yesdirect product factor
944C2C2×#551411yescharacteristic
945C2C2×#555311yescharacteristic
946C2C2×#556011yescharacteristic
947C2C2×#559211yescharacteristic
948C2C2×#564411yescharacteristic
949C2C2×#563011yescharacteristic
950C2C2×#566611yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#385C2
socleC24×C3C24
hypercenterC2×#385D3
hypocenterC3C2×#2714
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#930C2semidirect
2. C22×#898C2semidirect
3. C2×C3×#385C2semidirect
4. C2×#5213C2semidirect
5. C2×#4991C2semidirect
6. C2×#4988C2semidirect
7. C2×#4990C2semidirect
8. C2×#4960C2semidirect
9. C2×#4960C2semidirect
10. C2×#4957C2semidirect
11. C2×#4957C2semidirect
12. #74530C2direct (N × H)
13. C2×#4675C2semidirect
14. C2×#4671C2semidirect
15. C2×#4672C2semidirect
16. C2×#4654C2semidirect
31. C2×#930C22semidirect
50. C2×#898C22semidirect
51. C3×#385C22semidirect
54. #5213C22semidirect
59. #4991C22semidirect
60. #4990C22semidirect
61. #4988C22semidirect
62. #4960C22semidirect
63. #4960C22semidirect
64. #4957C22semidirect
65. #4957C22semidirect
66. #4675C22semidirect
67. #4672C22semidirect
68. #4671C22semidirect
69. #4654C22semidirect
85. C2×#385D3semidirect
164. C2×C4⋊Dic3D4semidirect
226. #385C2×D3semidirect
355. C4⋊Dic3C2×D4semidirect
870. C2×C3#2714semidirect
938. C3C2×#2714semidirect
943. C2#74530direct (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×#8982
C2×C3×#3852
C2×#52132
C2×#49912
C2×#49882
C2×#49902
C2×#49602
C2×#49572
#745302
C2×#46752
C2×#46712
C2×#46722
C2×#46542
C2×#27143