Finite Group Databasebeta

← C2×#76651 #11430409

Subgroups — C2×#76651 #11430409

Order 768.

3110 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#947C211yesmaximal, characteristic, complemented
2C22×#894C211yesmaximal, characteristic, complemented
3C2×C3×#391C211yesmaximal, characteristic, complemented
4C2×#5231C211yesmaximal, characteristic, complemented
5C2×#4993C211yesmaximal, characteristic, complemented
6C2×#4939C211yesmaximal, characteristic, complemented
7C2×#4940C211yesmaximal, characteristic, complemented
8#76651C2116yesmaximal, direct product factor
9C2×#4675C211yesmaximal, characteristic, complemented
10C2×#4671C211yesmaximal, characteristic
11C2×#4665C211yesmaximal, characteristic, complemented
12C2×#4668C211yesmaximal, characteristic, complemented
13C2×#4672C211yesmaximal, characteristic, complemented
14C2×#4672C211yesmaximal, characteristic, complemented
15C2×#4647C211yesmaximal, characteristic, complemented
16C2×#4669C211yesmaximal, characteristic, complemented
17C2×#2710—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C2×#947—28no—
26C2×#947C2218yescomplemented
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#894—28no—
48C2×#894C2218yescomplemented
49C3×#391C2218yescomplemented
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54#5231C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4993C2218yescomplemented
60#4940C2218yescomplemented
61#4939C2218yescomplemented
62#4675C2218yescomplemented
63#4672C2218yescomplemented
64#4672C2218yescomplemented
65#4671C2218yes—
66#4669C2218yescomplemented
67#4668C2218yescomplemented
68#4665C2218yescomplemented
69#4647C2218yescomplemented
70C22×#124—31no—
71C22×#123—31no—
72#2710—316no—
73C2×#399—31no—
74C2×#397—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#393—31no—
78C2×#392—31no—
79C2×#391D311yescharacteristic, complemented
80C2×#390—31no—
81C2×#389—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#386—31no—
85C2×#385—31no—
86C24×D3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C22×C3×Q8—24no—
90C22×C3×Q8—24no—
91C22×C3×Q8—42no—
92C22×C3×Q8C2314yes—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C22×D12—24no—
106C22×D12—24no—
107C22×D12—24no—
108C22×D12—24no—
109C22×D12—42no—
110C22×D12—42no—
111C22×D12—42no—
112C22×D12—42no—
113C22×D12—42no—
114C22×D12C2314yes—
115C22×D12C2314yes—
116C22×D12C2314yes—
117C22×C4×D3—24no—
118C22×C4×D3—42no—
119C22×C4×D3—42no—
120C22×C4×D3C2314yes—
121C2×C3×C4⋊C4—24no—
122C2×C3×C4⋊C4C2314yes—
123C2×C3×C42—42no—
124C2×C3×C42C2314yes—
125#947—232no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—24no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4—24no—
132C2×(C2×D3)⋊C4—24no—
133C2×(C2×D3)⋊C4—42no—
134C2×(C2×D3)⋊C4—42no—
135C2×(C2×D3)⋊C4—42no—
136C2×(C2×D3)⋊C4—42no—
137C2×(C2×D3)⋊C4—42no—
138C2×(C2×D3)⋊C4—42no—
139C2×(C2×D3)⋊C4D418yescomplemented
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×C4⋊Dic3—42no—
155C2×C4⋊Dic3C2314yes—
156C2×Dic3⋊C4—24no—
157C2×Dic3⋊C4—24no—
158C2×Dic3⋊C4—42no—
159C2×Dic3⋊C4—42no—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×C4×Dic3—24no—
165C2×C4×Dic3C2314yes—
166#894—232no—
167C3×#95C2314yes—
168C3×#95C2314yes—
169C3×#95C2314yes—
170C3×#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C23×Q8C2×D311yescharacteristic
176C23×D4—31no—
177C23×D4—31no—
178C23×D4—31no—
179C24×C4—31no—
180C2×#124—38no—
181C2×#124—68no—
182C2×#123—38no—
183C2×#123—68no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4C2×D311yescharacteristic
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊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×C42—31no—
205C22×C42C2×D311yescharacteristic
206#399—38no—
207#397—38no—
208#394—38no—
209#394—38no—
210#393—38no—
211#392—38no—
212#391C2×D318yescomplemented
213#390—38no—
214#389—38no—
215#388—38no—
216#388—38no—
217#386—38no—
218#385—38no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95C2×D311yescharacteristic
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C24×C3C2411yescharacteristic
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3—22no—
241C23×D3—22no—
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3C2×D414yes—
249C23×D3C2412yes—
250C23×D3C2412yes—
251C23×D3C2412yes—
252C2×C3×Q8—28no—
253C2×C3×Q8—28no—
254C2×C3×Q8—44no—
255C2×C3×Q8—416no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
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×C4C2×D414yes—
275C22×C3×C4#4114yes—
276C22×C3×C4#4114yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3C2×D414yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C2×D12—28no—
305C2×D12—28no—
306C2×D12—28no—
307C2×D12—28no—
308C2×D12—44no—
309C2×D12—44no—
310C2×D12—44no—
311C2×D12—44no—
312C2×D12—44no—
313C2×D12—416no—
314C2×D12—416no—
315C2×D12—416no—
316C2×C4×D3—28no—
317C2×C4×D3—44no—
318C2×C4×D3—44no—
319C2×C4×D3—416no—
320C3×C4⋊C4—28no—
321C3×C42—44no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—28no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—28no—
327(C2×D3)⋊C4—28no—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4C2×D4116yescomplemented
336C4⋊Dic3—44no—
337Dic3⋊C4—28no—
338Dic3⋊C4—28no—
339Dic3⋊C4—44no—
340Dic3⋊C4—44no—
341C4×Dic3—28no—
342C25—31no—
343C25—31no—
344C25—31no—
345C22×Q8—24no—
346C22×Q8—24no—
347C22×Q8—42no—
348C22×Q8C22×D314yes—
349C22×D4—34no—
350C22×D4—34no—
351C22×D4—34no—
352C22×D4—64no—
353C22×D4—64no—
354C22×D4—64no—
355C22×D4—64no—
356C22×D4—122no—
357C22×D4—122no—
358C22×D4—122no—
359C22×D4—122no—
360C22×D4—122no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—34no—
367C23×C4—64no—
368C23×C4—122no—
369C23×C4—122no—
370C23×C4C22×D311yescharacteristic
371C23×C4C22×D311yescharacteristic
372C23×C4C22×D311yescharacteristic
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377#124—632no—
378#123—632no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—64no—
386C2×C4⋊C4—64no—
387C2×C4⋊C4—122no—
388C2×C4⋊C4—122no—
389C2×C4⋊C4—122no—
390C2×C4⋊C4C22×D314yes—
391C2×C22⋊C4—38no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—64no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4—122no—
414C2×C22⋊C4—122no—
415C2×C22⋊C4—122no—
416C2×C22⋊C4—122no—
417C2×C22⋊C4—122no—
418C2×C22⋊C4—122no—
419C2×C42—34no—
420C2×C42—42no—
421C2×C42—64no—
422C2×C42C22×D314yes—
423#95—34no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95C22×D314yes—
428#95C22×D314yes—
429#95C22×D314yes—
430#95C22×D314yes—
431C23×C3C22×D412yes—
432C23×C3C2×#4112yes—
433C23×C3C2×#4112yes—
434C23×C3H(5,𝔽2)12yes—
435C23×C3H(5,𝔽2)12yes—
436C23×C3H(5,𝔽2)12yes—
437C23×C32−1+412yes—
438C23×C3C2511yescharacteristic
439C22×D3—28no—
440C22×D3—28no—
441C22×D3—28no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—44no—
463C22×D3—44no—
464C22×D3—44no—
465C22×D3—44no—
466C22×D3—44no—
467C22×D3—44no—
468C22×D3—44no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3—44no—
472C22×D3—44no—
473C22×D3—44no—
474C22×D3—44no—
475C22×D3—44no—
476C22×D3—44no—
477C22×D3—44no—
478C22×D3—44no—
479C22×D3—44no—
480C22×D3C22×D414yes—
481C3×Q8—416no—
482C2×C3×C4—28no—
483C2×C3×C4—28no—
484C2×C3×C4—28no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—44no—
504C2×C3×C4—44no—
505C2×C3×C4—44no—
506C2×C3×C4—44no—
507C2×C3×C4C22×D414yes—
508C2×C3×C4C2×#4114yes—
509C2×C3×C4C2×#4114yes—
510C2×Dic3—28no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—44no—
526C2×Dic3—44no—
527C2×Dic3—44no—
528C2×Dic3—44no—
529C2×Dic3C22×D414yes—
530D12—416no—
531D12—416no—
532D12—416no—
533C4×D3—416no—
534C24—34no—
535C24—32no—
536C24—32no—
537C24—32no—
538C24—62no—
539C24—62no—
540C24—62no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—62no—
546C24—62no—
547C24—62no—
548C24—62no—
549C24—62no—
550C24—62no—
551C24—62no—
552C24—62no—
553C24—62no—
554C24—62no—
555C24—62no—
556C24—62no—
557C24—62no—
558C24C23×D311yescharacteristic
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—44no—
562C2×Q8—416no—
563C2×D4—68no—
564C2×D4—68no—
565C2×D4—68no—
566C2×D4—68no—
567C2×D4—124no—
568C2×D4—124no—
569C2×D4—124no—
570C2×D4—124no—
571C2×D4—124no—
572C2×D4—1216no—
573C2×D4—1216no—
574C2×D4—1216no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—34no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—68no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—124no—
615C22×C4—124no—
616C22×C4—1216no—
617C22×C4#23514yes—
618C22×C4D3×D414yes—
619C22×C4#23914yes—
620C22×C4C23×D312yes—
621C22×C4C23×D312yes—
622C22×C4C23×D312yes—
623C22×C4C23×D312yes—
624C22×C4C23×D312yes—
625C22×C4C23×D312yes—
626C22×C4C23×D312yes—
627C4⋊C4—28no—
628C4⋊C4—68no—
629C4⋊C4—68no—
630C4⋊C4—124no—
631C4⋊C4—124no—
632C4⋊C4—124no—
633C22⋊C4—316no—
634C22⋊C4—68no—
635C22⋊C4—68no—
636C22⋊C4—68no—
637C22⋊C4—68no—
638C22⋊C4—68no—
639C22⋊C4—68no—
640C22⋊C4—68no—
641C22⋊C4—124no—
642C22⋊C4—124no—
643C22⋊C4—124no—
644C22⋊C4—124no—
645C22⋊C4—124no—
646C22⋊C4—124no—
647C42—44no—
648C42—68no—
649C22×C3#53514yes—
650C22×C3#53814yes—
651C22×C3#54214yes—
652C22×C3#54614yes—
653C22×C3#54714yes—
654C22×C3#55914yes—
655C22×C3#56214yes—
656C22×C3C23×D411yescharacteristic
657C22×C3C22×#4111yescharacteristic
658C22×C3C22×#4111yescharacteristic
659C22×C3C2×H(5,𝔽2)11yescharacteristic
660C22×C3C2×H(5,𝔽2)11yescharacteristic
661C22×C3C2×H(5,𝔽2)11yescharacteristic
662C22×C3C2×2−1+411yescharacteristic
663C2×D3—24no—
664C2×D3—24no—
665C2×D3—24no—
666C2×D3—42no—
667C2×D3—42no—
668C2×D3—416no—
669C2×D3—42no—
670C2×D3—42no—
671C2×D3—42no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—42no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—42no—
683C2×D3—42no—
684C2×D3—42no—
685C2×D3—88no—
686C2×D3—88no—
687C3×C4—24no—
688C3×C4—24no—
689C3×C4—24no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—42no—
693C3×C4—42no—
694Dic3—24no—
695Dic3—42no—
696Dic3—42no—
697Dic3—42no—
698Dic3—42no—
699C23—34no—
700C23—68no—
701C23—62no—
702C23—62no—
703C23—62no—
704C23—62no—
705C23—62no—
706C23—62no—
707C23—68no—
708C23—68no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23—62no—
714C23—62no—
715C23—62no—
716C23—62no—
717C23—62no—
718C23—62no—
719C23—62no—
720C23—62no—
721C23—62no—
722C23—62no—
723C23—124no—
724C23—124no—
725C23—124no—
726C23—124no—
727C23—124no—
728C23—124no—
729C23—124no—
730C23—124no—
731C23—124no—
732C23—124no—
733C23—124no—
734C23—124no—
735C23—124no—
736C23—124no—
737C23—124no—
738C23—124no—
739C23—124no—
740C23—124no—
741C23C2×#23512yes—
742C23C2×D3×D412yes—
743C23#100412yes—
744C23C2×#23912yes—
745C23#100712yes—
746C23#100912yes—
747C23#100912yes—
748C23C24×D311yescharacteristic
749Q8—416no—
750D4—1216no—
751D4—1216no—
752D4—1216no—
753C2×C4—28no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—34no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—68no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—1216no—
795C2×C4—124no—
796C2×C4—124no—
797C2×C4—124no—
798C2×C4—124no—
799C2×C4C2×#23514yes—
800C2×C4C2×D3×D414yes—
801C2×C4C2×#23914yes—
802C2×C3#271018yescomplemented
803C2×C3C2×#53511yescharacteristic
804C2×C3C2×#53811yescharacteristic
805C2×C3C2×#54211yescharacteristic
806C2×C3C2×#54611yescharacteristic
807C2×C3C2×#54711yescharacteristic
808C2×C3C2×#55911yescharacteristic
809C2×C3C2×#56211yescharacteristic
810D3—44no—
811D3—82no—
812D3—82no—
813C22—64no—
814C22—64no—
815C22—64no—
816C22—122no—
817C22—122no—
818C22—1216no—
819C22—122no—
820C22—122no—
821C22—122no—
822C22—122no—
823C22—122no—
824C22—122no—
825C22—122no—
826C22—122no—
827C22—122no—
828C22—122no—
829C22—122no—
830C22—122no—
831C22—122no—
832C22—122no—
833C22—122no—
834C22—122no—
835C22—248no—
836C22—248no—
837C22#549014yes—
838C22#558214yes—
839C22#558514yes—
840C22#564414yes—
841C22#564714yes—
842C22#567414yes—
843C22#572614yes—
844C22C22×#23511yescharacteristic
845C22C22×D3×D411yescharacteristic
846C22C2×#100411yescharacteristic
847C22C22×#23911yescharacteristic
848C22C2×#100711yescharacteristic
849C22C2×#100911yescharacteristic
850C22C2×#100911yescharacteristic
851C4—24no—
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—64no—
859C4—122no—
860C4—122no—
861C4—122no—
862C4—122no—
863C3C2×#271011yescharacteristic, complemented, Sylow
864C2—124no—
865C2—242no—
866C2—242no—
867C2#7665118yesdirect product factor
868C2C2×#549011yescharacteristic
869C2C2×#558511yescharacteristic
870C2C2×#558211yescharacteristic
871C2C2×#564411yescharacteristic
872C2C2×#564711yescharacteristic
873C2C2×#567411yescharacteristic
874C2C2×#572611yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#391C2
socleC24×C3C24
prime radicalC2×#4671C2
hypercenterC2×#391D3
hypocenterC3C2×#2710
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C22×#947C2semidirect
2. C22×#894C2semidirect
3. C2×C3×#391C2semidirect
4. C2×#5231C2semidirect
5. C2×#4993C2semidirect
6. C2×#4939C2semidirect
7. C2×#4940C2semidirect
8. #76651C2direct (N × H)
9. C2×#4675C2semidirect
11. C2×#4665C2semidirect
12. C2×#4668C2semidirect
13. C2×#4672C2semidirect
14. C2×#4672C2semidirect
15. C2×#4647C2semidirect
16. C2×#4669C2semidirect
26. C2×#947C22semidirect
48. C2×#894C22semidirect
49. C3×#391C22semidirect
54. #5231C22semidirect
59. #4993C22semidirect
60. #4940C22semidirect
61. #4939C22semidirect
62. #4675C22semidirect
63. #4672C22semidirect
64. #4672C22semidirect
66. #4669C22semidirect
67. #4668C22semidirect
68. #4665C22semidirect
69. #4647C22semidirect
79. C2×#391D3semidirect
139. C2×(C2×D3)⋊C4D4semidirect
212. #391C2×D3semidirect
335. (C2×D3)⋊C4C2×D4semidirect
802. C2×C3#2710semidirect
863. C3C2×#2710semidirect
867. C2#76651direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9472
C22×#8942
C2×C3×#3912
C2×#52312
C2×#49932
C2×#49392
C2×#49402
#766512
C2×#46752
C2×#46712
C2×#46652
C2×#46682
C2×#46722
C2×#46472
C2×#46692
C2×#27103