Finite Group Databasebeta

← #6450313

Subgroups — #6450313

Order 512.

1604 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34815C211yesmaximal, characteristic
2C2×#2355C211yesmaximal, characteristic
3#27380C212yesmaximal, complemented
4#27378C212yesmaximal, complemented
5#27377C212yesmaximal, complemented
6#27375C212yesmaximal, complemented
7#27364C212yesmaximal, complemented
8#27362C212yesmaximal, complemented
9#27361C212yesmaximal, complemented
10#27359C212yesmaximal, complemented
11#23745C211yesmaximal, characteristic
12#23658C211yesmaximal, characteristic
13#23629C211yesmaximal, characteristic
14#23619C211yesmaximal, characteristic
15#21170C211yesmaximal, characteristic
16#21094C211yesmaximal, characteristic
17#21061C211yesmaximal, characteristic
18#21033C211yesmaximal, characteristic
19#21033C211yesmaximal, characteristic
20#21023C211yesmaximal, characteristic
21#20874C211yesmaximal, characteristic
22#20874C211yesmaximal, characteristic
23C4×#428C211yesmaximal, characteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#428C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#423C2211yescharacteristic
30C2×#419C2211yescharacteristic
31C2×#419C2211yescharacteristic
32C2×#419C2211yescharacteristic
33C2×#419C2211yescharacteristic
34C2×C4×M16C2211yescharacteristic
35#2509C2211yescharacteristic
36#2509C2211yescharacteristic
37#2508C2211yescharacteristic
38#2508C2211yescharacteristic
39#2507C2211yescharacteristic
40#2507C2211yescharacteristic
41#2506C2211yescharacteristic
42#2506C2211yescharacteristic
43#2505—21no—
44#2505—21no—
45#2473—21no—
46#2473—21no—
47#2402—21no—
48#2402—21no—
49#2355—21no—
50#2355—21no—
51#2355—21no—
52#2355—21no—
53#2355C2212yes—
54#2355C2212yes—
55#2355C2212yes—
56#2355C2212yes—
57C4×#125—21no—
58C4×#125—21no—
59#2296C2211yescharacteristic
60#2296C2211yescharacteristic
61#2296C2211yescharacteristic
62#2296C2211yescharacteristic
63C2×#391C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#387—21no—
66C2×#387—21no—
67#2285C2211yescharacteristic
68C2×#384C2211yescharacteristic
69C2×#382—21no—
70C4×#117C2211yescharacteristic
71C2×C4×C4⋊C4—21no—
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75#2100C2212yes—
76#2100C2212yes—
77#2099C2212yes—
78#2099C2212yes—
79#2084C2212yes—
80#2084C2212yes—
81#2083C2212yes—
82#2083C2212yes—
83#2074C2212yes—
84#2074C2212yes—
85#2072C2212yes—
86#2072C2212yes—
87#2068C2212yes—
88#2068C2212yes—
89#2066C2212yes—
90#2066C2212yes—
91#1949C2212yes—
92#1949C2212yes—
93#1948C2212yes—
94#1947C2212yes—
95#1935C2212yes—
96#1935C2212yes—
97#1933C2212yes—
98#1933C2212yes—
99#1928C2212yes—
100#1928C2212yes—
101#1927C2212yes—
102#1927C2212yes—
103#1921C2212yes—
104#1921C2212yes—
105#1920C2212yes—
106#1920C2212yes—
107#1919C2212yes—
108#1919C2212yes—
109#1918C2212yes—
110#1918C2212yes—
111#1917C2212yes—
112#1917C2212yes—
113#1916C2212yes—
114#1916C2212yes—
115#1865C2212yes—
116#1865C2212yes—
117#1865C2212yes—
118#1865C2212yes—
119#1863C2212yes—
120#1863C2212yes—
121#1863C2212yes—
122#1863C2212yes—
123#1776C2212yes—
124#1776C2212yes—
125C4×#107C2212yes—
126C4×#106C2212yes—
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131#1736C2211yescharacteristic
132#1736C2211yescharacteristic
133#1736C2211yescharacteristic
134#1736C2211yescharacteristic
135#1728C2211yescharacteristic
136#1728C2211yescharacteristic
137#1728C2211yescharacteristic
138#1728C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C2×#125—21no—
145C2×#125—21no—
146C2×C4×Q8—24no—
147C2×C4×Q8—24no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×#117C2311yescharacteristic
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4D411yescharacteristic
160C22×C4⋊C4D411yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C42—21no—
165C22×C42—21no—
166C22×C42—21no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#428—24no—
171#428—24no—
172#428—24no—
173#428—24no—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#106C2312yes—
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182#423—24no—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185#419—24no—
186#419—24no—
187#419—24no—
188#419—24no—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C4×M16—24no—
198C2×#97C2312yes—
199C2×C4×C8C2312yes—
200#400—21no—
201#400—21no—
202#400—21no—
203#400—21no—
204#400—21no—
205#400—21no—
206#400—21no—
207#400—21no—
208#398—21no—
209#398—21no—
210#398—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#398—21no—
215#398—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391C2312yes—
221#391C2312yes—
222#391C2312yes—
223#391C2312yes—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389C2311yescharacteristic
229#389C2311yescharacteristic
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#387—21no—
245#387—21no—
246#387—21no—
247#387—21no—
248#387—21no—
249#387—21no—
250#387—21no—
251#387—21no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#385—21no—
261#385—21no—
262#385—21no—
263#385—21no—
264#385—21no—
265#385—21no—
266#385—21no—
267#385—21no—
268#384—21no—
269#384—21no—
270#384C2311yescharacteristic
271#384C2311yescharacteristic
272#384C2312yes—
273#384C2312yes—
274#382—22no—
275#382—22no—
276#382—22no—
277#382—22no—
278#382—21no—
279#382—21no—
280#382C2311yescharacteristic
281#382C2311yescharacteristic
282#380—21no—
283#380—21no—
284C4×C4⋊C4—22no—
285C4×C4⋊C4—22no—
286C4×C4⋊C4—22no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4D411yescharacteristic
303C4×C4⋊C4D411yescharacteristic
304C4×C4⋊C4D411yescharacteristic
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2312yes—
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320#376—21no—
321C2×#95—21no—
322C2×#95—21no—
323C2×#95—21no—
324C2×#95—21no—
325C2×#95—21no—
326C2×#95—21no—
327C2×#95D411yescharacteristic
328C2×#95D411yescharacteristic
329C43—21no—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351#336C2312yes—
352#336C2312yes—
353#336C2312yes—
354C22×Q8—21no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8#4114yes—
361C22×Q8C2412yes—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2411yescharacteristic
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—22no—
384C2×M16#4114yes—
385C22×C8C2412yes—
386C22×C8C2412yes—
387C22×C8C2412yes—
388C22×C8C2412yes—
389#125—44no—
390#125—44no—
391C4×Q8—28no—
392C4×Q8—28no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8—24no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117#4114yes—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—44no—
443C2×C4⋊C4—82no—
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D411yescharacteristic
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4#4114yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2411yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C42—28no—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—82no—
490C2×C42—82no—
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2×D411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503#107—24no—
504#107—24no—
505#107—24no—
506#107—24no—
507#106—24no—
508#106—24no—
509#106—24no—
510#106—24no—
511C4⋊C8—24no—
512C4⋊C8—24no—
513#103—24no—
514#103—24no—
515#103—24no—
516#103—24no—
517#103—24no—
518#103—24no—
519#103—24no—
520#103—24no—
521#97—24no—
522C4×C8—24no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563#95C2×D411yescharacteristic
564#95C2×D411yescharacteristic
565#95C2×D411yescharacteristic
566#95C2×D411yescharacteristic
567C24C22×D411yescharacteristic
568C2×Q8—24no—
569C2×Q8—22no—
570C2×Q8—28no—
571C2×Q8—28no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×Q8C2×#4114yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4C2×#4112yes—
639C22×C4C2×#4112yes—
640C22×C42−1+412yes—
641C22×C42−1+412yes—
642C22×C4C2511yescharacteristic
643M16—28no—
644M16—44no—
645M16—44no—
646M16—44no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8C2×#4114yes—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—24no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4—44no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—44no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—81no—
703C4⋊C4—81no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4—81no—
707C4⋊C4—81no—
708C4⋊C4—81no—
709C4⋊C4—81no—
710C4⋊C4—81no—
711C4⋊C4—81no—
712C4⋊C4—82no—
713C4⋊C4—82no—
714C4⋊C4#13714yes—
715C4⋊C4C2×#4112yes—
716C4⋊C4C2×#4112yes—
717C4⋊C4C2×#4114yes—
718C22⋊C4—24no—
719C22⋊C4—42no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C42—28no—
723C42—28no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—24no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—42no—
744C42—42no—
745C42—42no—
746C42—42no—
747C42—42no—
748C42—81no—
749C42—81no—
750C42—82no—
751C42—82no—
752C42—82no—
753C42—82no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23#52512yes—
759C23#54712yes—
760C23#54812yes—
761C23C23×D411yescharacteristic
762Q8—24no—
763Q8—24no—
764Q8—42no—
765Q8—42no—
766Q8—48no—
767C2×C4—28no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—48no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—48no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—82no—
842C2×C4—82no—
843C2×C4—84no—
844C2×C4—84no—
845C2×C4#52512yes—
846C2×C4#52914yes—
847C2×C4#54114yes—
848C2×C4#54712yes—
849C2×C4#54812yes—
850C2×C4#55214yes—
851C2×C4#55214yes—
852C2×C4C2×#13712yes—
853C2×C4C2×#13712yes—
854C2×C4C2×#13712yes—
855C2×C4#57512yes—
856C2×C4C22×#4111yescharacteristic
857C2×C4C22×#4111yescharacteristic
858C2×C4C22×#4111yescharacteristic
859C2×C4C22×#4111yescharacteristic
860C2×C4C2×2−1+411yescharacteristic
861C2×C4C2×2−1+411yescharacteristic
862C8—24no—
863C8—42no—
864C8—42no—
865C8—42no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22#247514yes—
873C22C2×#52511yescharacteristic
874C22C2×#54711yescharacteristic
875C22C2×#54811yescharacteristic
876C22C22×#13711yescharacteristic
877C22C2×#57511yescharacteristic
878C22#358511yescharacteristic
879C22#358611yescharacteristic
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—41no—
894C4—44no—
895C4—44no—
896C4—81no—
897C4—81no—
898C4—82no—
899C4—82no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4#247514yes—
905C4C2×#52911yescharacteristic
906C4C2×#54111yescharacteristic
907C4C2×#55211yescharacteristic
908C4C2×#55211yescharacteristic
909C2—24no—
910C2C2×#247511yescharacteristic
911C2#6056011yescharacteristic
912C2#6056511yescharacteristic
913C2#6125411yescharacteristic
914C2#6125711yescharacteristic
915C2#6132211yescharacteristic
916C2#6132411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #27380C2semidirect
4. #27378C2semidirect
5. #27377C2semidirect
6. #27375C2semidirect
7. #27364C2semidirect
8. #27362C2semidirect
9. #27361C2semidirect
10. #27359C2semidirect

Maximal subgroups

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

subgroupindex
#348152
C2×#23552
#273802
#273782
#273772
#273752
#273642
#273622
#273612
#273592
#237452
#236582
#236292
#236192
#211702
#210942
#210612
#210332
#210232
#208742
C4×#4282