Finite Group Databasebeta

← D4×#924 #10990515

Subgroups — D4×#924 #10990515

Order 768.

3488 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C22×#924C212yesmaximal, complemented
3C2×D4×Dic6C211yesmaximal, characteristic, complemented
4D4×#217C212yesmaximal
5#84031C212yesmaximal, complemented
6#82379C211yesmaximal, characteristic, complemented
7#82376C211yesmaximal, characteristic, complemented
8#82362C212yesmaximal, complemented
9#82360C214yesmaximal, complemented
10#82353C212yesmaximal, complemented
11#82349C212yesmaximal, complemented
12D4×Dic3⋊C4C212yesmaximal, complemented
13D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
14#82171C212yesmaximal, complemented
15#82110C214yesmaximal, complemented
16#82076C211yesmaximal, characteristic, complemented
17C4×#924C211yesmaximal, characteristic, complemented
18D4×C22⋊Q8—31nomaximal, Sylow
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2212yes—
21C23×Dic6C2212yescomplemented
22C2×C3×C4×D4—28no—
23C2×C3×C4×D4C2211yescharacteristic
24C2×C3×C4×D4C2212yes—
25C2×C3×C4×D4C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2212yes—
31C22×C3×C42C2211yescharacteristic
32C22×#217C2214yes—
33C2×D4×Dic3C2212yes—
34C2×D4×Dic3C2212yes—
35C22×C4⋊Dic3C2212yescomplemented
36C2×#924—216no—
37C2×#924C2212yes—
38C2×#924C2214yes—
39C2×#924C2211yescharacteristic
40C2×#924C2212yescomplemented
41C2×#924C2212yescomplemented
42C2×#924C2212yescomplemented
43C2×#924C2214yescomplemented
44C2×#924C2212yescomplemented
45C22×Dic3⋊C4C2214yescomplemented
46D4×Dic6—28no—
47C2×#888C2212yescomplemented
48C2×#878C2214yescomplemented
49C2×#869C2211yescharacteristic, complemented
50C2×C4×Dic6C2211yescharacteristic, complemented
51#5247C2214yes—
52#5221C2212yes—
53#5221C2212yes—
54#5220C2214yes—
55#5220C2214yes—
56#5212C2211yescharacteristic
57#5212C2212yes—
58#5212C2212yes—
59#5212C2212yescomplemented
60#5212C2212yescomplemented
61#5210C2214yes—
62#5210C2212yes—
63#5210C2214yescomplemented
64#5210C2214yescomplemented
65C4×#217C2212yes—
66#4984C2212yescomplemented
67#4982C2214yescomplemented
68#4979C2214yescomplemented
69#4975C2212yescomplemented
70#4972C2212yescomplemented
71#4950C2214yescomplemented
72#4949C2214yescomplemented
73#4948C2214yescomplemented
74#4948C2214yescomplemented
75#4947C2214yescomplemented
76#4946C2214yescomplemented
77#4942C2214yescomplemented
78#4935C2211yescharacteristic, complemented
79C4×C4⋊Dic3C2211yescharacteristic, complemented
80#4933C2212yescomplemented
81C4×Dic3⋊C4C2212yescomplemented
82#4929C2211yescharacteristic, complemented
83#4929C2212yescomplemented
84#4928C2211yescharacteristic, complemented
85#4928C2212yescomplemented
86#4928C2212yescomplemented
87C2×D4×Q8—31no—
88C22×C22⋊Q8—32no—
89C22×C4×D4D311yescharacteristic
90#2857—31no—
91#2848—32no—
92#2542—31no—
93#2538—31no—
94#2452—32no—
95#2449—34no—
96#2440—32no—
97#2437—34no—
98#2417—32no—
99#2409—32no—
100D4×C4⋊C4—31no—
101D4×C4⋊C4—32no—
102D4×C22⋊C4—32no—
103C4×C22⋊Q8—31no—
104C25×C3C2312yes—
105C22×C3×D4—24no—
106C22×C3×D4—24no—
107C22×C3×D4Q818yescomplemented
108C22×C3×D4C2312yes—
109C22×C3×D4C2311yescharacteristic
110C22×C3×D4C2311yescharacteristic
111C23×C3×C4—28no—
112C23×C3×C4—28no—
113C23×C3×C4—44no—
114C23×C3×C4C2312yes—
115C23×C3×C4C2312yes—
116C23×C3×C4C2312yes—
117C23×C3×C4C2312yes—
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2312yes—
120C23×C3×C4C2311yescharacteristic
121C23×C3×C4C2311yescharacteristic
122C23×Dic3C2314yes—
123C23×Dic3C2314yes—
124C22×Dic6—28no—
125C22×Dic6—28no—
126C22×Dic6—44no—
127C22×Dic6C2312yes—
128C22×Dic6C2314yes—
129C22×Dic6C2311yescharacteristic
130C3×C4×D4—24no—
131C3×C4×D4—28no—
132C3×C4×D4—24no—
133C3×C4×D4—28no—
134C3×C4×D4—24no—
135C3×C4×D4D418yes—
136C2×C3×C4⋊C4—24no—
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2312yes—
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C22⋊C4—28no—
141C2×C3×C22⋊C4C2312yes—
142C2×C3×C22⋊C4C2312yes—
143C2×C3×C22⋊C4C2312yes—
144C2×C3×C22⋊C4C2312yes—
145C2×C3×C42—24no—
146C2×C3×C42C2311yescharacteristic
147C2×C3×C42C2311yescharacteristic
148C2×C3×C42C2311yescharacteristic
149C2×C3×C42C2311yescharacteristic
150C2×#217—216no—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2312yes—
156C2×#217C2314yes—
157C2×#217C2314yes—
158C2×#217C2314yes—
159C2×#217C2312yes—
160D4×Dic3—28no—
161D4×Dic3—28no—
162C2×C4⋊Dic3—28no—
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2314yes—
170C2×C4⋊Dic3C2312yes—
171C2×C4⋊Dic3C2311yescharacteristic
172#924—28no—
173#924—28no—
174#924—28no—
175#924—216no—
176#924—28no—
177#924—216no—
178#924—44no—
179#924D418yesdirect product factor
180C2×Dic3⋊C4—216no—
181C2×Dic3⋊C4C2314yes—
182C2×Dic3⋊C4C2312yes—
183C2×Dic3⋊C4C2314yes—
184C2×Dic3⋊C4C2314yes—
185C2×Dic3⋊C4C2314yes—
186C2×Dic3⋊C4C2312yes—
187C2×Dic3⋊C4C2314yes—
188C2×Dic3⋊C4C2312yes—
189C2×C4×Dic3C2312yes—
190C2×C4×Dic3C2312yes—
191#888—28no—
192#878—216no—
193#869—24no—
194C4×Dic6—24no—
195C3⋊#95C2314yes—
196C3⋊#95C2314yes—
197C3⋊#95C2312yes—
198C3⋊#95C2312yes—
199C3⋊#95C2312yes—
200C3⋊#95C2312yes—
201C3⋊#95C2312yes—
202C3⋊#95C2314yes—
203C3⋊#95C2314yes—
204C23×Q8—32no—
205C23×D4C2×D311yescharacteristic
206C24×C4C2×D312yes—
207D4×Q8—68no—
208C2×C4⋊Q8—32no—
209C2×C4⋊Q8—31no—
210C2×C22⋊Q8—31no—
211C2×C22⋊Q8—32no—
212C2×C22⋊Q8—32no—
213C2×C22⋊Q8—32no—
214C2×C22⋊Q8—32no—
215C2×C22⋊Q8—34no—
216C2×C22⋊Q8—34no—
217C2×C22⋊Q8—32no—
218C2×C22⋊Q8—34no—
219C2×C22⋊Q8—616no—
220C2×C4×Q8—31no—
221C2×C4×D4—28no—
222C2×C4×D4—32no—
223C2×C4×D4—32no—
224C2×C4×D4C2×D311yescharacteristic
225C2×C4×D4C2×D312yes—
226C2×C4×D4C2×D312yes—
227C2×C4×D4C2×D311yescharacteristic
228C2×C4×D4C2×D311yescharacteristic
229C2×C4×D4C2×D311yescharacteristic
230C22×C4⋊C4—32no—
231C22×C4⋊C4—34no—
232C22×C4⋊C4C2×D311yescharacteristic
233C22×C22⋊C4—34no—
234C22×C22⋊C4C2×D312yes—
235C22×C42C2×D311yescharacteristic
236#399—34no—
237#398—34no—
238#396—34no—
239#396—34no—
240#395—34no—
241#393—34no—
242#391—32no—
243#391—31no—
244#390—32no—
245#390—32no—
246#389—32no—
247#389—32no—
248#389—32no—
249#389—32no—
250#389—31no—
251#387—32no—
252#386—34no—
253#386—34no—
254#385—34no—
255#385—34no—
256#385—34no—
257#385—32no—
258#385—34no—
259#385—34no—
260#384—32no—
261#384—31no—
262#380—31no—
263#380—32no—
264#380—32no—
265#380—32no—
266#380—32no—
267#380—34no—
268#379—34no—
269C4×C4⋊C4—32no—
270C4×C4⋊C4—31no—
271C4×C22⋊C4—32no—
272C24×C3—24no—
273C24×C3—24no—
274C24×C3—24no—
275C24×C3—24no—
276C24×C3—42no—
277C24×C3—42no—
278C24×C3C2×Q818yescomplemented
279C24×C3C2412yes—
280C24×C3C2412yes—
281C24×C3C2411yescharacteristic
282C2×C3×D4—24no—
283C2×C3×D4—24no—
284C2×C3×D4—232no—
285C2×C3×D4—22no—
286C2×C3×D4—22no—
287C2×C3×D4C2×D414yes—
288C2×C3×D4C2×Q814yes—
289C2×C3×D4C2×Q818yescomplemented
290C2×C3×D4C2×Q814yescomplemented
291C2×C3×D4#4114yes—
292C22×C3×C4—24no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—24no—
297C22×C3×C4—22no—
298C22×C3×C4—24no—
299C22×C3×C4—24no—
300C22×C3×C4—22no—
301C22×C3×C4—24no—
302C22×C3×C4—24no—
303C22×C3×C4—24no—
304C22×C3×C4—22no—
305C22×C3×C4—24no—
306C22×C3×C4—24no—
307C22×C3×C4—24no—
308C22×C3×C4—24no—
309C22×C3×C4—42no—
310C22×C3×C4—42no—
311C22×C3×C4—42no—
312C22×C3×C4—41no—
313C22×C3×C4—432no—
314C22×C3×C4C2×D414yes—
315C22×C3×C4C2×D418yes—
316C22×C3×C4C2×Q814yescomplemented
317C22×C3×C4C2411yescharacteristic
318C22×C3×C4C2412yes—
319C22×C3×C4C2411yescharacteristic
320C22×C3×C4C2411yescharacteristic
321C22×C3×C4C2412yes—
322C22×C3×C4C2411yescharacteristic
323C22×C3×C4C2411yescharacteristic
324C22×C3×C4C2411yescharacteristic
325C22×Dic3—28no—
326C22×Dic3—28no—
327C22×Dic3—28no—
328C22×Dic3—28no—
329C22×Dic3—44no—
330C22×Dic3—44no—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2414yes—
334C22×Dic3C2414yes—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C2×Dic6—22no—
338C2×Dic6—22no—
339C2×Dic6—24no—
340C2×Dic6—28no—
341C2×Dic6—24no—
342C2×Dic6—24no—
343C2×Dic6—28no—
344C2×Dic6—432no—
345C2×Dic6—44no—
346C2×Dic6C2×D414yescomplemented
347C3×C4⋊C4—24no—
348C3×C4⋊C4—22no—
349C3×C4⋊C4C2×D414yes—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—24no—
352C3×C22⋊C4—24no—
353C3×C22⋊C4C2×D418yes—
354C3×C42—22no—
355C3×C42—22no—
356C3×C42—22no—
357C3×C42C2×D414yes—
358#217—28no—
359#217—28no—
360#217—28no—
361#217—24no—
362#217—28no—
363#217—28no—
364#217—44no—
365#217—44no—
366#217C2×D418yes—
367C4⋊Dic3—22no—
368C4⋊Dic3—24no—
369C4⋊Dic3—24no—
370C4⋊Dic3—24no—
371C4⋊Dic3—24no—
372C4⋊Dic3—22no—
373C4⋊Dic3—28no—
374C4⋊Dic3—42no—
375C4⋊Dic3C2×D414yescomplemented
376Dic3⋊C4—24no—
377Dic3⋊C4—28no—
378Dic3⋊C4—28no—
379Dic3⋊C4—28no—
380Dic3⋊C4—28no—
381Dic3⋊C4—42no—
382Dic3⋊C4—44no—
383Dic3⋊C4C2×D418yescomplemented
384C4×Dic3—24no—
385C4×Dic3—24no—
386C25C22×D312yes—
387C22×Q8—31no—
388C22×Q8—32no—
389C22×Q8—34no—
390C22×Q8—68no—
391C22×Q8—68no—
392C22×Q8—124no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4Dic618yescomplemented
396C22×D4C22×D312yes—
397C22×D4C22×D311yescharacteristic
398C22×D4C22×D311yescharacteristic
399C23×C4—28no—
400C23×C4—28no—
401C23×C4—34no—
402C23×C4—34no—
403C23×C4—44no—
404C23×C4C22×D312yes—
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D312yes—
407C23×C4C22×D312yes—
408C23×C4C22×D312yes—
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D312yes—
412C4⋊Q8—68no—
413C4⋊Q8—64no—
414C22⋊Q8—38no—
415C22⋊Q8—616no—
416C22⋊Q8—616no—
417C22⋊Q8—68no—
418C22⋊Q8—68no—
419C22⋊Q8—68no—
420C22⋊Q8—68no—
421C22⋊Q8—616no—
422C22⋊Q8—124no—
423C4×Q8—64no—
424C4×D4—24no—
425C4×D4—28no—
426C4×D4—24no—
427C4×D4—28no—
428C4×D4—24no—
429C4×D4—68no—
430C4×D4—68no—
431C4×D4#6718yes—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—32no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—34no—
439C2×C4⋊C4—34no—
440C2×C4⋊C4—32no—
441C2×C4⋊C4—32no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—32no—
445C2×C4⋊C4—34no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—34no—
448C2×C4⋊C4—32no—
449C2×C4⋊C4—32no—
450C2×C4⋊C4—616no—
451C2×C4⋊C4—68no—
452C2×C4⋊C4C22×D311yescharacteristic
453C2×C4⋊C4C22×D312yes—
454C2×C4⋊C4C22×D311yescharacteristic
455C2×C22⋊C4—28no—
456C2×C22⋊C4—32no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4—34no—
460C2×C22⋊C4—34no—
461C2×C22⋊C4—34no—
462C2×C22⋊C4—32no—
463C2×C22⋊C4—34no—
464C2×C22⋊C4—34no—
465C2×C22⋊C4—616no—
466C2×C22⋊C4C22×D312yes—
467C2×C22⋊C4C22×D312yes—
468C2×C22⋊C4C22×D312yes—
469C2×C22⋊C4C22×D312yes—
470C2×C42—24no—
471C2×C42—32no—
472C2×C42—32no—
473C2×C42C22×D311yescharacteristic
474C2×C42C22×D311yescharacteristic
475C2×C42C22×D311yescharacteristic
476C2×C42C22×D311yescharacteristic
477#95—32no—
478#95—32no—
479#95—32no—
480#95—32no—
481#95—32no—
482#95—34no—
483#95—34no—
484#95—34no—
485#95—34no—
486C23×C3—22no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—22no—
490C23×C3—21no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—21no—
494C23×C3—216no—
495C23×C3—216no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—48no—
503C23×C3—48no—
504C23×C3—48no—
505C23×C3—48no—
506C23×C3—48no—
507C23×C3C22×D412yes—
508C23×C3C22×D414yes—
509C23×C3C22×Q814yes—
510C23×C3C22×Q814yes—
511C23×C3C22×Q812yes—
512C23×C3C2×#4114yes—
513C23×C32−1+412yes—
514C23×C3C2511yescharacteristic
515C3×D4—216no—
516C3×D4—28no—
517C3×D4C22⋊Q8116yescomplemented
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—28no—
527C2×C3×C4—216no—
528C2×C3×C4—28no—
529C2×C3×C4—22no—
530C2×C3×C4—21no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—48no—
536C2×C3×C4—44no—
537C2×C3×C4—48no—
538C2×C3×C4—48no—
539C2×C3×C4—48no—
540C2×C3×C4C22×D412yes—
541C2×C3×C4C22×D412yes—
542C2×C3×C4C22×D412yes—
543C2×C3×C4C22×D414yes—
544C2×C3×C4C22×D412yes—
545C2×C3×C4C22×D412yes—
546C2×C3×C4C22×Q812yes—
547C2×C3×C4C22×Q812yes—
548C2×C3×C4C2×#4112yes—
549C2×C3×C4H(5,𝔽2)12yes—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—24no—
556C2×Dic3—24no—
557C2×Dic3—24no—
558C2×Dic3—22no—
559C2×Dic3—24no—
560C2×Dic3—22no—
561C2×Dic3—24no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—24no—
566C2×Dic3—416no—
567C2×Dic3—416no—
568C2×Dic3C22×D414yes—
569C2×Dic3C22×D414yes—
570Dic6—28no—
571Dic6—416no—
572Dic6—48no—
573C24—24no—
574C24—24no—
575C24—24no—
576C24—24no—
577C24—42no—
578C24—42no—
579C24C2×Dic618yescomplemented
580C24C23×D312yes—
581C24C23×D312yes—
582C24C23×D311yescharacteristic
583C2×Q8—34no—
584C2×Q8—68no—
585C2×Q8—64no—
586C2×Q8—62no—
587C2×Q8—64no—
588C2×Q8—62no—
589C2×Q8—68no—
590C2×Q8—64no—
591C2×Q8—124no—
592C2×Q8—1232no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—232no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4C2×Dic614yes—
599C2×D4C2×Dic618yescomplemented
600C2×D4C2×Dic614yescomplemented
601C2×D4#23514yes—
602C2×D4C2×#6714yes—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—34no—
625C22×C4—34no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—432no—
631C22×C4—68no—
632C22×C4—68no—
633C22×C4—68no—
634C22×C4—68no—
635C22×C4—124no—
636C22×C4—124no—
637C22×C4C2×Dic614yescomplemented
638C22×C4D3×D414yes—
639C22×C4C2×#6718yes—
640C22×C4C23×D311yescharacteristic
641C22×C4C23×D312yes—
642C22×C4C23×D311yescharacteristic
643C22×C4C23×D311yescharacteristic
644C22×C4C23×D311yescharacteristic
645C22×C4C23×D312yes—
646C22×C4C23×D311yescharacteristic
647C22×C4C23×D311yescharacteristic
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—38no—
651C4⋊C4—34no—
652C4⋊C4—68no—
653C4⋊C4—68no—
654C4⋊C4—68no—
655C4⋊C4—64no—
656C4⋊C4—68no—
657C4⋊C4—64no—
658C4⋊C4—62no—
659C4⋊C4—64no—
660C4⋊C4—64no—
661C4⋊C4—62no—
662C4⋊C4—68no—
663C4⋊C4—64no—
664C4⋊C4—124no—
665C4⋊C4—122no—
666C4⋊C4—122no—
667C4⋊C4C2×#6714yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—38no—
672C22⋊C4—68no—
673C22⋊C4—68no—
674C22⋊C4—68no—
675C22⋊C4—68no—
676C22⋊C4—64no—
677C22⋊C4—68no—
678C22⋊C4—124no—
679C22⋊C4—124no—
680C22⋊C4C2×#6718yes—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—64no—
685C42—64no—
686C42C2×#6714yes—
687C22×C3—22no—
688C22×C3—24no—
689C22×C3—22no—
690C22×C3—24no—
691C22×C3—24no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—24no—
695C22×C3—22no—
696C22×C3—24no—
697C22×C3—22no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—432no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3C2×C22⋊Q818yescomplemented
708C22×C3D4×Q814yescomplemented
709C22×C3C23×D411yescharacteristic
710C22×C3C23×D411yescharacteristic
711C22×C3C23×Q811yescharacteristic
712C22×C3C22×#4111yescharacteristic
713C22×C3C2×H(5,𝔽2)11yescharacteristic
714C22×C3C2×2−1+411yescharacteristic
715C22×C3#58511yescharacteristic
716C3×C4—22no—
717C3×C4—24no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—42no—
721C3×C4—41no—
722C3×C4C2×C22⋊Q814yescomplemented
723C3×C4D4214yes—
724Dic3—24no—
725Dic3—24no—
726Dic3—44no—
727Dic3—44no—
728Dic3—42no—
729Dic3—42no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—216no—
745C23—216no—
746C23—48no—
747C23—48no—
748C23—48no—
749C23—48no—
750C23—48no—
751C23C22×Dic614yes—
752C23C22×Dic614yes—
753C23C22×Dic612yes—
754C23C2×#23514yes—
755C23C2×D3×D412yes—
756C23#101012yes—
757C23C22×#6714yes—
758C23C24×D311yescharacteristic
759Q8—68no—
760Q8—1216no—
761Q8—128no—
762D4—216no—
763D4—28no—
764D4#924116yesdirect product factor
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—216no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—34no—
783C2×C4—34no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—44no—
788C2×C4—48no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—64no—
795C2×C4—64no—
796C2×C4—64no—
797C2×C4—62no—
798C2×C4—64no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—64no—
803C2×C4—62no—
804C2×C4—64no—
805C2×C4—1216no—
806C2×C4—1216no—
807C2×C4C22×Dic612yes—
808C2×C4C22×Dic612yes—
809C2×C4C2×#23512yes—
810C2×C4C2×D3×D412yes—
811C2×C4C2×D3×D412yes—
812C2×C4#100412yes—
813C2×C4C22×#6712yes—
814C2×C4C22×#6714yes—
815C2×C4C22×#6712yes—
816C2×C4C22×#6712yes—
817C2×C3—24no—
818C2×C3—28no—
819C2×C3—44no—
820C2×C3C22×C22⋊Q811yescharacteristic
821C2×C3C2×D4211yescharacteristic
822C2×C3C2×D4×Q811yescharacteristic
823C2×C3D4×#4111yescharacteristic
824C2×C3#348911yescharacteristic
825C2×C3#350111yescharacteristic
826C2×C3#352011yescharacteristic
827C22—22no—
828C22—24no—
829C22—22no—
830C22—24no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—24no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—432no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22D4×Dic614yescomplemented
848C22C2×#92418yescomplemented
849C22C23×Dic611yescharacteristic
850C22C22×#23511yescharacteristic
851C22C22×D3×D411yescharacteristic
852C22C2×#100411yescharacteristic
853C22C2×#101011yescharacteristic
854C22#596411yescharacteristic
855C22C23×#6711yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—42no—
861C4—41no—
862C4—64no—
863C4—64no—
864C4—122no—
865C4—124no—
866C4—124no—
867C4—122no—
868C4C2×#92414yescomplemented
869C4D4×#6714yes—
870C3D4×C22⋊Q811yescharacteristic, complemented, Sylow
871C2—24no—
872C2—28no—
873C2—44no—
874C2C2×D4×Dic611yescharacteristic
875C2#8576611yescharacteristic
876C2#8576711yescharacteristic
877C2D4×#23511yescharacteristic
878C2C22×#92411yescharacteristic
879C2C2×D4×#6711yescharacteristic
880C2#8726411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC22×C3×C4×D4C2
prime radicalC23×C3×D4C22
hypercenterC22×C4×D4D3
hypocenterC3D4×C22⋊Q8
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#924C2semidirect
3. C2×D4×Dic6C2semidirect
5. #84031C2semidirect
6. #82379C2semidirect
7. #82376C2semidirect
8. #82362C2semidirect
9. #82360C2semidirect
10. #82353C2semidirect
11. #82349C2semidirect
12. D4×Dic3⋊C4C2semidirect
13. D4×C4⋊Dic3C2semidirect
14. #82171C2semidirect
15. #82110C2semidirect
16. #82076C2semidirect
17. C4×#924C2semidirect
21. C23×Dic6C22semidirect
35. C22×C4⋊Dic3C22semidirect
40. C2×#924C22semidirect
41. C2×#924C22semidirect
42. C2×#924C22semidirect
43. C2×#924C22semidirect
44. C2×#924C22semidirect
45. C22×Dic3⋊C4C22semidirect
47. C2×#888C22semidirect
48. C2×#878C22semidirect
49. C2×#869C22semidirect
50. C2×C4×Dic6C22semidirect
59. #5212C22semidirect
60. #5212C22semidirect
63. #5210C22semidirect
64. #5210C22semidirect
66. #4984C22semidirect
67. #4982C22semidirect
68. #4979C22semidirect
69. #4975C22semidirect
70. #4972C22semidirect
71. #4950C22semidirect
72. #4949C22semidirect
73. #4948C22semidirect
74. #4948C22semidirect
75. #4947C22semidirect
76. #4946C22semidirect
77. #4942C22semidirect
78. #4935C22semidirect
79. C4×C4⋊Dic3C22semidirect
80. #4933C22semidirect
81. C4×Dic3⋊C4C22semidirect
82. #4929C22semidirect
83. #4929C22semidirect
84. #4928C22semidirect
85. #4928C22semidirect
86. #4928C22semidirect
107. C22×C3×D4Q8semidirect
179. #924D4direct (N × H)
278. C24×C3C2×Q8semidirect
289. C2×C3×D4C2×Q8semidirect
290. C2×C3×D4C2×Q8semidirect
316. C22×C3×C4C2×Q8semidirect
346. C2×Dic6C2×D4semidirect
375. C4⋊Dic3C2×D4semidirect
383. Dic3⋊C4C2×D4semidirect
395. C22×D4Dic6semidirect
517. C3×D4C22⋊Q8semidirect
579. C24C2×Dic6semidirect
599. C2×D4C2×Dic6semidirect
600. C2×D4C2×Dic6semidirect
637. C22×C4C2×Dic6semidirect
707. C22×C3C2×C22⋊Q8semidirect
708. C22×C3D4×Q8semidirect
722. C3×C4C2×C22⋊Q8semidirect
764. D4#924direct (N × H)
847. C22D4×Dic6semidirect
848. C22C2×#924semidirect
868. C4C2×#924semidirect
870. C3D4×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C22×#9242
C2×D4×Dic62
D4×#2172
#840312
#823792
#823762
#823622
#823602
#823532
#823492
D4×Dic3⋊C42
D4×C4⋊Dic32
#821712
#821102
#820762
C4×#9242
D4×C22⋊Q83