Finite Group Databasebeta

← C2×#77432 #11429929

Subgroups — C2×#77432 #11429929

Order 768.

3934 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic, complemented
3C22×#883C211yesmaximal, characteristic, complemented
4C22×#884C211yesmaximal, characteristic, complemented
5C2×C3×#396C211yesmaximal, characteristic, complemented
6C2×#4994C211yesmaximal, characteristic, complemented
7C2×#4989C211yesmaximal, characteristic, complemented
8C2×#4988C211yesmaximal, characteristic, complemented
9C2×#4976C211yesmaximal, characteristic, complemented
10C2×#4959C211yesmaximal, characteristic, complemented
11C2×#4960C211yesmaximal, characteristic, complemented
12C2×#4960C211yesmaximal, characteristic, complemented
13C2×#4957C211yesmaximal, characteristic, complemented
14#77432C2116yesmaximal, direct product factor
15C2×#4668C211yesmaximal, characteristic, complemented
16C2×#4672C211yesmaximal, characteristic, complemented
17C2×#2682—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×C4×D3C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#895—28no—
50C2×#895C2218yescomplemented
51C2×#894—28no—
52C2×#894C2218yescomplemented
53C2×#884—28no—
54C2×#884C2218yescomplemented
55C2×#883—28no—
56C2×#883C2218yescomplemented
57C3×#396C2218yescomplemented
58C2×C3×#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4994C2218yescomplemented
63#4989C2218yescomplemented
64#4988C2218yescomplemented
65#4976C2218yescomplemented
66#4960C2218yescomplemented
67#4960C2218yescomplemented
68#4959C2218yescomplemented
69#4957C2218yescomplemented
70#4672C2218yescomplemented
71#4668C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2682—316no—
77C2×#396—31no—
78C2×#396D311yescharacteristic, complemented
79C2×#394—31no—
80C2×#394—31no—
81C2×#392—31no—
82C2×#392—31no—
83C2×#390—31no—
84C2×#390—31no—
85C2×#389—31no—
86C2×#385—31no—
87C2×#385—31no—
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C22×#67—24no—
99C22×#67—24no—
100C22×#67—24no—
101C22×#67—24no—
102C22×#67—42no—
103C22×#67—42no—
104C22×#67—42no—
105C22×#67—42no—
106C22×#67—42no—
107C22×#67C2314yes—
108C22×#67C2314yes—
109C22×#67C2314yes—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C22×D12—24no—
116C22×D12—24no—
117C22×D12—24no—
118C22×D12—42no—
119C22×D12—42no—
120C22×D12—42no—
121C22×D12—42no—
122C22×D12—42no—
123C22×D12D418yescomplemented
124C22×D12C2314yes—
125C22×D12C2314yes—
126C22×D12C2314yes—
127C22×C4×D3—24no—
128C22×C4×D3—24no—
129C22×C4×D3—24no—
130C22×C4×D3—24no—
131C22×C4×D3—42no—
132C22×C4×D3—42no—
133C22×C4×D3C2314yes—
134C22×C4×D3C2314yes—
135C2×C3×C4⋊C4—24no—
136C2×C3×C4⋊C4—24no—
137C2×C3×C4⋊C4—42no—
138C2×C3×C4⋊C4C2314yes—
139C2×C3×C4⋊C4C2314yes—
140C2×C3×C4⋊C4C2314yes—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4—42no—
144C2×C3×C22⋊C4C2314yes—
145C2×C3×C22⋊C4C2314yes—
146C2×C3×C22⋊C4C2314yes—
147C2×#217—24no—
148C2×#217C2314yes—
149C2×(C2×D3)⋊C4—24no—
150C2×(C2×D3)⋊C4—24no—
151C2×(C2×D3)⋊C4—24no—
152C2×(C2×D3)⋊C4—24no—
153C2×(C2×D3)⋊C4—24no—
154C2×(C2×D3)⋊C4—24no—
155C2×(C2×D3)⋊C4—24no—
156C2×(C2×D3)⋊C4—24no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—42no—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×C4⋊Dic3—24no—
170C2×C4⋊Dic3C2314yes—
171C2×Dic3⋊C4—24no—
172C2×Dic3⋊C4—42no—
173C2×Dic3⋊C4—42no—
174C2×Dic3⋊C4D418yescomplemented
175C2×Dic3⋊C4C2314yes—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×C4×Dic3—42no—
180C2×C4×Dic3C2314yes—
181#895—232no—
182#894—232no—
183#884—232no—
184#883—232no—
185C3×#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4—31no—
193C23×D4—31no—
194C23×D4—31no—
195C24×C4—31no—
196C24×C4—31no—
197C2×#123—38no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#123—68no—
201C2×#121—38no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121—68no—
205C22×C4⋊C4—31no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4C2×D311yescharacteristic
211C22×C4⋊C4C2×D311yescharacteristic
212C22×C4⋊C4C2×D311yescharacteristic
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×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226C22×C22⋊C4C2×D311yescharacteristic
227C22×C42—31no—
228#396—38no—
229#396C2×D318yescomplemented
230#394—38no—
231#394—38no—
232#392—38no—
233#392—38no—
234#390—38no—
235#390—38no—
236#389—38no—
237#385—38no—
238#385—38no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95C2×D311yescharacteristic
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3C2412yes—
251C24×C3C2411yescharacteristic
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×D3—22no—
264C23×D3—22no—
265C23×D3—22no—
266C23×D3—22no—
267C23×D3—22no—
268C23×D3—22no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3C2×D414yes—
272C23×D3C2×D414yes—
273C23×D3C2412yes—
274C23×D3C2412yes—
275C23×D3C2412yes—
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—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4C2×D414yes—
293C22×C3×C4C2×D414yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C2×#67—28no—
301C2×#67—28no—
302C2×#67—28no—
303C2×#67—28no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—44no—
309C2×#67—416no—
310C2×#67—416no—
311C2×#67—416no—
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×Dic3C2×D414yes—
325C22×Dic3C2×D414yes—
326C22×Dic3#4114yes—
327C22×Dic3C2412yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C2×D12—28no—
333C2×D12—28no—
334C2×D12—28no—
335C2×D12—416no—
336C2×D12—44no—
337C2×D12—44no—
338C2×D12—44no—
339C2×D12—44no—
340C2×D12—44no—
341C2×D12—416no—
342C2×D12—416no—
343C2×D12C2×D4116yescomplemented
344C2×C4×D3—28no—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—28no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—416no—
351C2×C4×D3—416no—
352C3×C4⋊C4—28no—
353C3×C4⋊C4—28no—
354C3×C4⋊C4—44no—
355C3×C22⋊C4—28no—
356C3×C22⋊C4—28no—
357C3×C22⋊C4—44no—
358#217—28no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—28no—
362(C2×D3)⋊C4—28no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—44no—
369C4⋊Dic3—28no—
370Dic3⋊C4—28no—
371Dic3⋊C4—44no—
372Dic3⋊C4—44no—
373Dic3⋊C4C2×D4116yescomplemented
374C4×Dic3—44no—
375C25—31no—
376C25—31no—
377C25—31no—
378C25C22×D311yescharacteristic
379C22×D4—34no—
380C22×D4—34no—
381C22×D4—34no—
382C22×D4—38no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—64no—
387C22×D4—64no—
388C22×D4—64no—
389C22×D4—64no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—122no—
394C22×D4—122no—
395C22×D4—122no—
396C22×D4—122no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4—122no—
400C22×D4—122no—
401C22×D4—122no—
402C22×D4—122no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—34no—
409C23×C4—34no—
410C23×C4—64no—
411C23×C4—64no—
412C23×C4—64no—
413C23×C4—64no—
414C23×C4—122no—
415C23×C4—122no—
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422#123—632no—
423#123—632no—
424#121—632no—
425#121—632no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—38no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—34no—
431C2×C4⋊C4—34no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—64no—
436C2×C4⋊C4—64no—
437C2×C4⋊C4—122no—
438C2×C4⋊C4—122no—
439C2×C4⋊C4C22×D314yes—
440C2×C4⋊C4C22×D314yes—
441C2×C4⋊C4C22×D314yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—34no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—64no—
457C2×C22⋊C4—64no—
458C2×C22⋊C4—64no—
459C2×C22⋊C4—64no—
460C2×C22⋊C4—64no—
461C2×C22⋊C4—64no—
462C2×C22⋊C4—64no—
463C2×C22⋊C4—64no—
464C2×C22⋊C4—64no—
465C2×C22⋊C4—64no—
466C2×C22⋊C4—122no—
467C2×C22⋊C4C22×D314yes—
468C2×C22⋊C4C22×D314yes—
469C2×C22⋊C4C22×D314yes—
470C2×C42—34no—
471C2×C42—122no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95C22×D314yes—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—44no—
484C23×C3—44no—
485C23×C3—44no—
486C23×C3—44no—
487C23×C3—44no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3C22×D412yes—
491C23×C3C22×D412yes—
492C23×C3C2×#4112yes—
493C23×C3H(5,𝔽2)12yes—
494C23×C3H(5,𝔽2)12yes—
495C23×C3H(5,𝔽2)12yes—
496C23×C32−1+412yes—
497C23×C3C2511yescharacteristic
498C22×D3—28no—
499C22×D3—28no—
500C22×D3—28no—
501C22×D3—28no—
502C22×D3—28no—
503C22×D3—28no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—44no—
524C22×D3—44no—
525C22×D3—44no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3—44no—
529C22×D3—44no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3—44no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3C22×D414yes—
539C22×D3C22×D414yes—
540C2×C3×C4—28no—
541C2×C3×C4—28no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—44no—
559C2×C3×C4—44no—
560C2×C3×C4—44no—
561C2×C3×C4—44no—
562C2×C3×C4C22×D414yes—
563C2×C3×C4C22×D414yes—
564#67—416no—
565#67—416no—
566#67—416no—
567C2×Dic3—28no—
568C2×Dic3—28no—
569C2×Dic3—28no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—44no—
583C2×Dic3—44no—
584C2×Dic3C22×D414yes—
585C2×Dic3C22×D414yes—
586C2×Dic3C2×#4114yes—
587D12—416no—
588D12—416no—
589D12—416no—
590C4×D3—416no—
591C4×D3—416no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—34no—
600C24—34no—
601C24—32no—
602C24—32no—
603C24—32no—
604C24—62no—
605C24—62no—
606C24—62no—
607C24—62no—
608C24—62no—
609C24—62no—
610C24—62no—
611C24—62no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24—62no—
622C24—62no—
623C24C23×D312yes—
624C24C23×D311yescharacteristic
625C2×D4—316no—
626C2×D4—68no—
627C2×D4—68no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—68no—
631C2×D4—68no—
632C2×D4—68no—
633C2×D4—124no—
634C2×D4—124no—
635C2×D4—124no—
636C2×D4—1216no—
637C2×D4—124no—
638C2×D4—124no—
639C2×D4—1216no—
640C2×D4—1216no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—124no—
646C2×D4—1216no—
647C2×D4—1216no—
648C2×D4—1216no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—34no—
666C22×C4—34no—
667C22×C4—34no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—68no—
674C22×C4—68no—
675C22×C4—68no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—68no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—1216no—
692C22×C4—1216no—
693C22×C4D3×D414yes—
694C22×C4D3×D414yes—
695C22×C4C23×D312yes—
696C22×C4C23×D312yes—
697C22×C4C23×D312yes—
698C22×C4C23×D312yes—
699C22×C4C23×D312yes—
700C22×C4C23×D312yes—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—316no—
704C4⋊C4—44no—
705C4⋊C4—68no—
706C4⋊C4—68no—
707C4⋊C4—124no—
708C4⋊C4—124no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—44no—
712C22⋊C4—68no—
713C22⋊C4—68no—
714C22⋊C4—68no—
715C22⋊C4—68no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—124no—
723C42—124no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—88no—
732C22×C3#53414yes—
733C22×C3#53714yes—
734C22×C3#53814yes—
735C22×C3D4214yes—
736C22×C3#54714yes—
737C22×C3#55014yes—
738C22×C3#56214yes—
739C22×C3C23×D411yescharacteristic
740C22×C3C23×D411yescharacteristic
741C22×C3C22×#4111yescharacteristic
742C22×C3C2×H(5,𝔽2)11yescharacteristic
743C22×C3C2×H(5,𝔽2)11yescharacteristic
744C22×C3C2×H(5,𝔽2)11yescharacteristic
745C22×C3C2×2−1+411yescharacteristic
746C2×D3—24no—
747C2×D3—24no—
748C2×D3—24no—
749C2×D3—24no—
750C2×D3—24no—
751C2×D3—24no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—416no—
755C2×D3—416no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—42no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—88no—
770C3×C4—24no—
771C3×C4—24no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—42no—
775C3×C4—42no—
776Dic3—24no—
777Dic3—24no—
778Dic3—24no—
779Dic3—42no—
780Dic3—42no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—34no—
789C23—34no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—68no—
810C23—68no—
811C23—68no—
812C23—68no—
813C23—68no—
814C23—68no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—62no—
822C23—124no—
823C23—124no—
824C23—124no—
825C23—124no—
826C23—124no—
827C23—124no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23C2×D3×D412yes—
838C23C2×D3×D412yes—
839C23#100412yes—
840C23#100712yes—
841C23D3×#4112yes—
842C23#100912yes—
843C23#100912yes—
844C23C24×D311yescharacteristic
845D4—1216no—
846D4—1216no—
847D4—1216no—
848D4—1216no—
849D4—1216no—
850D4—1216no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—34no—
870C2×C4—34no—
871C2×C4—34no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—62no—
877C2×C4—68no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—68no—
884C2×C4—68no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—1216no—
892C2×C4—1216no—
893C2×C4—124no—
894C2×C4—124no—
895C2×C4C2×D3×D414yes—
896C2×C4C2×D3×D414yes—
897C2×C3—82no—
898C2×C3#268218yescomplemented
899C2×C3C2×#53411yescharacteristic
900C2×C3C2×#53711yescharacteristic
901C2×C3C2×#53811yescharacteristic
902C2×C3C2×D4211yescharacteristic
903C2×C3C2×#54711yescharacteristic
904C2×C3C2×#55011yescharacteristic
905C2×C3C2×#56211yescharacteristic
906D3—44no—
907D3—44no—
908D3—82no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—64no—
917C22—64no—
918C22—64no—
919C22—64no—
920C22—64no—
921C22—64no—
922C22—88no—
923C22—122no—
924C22—122no—
925C22—1216no—
926C22—1216no—
927C22—122no—
928C22—122no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—122no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—248no—
941C22#559914yes—
942C22#560514yes—
943C22#560914yes—
944C22#562914yes—
945C22#563114yes—
946C22#564714yes—
947C22#570414yes—
948C22C22×D3×D411yescharacteristic
949C22C22×D3×D411yescharacteristic
950C22C2×#100411yescharacteristic
951C22C2×#100711yescharacteristic
952C22C2×D3×#4111yescharacteristic
953C22C2×#100911yescharacteristic
954C22C2×#100911yescharacteristic
955C4—24no—
956C4—24no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—64no—
962C4—64no—
963C4—64no—
964C4—122no—
965C4—122no—
966C3C2×#268211yescharacteristic, complemented, Sylow
967C2—82no—
968C2—124no—
969C2—124no—
970C2—242no—
971C2#7743218yesdirect product factor
972C2C2×#559911yescharacteristic
973C2C2×#560511yescharacteristic
974C2C2×#560911yescharacteristic
975C2C2×#562911yescharacteristic
976C2C2×#563111yescharacteristic
977C2C2×#564711yescharacteristic
978C2C2×#570411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#396C2
socleC24×C3C24
hypercenterC2×#396D3
hypocenterC3C2×#2682
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#895C2semidirect
3. C22×#883C2semidirect
4. C22×#884C2semidirect
5. C2×C3×#396C2semidirect
6. C2×#4994C2semidirect
7. C2×#4989C2semidirect
8. C2×#4988C2semidirect
9. C2×#4976C2semidirect
10. C2×#4959C2semidirect
11. C2×#4960C2semidirect
12. C2×#4960C2semidirect
13. C2×#4957C2semidirect
14. #77432C2direct (N × H)
15. C2×#4668C2semidirect
16. C2×#4672C2semidirect
50. C2×#895C22semidirect
52. C2×#894C22semidirect
54. C2×#884C22semidirect
56. C2×#883C22semidirect
57. C3×#396C22semidirect
62. #4994C22semidirect
63. #4989C22semidirect
64. #4988C22semidirect
65. #4976C22semidirect
66. #4960C22semidirect
67. #4960C22semidirect
68. #4959C22semidirect
69. #4957C22semidirect
70. #4672C22semidirect
71. #4668C22semidirect
78. C2×#396D3semidirect
123. C22×D12D4semidirect
174. C2×Dic3⋊C4D4semidirect
229. #396C2×D3semidirect
343. C2×D12C2×D4semidirect
373. Dic3⋊C4C2×D4semidirect
898. C2×C3#2682semidirect
966. C3C2×#2682semidirect
971. C2#77432direct (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×#8952
C22×#8832
C22×#8842
C2×C3×#3962
C2×#49942
C2×#49892
C2×#49882
C2×#49762
C2×#49592
C2×#49602
C2×#49572
#774322
C2×#46682
C2×#46722
C2×#26823