Finite Group Databasebeta

← #365361

Subgroups — #365361

Order 512.

1670 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2933C211yesmaximal, characteristic
2C2×#1896C211yesmaximal, characteristic
3#20908C211yesmaximal, characteristic
4C2×#1866C211yesmaximal, characteristic, complemented
5C2×#1855C211yesmaximal, characteristic, complemented
6#20628C211yesmaximal, characteristic, complemented
7C22×#339C211yesmaximal, characteristic, complemented
8#11329C211yesmaximal, characteristic, complemented
9#11291C211yesmaximal, characteristic, complemented
10#11125C211yesmaximal, characteristic, complemented
11#11068C211yesmaximal, characteristic, complemented
12#10910C211yesmaximal, characteristic, complemented
13#10887C211yesmaximal, characteristic, complemented
14#10791C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C22×#131C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C2×#525C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C42C2211yescharacteristic
21#2933—24no—
22#2933—24no—
23C2×#436—21no—
24C2×#435—21no—
25C2×#435—21no—
26C2×C8×D4—21no—
27C22×#108C2211yescharacteristic
28C22×#108C2211yescharacteristic
29C2×#424C2211yescharacteristic
30C2×#424C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C22×#104C2211yescharacteristic
33C22×#104C2211yescharacteristic
34C2×#416C2211yescharacteristic
35C2×#416C2211yescharacteristic
36C2×#408C2211yescharacteristic
37C2×#407C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C2×#405C2211yescharacteristic
41#1896—24no—
42#1875C411yescharacteristic, complemented
43#1875C411yescharacteristic, complemented
44#1874C411yescharacteristic, complemented
45#1874C411yescharacteristic, complemented
46#1873C411yescharacteristic, complemented
47#1873C411yescharacteristic, complemented
48#1872C411yescharacteristic, complemented
49#1872C411yescharacteristic, complemented
50#1866—24no—
51#1855—24no—
52#1798—21no—
53#1798—21no—
54#1797—21no—
55#1797—21no—
56C2×#341C2211yescharacteristic
57C2×#341C2211yescharacteristic
58#1735C2211yescharacteristic
59#1735C2211yescharacteristic
60C2×#339—24no—
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66C2×#339C2211yescharacteristic
67#1729C2211yescharacteristic
68#1729C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C2×#336C2211yescharacteristic
71C2×#336C2211yescharacteristic
72C2×#336C2211yescharacteristic
73C22×#41C2311yescharacteristic
74C24×C4—21no—
75C24×C4C2311yescharacteristic
76C2×#131—22no—
77C2×#131—22no—
78C2×#131—22no—
79C2×#131—22no—
80C2×#131—41no—
81C2×#131—41no—
82C22×M16—21no—
83C22×M16—22no—
84C22×M16—21no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—41no—
88C22×M16—41no—
89C22×M16D414yes—
90C22×M16C2311yescharacteristic
91C22×M16C2311yescharacteristic
92C22×M16C2311yescharacteristic
93C22×M16C2311yescharacteristic
94C23×C8—21no—
95C23×C8—21no—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100#525—22no—
101#525—22no—
102#525D414yes—
103#525Q814yes—
104C2×#123—21no—
105C2×C22⋊Q8C2×C411yescharacteristic
106C2×C22⋊Q8C2×C411yescharacteristic
107C2×#121C2×C411yescharacteristic
108C2×#121C2×C411yescharacteristic
109C2×#120—21no—
110C2×C4×D4—21no—
111C2×C4×D4—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—22no—
115C2×#117—22no—
116C2×#117—41no—
117C2×#117—41no—
118C2×#117C2×C411yescharacteristic
119C2×#117C2×C411yescharacteristic
120C2×#117C2311yescharacteristic
121C2×#117C2311yescharacteristic
122C2×#117C2311yescharacteristic
123C22×C4⋊C4C2×C411yescharacteristic
124C22×C4⋊C4C2×C411yescharacteristic
125C22×C22⋊C4—21no—
126C22×C42—22no—
127C22×C42—22no—
128C22×C42—22no—
129C22×C42—21no—
130C22×C42—22no—
131C22×C42—21no—
132C22×C42—41no—
133C22×C42—41no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136#436—28no—
137#435—28no—
138#435—28no—
139C8×D4—28no—
140C2×#108—22no—
141C2×#108—22no—
142C2×#108—22no—
143C2×#108—22no—
144C2×#108—41no—
145C2×#108—41no—
146#424—22no—
147#424—22no—
148#424—22no—
149#424—22no—
150#424—41no—
151#424—41no—
152C2×C4⋊C8—21no—
153C2×C4⋊C8—21no—
154C2×C4⋊C8—21no—
155C2×C4⋊C8—21no—
156C2×C4⋊C8—21no—
157C2×C4⋊C8—21no—
158C2×#104—22no—
159C2×#104—22no—
160C2×#104—22no—
161C2×#104—22no—
162C2×#104—41no—
163C2×#104—41no—
164#416—22no—
165#416—22no—
166#416—41no—
167#416—41no—
168C2×#103C2×C411yescharacteristic, complemented
169C2×#103C2×C411yescharacteristic, complemented
170C2×#103C2×C411yescharacteristic, complemented
171C2×#103C2×C411yescharacteristic, complemented
172C2×#102C2×C411yescharacteristic, complemented
173C2×#102C2×C411yescharacteristic, complemented
174C2×#102C2×C411yescharacteristic, complemented
175C2×#102C2×C411yescharacteristic, complemented
176#408—22no—
177#408—22no—
178#407—22no—
179#407—22no—
180C2×C22⋊C8—22no—
181C2×C22⋊C8—22no—
182C2×C22⋊C8—22no—
183C2×C22⋊C8—22no—
184C2×C22⋊C8—21no—
185C2×C22⋊C8—21no—
186C2×C22⋊C8—21no—
187C2×C22⋊C8—21no—
188C2×C22⋊C8C2×C411yescharacteristic
189C2×C22⋊C8C2×C411yescharacteristic
190C2×C22⋊C8C2×C411yescharacteristic
191C2×C22⋊C8C2×C411yescharacteristic
192C2×C22⋊C8D411yescharacteristic
193C2×C22⋊C8D411yescharacteristic
194C2×C22⋊C8D411yescharacteristic
195C2×C22⋊C8D411yescharacteristic
196#405—22no—
197#405—22no—
198C2×#97—21no—
199C2×C4×C8—21no—
200#341—22no—
201#341—22no—
202#340C2×C411yescharacteristic, complemented
203#340C2×C411yescharacteristic, complemented
204#340C2×C411yescharacteristic, complemented
205#340C2×C411yescharacteristic, complemented
206#340C2×C411yescharacteristic, complemented
207#340C2×C411yescharacteristic, complemented
208#340C2×C411yescharacteristic, complemented
209#340C2×C411yescharacteristic, complemented
210#339—22no—
211#339—22no—
212#339—22no—
213#339—22no—
214#339—22no—
215#339D414yescomplemented
216#336—21no—
217#336—21no—
218#336—21no—
219#336—21no—
220#336—22no—
221#336—22no—
222#336—41no—
223#336—41no—
224C25#4111yescharacteristic
225C2×#41—21no—
226C2×#41—21no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41—21no—
232C2×#41—21no—
233C2×#41—21no—
234C2×#41—21no—
235C2×#41C2×D412yes—
236C2×#41C2×Q812yes—
237C22×Q8C22×C411yescharacteristic
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4C22×C411yescharacteristic
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—24no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×Q812yes—
269C23×C4#4111yescharacteristic
270C23×C4#4112yes—
271C23×C4C2411yescharacteristic
272#131—44no—
273#131—44no—
274#131—44no—
275#131—44no—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—21no—
279C2×M16—24no—
280C2×M16—24no—
281C2×M16—21no—
282C2×M16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C2×M16—28no—
287C2×M16—21no—
288C2×M16—21no—
289C2×M16—21no—
290C2×M16—21no—
291C2×M16—21no—
292C2×M16—21no—
293C2×M16—21no—
294C2×M16—21no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—42no—
300C2×M16—42no—
301C2×M16—42no—
302C2×M16—42no—
303C2×M16—44no—
304C2×M16—44no—
305C2×M16—44no—
306C2×M16C2×D412yes—
307C2×M16C2×D412yes—
308C2×M16C2×D412yes—
309C2×M16#4112yes—
310C22×C8—21no—
311C22×C8—24no—
312C22×C8—24no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8—21no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—21no—
340C22×C8—42no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8—42no—
344C22×C8C22×C411yescharacteristic
345C22×C8C22×C411yescharacteristic
346C22×C8C22×C411yescharacteristic
347C22×C8C22×C411yescharacteristic
348C22×C8C2×D411yescharacteristic
349C22×C8C2×D411yescharacteristic
350C22×C8C2×D411yescharacteristic
351C22×C8C2×D411yescharacteristic
352#123—24no—
353#123—24no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8C4⋊C414yes—
357C22⋊Q8C4⋊C414yes—
358#121—22no—
359#121—22no—
360#121C4⋊C414yes—
361#121C4⋊C414yes—
362#120—24no—
363#120—24no—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—22no—
377#117—22no—
378#117—42no—
379#117—42no—
380#117—42no—
381#117—42no—
382#117—41no—
383#117—41no—
384#117C2×D412yes—
385#117C2×D412yes—
386#117C2×Q812yes—
387#117#4112yes—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4C22×C411yescharacteristic
397C2×C4⋊C4C22×C411yescharacteristic
398C2×C4⋊C4C22×C411yescharacteristic
399C2×C4⋊C4C22×C411yescharacteristic
400C2×C4⋊C4C22×C411yescharacteristic
401C2×C4⋊C4C22×C411yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—28no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—44no—
432C2×C42—44no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—44no—
436C2×C42—42no—
437C2×C42C2×D412yes—
438C2×C42#4112yes—
439#108—44no—
440#108—44no—
441C4⋊C8—24no—
442C4⋊C8—24no—
443C4⋊C8—42no—
444C4⋊C8—42no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447#104—44no—
448#104—44no—
449#103—22no—
450#103—22no—
451#103—41no—
452#103—41no—
453#102—22no—
454#102—22no—
455#102—41no—
456#102—41no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8—22no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C22⋊C8—42no—
468C22⋊C8—42no—
469#97—24no—
470C4×C8—24no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—41no—
479C24—41no—
480C24C4×D411yescharacteristic
481C24C4×D411yescharacteristic
482C24C22⋊Q812yes—
483C24#12312yes—
484C24C2×#4111yescharacteristic
485#41—22no—
486#41—22no—
487#41—22no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—22no—
492#41—22no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—41no—
500#41—41no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×C4⋊C412yes—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4C2×C4⋊C412yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—48no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4C2×C4⋊C412yes—
602C22×C4C2×C4⋊C412yes—
603C22×C4C4×D412yes—
604C22×C4C4×D412yes—
605C22×C4C4×D411yescharacteristic
606C22×C4C4×D411yescharacteristic
607C22×C4#12012yes—
608C22×C4#12012yes—
609C22×C4C22⋊Q812yes—
610C22×C4C22⋊Q812yes—
611C22×C4C22⋊Q812yes—
612C22×C4#12312yes—
613C22×C4C23×C411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×Q811yescharacteristic
619C22×C4C2×#4111yescharacteristic
620C22×C4C2×#4111yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4H(5,𝔽2)11yescharacteristic
624C22×C4H(5,𝔽2)11yescharacteristic
625C22×C4H(5,𝔽2)11yescharacteristic
626C22×C42−1+411yescharacteristic
627M16—22no—
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—48no—
633M16—48no—
634M16—41no—
635M16—41no—
636M16—41no—
637M16—41no—
638M16—41no—
639M16—41no—
640M16—41no—
641M16—41no—
642M16—41no—
643M16—41no—
644M16#12114yes—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—22no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—48no—
674C2×C8—48no—
675C2×C8—41no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—41no—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8—41no—
686C2×C8—41no—
687C2×C8—41no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4C2×C4⋊C412yes—
712C4⋊C4C2×C4⋊C412yes—
713C4⋊C4C4×D412yes—
714C4⋊C4C4×D412yes—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—41no—
726C22⋊C4—41no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—22no—
731C42—22no—
732C42—22no—
733C42—22no—
734C42—22no—
735C42—42no—
736C42—42no—
737C42—48no—
738C42—41no—
739C42—41no—
740C42—41no—
741C42—41no—
742C42—41no—
743C42—41no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—24no—
756C23—24no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#38512yes—
782C23#38512yes—
783C23#44312yes—
784C23#44412yes—
785C23C2×C4×D411yescharacteristic
786C23C2×C22⋊Q811yescharacteristic
787C23C2×#12311yescharacteristic
788C23#54611yescharacteristic
789C23#55111yescharacteristic
790C23#55111yescharacteristic
791C23#55211yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—42no—
799D4—48no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—41no—
804D4—41no—
805D4—84no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—432no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—84no—
871C2×C4—84no—
872C2×C4#38512yes—
873C2×C4#38512yes—
874C2×C4C22×C4⋊C411yescharacteristic
875C2×C4C2×C4×D411yescharacteristic
876C2×C4C2×C4×D411yescharacteristic
877C2×C4C4×#4111yescharacteristic
878C2×C4#51811yescharacteristic
879C2×C4#52011yescharacteristic
880C2×C4C2×#12011yescharacteristic
881C2×C4C2×#12111yescharacteristic
882C2×C4C2×C22⋊Q811yescharacteristic
883C2×C4#52511yescharacteristic
884C2×C4#52911yescharacteristic
885C2×C4#53211yescharacteristic
886C2×C4#53411yescharacteristic
887C2×C4#53711yescharacteristic
888C2×C4#53811yescharacteristic
889C2×C4#53911yescharacteristic
890C2×C4D4211yescharacteristic
891C2×C4D4211yescharacteristic
892C2×C4#54611yescharacteristic
893C2×C4#54611yescharacteristic
894C2×C4#54611yescharacteristic
895C2×C4#54611yescharacteristic
896C2×C4#54711yescharacteristic
897C2×C4#54711yescharacteristic
898C2×C4D4×Q811yescharacteristic
899C2×C4#55411yescharacteristic
900C2×C4#55411yescharacteristic
901C2×C4#55411yescharacteristic
902C8—24no—
903C8—41no—
904C8—41no—
905C8—41no—
906C8—41no—
907C8—42no—
908C8—41no—
909C8—41no—
910C8—41no—
911C8—41no—
912C8—81no—
913C8—81no—
914C22—21no—
915C22—22no—
916C22—21no—
917C22—21no—
918C22—22no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—22no—
926C22—21no—
927C22—21no—
928C22—22no—
929C22—21no—
930C22—21no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22—81no—
950C22#186614yescomplemented
951C22C2×#38511yescharacteristic
952C22#235811yescharacteristic
953C22#235911yescharacteristic
954C22#241711yescharacteristic
955C22#241811yescharacteristic
956C22#241911yescharacteristic
957C22#256411yescharacteristic
958C22C2×#44311yescharacteristic
959C22C2×#44411yescharacteristic
960C22#295611yescharacteristic
961C22#295611yescharacteristic
962C4—22no—
963C4—22no—
964C4—44no—
965C4—44no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—81no—
972C4—81no—
973C4C4×#12111yescharacteristic
974C4#232511yescharacteristic
975C4D4×C4⋊C411yescharacteristic
976C4#234911yescharacteristic
977C4#241011yescharacteristic
978C4#243011yescharacteristic
979C4#244911yescharacteristic
980C4#245011yescharacteristic
981C2—21no—
982C2—21no—
983C2—24no—
984C2—21no—
985C2—21no—
986C2—42no—
987C2—82no—
988C2#1397511yescharacteristic
989C2C2×#186611yescharacteristic
990C2#2088511yescharacteristic
991C2#2288611yescharacteristic
992C2#2288811yescharacteristic
993C2#2294811yescharacteristic
994C2#2295011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1866C2semidirect
5. C2×#1855C2semidirect
6. #20628C2semidirect
7. C22×#339C2semidirect
8. #11329C2semidirect
9. #11291C2semidirect
10. #11125C2semidirect
11. #11068C2semidirect
12. #10910C2semidirect
13. #10887C2semidirect
14. #10791C2semidirect
15. #10712C2semidirect
42. #1875C4semidirect
43. #1875C4semidirect
44. #1874C4semidirect
45. #1874C4semidirect
46. #1873C4semidirect
47. #1873C4semidirect
48. #1872C4semidirect
49. #1872C4semidirect
168. C2×#103C2×C4semidirect
169. C2×#103C2×C4semidirect
170. C2×#103C2×C4semidirect
171. C2×#103C2×C4semidirect
172. C2×#102C2×C4semidirect
173. C2×#102C2×C4semidirect
174. C2×#102C2×C4semidirect
175. C2×#102C2×C4semidirect
202. #340C2×C4semidirect
203. #340C2×C4semidirect
204. #340C2×C4semidirect
205. #340C2×C4semidirect
206. #340C2×C4semidirect
207. #340C2×C4semidirect
208. #340C2×C4semidirect
209. #340C2×C4semidirect
215. #339D4semidirect
950. C22#1866semidirect

Maximal subgroups

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

subgroupindex
C2×#29332
C2×#18962
#209082
C2×#18662
C2×#18552
#206282
C22×#3392
#113292
#112912
#111252
#110682
#109102
#108872
#107912
#107122