Finite Group Databasebeta

← C2×#15614 #609229

Subgroups — C2×#15614 #609229

Order 512.

6586 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C22×#398C211yesmaximal, characteristic, complemented
3C22×#396C211yesmaximal, characteristic
4C22×#395C211yesmaximal, characteristic, complemented
5C22×#389C211yesmaximal, characteristic, complemented
6C22×#385C211yesmaximal, characteristic
7#15614C2116yesmaximal, direct product factor
8C2×#1446C211yesmaximal, characteristic, complemented
9C2×#1444C211yesmaximal, characteristic, complemented
10C2×#1441C211yesmaximal, characteristic, complemented
11C2×#1441C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic
13C2×#1439C211yesmaximal, characteristic
14C2×#1437C211yesmaximal, characteristic
15C2×C4⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8—28no—
20C22×C22⋊Q8—28no—
21C22×C22⋊Q8—28no—
22C22×C22⋊Q8C2218yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C42C2211yescharacteristic
40C2×#398—28no—
41C2×#398C2218yescomplemented
42C2×#396—28no—
43C2×#396C2218yes—
44C2×#395—28no—
45C2×#395C2218yescomplemented
46C2×#389—28no—
47C2×#389C2218yescomplemented
48C2×#385—28no—
49C2×#385C2218yes—
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66#1446C2218yescomplemented
67#1444C2218yescomplemented
68#1441C2218yescomplemented
69#1441C2218yescomplemented
70#1439C2218yes—
71#1439C2218yes—
72#1437C2218yes—
73C4⋊#95C2218yescomplemented
74C22⋊#95C2218yes—
75C26C2311yescharacteristic
76C23×Q8—24no—
77C23×Q8—24no—
78C23×Q8—24no—
79C23×Q8—24no—
80C23×Q8—24no—
81C23×Q8—42no—
82C23×Q8—42no—
83C23×Q8C2314yes—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2314yes—
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C2×C22⋊Q8—2128no—
107C2×C22⋊Q8—232no—
108C2×C22⋊Q8—232no—
109C2×C22⋊Q8—232no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4—42no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4—42no—
136C22×C4⋊C4—42no—
137C22×C4⋊C4D418yes—
138C22×C4⋊C4D418yes—
139C22×C4⋊C4D418yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2314yes—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—24no—
158C22×C22⋊C4—24no—
159C22×C22⋊C4—24no—
160C22×C22⋊C4—24no—
161C22×C22⋊C4—42no—
162C22×C22⋊C4—42no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4D418yes—
166C22×C22⋊C4Q818yescomplemented
167C22×C22⋊C4Q818yescomplemented
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C42—24no—
175C22×C42—24no—
176C22×C42—42no—
177C22×C42C2314yes—
178#398—232no—
179#396—232no—
180#395—232no—
181#389—232no—
182#385—232no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—24no—
193C2×#95—24no—
194C2×#95—24no—
195C2×#95—42no—
196C2×#95—42no—
197C2×#95—42no—
198C2×#95—42no—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25C2×D414yes—
228C25C2×Q814yes—
229C25C2×Q814yes—
230C25C2412yes—
231C25C2411yescharacteristic
232C22×Q8—232no—
233C22×Q8—28no—
234C22×Q8—28no—
235C22×Q8—28no—
236C22×Q8—28no—
237C22×Q8—28no—
238C22×Q8—44no—
239C22×Q8—44no—
240C22×Q8—416no—
241C22×Q8—416no—
242C22×Q8—416no—
243C22×Q8—416no—
244C22×Q8—416no—
245C22×Q8—416no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—232no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—28no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—28no—
315C23×C4—28no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—28no—
331C23×C4—28no—
332C23×C4—44no—
333C23×C4—44no—
334C23×C4—416no—
335C23×C4—416no—
336C23×C4—416no—
337C23×C4—416no—
338C23×C4—416no—
339C23×C4—416no—
340C23×C4C2×D414yes—
341C23×C4C2×D414yes—
342C23×C4C2×D414yes—
343C23×C4C2×D414yes—
344C23×C4C2×D414yes—
345C23×C4C2×D414yes—
346C23×C4C2×D414yes—
347C23×C4C2×D414yes—
348C23×C4C2×D414yes—
349C23×C4C2×D414yes—
350C23×C4C2×D414yes—
351C23×C4C2×Q814yes—
352C23×C4C2×Q814yes—
353C23×C4C2×Q814yes—
354C23×C4C2×Q814yes—
355C23×C4#4114yes—
356C23×C4#4114yes—
357C23×C4#4114yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C22⋊Q8—2256no—
373C2×C4⋊C4—232no—
374C2×C4⋊C4—232no—
375C2×C4⋊C4—232no—
376C2×C4⋊C4—232no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—28no—
398C2×C4⋊C4—28no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—416no—
405C2×C4⋊C4—416no—
406C2×C4⋊C4—416no—
407C2×C4⋊C4—416no—
408C2×C4⋊C4—416no—
409C2×C4⋊C4—416no—
410C2×C4⋊C4C2×D4116yes—
411C2×C4⋊C4C2×D4116yes—
412C2×C4⋊C4C2×D4116yes—
413C2×C22⋊C4—232no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—232no—
416C2×C22⋊C4—232no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—416no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—416no—
433C2×C22⋊C4—416no—
434C2×C22⋊C4C2×D4116yes—
435C2×C22⋊C4C2×Q8116yescomplemented
436C2×C22⋊C4C2×Q8116yescomplemented
437C2×C42—28no—
438C2×C42—28no—
439C2×C42—44no—
440C2×C42—416no—
441#95—28no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—28no—
469C24—28no—
470C24—28no—
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24—44no—
491C24—44no—
492C24—44no—
493C24—44no—
494C24—44no—
495C24—44no—
496C24—44no—
497C24—44no—
498C24—44no—
499C24—44no—
500C24—44no—
501C24—44no—
502C24—44no—
503C24C4⋊Q8116yes—
504C24C22×D414yes—
505C24C22×D412yes—
506C24C22×D412yes—
507C24C22×D412yes—
508C24C22×D412yes—
509C24C22×Q814yes—
510C24C22×Q814yes—
511C24C22×Q812yes—
512C24C22×Q812yes—
513C24C2×#4112yes—
514C24C2×#4112yes—
515C24C2×#4112yes—
516C24H(5,𝔽2)12yes—
517C24H(5,𝔽2)12yes—
518C24H(5,𝔽2)12yes—
519C242−1+412yes—
520C242−1+412yes—
521C242−1+412yes—
522C24C2511yescharacteristic
523C2×Q8—232no—
524C2×Q8—416no—
525C2×Q8—416no—
526C2×Q8—416no—
527C2×Q8—416no—
528C2×Q8—4128no—
529C2×Q8—416no—
530C2×Q8—416no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—232no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
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—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
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—416no—
658C22×C4—416no—
659C22×C4—416no—
660C22×C4—416no—
661C22×C4—4128no—
662C22×C4—416no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—416no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4#120116yes—
715C22×C4#121116yes—
716C22×C4C22⋊Q8116yescomplemented
717C22×C4C22×D414yes—
718C22×C4C22×D414yes—
719C22×C4C22×D414yes—
720C22×C4C22×D414yes—
721C22×C4C22×D414yes—
722C22×C4C22×D414yes—
723C22×C4C22×D414yes—
724C22×C4C22×D414yes—
725C22×C4C22×D414yes—
726C22×C4C22×D414yes—
727C22×C4C22×D414yes—
728C22×C4C22×Q814yes—
729C22×C4C22×Q814yes—
730C22×C4C22×Q814yes—
731C22×C4C22×Q814yes—
732C22×C4C2×#4114yes—
733C22×C4C2×#4114yes—
734C22×C4C2×#4114yes—
735C4⋊C4—232no—
736C4⋊C4—232no—
737C4⋊C4—232no—
738C4⋊C4—232no—
739C4⋊C4—416no—
740C4⋊C4—416no—
741C4⋊C4—416no—
742C4⋊C4—416no—
743C4⋊C4—416no—
744C4⋊C4—416no—
745C22⋊C4—232no—
746C22⋊C4—232no—
747C22⋊C4—232no—
748C22⋊C4—416no—
749C22⋊C4—416no—
750C22⋊C4—416no—
751C42—416no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—232no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—232no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—232no—
773C23—416no—
774C23—42no—
775C23—416no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—416no—
781C23—416no—
782C23—42no—
783C23—416no—
784C23—42no—
785C23—416no—
786C23—42no—
787C23—416no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—416no—
794C23—42no—
795C23—416no—
796C23—416no—
797C23—416no—
798C23—42no—
799C23—42no—
800C23—416no—
801C23C2×#12014yes—
802C23C2×#12114yes—
803C23C2×C22⋊Q814yes—
804C23C2×C4⋊Q818yes—
805C23C2×C4⋊Q814yes—
806C23#53214yes—
807C23#53314yes—
808C23#53514yes—
809C23#53614yes—
810C23#53714yes—
811C23#53714yes—
812C23#53914yes—
813C23#54114yes—
814C23#54214yes—
815C23#54314yes—
816C23#54414yes—
817C23D4214yes—
818C23D4214yes—
819C23#54614yes—
820C23#54614yes—
821C23#54614yes—
822C23#54614yes—
823C23#54714yes—
824C23#54714yes—
825C23#54814yes—
826C23D4×Q814yes—
827C23D4×Q814yes—
828C23D4×Q814yes—
829C23D4×Q814yes—
830C23D4×Q814yes—
831C23#55214yes—
832C23#55414yes—
833C23#55414yes—
834C23#55414yes—
835C23#56214yes—
836C23#56314yes—
837C23C23×D411yescharacteristic
838C23C23×D411yescharacteristic
839C23C23×D411yescharacteristic
840C23C23×D411yescharacteristic
841C23C23×Q811yescharacteristic
842C23C23×Q811yescharacteristic
843C23C22×#4111yescharacteristic
844C23C22×#4111yescharacteristic
845C23C22×#4111yescharacteristic
846C23C2×H(5,𝔽2)11yescharacteristic
847C23C2×H(5,𝔽2)11yescharacteristic
848C23C2×H(5,𝔽2)11yescharacteristic
849C23C2×2−1+411yescharacteristic
850C23C2×2−1+411yescharacteristic
851C23C2×2−1+411yescharacteristic
852Q8—464no—
853C2×C4—24no—
854C2×C4—232no—
855C2×C4—24no—
856C2×C4—232no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—232no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—464no—
902C2×C4—42no—
903C2×C4—416no—
904C2×C4—416no—
905C2×C4—416no—
906C2×C4—416no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—416no—
923C2×C4—416no—
924C2×C4—416no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—416no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—416no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—88no—
962C2×C4—88no—
963C2×C4C2×#12018yes—
964C2×C4C2×#12118yes—
965C2×C4C2×C22⋊Q818yescomplemented
966C22—28no—
967C22—28no—
968C22—28no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—464no—
982C22#240818yes—
983C22#241718yes—
984C22#242918yes—
985C22#243018yes—
986C22#243418yes—
987C22#244018yes—
988C22#245218yes—
989C22#254918yes—
990C22#255618yes—
991C22#268118yes—
992C22#268318yes—
993C22#269218yes—
994C22#269818yes—
995C22#270418yes—
996C22#272018yes—
997C22C22×#12011yescharacteristic
998C22C22×#12111yescharacteristic
999C22C22×C22⋊Q811yescharacteristic
1000C22C22×C4⋊Q811yescharacteristic
1001C22C2×#53211yescharacteristic
1002C22C2×#53311yescharacteristic
1003C22C2×#53511yescharacteristic
1004C22C2×#53611yescharacteristic
1005C22C2×#53711yescharacteristic
1006C22C2×#53711yescharacteristic
1007C22C2×#53911yescharacteristic
1008C22C2×#54111yescharacteristic
1009C22C2×#54211yescharacteristic
1010C22C2×#54311yescharacteristic
1011C22C2×#54411yescharacteristic
1012C22C2×D4211yescharacteristic
1013C22C2×D4211yescharacteristic
1014C22C2×#54611yescharacteristic
1015C22C2×#54611yescharacteristic
1016C22C2×#54611yescharacteristic
1017C22C2×#54611yescharacteristic
1018C22C2×#54711yescharacteristic
1019C22C2×#54711yescharacteristic
1020C22C2×#54811yescharacteristic
1021C22C2×D4×Q811yescharacteristic
1022C22C2×D4×Q811yescharacteristic
1023C22C2×D4×Q811yescharacteristic
1024C22C2×D4×Q811yescharacteristic
1025C22C2×D4×Q811yescharacteristic
1026C22C2×#55211yescharacteristic
1027C22C2×#55411yescharacteristic
1028C22C2×#55411yescharacteristic
1029C22C2×#55411yescharacteristic
1030C22C2×#56211yescharacteristic
1031C22C2×#56311yescharacteristic
1032C4—28no—
1033C4—28no—
1034C4—28no—
1035C4—44no—
1036C4—44no—
1037C4—44no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4—44no—
1043C4—44no—
1044C4—82no—
1045C4—82no—
1046C2—48no—
1047C2#15614116yesdirect product factor
1048C2C2×#240811yescharacteristic
1049C2C2×#244011yescharacteristic
1050C2C2×#245211yescharacteristic
1051C2C2×#241711yescharacteristic
1052C2C2×#243411yescharacteristic
1053C2C2×#242911yescharacteristic
1054C2C2×#243011yescharacteristic
1055C2C2×#254911yescharacteristic
1056C2C2×#255611yescharacteristic
1057C2C2×#268111yescharacteristic
1058C2C2×#268311yescharacteristic
1059C2C2×#269211yescharacteristic
1060C2C2×#269811yescharacteristic
1061C2C2×#270411yescharacteristic
1062C2C2×#272011yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#398C2semidirect
4. C22×#395C2semidirect
5. C22×#389C2semidirect
7. #15614C2direct (N × H)
8. C2×#1446C2semidirect
9. C2×#1444C2semidirect
10. C2×#1441C2semidirect
11. C2×#1441C2semidirect
15. C2×C4⋊#95C2semidirect
41. C2×#398C22semidirect
45. C2×#395C22semidirect
47. C2×#389C22semidirect
66. #1446C22semidirect
67. #1444C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
73. C4⋊#95C22semidirect
166. C22×C22⋊C4Q8semidirect
167. C22×C22⋊C4Q8semidirect
435. C2×C22⋊C4C2×Q8semidirect
436. C2×C22⋊C4C2×Q8semidirect
716. C22×C4C22⋊Q8semidirect
965. C2×C4C2×C22⋊Q8semidirect
1047. C2#15614direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C22×#3982
C22×#3962
C22×#3952
C22×#3892
C22×#3852
#156142
C2×#14462
C2×#14442
C2×#14412
C2×#14392
C2×#14372
C2×C4⋊#952
C2×C22⋊#952