Finite Group Databasebeta

← #7506542

Subgroups — #7506542

Order 512.

1619 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35515C211yesmaximal, characteristic
2#35159C211yesmaximal, characteristic, complemented
3#31895C212yesmaximal, complemented
4#31890C212yesmaximal, complemented
5#31886C212yesmaximal, complemented
6#31883C212yesmaximal, complemented
7#31878C212yesmaximal, complemented
8#31875C212yesmaximal, complemented
9#31871C212yesmaximal, complemented
10#31866C212yesmaximal, complemented
11#23671C211yesmaximal, characteristic, complemented
12#23669C211yesmaximal, characteristic, complemented
13#23660C211yesmaximal, characteristic, complemented
14#23618C211yesmaximal, characteristic
15#23612C211yesmaximal, characteristic
16#23551C211yesmaximal, characteristic, complemented
17#21312C211yesmaximal, characteristic, complemented
18#21156C211yesmaximal, characteristic, complemented
19#21148C211yesmaximal, characteristic, complemented
20#21089C211yesmaximal, characteristic
21C2×#1925C211yesmaximal, characteristic
22#20879C211yesmaximal, characteristic
23#20650C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#518C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#427C2211yescharacteristic
28C2×#427C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C2×#424C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#423C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C2×#418C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C2×#405C2211yescharacteristic
38#2851—22no—
39#2646—22no—
40#2580—21no—
41#2580—21no—
42#2538—21no—
43#2538—21no—
44#2509—21no—
45#2509C2212yescomplemented
46#2508—21no—
47#2508C2212yescomplemented
48#2507—21no—
49#2507C2212yescomplemented
50#2506—21no—
51#2506C2212yescomplemented
52#2454C2212yes—
53#2454C2212yes—
54#2452C2212yes—
55#2452C2212yes—
56#2437—22no—
57#2437—22no—
58#2317C2211yescharacteristic
59#2317C2211yescharacteristic
60#2317C2211yescharacteristic
61#2316C2211yescharacteristic
62#2316C2211yescharacteristic
63#2316C2211yescharacteristic
64#2309C2211yescharacteristic
65#2296C2211yescharacteristic
66#2296C2211yescharacteristic
67C2×#390C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69#2088C2212yescomplemented
70#2088C2212yescomplemented
71#2088C2212yescomplemented
72#2088C2212yescomplemented
73#2087C2212yescomplemented
74#2087C2212yescomplemented
75#2086C2212yescomplemented
76#2086C2212yescomplemented
77#2085C2212yescomplemented
78#2085C2212yescomplemented
79#2083C2212yescomplemented
80#2083C2212yescomplemented
81#2067C2212yes—
82#2067C2212yes—
83#2067C2212yes—
84#2067C2212yes—
85#2065C2212yes—
86#2065C2212yes—
87#2065C2212yes—
88#2065C2212yes—
89#2059C2211yescharacteristic, complemented
90#2059C2211yescharacteristic, complemented
91#2059C2211yescharacteristic, complemented
92#2059C2211yescharacteristic, complemented
93#2058C2211yescharacteristic, complemented
94#2058C2211yescharacteristic, complemented
95#2057C2211yescharacteristic, complemented
96#2057C2211yescharacteristic, complemented
97#1989C2212yescomplemented
98#1989C2212yescomplemented
99#1988C2212yescomplemented
100#1987C2212yescomplemented
101#1944C2212yescomplemented
102#1944C2212yescomplemented
103#1942C2212yescomplemented
104#1942C2212yescomplemented
105#1940C2212yescomplemented
106#1940C2212yescomplemented
107#1939C2212yescomplemented
108#1939C2212yescomplemented
109#1936C2212yes—
110#1936C2212yes—
111#1934C2212yes—
112#1934C2212yes—
113#1925C2212yes—
114#1925C2212yes—
115#1925C2212yes—
116#1925C2212yes—
117#1864C2212yes—
118#1864C2212yes—
119#1862C2212yes—
120#1862C2212yes—
121#1804C2212yes—
122#1804C2212yes—
123#1802C2212yes—
124#1802C2212yes—
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130#1735C2211yescharacteristic
131#1735C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140#533—24no—
141#533—42no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×#125—22no—
145C2×#125C2311yescharacteristic
146C2×#125C2311yescharacteristic
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151#518—24no—
152#518—42no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×D4—21no—
156C2×C4×D4—21no—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×#117C2311yescharacteristic
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—22no—
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173#428—42no—
174#427—24no—
175#427—42no—
176C2×#107—42no—
177C2×#107C2311yescharacteristic
178C2×#107C2311yescharacteristic
179C2×#107C2311yescharacteristic
180C2×#107C2311yescharacteristic
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#106C2311yescharacteristic
185C2×#106C2311yescharacteristic
186C2×#106C2311yescharacteristic
187C2×#106C2311yescharacteristic
188C2×#106C2312yes—
189#424—42no—
190#424—42no—
191#423—42no—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198#418—42no—
199#418—42no—
200C2×#102—42no—
201C2×#102Q818yescomplemented
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210#405—42no—
211C2×#97C2312yes—
212C2×C4×C8C2312yes—
213#400—22no—
214#400—22no—
215#400—22no—
216#400—22no—
217#399—22no—
218#399—22no—
219#398—22no—
220#398—22no—
221#398—22no—
222#398—22no—
223#396—22no—
224#396—22no—
225#396—22no—
226#396—22no—
227#393—22no—
228#393—22no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390—21no—
233#390C2312yes—
234#390C2312yes—
235#390C2312yes—
236#390C2312yes—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—22no—
246#389—22no—
247#389D411yescharacteristic
248#389D411yescharacteristic
249#389D411yescharacteristic
250#389D411yescharacteristic
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#389C2312yes—
259#389C2312yes—
260#389C2312yes—
261#389C2312yes—
262#389C2312yes—
263#389C2312yes—
264#389C2312yes—
265#387—22no—
266#387—22no—
267#387—22no—
268#387—22no—
269#385—21no—
270#385—21no—
271#385—22no—
272#385—22no—
273#385—22no—
274#385—22no—
275#385—22no—
276#385—22no—
277#385—22no—
278#385D412yes—
279#385D412yes—
280#384—21no—
281#384—21no—
282#384C2312yes—
283#382—21no—
284#382—21no—
285#382—22no—
286#382C2312yes—
287#380—22no—
288#380—22no—
289#380—22no—
290#380—22no—
291#380—22no—
292#379—22no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2312yes—
301C2×#95—21no—
302#340C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2312yes—
327#336C2312yes—
328C25—21no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×D4—21no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4C2×Q814yes—
338C22×D4C2412yes—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2411yescharacteristic
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8C2×Q814yes—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—41no—
368C4⋊Q8—41no—
369#125—22no—
370#125—22no—
371#125—41no—
372#125—41no—
373#125—84no—
374C22⋊Q8—44no—
375C22⋊Q8—44no—
376C22⋊Q8—84no—
377C22⋊Q8—84no—
378C4×Q8—44no—
379C4×Q8—44no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—44no—
385C4×D4—44no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117#4114yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
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—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×Q814yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—48no—
463C2×C22⋊C4—82no—
464C2×C22⋊C4—82no—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—82no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2412yes—
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482#107—22no—
483#107—22no—
484#107—42no—
485#107—42no—
486#107—41no—
487#107—41no—
488#107—42no—
489#106—22no—
490#106—22no—
491#106—41no—
492#106—41no—
493#106—42no—
494C4⋊C8—42no—
495C4⋊C8—42no—
496C4⋊C8—42no—
497C4⋊C8—42no—
498C4⋊C8—42no—
499C4⋊C8—42no—
500#102—42no—
501#102—42no—
502#102—42no—
503#102—42no—
504#102—42no—
505#102—42no—
506#102C2×Q818yes—
507#102C2×Q818yes—
508#97—42no—
509C4×C8—42no—
510#95—22no—
511#95—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95C2×D412yes—
529#95C2×D412yes—
530#95C2×D412yes—
531#95C2×D412yes—
532C24—22no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24—81no—
537C24—81no—
538C24—81no—
539C24—81no—
540C24C22×D411yescharacteristic
541C2×Q8—42no—
542C2×Q8—42no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—81no—
546C2×Q8—81no—
547C2×D4—28no—
548C2×D4—24no—
549C2×D4—28no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—42no—
556C2×D4—44no—
557C2×D4—42no—
558C2×D4—44no—
559C2×D4C22×Q814yes—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C22×D412yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D412yes—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×Q812yes—
602C22×C4C2×#4112yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C42−1+412yes—
606C22×C42−1+412yes—
607C22×C4C2511yescharacteristic
608M16—44no—
609M16—44no—
610C2×C8—28no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—22no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—44no—
628C2×C8C22×Q812yes—
629C2×C8C22×Q812yes—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4C22×Q814yes—
683C4⋊C4C2×#4112yes—
684C4⋊C4C2×#4112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C42—22no—
702C42—22no—
703C42—24no—
704C42—21no—
705C42—21no—
706C42—22no—
707C42—22no—
708C42—21no—
709C42—21no—
710C42—22no—
711C42—22no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—44no—
716C42—82no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—24no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—48no—
729C23—84no—
730C23—84no—
731C23—162no—
732C23—162no—
733C23—162no—
734C23—162no—
735C23#53712yes—
736C23#54612yes—
737C23D4×Q812yes—
738C23C23×D411yescharacteristic
739Q8—84no—
740Q8—84no—
741D4—24no—
742D4—24no—
743D4—42no—
744D4—48no—
745D4—42no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—82no—
804C2×C4—84no—
805C2×C4—84no—
806C2×C4—164no—
807C2×C4—164no—
808C2×C4—162no—
809C2×C4#53712yes—
810C2×C4#54114yes—
811C2×C4#54414yes—
812C2×C4#54612yes—
813C2×C4D4×Q812yes—
814C2×C4#55414yes—
815C2×C4#56214yes—
816C2×C4#57612yes—
817C2×C4C23×Q811yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×H(5,𝔽2)11yescharacteristic
821C2×C4C2×2−1+411yescharacteristic
822C2×C4C2×2−1+411yescharacteristic
823C8—22no—
824C8—22no—
825C8—41no—
826C8—41no—
827C8—42no—
828C8—42no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—168no—
843C22#270414yes—
844C22C2×#53711yescharacteristic
845C22C2×#54611yescharacteristic
846C22C2×D4×Q811yescharacteristic
847C22C2×#57611yescharacteristic
848C22#358411yescharacteristic
849C22#358511yescharacteristic
850C22#358611yescharacteristic
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—41no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—44no—
860C4—42no—
861C4—42no—
862C4—81no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—82no—
868C4—82no—
869C4—81no—
870C4#270414yes—
871C4C2×#54111yescharacteristic
872C4C2×#54411yescharacteristic
873C4C2×#55411yescharacteristic
874C4C2×#56211yescharacteristic
875C2—24no—
876C2—84no—
877C2C2×#270411yescharacteristic
878C2#6092211yescharacteristic
879C2#6092711yescharacteristic
880C2#6119111yescharacteristic
881C2#6119511yescharacteristic
882C2#6137011yescharacteristic
883C2#6137711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35159C2semidirect
3. #31895C2semidirect
4. #31890C2semidirect
5. #31886C2semidirect
6. #31883C2semidirect
7. #31878C2semidirect
8. #31875C2semidirect
9. #31871C2semidirect
10. #31866C2semidirect
11. #23671C2semidirect
12. #23669C2semidirect
13. #23660C2semidirect
16. #23551C2semidirect
17. #21312C2semidirect
18. #21156C2semidirect
19. #21148C2semidirect
45. #2509C22semidirect
47. #2508C22semidirect
49. #2507C22semidirect
51. #2506C22semidirect
69. #2088C22semidirect
70. #2088C22semidirect
71. #2088C22semidirect
72. #2088C22semidirect
73. #2087C22semidirect
74. #2087C22semidirect
75. #2086C22semidirect
76. #2086C22semidirect
77. #2085C22semidirect
78. #2085C22semidirect
79. #2083C22semidirect
80. #2083C22semidirect
89. #2059C22semidirect
90. #2059C22semidirect
91. #2059C22semidirect
92. #2059C22semidirect
93. #2058C22semidirect
94. #2058C22semidirect
95. #2057C22semidirect
96. #2057C22semidirect
97. #1989C22semidirect
98. #1989C22semidirect
99. #1988C22semidirect
100. #1987C22semidirect
101. #1944C22semidirect
102. #1944C22semidirect
103. #1942C22semidirect
104. #1942C22semidirect
105. #1940C22semidirect
106. #1940C22semidirect
107. #1939C22semidirect
108. #1939C22semidirect
201. C2×#102Q8semidirect

Maximal subgroups

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

subgroupindex
#355152
#351592
#318952
#318902
#318862
#318832
#318782
#318752
#318712
#318662
#236712
#236692
#236602
#236182
#236122
#235512
#213122
#211562
#211482
#210892
C2×#19252
#208792
#206502