Finite Group Databasebeta

← C2×#76259 #11429915

Subgroups — C2×#76259 #11429915

Order 768.

3610 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#896C211yesmaximal, characteristic, complemented
3C22×#897C211yesmaximal, characteristic, complemented
4C22×#895C211yesmaximal, characteristic
5C2×C3×#389C211yesmaximal, characteristic, complemented
6C2×#4994C211yesmaximal, characteristic, complemented
7C2×#4991C211yesmaximal, characteristic, complemented
8C2×#4991C211yesmaximal, characteristic, complemented
9C2×#4981C211yesmaximal, characteristic, complemented
10C2×#4939C211yesmaximal, characteristic, complemented
11C2×#4940C211yesmaximal, characteristic, complemented
12#76259C2116yesmaximal, direct product factor
13C2×#4673C211yesmaximal, characteristic, complemented
14C2×#4665C211yesmaximal, characteristic, complemented
15C2×#4668C211yesmaximal, characteristic, complemented
16C2×#4672C211yesmaximal, characteristic, complemented
17C2×#2681—31nomaximal, Sylow
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C23×Dic6C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
42C22×C4⋊Dic3C2211yescharacteristic
43C22×C4⋊Dic3C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C2×#897—28no—
48C2×#897C2218yescomplemented
49C2×#896—28no—
50C2×#896C2218yescomplemented
51C2×#895—28no—
52C2×#895C2218yes—
53C2×#894—28no—
54C2×#894C2218yescomplemented
55C3×#389C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4994C2218yescomplemented
63#4991C2218yescomplemented
64#4991C2218yescomplemented
65#4981C2218yescomplemented
66#4940C2218yescomplemented
67#4939C2218yescomplemented
68#4673C2218yescomplemented
69#4672C2218yescomplemented
70#4668C2218yescomplemented
71#4665C2218yescomplemented
72C22×#123—31no—
73C22×C22⋊Q8—31no—
74C22×C22⋊Q8—31no—
75C22×#121—31no—
76#2681—316no—
77C2×#398—31no—
78C2×#396—31no—
79C2×#394—31no—
80C2×#394—31no—
81C2×#394—31no—
82C2×#393—31no—
83C2×#390—31no—
84C2×#389D311yescharacteristic, complemented
85C2×#388—31no—
86C2×#386—31no—
87C2×#385—31no—
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C22×D12—24no—
104C22×D12—24no—
105C22×D12—24no—
106C22×D12—24no—
107C22×D12—24no—
108C22×D12—24no—
109C22×D12—42no—
110C22×D12—42no—
111C22×D12—42no—
112C22×D12C2314yes—
113C22×D12C2314yes—
114C22×D12C2314yes—
115C22×C4×D3—24no—
116C22×C4×D3—24no—
117C22×C4×D3—24no—
118C22×C4×D3—24no—
119C22×C4×D3—42no—
120C22×C4×D3—42no—
121C22×C4×D3C2314yes—
122C22×C4×D3C2314yes—
123C22×Dic6—24no—
124C22×Dic6—24no—
125C22×Dic6—42no—
126C22×Dic6C2314yes—
127C2×C3×C4⋊C4—24no—
128C2×C3×C4⋊C4—24no—
129C2×C3×C4⋊C4—42no—
130C2×C3×C4⋊C4D418yescomplemented
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C42—42no—
136C2×C3×C42C2314yes—
137C2×(C2×D3)⋊C4—24no—
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—24no—
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—42no—
146C2×(C2×D3)⋊C4—42no—
147C2×(C2×D3)⋊C4—42no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4D418yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
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×C4⋊Dic3—24no—
164C2×C4⋊Dic3—24no—
165C2×C4⋊Dic3C2314yes—
166C2×C4⋊Dic3C2314yes—
167C2×Dic3⋊C4—24no—
168C2×Dic3⋊C4—24no—
169C2×Dic3⋊C4—24no—
170C2×Dic3⋊C4C2314yes—
171C2×Dic3⋊C4C2314yes—
172C2×Dic3⋊C4C2314yes—
173#897—232no—
174#896—232no—
175#895—232no—
176#894—232no—
177C3×#95C2314yes—
178C3×#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C23×Q8—31no—
184C23×D4—31no—
185C23×D4—31no—
186C23×D4—31no—
187C24×C4—31no—
188C24×C4—31no—
189C2×#123—38no—
190C2×#123—68no—
191C2×C22⋊Q8—38no—
192C2×C22⋊Q8—38no—
193C2×C22⋊Q8—68no—
194C2×C22⋊Q8—68no—
195C2×#121—38no—
196C2×#121—68no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4C2×D311yescharacteristic
203C22×C4⋊C4C2×D311yescharacteristic
204C22×C4⋊C4C2×D311yescharacteristic
205C22×C4⋊C4C2×D311yescharacteristic
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C42C2×D311yescharacteristic
220#398—38no—
221#396—38no—
222#394—38no—
223#394—38no—
224#394—38no—
225#393—38no—
226#390—38no—
227#389C2×D318yescomplemented
228#388—38no—
229#386—38no—
230#385—38no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95C2×D311yescharacteristic
236C2×#95C2×D311yescharacteristic
237C24×C3C2411yescharacteristic
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×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×D3C2×D414yes—
258C23×D3#4114yes—
259C23×D3C2412yes—
260C23×D3C2412yes—
261C23×D3C2412yes—
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×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4C2×D414yes—
280C22×C3×C4C2×D414yes—
281C22×C3×C4C2×D414yes—
282C22×C3×C4C2×D414yes—
283C22×C3×C4C2412yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
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×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3C2×D414yes—
305C22×Dic3C2412yes—
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309C22×Dic3C2412yes—
310C2×D12—28no—
311C2×D12—28no—
312C2×D12—28no—
313C2×D12—28no—
314C2×D12—28no—
315C2×D12—28no—
316C2×D12—44no—
317C2×D12—44no—
318C2×D12—44no—
319C2×D12—416no—
320C2×D12—416no—
321C2×D12—416no—
322C2×C4×D3—28no—
323C2×C4×D3—28no—
324C2×C4×D3—28no—
325C2×C4×D3—28no—
326C2×C4×D3—44no—
327C2×C4×D3—44no—
328C2×C4×D3—416no—
329C2×C4×D3—416no—
330C2×Dic6—28no—
331C2×Dic6—28no—
332C2×Dic6—44no—
333C2×Dic6—416no—
334C3×C4⋊C4—28no—
335C3×C4⋊C4—28no—
336C3×C4⋊C4—44no—
337C3×C4⋊C4C2×D4116yescomplemented
338C3×C42—44no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—28no—
341(C2×D3)⋊C4—28no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4C2×D4116yes—
352C4⋊Dic3—28no—
353C4⋊Dic3—28no—
354Dic3⋊C4—28no—
355Dic3⋊C4—28no—
356Dic3⋊C4—28no—
357C25—31no—
358C25—31no—
359C25—31no—
360C22×Q8—34no—
361C22×Q8—64no—
362C22×Q8—64no—
363C22×Q8—122no—
364C22×D4—34no—
365C22×D4—34no—
366C22×D4—34no—
367C22×D4—64no—
368C22×D4—64no—
369C22×D4—64no—
370C22×D4—64no—
371C22×D4—64no—
372C22×D4—64no—
373C22×D4—122no—
374C22×D4—122no—
375C22×D4—122no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—34no—
382C23×C4—34no—
383C23×C4—64no—
384C23×C4—64no—
385C23×C4—64no—
386C23×C4—64no—
387C23×C4—122no—
388C23×C4—122no—
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396#123—632no—
397C22⋊Q8—632no—
398C22⋊Q8—632no—
399#121—632no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4—64no—
410C2×C4⋊C4—64no—
411C2×C4⋊C4—64no—
412C2×C4⋊C4—64no—
413C2×C4⋊C4D1218yescomplemented
414C2×C4⋊C4C22×D314yes—
415C2×C4⋊C4C22×D314yes—
416C2×C4⋊C4C22×D314yes—
417C2×C4⋊C4C22×D314yes—
418C2×C22⋊C4—38no—
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—34no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—64no—
438C2×C22⋊C4—64no—
439C2×C22⋊C4—64no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4—122no—
444C2×C42—42no—
445C2×C42C22×D314yes—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95C22×D314yes—
451#95C22×D314yes—
452C23×C3C22×D412yes—
453C23×C3C22×D412yes—
454C23×C3C2×#4112yes—
455C23×C3H(5,𝔽2)12yes—
456C23×C3H(5,𝔽2)12yes—
457C23×C32−1+412yes—
458C23×C32−1+412yes—
459C23×C3C2511yescharacteristic
460C22×D3—28no—
461C22×D3—28no—
462C22×D3—28no—
463C22×D3—28no—
464C22×D3—28no—
465C22×D3—28no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
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—44no—
486C22×D3—44no—
487C22×D3—44no—
488C22×D3—44no—
489C22×D3—44no—
490C22×D3—44no—
491C22×D3—44no—
492C22×D3—44no—
493C22×D3—44no—
494C22×D3—44no—
495C22×D3—44no—
496C22×D3—44no—
497C22×D3—44no—
498C22×D3—44no—
499C22×D3—44no—
500C22×D3C22×D414yes—
501C22×D3C2×#4114yes—
502C2×C3×C4—28no—
503C2×C3×C4—28no—
504C2×C3×C4—28no—
505C2×C3×C4—28no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—44no—
524C2×C3×C4—44no—
525C2×C3×C4—44no—
526C2×C3×C4C22×D414yes—
527C2×C3×C4C22×D414yes—
528C2×C3×C4C22×D414yes—
529C2×C3×C4C22×D414yes—
530C2×Dic3—28no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—44no—
546C2×Dic3—44no—
547C2×Dic3—44no—
548C2×Dic3—44no—
549C2×Dic3C22×D414yes—
550D12—416no—
551D12—416no—
552D12—416no—
553C4×D3—416no—
554C4×D3—416no—
555Dic6—416no—
556C24—34no—
557C24—34no—
558C24—32no—
559C24—32no—
560C24—32no—
561C24—62no—
562C24—62no—
563C24—62no—
564C24—62no—
565C24—62no—
566C24—62no—
567C24—62no—
568C24—62no—
569C24—62no—
570C24—62no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—62no—
575C24—62no—
576C24—62no—
577C24—62no—
578C24—62no—
579C24—62no—
580C24C23×D311yescharacteristic
581C2×Q8—68no—
582C2×Q8—68no—
583C2×Q8—124no—
584C2×Q8—1216no—
585C2×D4—68no—
586C2×D4—68no—
587C2×D4—68no—
588C2×D4—68no—
589C2×D4—68no—
590C2×D4—68no—
591C2×D4—124no—
592C2×D4—124no—
593C2×D4—124no—
594C2×D4—1216no—
595C2×D4—1216no—
596C2×D4—1216no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—34no—
615C22×C4—32no—
616C22×C4—32no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—68no—
621C22×C4—68no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—68no—
637C22×C4—68no—
638C22×C4—124no—
639C22×C4—124no—
640C22×C4—1216no—
641C22×C4—1216no—
642C22×C4C2×D1214yes—
643C22×C4C2×D1214yes—
644C22×C4C2×D1214yes—
645C22×C4D3×D414yes—
646C22×C4C23×D312yes—
647C22×C4C23×D312yes—
648C22×C4C23×D312yes—
649C22×C4C23×D312yes—
650C22×C4C23×D312yes—
651C22×C4C23×D312yes—
652C22×C4C23×D312yes—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—44no—
656C4⋊C4—68no—
657C4⋊C4—68no—
658C4⋊C4—68no—
659C4⋊C4—68no—
660C4⋊C4—68no—
661C4⋊C4C2×D12116yescomplemented
662C22⋊C4—316no—
663C22⋊C4—68no—
664C22⋊C4—68no—
665C22⋊C4—68no—
666C22⋊C4—68no—
667C22⋊C4—68no—
668C22⋊C4—68no—
669C22⋊C4—68no—
670C22⋊C4—68no—
671C22⋊C4—124no—
672C22⋊C4—124no—
673C22⋊C4—124no—
674C22⋊C4—124no—
675C42—44no—
676C22×C3#53614yes—
677C22×C3#53714yes—
678C22×C3#53914yes—
679C22×C3D4214yes—
680C22×C3#54614yes—
681C22×C3#54814yes—
682C22×C3#56214yes—
683C22×C3C23×D411yescharacteristic
684C22×C3C23×D411yescharacteristic
685C22×C3C22×#4111yescharacteristic
686C22×C3C2×H(5,𝔽2)11yescharacteristic
687C22×C3C2×H(5,𝔽2)11yescharacteristic
688C22×C3C2×2−1+411yescharacteristic
689C22×C3C2×2−1+411yescharacteristic
690C2×D3—24no—
691C2×D3—24no—
692C2×D3—24no—
693C2×D3—24no—
694C2×D3—24no—
695C2×D3—24no—
696C2×D3—42no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—416no—
700C2×D3—416no—
701C2×D3—42no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—42no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—88no—
714C3×C4—24no—
715C3×C4—24no—
716C3×C4—24no—
717C3×C4—24no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721Dic3—24no—
722Dic3—42no—
723Dic3—42no—
724Dic3—42no—
725Dic3—42no—
726C23—34no—
727C23—34no—
728C23—68no—
729C23—62no—
730C23—62no—
731C23—62no—
732C23—62no—
733C23—62no—
734C23—62no—
735C23—62no—
736C23—62no—
737C23—62no—
738C23—62no—
739C23—62no—
740C23—62no—
741C23—68no—
742C23—68no—
743C23—68no—
744C23—68no—
745C23—68no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—124no—
754C23—124no—
755C23—124no—
756C23—124no—
757C23—124no—
758C23—124no—
759C23—124no—
760C23—124no—
761C23—124no—
762C23—124no—
763C23—124no—
764C23—124no—
765C23—124no—
766C23—124no—
767C23—124no—
768C23C22×D1212yes—
769C23C2×D3×D412yes—
770C23#100412yes—
771C23#100712yes—
772C23#100712yes—
773C23D3×#4112yes—
774C23#100912yes—
775C23C24×D311yescharacteristic
776Q8—1216no—
777D4—1216no—
778D4—1216no—
779D4—1216no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—34no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—68no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—1216no—
821C2×C4—1216no—
822C2×C4—124no—
823C2×C4—124no—
824C2×C4—124no—
825C2×C4—124no—
826C2×C4C22×D1214yes—
827C2×C4C22×D1214yes—
828C2×C4C22×D1214yes—
829C2×C4C2×D3×D414yes—
830C2×C3#268118yescomplemented
831C2×C3C2×#53611yescharacteristic
832C2×C3C2×#53711yescharacteristic
833C2×C3C2×#53911yescharacteristic
834C2×C3C2×D4211yescharacteristic
835C2×C3C2×#54611yescharacteristic
836C2×C3C2×#54811yescharacteristic
837C2×C3C2×#56211yescharacteristic
838D3—44no—
839D3—44no—
840D3—82no—
841C22—64no—
842C22—64no—
843C22—64no—
844C22—64no—
845C22—64no—
846C22—64no—
847C22—122no—
848C22—122no—
849C22—122no—
850C22—122no—
851C22—122no—
852C22—122no—
853C22—1216no—
854C22—1216no—
855C22—122no—
856C22—122no—
857C22—122no—
858C22—122no—
859C22—122no—
860C22—122no—
861C22—122no—
862C22—122no—
863C22—122no—
864C22—248no—
865C22#551014yes—
866C22D4×D1214yes—
867C22#557614yes—
868C22#561014yes—
869C22#564714yes—
870C22#569214yes—
871C22#572414yes—
872C22C23×D1211yescharacteristic
873C22C22×D3×D411yescharacteristic
874C22C2×#100411yescharacteristic
875C22C2×#100711yescharacteristic
876C22C2×#100711yescharacteristic
877C22C2×D3×#4111yescharacteristic
878C22C2×#100911yescharacteristic
879C4—24no—
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—64no—
887C4—122no—
888C4—122no—
889C4—122no—
890C4—122no—
891C3C2×#268111yescharacteristic, complemented, Sylow
892C2—124no—
893C2—124no—
894C2—242no—
895C2#7625918yesdirect product factor
896C2C2×#551011yescharacteristic
897C2C2×D4×D1211yescharacteristic
898C2C2×#557611yescharacteristic
899C2C2×#561011yescharacteristic
900C2C2×#564711yescharacteristic
901C2C2×#569211yescharacteristic
902C2C2×#572411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#389C2
socleC24×C3C24
prime radicalC22×#895C2
hypercenterC2×#389D3
hypocenterC3C2×#2681
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#896C2semidirect
3. C22×#897C2semidirect
5. C2×C3×#389C2semidirect
6. C2×#4994C2semidirect
7. C2×#4991C2semidirect
8. C2×#4991C2semidirect
9. C2×#4981C2semidirect
10. C2×#4939C2semidirect
11. C2×#4940C2semidirect
12. #76259C2direct (N × H)
13. C2×#4673C2semidirect
14. C2×#4665C2semidirect
15. C2×#4668C2semidirect
16. C2×#4672C2semidirect
48. C2×#897C22semidirect
50. C2×#896C22semidirect
54. C2×#894C22semidirect
55. C3×#389C22semidirect
62. #4994C22semidirect
63. #4991C22semidirect
64. #4991C22semidirect
65. #4981C22semidirect
66. #4940C22semidirect
67. #4939C22semidirect
68. #4673C22semidirect
69. #4672C22semidirect
70. #4668C22semidirect
71. #4665C22semidirect
84. C2×#389D3semidirect
130. C2×C3×C4⋊C4D4semidirect
227. #389C2×D3semidirect
337. C3×C4⋊C4C2×D4semidirect
413. C2×C4⋊C4D12semidirect
661. C4⋊C4C2×D12semidirect
830. C2×C3#2681semidirect
891. C3C2×#2681semidirect
895. C2#76259direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8962
C22×#8972
C22×#8952
C2×C3×#3892
C2×#49942
C2×#49912
C2×#49812
C2×#49392
C2×#49402
#762592
C2×#46732
C2×#46652
C2×#46682
C2×#46722
C2×#26813