Finite Group Databasebeta

← #10963951

Subgroups — #10963951

Order 768.

3578 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic, complemented
2C2×#5791C211yesmaximal, characteristic, complemented
3C2×#5791C211yesmaximal, characteristic, complemented
4C22×#926C211yesmaximal, characteristic, complemented
5#84048C212yesmaximal, complemented
6#84027C211yesmaximal, characteristic, complemented
7#82353C212yesmaximal, complemented
8#82352C212yesmaximal, complemented
9#82351C212yesmaximal, complemented
10#82350C212yesmaximal, complemented
11#82345C214yesmaximal, complemented
12C4×#939C214yesmaximal, complemented
13#82170C212yesmaximal, complemented
14#82107C212yesmaximal, complemented
15#82106C212yesmaximal, complemented
16#82070C211yesmaximal, characteristic, complemented
17#82069C211yesmaximal, characteristic, complemented
18#34737—31nomaximal, Sylow
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C22×#235C2211yescharacteristic
23C2×C3×C4×D4—28no—
24C2×C3×C4×D4C2212yes—
25C2×C3×C4×D4C2212yes—
26C2×C3×C4×D4C2212yes—
27C2×C3×C4×D4C2212yes—
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C42C2211yescharacteristic
32C2×#953C2212yes—
33C2×#953C2212yes—
34C22×#217C2212yes—
35C2×#939C2214yes—
36#5791—28no—
37#5791—28no—
38C2×#930C2211yescharacteristic, complemented
39C2×#930C2212yescomplemented
40C2×#930C2211yescharacteristic, complemented
41C2×#929C2212yes—
42C2×#929C2212yes—
43C2×C4×#67C2212yescomplemented
44C2×C4×#67C2214yescomplemented
45C2×C4×#67C2212yescomplemented
46C2×#926—28no—
47C2×#926C2211yescharacteristic
48C2×#926C2211yescharacteristic
49C2×#926C2212yes—
50C2×#926C2211yescharacteristic
51C2×#926C2212yescomplemented
52C2×#926C2212yescomplemented
53C22×C4⋊Dic3C2212yescomplemented
54C2×#924C2211yescharacteristic, complemented
55C2×#924C2212yescomplemented
56C2×#924C2211yescharacteristic, complemented
57C22×C4×Dic3C2212yescomplemented
58#5247C2212yes—
59#5223C2214yes—
60#5222C2214yes—
61#5220C2214yes—
62#5213C2212yes—
63#5213C2212yes—
64#5212C2212yescomplemented
65#5212C2212yescomplemented
66#5211C2212yes—
67#5210C2212yes—
68#5210C2212yes—
69C4×#217C2214yescomplemented
70#4994C2214yescomplemented
71#4990C2214yescomplemented
72#4982C2214yescomplemented
73#4976C2214yescomplemented
74#4961C2214yescomplemented
75#4959C2214yescomplemented
76#4958C2214yescomplemented
77#4957C2214yescomplemented
78#4952C2214yescomplemented
79#4948C2214yescomplemented
80#4945C2214yescomplemented
81#4942C2214yescomplemented
82#4939C2212yescomplemented
83C4×(C2×D3)⋊C4C2214yescomplemented
84C4×Dic3⋊C4C2214yescomplemented
85#4929C2212yescomplemented
86#4928C2212yescomplemented
87#4928C2212yescomplemented
88C2×#525—31no—
89C2×#525—31no—
90C22×C4×D4D311yescharacteristic, complemented
91C22×#117—31no—
92#2417—32no—
93#2416—32no—
94#2415—32no—
95#2414—32no—
96#2413—32no—
97#2412—32no—
98#2411—32no—
99#2410—32no—
100#2392—34no—
101C4×#121—34no—
102#2297—31no—
103#2296—31no—
104#2280—31no—
105C25×C3C2311yescharacteristic
106C25×C3C2311yescharacteristic
107C22×C3×D4—24no—
108C22×C3×D4—28no—
109C22×C3×D4C2312yes—
110C22×C3×D4C2312yes—
111C23×C3×C4—24no—
112C23×C3×C4—24no—
113C23×C3×C4—24no—
114C23×C3×C4—24no—
115C23×C3×C4—24no—
116C23×C3×C4D418yescomplemented
117C23×C3×C4C2312yes—
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2312yes—
120C23×C3×C4C2311yescharacteristic
121C23×C3×C4C2311yescharacteristic
122C23×C3×C4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2311yescharacteristic
126C23×C3×C4C2311yescharacteristic
127C23×C3×C4C2311yescharacteristic
128C22×#67C2312yes—
129C22×#67C2312yes—
130C22×#67C2314yes—
131C22×#67C2312yes—
132C23×Dic3C2314yes—
133C2×#235—24no—
134C2×#235—24no—
135C2×#235—24no—
136C22×D12C2311yescharacteristic
137C22×C4×D3C2312yes—
138C22×Dic6C2311yescharacteristic
139C3×C4×D4—28no—
140C3×C4×D4—28no—
141C3×C4×D4—28no—
142C3×C4×D4—28no—
143C2×C3×C4⋊C4—24no—
144C2×C3×C4⋊C4C2312yes—
145C2×C3×C4⋊C4C2312yes—
146C2×C3×C22⋊C4—24no—
147C2×C3×C22⋊C4—24no—
148C2×C3×C22⋊C4C2312yes—
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C22⋊C4C2312yes—
151C2×C3×C22⋊C4C2312yes—
152C2×C3×C42—24no—
153C2×C3×C42C2312yes—
154C2×C3×C42C2312yes—
155#953—28no—
156#953—28no—
157C2×#217—28no—
158C2×#217C2312yes—
159C2×#217C2314yes—
160C2×#217C2314yes—
161C2×#217C2312yes—
162C2×#217C2314yes—
163C2×#217C2312yes—
164C2×#217C2312yes—
165C2×#217C2314yes—
166C2×#217C2312yes—
167#939—216no—
168#930—24no—
169#930—24no—
170#930—28no—
171#929—28no—
172#929—28no—
173C4×#67—28no—
174C4×#67—28no—
175C4×#67—216no—
176C2×(C2×D3)⋊C4C2314yes—
177C2×(C2×D3)⋊C4C2312yes—
178C2×(C2×D3)⋊C4C2314yes—
179C2×(C2×D3)⋊C4C2312yes—
180C2×(C2×D3)⋊C4C2314yes—
181#926—24no—
182#926—24no—
183#926—28no—
184#926—28no—
185#926—28no—
186#926D418yescomplemented
187C2×C4⋊Dic3—28no—
188C2×C4⋊Dic3C2311yescharacteristic
189C2×C4⋊Dic3C2311yescharacteristic
190C2×C4⋊Dic3C2312yes—
191C2×C4⋊Dic3C2314yes—
192C2×C4⋊Dic3C2312yes—
193#924—24no—
194#924—24no—
195#924—28no—
196C2×Dic3⋊C4C2314yes—
197C2×Dic3⋊C4C2314yes—
198C2×Dic3⋊C4C2312yes—
199C2×Dic3⋊C4C2312yes—
200C2×Dic3⋊C4C2314yes—
201C2×C4×Dic3—28no—
202C2×C4×Dic3C2312yes—
203C2×C4×Dic3C2312yes—
204C2×C4×Dic3C2314yes—
205C2×C4×Dic3C2312yes—
206C3⋊#95C2314yes—
207C3⋊#95C2314yes—
208C3⋊#95C2314yes—
209C3⋊#95C2314yes—
210C3⋊#95C2314yes—
211C3⋊#95C2314yes—
212C22×#41—31no—
213C23×D4C2×D311yescharacteristic
214C24×C4C2×D311yescharacteristic
215C24×C4C2×D311yescharacteristic
216#525—68no—
217#525—68no—
218C2×#123—32no—
219C2×#123—32no—
220C2×C22⋊Q8—31no—
221C2×C22⋊Q8—32no—
222C2×C22⋊Q8—31no—
223C2×#121—34no—
224C2×#121—31no—
225C2×#121—32no—
226C2×#121—31no—
227C2×#120—32no—
228C2×#120—32no—
229C2×C4×D4—28no—
230C2×C4×D4—32no—
231C2×C4×D4—34no—
232C2×C4×D4—32no—
233C2×C4×D4C2×D312yes—
234C2×C4×D4C2×D312yes—
235C2×C4×D4C2×D312yes—
236C2×C4×D4C2×D312yes—
237C2×#117—31no—
238C2×#117—32no—
239C2×#117—32no—
240C2×#117—32no—
241C2×#117—31no—
242C2×#117—31no—
243C2×#117—68no—
244C22×C4⋊C4—32no—
245C22×C4⋊C4C2×D311yescharacteristic
246C22×C22⋊C4—32no—
247C22×C22⋊C4C2×D311yescharacteristic
248C22×C22⋊C4C2×D311yescharacteristic
249C22×C42—32no—
250C22×C42C2×D311yescharacteristic
251#398—34no—
252#397—34no—
253#396—34no—
254#396—34no—
255#394—34no—
256#394—34no—
257#394—34no—
258#392—34no—
259#391—32no—
260#390—34no—
261#390—32no—
262#389—34no—
263#389—32no—
264#389—32no—
265#388—34no—
266#388—34no—
267#386—34no—
268#386—32no—
269#386—32no—
270#386—34no—
271#385—32no—
272#385—32no—
273#381—32no—
274#380—32no—
275#380—32no—
276#380—34no—
277#379—32no—
278C4×C4⋊C4—34no—
279C4×C22⋊C4—34no—
280C4×C22⋊C4—34no—
281C24×C3—22no—
282C24×C3—22no—
283C24×C3—22no—
284C24×C3—24no—
285C24×C3—24no—
286C24×C3—22no—
287C24×C3—22no—
288C24×C3—42no—
289C24×C3—42no—
290C24×C3C2×D414yes—
291C24×C3C2411yescharacteristic
292C24×C3C2412yes—
293C24×C3C2411yescharacteristic
294C24×C3C2411yescharacteristic
295C23×D3C2412yes—
296C2×C3×D4—232no—
297C2×C3×D4—24no—
298C2×C3×D4—24no—
299C2×C3×D4—24no—
300C2×C3×D4—24no—
301C2×C3×D4—24no—
302C2×C3×D4#4118yescomplemented
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—232no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—24no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—24no—
321C22×C3×C4—24no—
322C22×C3×C4—24no—
323C22×C3×C4—24no—
324C22×C3×C4—24no—
325C22×C3×C4—24no—
326C22×C3×C4—42no—
327C22×C3×C4—416no—
328C22×C3×C4C2×D414yes—
329C22×C3×C4C2×D414yes—
330C22×C3×C4C2×D414yes—
331C22×C3×C4C2×D414yes—
332C22×C3×C4C2×D414yes—
333C22×C3×C4C2×D414yes—
334C22×C3×C4C2×D414yes—
335C22×C3×C4#4114yes—
336C22×C3×C4C2412yes—
337C22×C3×C4C2412yes—
338C22×C3×C4C2411yescharacteristic
339C22×C3×C4C2411yescharacteristic
340C22×C3×C4C2412yes—
341C22×C3×C4C2411yescharacteristic
342C22×C3×C4C2411yescharacteristic
343C2×#67—24no—
344C2×#67—24no—
345C2×#67—24no—
346C2×#67—24no—
347C2×#67—28no—
348C2×#67—28no—
349C2×#67—24no—
350C2×#67—28no—
351C2×#67—44no—
352C2×#67—44no—
353C22×Dic3—28no—
354C22×Dic3—28no—
355C22×Dic3—44no—
356C22×Dic3C2414yes—
357C22×Dic3C2412yes—
358C22×Dic3C2412yes—
359C22×Dic3C2412yes—
360C22×Dic3C2414yes—
361#235—416no—
362C2×D12—22no—
363C2×D12—22no—
364C2×D12—22no—
365C2×C4×D3—24no—
366C2×C4×D3—24no—
367C2×C4×D3—24no—
368C2×Dic6—22no—
369C2×Dic6—22no—
370C2×Dic6—22no—
371C3×C4⋊C4—24no—
372C3×C4⋊C4—24no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—24no—
375C3×C22⋊C4—24no—
376C3×C22⋊C4—24no—
377C3×C42—24no—
378C3×C42—24no—
379#217—24no—
380#217—24no—
381#217—24no—
382#217—24no—
383#217—28no—
384#217—28no—
385#217—28no—
386#217—44no—
387#217C2×D418yes—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4—28no—
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—44no—
393C4⋊Dic3—22no—
394C4⋊Dic3—22no—
395C4⋊Dic3—24no—
396C4⋊Dic3—28no—
397C4⋊Dic3C2×D418yescomplemented
398Dic3⋊C4—24no—
399Dic3⋊C4—24no—
400Dic3⋊C4—28no—
401Dic3⋊C4—28no—
402Dic3⋊C4—44no—
403C4×Dic3—24no—
404C4×Dic3—24no—
405C4×Dic3—28no—
406C4×Dic3C2×D418yescomplemented
407C25C22×D311yescharacteristic
408C25C22×D311yescharacteristic
409C2×#41—64no—
410C2×#41—64no—
411C2×#41—64no—
412C22×Q8—31no—
413C22×D4—24no—
414C22×D4—28no—
415C22×D4—32no—
416C22×D4—32no—
417C22×D4—34no—
418C22×D4—32no—
419C22×D4—31no—
420C22×D4C22×D312yes—
421C22×D4C22×D312yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—34no—
428C23×C4—32no—
429C23×C4#6718yescomplemented
430C23×C4C22×D311yescharacteristic
431C23×C4C22×D311yescharacteristic
432C23×C4C22×D312yes—
433C23×C4C22×D312yes—
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C23×C4C22×D311yescharacteristic
441#123—68no—
442#123—68no—
443C22⋊Q8—68no—
444C22⋊Q8—64no—
445C22⋊Q8—64no—
446#121—68no—
447#121—616no—
448#121—64no—
449#121—64no—
450#120—68no—
451#120—68no—
452C4×D4—28no—
453C4×D4—28no—
454C4×D4—28no—
455C4×D4—28no—
456C4×D4—616no—
457C4×D4—68no—
458C4×D4—68no—
459#117—38no—
460#117—68no—
461#117—68no—
462#117—68no—
463#117—64no—
464#117—64no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—32no—
467C2×C4⋊C4—32no—
468C2×C4⋊C4—34no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—34no—
472C2×C4⋊C4—32no—
473C2×C4⋊C4—32no—
474C2×C4⋊C4—34no—
475C2×C4⋊C4—34no—
476C2×C4⋊C4—68no—
477C2×C4⋊C4C22×D312yes—
478C2×C4⋊C4C22×D312yes—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—32no—
482C2×C22⋊C4—32no—
483C2×C22⋊C4—34no—
484C2×C22⋊C4—32no—
485C2×C22⋊C4—32no—
486C2×C22⋊C4—34no—
487C2×C22⋊C4—32no—
488C2×C22⋊C4—34no—
489C2×C22⋊C4—34no—
490C2×C22⋊C4—32no—
491C2×C22⋊C4—32no—
492C2×C22⋊C4—34no—
493C2×C22⋊C4—34no—
494C2×C22⋊C4—34no—
495C2×C22⋊C4—68no—
496C2×C22⋊C4C22×D312yes—
497C2×C22⋊C4C22×D312yes—
498C2×C22⋊C4C22×D312yes—
499C2×C22⋊C4C22×D312yes—
500C2×C42—24no—
501C2×C42—32no—
502C2×C42—34no—
503C2×C42—32no—
504C2×C42—32no—
505C2×C42—68no—
506C2×C42C22×D312yes—
507C2×C42C22×D312yes—
508#95—34no—
509#95—34no—
510#95—34no—
511#95—34no—
512#95—34no—
513#95—34no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—28no—
520C23×C3—28no—
521C23×C3—28no—
522C23×C3—21no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—21no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—44no—
533C23×C3—48no—
534C23×C3—48no—
535C23×C3—48no—
536C23×C3—48no—
537C23×C3—44no—
538C23×C3—44no—
539C23×C3C22×D412yes—
540C23×C3C22×D412yes—
541C23×C3C22×D412yes—
542C23×C3C22×D412yes—
543C23×C3C2×#4114yes—
544C23×C3C2×#4114yes—
545C23×C3C2×#4112yes—
546C23×C3C2511yescharacteristic
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—24no—
550C22×D3—22no—
551C22×D3—24no—
552C3×D4—216no—
553C3×D4—216no—
554C2×C3×C4—28no—
555C2×C3×C4—28no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—22no—
562C2×C3×C4—28no—
563C2×C3×C4—28no—
564C2×C3×C4—28no—
565C2×C3×C4—28no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—44no—
573C2×C3×C4—44no—
574C2×C3×C4—48no—
575C2×C3×C4—48no—
576C2×C3×C4#121116yescomplemented
577C2×C3×C4C22×D412yes—
578C2×C3×C4C22×D412yes—
579C2×C3×C4C22×D412yes—
580C2×C3×C4C22×D412yes—
581C2×C3×C4C22×D412yes—
582C2×C3×C4C22×D412yes—
583C2×C3×C4C2×#4114yes—
584C2×C3×C4C2×#4112yes—
585C2×C3×C4C2×#4112yes—
586#67—416no—
587#67—48no—
588#67—48no—
589#67—48no—
590C2×Dic3—24no—
591C2×Dic3—24no—
592C2×Dic3—24no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—24no—
598C2×Dic3—24no—
599C2×Dic3—22no—
600C2×Dic3—24no—
601C2×Dic3—24no—
602C2×Dic3—416no—
603C2×Dic3C22×D418yes—
604D12—44no—
605C4×D3—48no—
606Dic6—44no—
607C24—24no—
608C24—24no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—32no—
615C24—42no—
616C24—42no—
617C24C2×#6714yes—
618C24C23×D312yes—
619C24C23×D311yescharacteristic
620C24C23×D311yescharacteristic
621C24C23×D311yescharacteristic
622#41—1216no—
623C2×Q8—62no—
624C2×Q8—62no—
625C2×Q8—62no—
626C2×D4—232no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—64no—
636C2×D4—64no—
637C2×D4—64no—
638C2×D4—64no—
639C2×D4—64no—
640C2×D4—62no—
641C2×D4—62no—
642C2×D4—62no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4#23518yescomplemented
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—232no—
650C22×C4—24no—
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—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—34no—
670C22×C4—34no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—42no—
675C22×C4—416no—
676C22×C4—68no—
677C22×C4—68no—
678C22×C4—64no—
679C22×C4—64no—
680C22×C4—64no—
681C22×C4—124no—
682C22×C4D3×D414yes—
683C22×C4#23714yes—
684C22×C4C2×#6714yes—
685C22×C4C2×#6714yes—
686C22×C4C2×#6714yes—
687C22×C4C2×#6714yes—
688C22×C4C2×#6714yes—
689C22×C4C2×#6714yes—
690C22×C4C23×D312yes—
691C22×C4C23×D312yes—
692C22×C4C23×D312yes—
693C22×C4C23×D311yescharacteristic
694C22×C4C23×D311yescharacteristic
695C22×C4C23×D311yescharacteristic
696C22×C4C23×D311yescharacteristic
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—38no—
700C4⋊C4—68no—
701C4⋊C4—68no—
702C4⋊C4—68no—
703C4⋊C4—64no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—64no—
707C4⋊C4—64no—
708C4⋊C4—124no—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—38no—
714C22⋊C4—68no—
715C22⋊C4—68no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—64no—
719C22⋊C4—64no—
720C22⋊C4—64no—
721C22⋊C4—64no—
722C22⋊C4—68no—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C22⋊C4—124no—
726C22⋊C4—124no—
727C42—24no—
728C42—24no—
729C42—38no—
730C42—68no—
731C42—64no—
732C42—64no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—24no—
738C22×C3—24no—
739C22×C3—24no—
740C22×C3—24no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—24no—
744C22×C3—22no—
745C22×C3—24no—
746C22×C3—24no—
747C22×C3—416no—
748C22×C3—416no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3C2×#12114yes—
756C22×C3#52514yescomplemented
757C22×C3C23×D411yescharacteristic
758C22×C3C23×D411yescharacteristic
759C22×C3C22×#4112yes—
760C22×C3C22×#4111yescharacteristic
761C22×C3#58512yes—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—44no—
766C2×D3—44no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—24no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4C2×#12114yes—
773C3×C4C2×#12114yes—
774Dic3—28no—
775Dic3—42no—
776Dic3—42no—
777Dic3—42no—
778Dic3—44no—
779C23—22no—
780C23—21no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—28no—
785C23—22no—
786C23—22no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—28no—
796C23—28no—
797C23—44no—
798C23—48no—
799C23—48no—
800C23—48no—
801C23—48no—
802C23—44no—
803C23—44no—
804C23—64no—
805C23—62no—
806C23—62no—
807C23—64no—
808C23—62no—
809C23C2×#23514yes—
810C23C2×#23514yes—
811C23C2×D3×D412yes—
812C23C2×#23712yes—
813C23C22×#6712yes—
814C23C22×#6712yes—
815C23C22×#6712yes—
816C23C24×D311yescharacteristic
817Q8—124no—
818D4—216no—
819D4—216no—
820D4—1216no—
821D4—128no—
822D4—128no—
823D4—128no—
824D4—124no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—28no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—38no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—48no—
847C2×C4—48no—
848C2×C4—64no—
849C2×C4—64no—
850C2×C4—64no—
851C2×C4—64no—
852C2×C4—64no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—64no—
856C2×C4—64no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—1216no—
861C2×C4—128no—
862C2×C4#939116yescomplemented
863C2×C4C2×#23514yes—
864C2×C4C2×D3×D412yes—
865C2×C4C2×D3×D412yes—
866C2×C4C2×#23712yes—
867C2×C4C2×#23712yes—
868C2×C4C22×#6712yes—
869C2×C4C22×#6712yes—
870C2×C4C22×#6712yes—
871C2×C4C22×#6712yes—
872C2×C3—24no—
873C2×C3—24no—
874C2×C3—42no—
875C2×C3—44no—
876C2×C3C22×#12111yescharacteristic
877C2×C3C2×#52511yescharacteristic
878C2×C3#344911yescharacteristic
879C2×C3D4×#4112yes—
880C2×C3#347512yes—
881D3—82no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—416no—
897C22—416no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—124no—
905C22—124no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22#579114yescomplemented
910C22C2×#93914yes—
911C22C22×#23512yes—
912C22C22×D3×D411yescharacteristic
913C22C22×#23711yescharacteristic
914C22#596412yes—
915C22C23×#6711yescharacteristic
916C4—24no—
917C4—22no—
918C4—22no—
919C4—42no—
920C4—42no—
921C4—68no—
922C4—124no—
923C4—122no—
924C4—122no—
925C4—122no—
926C4C2×#93914yes—
927C4C2×#93914yes—
928C3#3473711yescharacteristic, complemented, Sylow
929C2—24no—
930C2—24no—
931C2—44no—
932C2—42no—
933C2—242no—
934C2#8576412yes—
935C2D4×#23512yes—
936C2C2×#579111yescharacteristic
937C2C22×#93911yescharacteristic
938C2#8726811yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutator, socle, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×C4×D4C2
hypercenterC22×C4×D4D3
hypocenterC3#34737
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×D4C2semidirect
2. C2×#5791C2semidirect
3. C2×#5791C2semidirect
4. C22×#926C2semidirect
5. #84048C2semidirect
6. #84027C2semidirect
7. #82353C2semidirect
8. #82352C2semidirect
9. #82351C2semidirect
10. #82350C2semidirect
11. #82345C2semidirect
12. C4×#939C2semidirect
13. #82170C2semidirect
14. #82107C2semidirect
15. #82106C2semidirect
16. #82070C2semidirect
17. #82069C2semidirect
38. C2×#930C22semidirect
39. C2×#930C22semidirect
40. C2×#930C22semidirect
43. C2×C4×#67C22semidirect
44. C2×C4×#67C22semidirect
45. C2×C4×#67C22semidirect
51. C2×#926C22semidirect
52. C2×#926C22semidirect
53. C22×C4⋊Dic3C22semidirect
54. C2×#924C22semidirect
55. C2×#924C22semidirect
56. C2×#924C22semidirect
57. C22×C4×Dic3C22semidirect
64. #5212C22semidirect
65. #5212C22semidirect
69. C4×#217C22semidirect
70. #4994C22semidirect
71. #4990C22semidirect
72. #4982C22semidirect
73. #4976C22semidirect
74. #4961C22semidirect
75. #4959C22semidirect
76. #4958C22semidirect
77. #4957C22semidirect
78. #4952C22semidirect
79. #4948C22semidirect
80. #4945C22semidirect
81. #4942C22semidirect
82. #4939C22semidirect
83. C4×(C2×D3)⋊C4C22semidirect
84. C4×Dic3⋊C4C22semidirect
85. #4929C22semidirect
86. #4928C22semidirect
87. #4928C22semidirect
90. C22×C4×D4D3semidirect
116. C23×C3×C4D4semidirect
186. #926D4semidirect
302. C2×C3×D4#41semidirect
397. C4⋊Dic3C2×D4semidirect
406. C4×Dic3C2×D4semidirect
429. C23×C4#67semidirect
576. C2×C3×C4#121semidirect
645. C2×D4#235semidirect
756. C22×C3#525semidirect
862. C2×C4#939semidirect
909. C22#5791semidirect
928. C3#34737semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×#57912
C22×#9262
#840482
#840272
#823532
#823522
#823512
#823502
#823452
C4×#9392
#821702
#821072
#821062
#820702
#820692
#347373