Finite Group Databasebeta

← #6500046

Subgroups — #6500046

Order 512.

3298 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C211yesmaximal, characteristic
2C2×#3195C211yesmaximal, characteristic, complemented
3C22×#470C211yesmaximal, characteristic, complemented
4#35084C211yesmaximal, characteristic
5#25561C214yesmaximal, complemented
6#25504C214yesmaximal, complemented
7#24453C214yesmaximal, complemented
8#24386C214yesmaximal, complemented
9#24097C212yesmaximal, complemented
10#24041C212yesmaximal, complemented
11#23970C212yesmaximal, complemented
12#23856C212yesmaximal, complemented
13#21768C211yesmaximal, characteristic, complemented
14#20972C211yesmaximal, characteristic, complemented
15#20898C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic, complemented
17C23×M16C2211yescharacteristic
18#3501—28no—
19#3501—28no—
20C2×#554—22no—
21C2×#554—22no—
22C2×#554C2212yes—
23C2×#554C2212yes—
24C2×D4×Q8C2212yes—
25C2×D4×Q8C2212yes—
26C2×#544—21no—
27C2×#543—21no—
28C2×#543—21no—
29C2×#533C2212yes—
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#518—21no—
35C22×C4×D4C2211yescharacteristic
36#3195—28no—
37C2×#483C2212yescomplemented
38C2×#483C2212yescomplemented
39C2×#470—28no—
40C2×#470C2214yes—
41C2×#470C2214yes—
42C2×#470C2214yescomplemented
43C2×#451C2212yescomplemented
44C2×#451C2212yescomplemented
45C2×#451C2214yescomplemented
46C22×#106C2211yescharacteristic, complemented
47C2×#419C2212yescomplemented
48C22×#103C2211yescharacteristic, complemented
49C22×#103C2211yescharacteristic, complemented
50C2×#407C2211yescharacteristic
51C2×#407C2212yes—
52#2855C2212yes—
53#2848C2212yes—
54#2638—22no—
55#2583—21no—
56#2561—21no—
57#2486C2212yes—
58#2483—21no—
59#2415C2214yes—
60#2409C2212yes—
61#2405—21no—
62#2322—22no—
63#2280C2211yescharacteristic
64#2058C2214yescomplemented
65#2043C2214yescomplemented
66#2035C2214yescomplemented
67#2035C2214yescomplemented
68#2024C2214yescomplemented
69#2016C2214yescomplemented
70#2001C2214yescomplemented
71#2001C2214yescomplemented
72#1894C2214yes—
73#1894C2214yes—
74#1892C2212yescomplemented
75#1892C2212yescomplemented
76#1878C2214yescomplemented
77#1878C2214yescomplemented
78#1873C2214yescomplemented
79#1872C2214yescomplemented
80#1870C2214yes—
81#1869C2212yes—
82#1869C2212yes—
83#1865C2214yescomplemented
84#1865C2214yescomplemented
85#1853C2214yescomplemented
86#1824C2212yescomplemented
87#1787C2212yescomplemented
88#1787C2214yescomplemented
89#1736C2212yescomplemented
90#1728C2212yes—
91C23×Q8C2311yescharacteristic
92C23×Q8C2312yes—
93C23×Q8C2311yescharacteristic
94C23×Q8C2311yescharacteristic
95C23×D4D411yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C22×Q16—24no—
99C22×Q16—44no—
100C22×Q16C2314yes—
101C22×Q16C2314yes—
102C22×M16—24no—
103C22×M16—44no—
104C22×M16C2312yes—
105C22×M16C2312yes—
106C22×M16C2312yes—
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109#554—232no—
110#554—232no—
111#554—28no—
112#554—28no—
113#554—28no—
114#554—28no—
115D4×Q8—28no—
116D4×Q8—28no—
117D4×Q8—28no—
118D4×Q8—28no—
119#544—216no—
120#543—216no—
121#543—216no—
122#533—28no—
123#533—28no—
124C2×C4⋊Q8—22no—
125C2×C4⋊Q8—22no—
126C2×C4⋊Q8C2312yes—
127C2×C4⋊Q8C2312yes—
128C2×#125—22no—
129C2×#125—22no—
130C2×#125—22no—
131C2×#123—22no—
132C2×C22⋊Q8—22no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—22no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—24no—
139C2×C22⋊Q8—24no—
140C2×C22⋊Q8—22no—
141C2×C22⋊Q8—28no—
142C2×C22⋊Q8—28no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—22no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8—22no—
148C2×C22⋊Q8—22no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8D418yes—
156C2×C22⋊Q8D418yes—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2312yes—
161C2×C22⋊Q8C2312yes—
162C2×C22⋊Q8C2312yes—
163C2×C22⋊Q8C2312yes—
164C2×C22⋊Q8C2312yes—
165C2×C22⋊Q8C2314yes—
166#518—216no—
167C2×C4×Q8—22no—
168C2×C4×Q8C2312yes—
169C2×C4×Q8C2312yes—
170C2×C4×D4—22no—
171C2×C4×D4—22no—
172C2×C4×D4—22no—
173C2×C4×D4—22no—
174C2×C4×D4—24no—
175C2×C4×D4—24no—
176C2×C4×D4D412yes—
177C2×C4×D4D412yes—
178C2×C4×D4C2312yes—
179C2×C4×D4C2312yes—
180C2×#117—22no—
181C2×#117C2312yes—
182C22×C4⋊C4—22no—
183C22×C4⋊C4—21no—
184C22×C4⋊C4—21no—
185C22×C4⋊C4—21no—
186C22×C4⋊C4D411yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C22⋊C4—22no—
192C22×C22⋊C4—21no—
193C22×C22⋊C4—21no—
194C22×C22⋊C4—21no—
195C22×C22⋊C4D411yescharacteristic
196C22×C22⋊C4D411yescharacteristic
197C22×C42C2311yescharacteristic
198#483—28no—
199#483—28no—
200#470—216no—
201#470—216no—
202#470—216no—
203#451—28no—
204#451—28no—
205#451—48no—
206C2×#106—24no—
207C2×#106C2314yes—
208C2×#106C2314yes—
209#419—44no—
210C2×#103—24no—
211C2×#103—24no—
212C2×#103C2314yes—
213C2×#103C2314yes—
214C2×#103C2314yes—
215C2×#103C2314yes—
216C2×#103C2314yes—
217C2×#103C2314yes—
218C2×#103C2314yes—
219C2×#103C2314yes—
220#407—24no—
221#407—44no—
222C2×C22⋊C8C2312yes—
223C2×C22⋊C8C2312yes—
224C2×C22⋊C8C2314yes—
225C2×C22⋊C8C2314yes—
226#398—22no—
227#397—22no—
228#397—24no—
229#395—22no—
230#394—24no—
231#393—22no—
232#391C2314yes—
233#389—24no—
234#389C2314yes—
235#388—24no—
236#387—24no—
237#386—22no—
238#385—24no—
239#385—22no—
240#385—22no—
241#385—22no—
242#381—22no—
243#381—21no—
244#381—22no—
245#380C2312yes—
246#380C2312yes—
247#380C2314yes—
248#379—22no—
249#379—21no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2314yes—
257#336C2314yes—
258C25C2×D411yescharacteristic
259C25C2×D411yescharacteristic
260C22×Q8—24no—
261C22×Q8—24no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—21no—
265C22×Q8—21no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—21no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—42no—
272C22×Q8—42no—
273C22×Q8—42no—
274C22×Q8—42no—
275C22×Q8—42no—
276C22×Q8—42no—
277C22×Q8—44no—
278C22×Q8—44no—
279C22×Q8C2×D414yes—
280C22×Q8C2×D414yes—
281C22×Q8C2412yes—
282C22×Q8C2412yes—
283C22×Q8C2412yes—
284C22×D4—24no—
285C22×D4—28no—
286C22×D4C2×D412yes—
287C22×D4C2×D412yes—
288C23×C4—22no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D414yes—
310C23×C4C2×D414yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×Q16—28no—
316C2×Q16—28no—
317C2×Q16—28no—
318C2×Q16—44no—
319C2×Q16—416no—
320C2×Q16—44no—
321C2×Q16—44no—
322C2×M16—24no—
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—42no—
328C2×M16—42no—
329C2×M16—42no—
330C2×M16—42no—
331C2×M16—416no—
332C22×C8—22no—
333C22×C8—24no—
334C22×C8—22no—
335C22×C8—42no—
336C22×C8C2412yes—
337C22×C8C2414yes—
338C22×C8C2412yes—
339C4⋊Q8—216no—
340C4⋊Q8—216no—
341C4⋊Q8—24no—
342C4⋊Q8—24no—
343C4⋊Q8—24no—
344C4⋊Q8—24no—
345#125—216no—
346#125—216no—
347#125—216no—
348#123—48no—
349C22⋊Q8—216no—
350C22⋊Q8—216no—
351C22⋊Q8—216no—
352C22⋊Q8—216no—
353C22⋊Q8—216no—
354C22⋊Q8—216no—
355C22⋊Q8—216no—
356C22⋊Q8—216no—
357C22⋊Q8—216no—
358C22⋊Q8—216no—
359C22⋊Q8—216no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362C22⋊Q8—28no—
363C22⋊Q8—28no—
364C22⋊Q8—28no—
365C22⋊Q8—28no—
366C22⋊Q8—24no—
367C22⋊Q8—24no—
368C22⋊Q8—24no—
369C22⋊Q8—24no—
370C22⋊Q8—24no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—24no—
375C22⋊Q8—24no—
376C22⋊Q8—44no—
377C22⋊Q8—44no—
378C22⋊Q8—44no—
379C22⋊Q8—44no—
380C22⋊Q8C2×D418yes—
381C22⋊Q8C2×D418yes—
382C22⋊Q8C2×D418yes—
383C22⋊Q8C2×D418yes—
384C4×Q8—216no—
385C4×Q8—24no—
386C4×Q8—24no—
387C4×Q8—24no—
388C4×Q8—24no—
389C4×D4—216no—
390C4×D4—216no—
391C4×D4—216no—
392C4×D4—216no—
393C4×D4—28no—
394C4×D4—28no—
395C4×D4—24no—
396C4×D4—24no—
397C4×D4—24no—
398C4×D4—24no—
399#117—216no—
400#117—42no—
401#117—42no—
402C2×C4⋊C4—216no—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D414yes—
435C2×C4⋊C4C2×D414yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C22⋊C4—216no—
441C2×C22⋊C4—28no—
442C2×C22⋊C4—28no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—44no—
459C2×C22⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42C2×D412yes—
469C2×C42C2412yes—
470#106—28no—
471#106—28no—
472#103—28no—
473#103—28no—
474#103—28no—
475#103—28no—
476#103—28no—
477#103—44no—
478#103—44no—
479#103—44no—
480C22⋊C8—24no—
481C22⋊C8—24no—
482C22⋊C8—28no—
483C22⋊C8—44no—
484#95—22no—
485#95—22no—
486#95—24no—
487#95—24no—
488#95—24no—
489#95—24no—
490C24—22no—
491C24—24no—
492C24—24no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24#12014yes—
498C24C22×D411yescharacteristic
499C24C22×D411yescharacteristic
500C24C22×D412yes—
501C24C22×D411yescharacteristic
502C2×Q8—28no—
503C2×Q8—28no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—24no—
511C2×Q8—24no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—24no—
515C2×Q8—24no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—48no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8—42no—
522C2×Q8—84no—
523C2×Q8—82no—
524C2×Q8—82no—
525C2×Q8—82no—
526C2×Q8—84no—
527C2×Q8—82no—
528C2×Q8—82no—
529C2×Q8—84no—
530C2×Q8—84no—
531C2×Q8—84no—
532C2×Q8—84no—
533C2×Q8—88no—
534C2×Q8C22×D414yes—
535C2×Q8C22×D414yes—
536C2×D4—232no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4#13718yes—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—84no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—84no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—84no—
592C22×C4—82no—
593C22×C4#12014yes—
594C22×C4#12014yes—
595C22×C4#12014yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C2511yescharacteristic
609Q16—416no—
610Q16—88no—
611M16—48no—
612M16—48no—
613M16—84no—
614C2×C8—28no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—24no—
618C2×C8—22no—
619C2×C8—24no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—24no—
623C2×C8—44no—
624C2×C8H(5,𝔽2)14yes—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—48no—
651C4⋊C4—84no—
652C4⋊C4C22×D414yes—
653C4⋊C4C22×D414yes—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—48no—
669C22⋊C4—82no—
670C22⋊C4—84no—
671C42—28no—
672C42—28no—
673C42—24no—
674C42—22no—
675C42—22no—
676C42—82no—
677C23—22no—
678C23—22no—
679C23—28no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—28no—
691C23—44no—
692C23—44no—
693C23—82no—
694C23—88no—
695C23—88no—
696C23—82no—
697C23C2×#12012yes—
698C23C2×#12012yes—
699C23C2×#12012yes—
700C23C2×#13714yes—
701C23C2×#13714yes—
702C23C23×D411yescharacteristic
703Q8—24no—
704Q8—24no—
705Q8—28no—
706Q8—42no—
707Q8—42no—
708Q8—44no—
709Q8—42no—
710Q8—42no—
711Q8—44no—
712Q8—84no—
713Q8—84no—
714Q8—84no—
715Q8—88no—
716Q8—88no—
717D4—216no—
718D4—216no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—84no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4—88no—
767C2×C4—88no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4C2×#12012yes—
771C2×C4C2×#12012yes—
772C2×C4C2×#12012yes—
773C2×C4C2×#13714yes—
774C2×C4C23×D411yescharacteristic
775C2×C4C23×D411yescharacteristic
776C2×C4C2×H(5,𝔽2)12yes—
777C2×C4#58512yes—
778C8—24no—
779C8—42no—
780C8—44no—
781C22—22no—
782C22—28no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—28no—
787C22—22no—
788C22—22no—
789C22—24no—
790C22—22no—
791C22—22no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—88no—
798C22—88no—
799C22#300414yes—
800C22C22×#12011yescharacteristic
801C22#349612yes—
802C22C22×#13712yes—
803C22#358612yes—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—24no—
808C4—42no—
809C4—44no—
810C4—44no—
811C4—42no—
812C4—44no—
813C4—44no—
814C4—82no—
815C4—84no—
816C4—82no—
817C4#348411yescharacteristic
818C4#348511yescharacteristic
819C4#349612yes—
820C2—24no—
821C2—42no—
822C2—44no—
823C2—42no—
824C2#3534711yescharacteristic
825C2C2×#300411yescharacteristic
826C2#6037011yescharacteristic
827C2#6230014yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3195C2semidirect
3. C22×#470C2semidirect
5. #25561C2semidirect
6. #25504C2semidirect
7. #24453C2semidirect
8. #24386C2semidirect
9. #24097C2semidirect
10. #24041C2semidirect
11. #23970C2semidirect
12. #23856C2semidirect
13. #21768C2semidirect
14. #20972C2semidirect
16. C23×Q16C22semidirect
37. C2×#483C22semidirect
38. C2×#483C22semidirect
42. C2×#470C22semidirect
43. C2×#451C22semidirect
44. C2×#451C22semidirect
45. C2×#451C22semidirect
46. C22×#106C22semidirect
47. C2×#419C22semidirect
48. C22×#103C22semidirect
49. C22×#103C22semidirect
64. #2058C22semidirect
65. #2043C22semidirect
66. #2035C22semidirect
67. #2035C22semidirect
68. #2024C22semidirect
69. #2016C22semidirect
70. #2001C22semidirect
71. #2001C22semidirect
74. #1892C22semidirect
75. #1892C22semidirect
76. #1878C22semidirect
77. #1878C22semidirect
78. #1873C22semidirect
79. #1872C22semidirect
83. #1865C22semidirect
84. #1865C22semidirect
85. #1853C22semidirect
86. #1824C22semidirect
87. #1787C22semidirect
88. #1787C22semidirect
89. #1736C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35012
C2×#31952
C22×#4702
#350842
#255612
#255042
#244532
#243862
#240972
#240412
#239702
#238562
#217682
#209722
#208982