Finite Group Databasebeta

← #6343119

Subgroups — #6343119

Order 512.

3027 conjugacy classes of subgroups.

The subgroup lattice has 983 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3475C211yesmaximal, characteristic
2#60277C211yesmaximal, characteristic, complemented
3#60125C211yesmaximal, characteristic, complemented
4#17513C2116yesmaximal, complemented
5#17492C212yesmaximal, complemented
6#17491C212yesmaximal, complemented
7#17487C212yesmaximal, complemented
8#17451C212yesmaximal, complemented
9#17448C212yesmaximal, complemented
10#17443C212yesmaximal, complemented
11#3475—24no—
12#3475—24no—
13#3475C418yes—
14#3475C2218yes—
15C2×#556C411yescharacteristic
16C2×#555C411yescharacteristic
17C2×#554C411yescharacteristic
18C2×#553—21no—
19C2×#552—21no—
20C2×#552C411yescharacteristic
21C2×#552C411yescharacteristic
22C2×#551—21no—
23C2×#551—21no—
24C2×#547C411yescharacteristic
25C2×#546C411yescharacteristic
26C2×#546C411yescharacteristic
27C2×#533C2211yescharacteristic
28C2×#529—21no—
29C2×#529—21no—
30C2×#529C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C2×#525—21no—
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C22×#117—21no—
38#2989—24no—
39#2983—21no—
40#2975—21no—
41#2973—21no—
42#2973—21no—
43#2965C2218yescomplemented
44#2925—24no—
45#2925C2218yescomplemented
46#2921—21no—
47#2921—21no—
48#2920C2212yes—
49#2920C2212yes—
50#2920C2212yescomplemented
51#2920C2212yescomplemented
52C2×#431C2212yescomplemented
53C2×#423C2212yescomplemented
54#2879—21no—
55#2873—21no—
56#1497C2218yescomplemented
57#1495C2218yescomplemented
58#1494C2218yescomplemented
59#1490C2218yescomplemented
60#1489C2218yescomplemented
61#1488C2218yescomplemented
62#1487C2214yescomplemented
63#1487C2214yescomplemented
64#1486C2214yes—
65#1486C2214yes—
66#1485C2218yescomplemented
67#1483C2218yescomplemented
68#1482C2218yescomplemented
69#1478C2218yescomplemented
70#1477C2218yescomplemented
71#1476C2218yescomplemented
72C22×#41C2×C411yescharacteristic
73C22×#41C2×C411yescharacteristic
74C22×#41D411yescharacteristic
75C23×D4C2×C411yescharacteristic
76C24×C4—21no—
77C22×M16—22no—
78#556—24no—
79#556C2×C418yes—
80#555—24no—
81#555C2×C418yes—
82#554—24no—
83#554C2×C418yes—
84#553—28no—
85#553—28no—
86#552—28no—
87#552—28no—
88#552—24no—
89#552—24no—
90#552C2×C418yes—
91#552C2×C418yes—
92#551—28no—
93#551—28no—
94#551—28no—
95#551—28no—
96#547—24no—
97#547C2×C418yes—
98#546—24no—
99#546—24no—
100#546C2×C418yes—
101#546C2×C418yes—
102#533—22no—
103#533—22no—
104#533C2×C414yes—
105#533C2314yes—
106C2×C4⋊Q8C2×C411yescharacteristic
107C2×C4⋊Q8C2×C411yescharacteristic
108#529—28no—
109#529—28no—
110#529—28no—
111#529—28no—
112#529—22no—
113#529—22no—
114#529—22no—
115#529—22no—
116#529C2×C414yes—
117#529C2×C414yes—
118#529C2314yes—
119#529C2314yes—
120C2×#126—21no—
121C2×#126—21no—
122C2×#126—21no—
123C2×#126—21no—
124C2×#126—21no—
125C2×#126—21no—
126C2×#125—21no—
127C2×#125—21no—
128C2×#125—21no—
129C2×#125C2×C411yescharacteristic
130C2×#125C2×C411yescharacteristic
131C2×#124—21no—
132C2×#124—21no—
133C2×#124C2×C411yescharacteristic
134C2×#124C2×C411yescharacteristic
135#525—28no—
136#525—28no—
137C2×#123—21no—
138C2×#123—21no—
139C2×#123—21no—
140C2×#123—21no—
141C2×#123—21no—
142C2×#123—21no—
143C2×#123—21no—
144C2×#123—21no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8C2×C411yescharacteristic
151C2×C22⋊Q8C2×C411yescharacteristic
152C2×C22⋊Q8C2×C411yescharacteristic
153C2×C22⋊Q8C2×C411yescharacteristic
154C2×#121—21no—
155C2×#121—21no—
156C2×#121—21no—
157C2×#121—21no—
158C2×#121C2×C411yescharacteristic
159C2×#121C2×C411yescharacteristic
160C2×#120—21no—
161C2×#120—21no—
162C4×#41—22no—
163C4×#41—22no—
164C4×#41—22no—
165C4×#41—22no—
166C4×#41C2×C414yes—
167C4×#41C2×C414yes—
168C4×#41C2×C414yes—
169C4×#41D414yes—
170C4×#41D414yes—
171C4×#41C2314yes—
172C4×#41C2314yes—
173C4×#41C2314yes—
174C2×C4×Q8—21no—
175C2×C4×Q8C2×C411yescharacteristic
176C2×C4×Q8C2×C411yescharacteristic
177C2×C4×Q8C2×C411yescharacteristic
178C2×C4×Q8D411yescharacteristic
179C2×C4×Q8C2311yescharacteristic
180C2×C4×Q8C2311yescharacteristic
181C2×C4×D4—21no—
182C2×C4×D4—21no—
183C2×C4×D4—21no—
184C2×C4×D4—21no—
185C2×C4×D4—21no—
186C2×C4×D4—21no—
187C2×C4×D4—21no—
188C2×C4×D4—21no—
189C2×C4×D4—22no—
190C2×C4×D4—22no—
191C2×C4×D4C2×C411yescharacteristic
192C2×C4×D4C2×C411yescharacteristic
193C2×C4×D4C2×C414yes—
194C2×C4×D4C2×C411yescharacteristic
195C2×C4×D4C2×C411yescharacteristic
196C2×C4×D4C2×C411yescharacteristic
197C2×C4×D4C2×C411yescharacteristic
198C2×C4×D4C2×C411yescharacteristic
199C2×C4×D4D411yescharacteristic
200C2×C4×D4D411yescharacteristic
201C2×C4×D4D411yescharacteristic
202C2×C4×D4C2311yescharacteristic
203C2×C4×D4C2311yescharacteristic
204C2×C4×D4C2314yes—
205C2×#117—21no—
206C2×#117—28no—
207C2×#117—28no—
208C2×#117—21no—
209C2×#117—21no—
210C2×#117—21no—
211C2×#117—21no—
212C2×#117—21no—
213C2×#117—21no—
214C2×#117—21no—
215C2×#117—21no—
216C2×#117C2×C411yescharacteristic
217C2×#117C2×C411yescharacteristic
218C2×#117D411yescharacteristic
219C2×#117D411yescharacteristic
220C2×#117D411yescharacteristic
221C22×C4⋊C4—21no—
222C22×C4⋊C4—21no—
223C22×C4⋊C4C2×C411yescharacteristic
224C22×C22⋊C4—21no—
225C22×C22⋊C4—21no—
226C22×C22⋊C4—21no—
227C22×C42—21no—
228C22×C42—21no—
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#446—28no—
233#436—28no—
234#435—28no—
235#435—28no—
236#433—28no—
237#433—28no—
238#432—22no—
239#432—22no—
240#432—22no—
241#432—22no—
242#432—22no—
243#432—22no—
244#432C2314yes—
245#432C2314yescomplemented
246#431—22no—
247#431—22no—
248#431—22no—
249#431—22no—
250#431C2314yes—
251#431C2314yes—
252#431C2314yes—
253#431C2314yescomplemented
254#431C2314yescomplemented
255#431C2314yescomplemented
256#423—22no—
257#423—22no—
258#423—22no—
259#423—22no—
260#423C2314yes—
261#423C2314yescomplemented
262C2×C4⋊C8—22no—
263C2×C4⋊C8—22no—
264C2×C4⋊C8C2314yescomplemented
265#408—28no—
266#407—22no—
267#407—22no—
268#407—22no—
269#407—22no—
270C2×C22⋊C8—22no—
271#405—28no—
272C4×M16—22no—
273C4×M16—22no—
274C4×M16C2314yes—
275C4×M16C2314yescomplemented
276C2×C4×C8C2314yescomplemented
277Q8⋊C8C23116yescomplemented
278Q8⋊C8C23116yescomplemented
279D4⋊C8C23116yes—
280D4⋊C8C23116yes—
281C25—21no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—44no—
285C2×#41—44no—
286C2×#41—44no—
287C2×#41C22⋊C414yes—
288C2×#41C22×C414yes—
289C2×#41C22×C414yes—
290C2×#41C2×D414yes—
291C22×Q8—21no—
292C22×Q8C22⋊C411yescharacteristic
293C22×Q8C22×C411yescharacteristic
294C22×Q8C22×C411yescharacteristic
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4—22no—
301C22×D4—44no—
302C22×D4C22⋊C411yescharacteristic
303C22×D4C22⋊C411yescharacteristic
304C22×D4C22⋊C411yescharacteristic
305C22×D4C22×C411yescharacteristic
306C22×D4C22×C414yes—
307C22×D4C22×C411yescharacteristic
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4—24no—
314C23×C4—21no—
315C23×C4—24no—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—48no—
320C23×C4C22×C411yescharacteristic
321C23×C4C22×C411yescharacteristic
322C23×C4C22×C411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—48no—
334C22×C8—24no—
335C22×C8—24no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8C22×C414yes—
339C4⋊Q8C22×C414yes—
340#126—28no—
341#126—28no—
342#126—28no—
343#126—28no—
344#126—24no—
345#126—24no—
346#126—24no—
347#126—24no—
348#125—28no—
349#125—28no—
350#125—24no—
351#125—22no—
352#125—22no—
353#125—24no—
354#125C22×C414yes—
355#125C22×C414yes—
356#124—28no—
357#124—28no—
358#124—22no—
359#124—22no—
360#124C22×C414yes—
361#124C22×C414yes—
362#123—28no—
363#123—28no—
364#123—24no—
365#123—24no—
366#123—24no—
367#123—24no—
368#123—28no—
369#123—28no—
370#123—28no—
371#123—28no—
372C22⋊Q8—28no—
373C22⋊Q8—28no—
374C22⋊Q8—24no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—24no—
380C22⋊Q8—28no—
381C22⋊Q8—28no—
382C22⋊Q8C22×C414yes—
383C22⋊Q8C22×C414yes—
384C22⋊Q8C22×C414yes—
385C22⋊Q8C22×C414yes—
386#121—28no—
387#121—28no—
388#121—22no—
389#121—22no—
390#121—28no—
391#121—28no—
392#121C22×C414yes—
393#121C22×C414yes—
394#120—28no—
395#120—28no—
396C4×Q8—24no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—24no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8C22⋊C414yes—
405C4×Q8C22⋊C414yes—
406C4×Q8C22×C414yes—
407C4×Q8C22×C414yes—
408C4×Q8C22×C412yes—
409C4×Q8C22×C412yes—
410C4×Q8C22×C414yes—
411C4×Q8C2×D414yes—
412C4×Q8C2412yes—
413C4×Q8C2412yes—
414C4×D4—24no—
415C4×D4—24no—
416C4×D4—24no—
417C4×D4—24no—
418C4×D4—24no—
419C4×D4—24no—
420C4×D4—24no—
421C4×D4—24no—
422C4×D4—24no—
423C4×D4—24no—
424C4×D4—24no—
425C4×D4—24no—
426C4×D4—24no—
427C4×D4—22no—
428C4×D4—24no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—24no—
436C4×D4—21no—
437C4×D4—24no—
438C4×D4C22⋊C414yes—
439C4×D4C22⋊C414yes—
440C4×D4C22⋊C414yes—
441C4×D4C22⋊C414yes—
442C4×D4C22⋊C414yes—
443C4×D4C22⋊C414yes—
444C4×D4C22×C412yes—
445C4×D4C22×C412yes—
446C4×D4C22×C414yes—
447C4×D4C22×C414yes—
448C4×D4C22×C414yes—
449C4×D4C22×C414yes—
450C4×D4C22×C414yes—
451C4×D4C22×C414yes—
452C4×D4C22×C414yes—
453C4×D4C2×D414yes—
454C4×D4C2×D414yes—
455C4×D4C2×D414yes—
456C4×D4C2412yes—
457C4×D4C2412yes—
458#117—24no—
459#117—22no—
460#117—22no—
461#117—24no—
462#117—28no—
463#117—28no—
464#117—28no—
465#117—28no—
466#117—24no—
467#117—24no—
468#117—24no—
469#117—24no—
470#117—24no—
471#117—24no—
472#117—24no—
473#117—24no—
474#117C22⋊C414yes—
475#117C22⋊C414yes—
476#117C22⋊C414yes—
477#117C22×C414yes—
478#117C22×C414yes—
479#117C2×D414yes—
480#117C2×D414yes—
481#117C2×D414yes—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—28no—
500C2×C4⋊C4—28no—
501C2×C4⋊C4C22⋊C411yescharacteristic
502C2×C4⋊C4C22⋊C411yescharacteristic
503C2×C4⋊C4C22⋊C411yescharacteristic
504C2×C4⋊C4C22⋊C411yescharacteristic
505C2×C4⋊C4C22⋊C411yescharacteristic
506C2×C4⋊C4C22⋊C411yescharacteristic
507C2×C4⋊C4C22×C411yescharacteristic
508C2×C4⋊C4C22×C411yescharacteristic
509C2×C4⋊C4C22×C414yes—
510C2×C4⋊C4C22×C411yescharacteristic
511C2×C4⋊C4C22×C411yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—28no—
533C2×C22⋊C4—28no—
534C2×C22⋊C4C22⋊C411yescharacteristic
535C2×C22⋊C4C22⋊C411yescharacteristic
536C2×C22⋊C4C22⋊C411yescharacteristic
537C2×C22⋊C4C22⋊C411yescharacteristic
538C2×C22⋊C4C22⋊C411yescharacteristic
539C2×C22⋊C4C22⋊C411yescharacteristic
540C2×C42—21no—
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—24no—
550C2×C42C22×C411yescharacteristic
551C2×C42C22×C411yescharacteristic
552C2×C42C22×C411yescharacteristic
553C2×C42C22×C412yes—
554C2×C42C22×C412yes—
555C2×C42C22×C412yes—
556C2×C42C2×D411yescharacteristic
557C2×C42C2×D411yescharacteristic
558C2×C42C2×D411yescharacteristic
559C2×C42C2×D411yescharacteristic
560C2×C42C2×D411yescharacteristic
561C2×C42C2×D411yescharacteristic
562C2×C42C2×D412yes—
563C2×C42C2×D412yes—
564C2×C42C2×D412yes—
565C2×C42C2×D412yes—
566C2×C42C2×D412yes—
567C2×C42C2×D412yes—
568C2×C42C2411yescharacteristic
569C2×C42C2412yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C4⋊C8—24no—
573C4⋊C8—24no—
574C4⋊C8—24no—
575C4⋊C8—24no—
576C4⋊C8—24no—
577C4⋊C8—24no—
578C4⋊C8—24no—
579C4⋊C8C2418yes—
580C22⋊C8—24no—
581C22⋊C8—24no—
582C22⋊C8—24no—
583C22⋊C8—24no—
584C22⋊C8—24no—
585C22⋊C8—24no—
586C22⋊C8—24no—
587C22⋊C8—24no—
588#97—24no—
589#97—24no—
590#97—24no—
591#97—24no—
592C4×C8—24no—
593C4×C8—24no—
594C4×C8—24no—
595C4×C8C2418yes—
596C24—21no—
597C24—21no—
598C24—24no—
599C24—44no—
600C24—44no—
601C24—82no—
602C24C2×C22⋊C411yescharacteristic
603C24C2×C22⋊C411yescharacteristic
604C24C2×C22⋊C411yescharacteristic
605#41—28no—
606#41—28no—
607#41—48no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612#41—48no—
613#41—48no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—24no—
617C2×Q8—42no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—82no—
621C2×Q8C2×C22⋊C414yes—
622C2×Q8C23×C412yes—
623C2×Q8C23×C412yes—
624C2×D4—24no—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—48no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—82no—
643C2×D4—82no—
644C2×D4C2×C22⋊C414yes—
645C2×D4C2×C22⋊C414yes—
646C2×D4C2×C22⋊C414yes—
647C2×D4C23×C412yes—
648C2×D4C23×C412yes—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—24no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—22no—
664C22×C4—24no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—416no—
675C22×C4—416no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—81no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4—82no—
685C22×C4—82no—
686C22×C4C2×C22⋊C411yescharacteristic
687C22×C4C2×C22⋊C411yescharacteristic
688C22×C4C2×C22⋊C411yescharacteristic
689C22×C4C2×C22⋊C412yes—
690C22×C4C2×C22⋊C412yes—
691C22×C4C2×C22⋊C412yes—
692C22×C4C2×C22⋊C411yescharacteristic
693C22×C4C2×C22⋊C411yescharacteristic
694C22×C4C2×C22⋊C411yescharacteristic
695C22×C4C2×C22⋊C411yescharacteristic
696C22×C4C2×C22⋊C411yescharacteristic
697C22×C4C2×C22⋊C412yes—
698C22×C4C2×C22⋊C412yes—
699C22×C4C2×C22⋊C412yes—
700C22×C4C2×C22⋊C411yescharacteristic
701C22×C4C2×C22⋊C412yes—
702C22×C4C2×C22⋊C412yes—
703C22×C4C2×C22⋊C412yes—
704C22×C4C23×C411yescharacteristic
705C22×C4C23×C412yes—
706C22×C4C23×C412yes—
707C22×C4C23×C412yes—
708C22×C4C22×D412yes—
709C22×C4C22×D412yes—
710C22×C4C22×D412yes—
711C22×C4C22×D411yescharacteristic
712C22×C4C22×D412yes—
713C22×C4C22×D412yes—
714C22×C4C22×D412yes—
715C22×C4C22×D411yescharacteristic
716M16—48no—
717M16—48no—
718M16—84no—
719M16—84no—
720C2×C8—28no—
721C2×C8—28no—
722C2×C8—48no—
723C2×C8—84no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—24no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4C2×C22⋊C414yes—
747C4⋊C4C2×C22⋊C414yes—
748C4⋊C4C2×C22⋊C414yes—
749C4⋊C4C2×C22⋊C414yes—
750C4⋊C4C2×C22⋊C414yes—
751C4⋊C4C2×C22⋊C414yes—
752C4⋊C4C23×C412yes—
753C4⋊C4C23×C412yes—
754C4⋊C4C23×C412yes—
755C4⋊C4C23×C412yes—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—22no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4C2×C22⋊C414yes—
777C22⋊C4C2×C22⋊C414yes—
778C22⋊C4C2×C22⋊C414yes—
779C22⋊C4C2×C22⋊C414yes—
780C22⋊C4C2×C22⋊C414yes—
781C22⋊C4C2×C22⋊C414yes—
782C42—24no—
783C42—24no—
784C42—22no—
785C42—22no—
786C42—24no—
787C42—24no—
788C42—22no—
789C42—22no—
790C42C2×C22⋊C412yes—
791C42C2×C22⋊C412yes—
792C42C2×C22⋊C412yes—
793C42C2×C22⋊C412yes—
794C42C2×C22⋊C412yes—
795C42C2×C22⋊C412yes—
796C42C2×C22⋊C412yes—
797C42C2×C22⋊C412yes—
798C42C2×C22⋊C412yes—
799C42C23×C411yescharacteristic
800C42C23×C412yes—
801C42C23×C412yes—
802C42C23×C412yes—
803C42C22×D412yes—
804C42C22×D412yes—
805C42C22×D412yes—
806C42C22×D411yescharacteristic
807C42C22×D412yes—
808C42C22×D412yes—
809C42C22×D412yes—
810C42C22×D411yescharacteristic
811C42C2511yescharacteristic
812C23—24no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—48no—
825C23—42no—
826C23—48no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—84no—
832C23—816no—
833C23C22×C22⋊C412yes—
834C23C22×C22⋊C412yes—
835C23C22×C22⋊C412yes—
836C23C22×C22⋊C411yescharacteristic
837Q8—24no—
838Q8—24no—
839Q8—44no—
840Q8—42no—
841Q8—42no—
842Q8—84no—
843D4—24no—
844D4—22no—
845D4—24no—
846D4—44no—
847D4—44no—
848D4—44no—
849D4—48no—
850D4—42no—
851D4—48no—
852D4—48no—
853D4—84no—
854D4—84no—
855D4#56814yes—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—41no—
892C2×C4—48no—
893C2×C4—48no—
894C2×C4—48no—
895C2×C4—48no—
896C2×C4—48no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—84no—
908C2×C4—84no—
909C2×C4C22×C22⋊C412yes—
910C2×C4C22×C22⋊C412yes—
911C2×C4C22×C22⋊C412yes—
912C2×C4C22×C22⋊C412yes—
913C2×C4C22×C22⋊C411yescharacteristic
914C2×C4C22×C22⋊C411yescharacteristic
915C2×C4C22×C22⋊C412yes—
916C2×C4C22×C22⋊C412yes—
917C2×C4C22×C22⋊C412yes—
918C2×C4C22×C22⋊C412yes—
919C2×C4C22×C22⋊C412yes—
920C2×C4C22×C22⋊C411yescharacteristic
921C2×C4#57514yes—
922C2×C4C24×C411yescharacteristic
923C2×C4C23×D411yescharacteristic
924C2×C4C23×D411yescharacteristic
925C8—48no—
926C8—48no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—48no—
940C22—44no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—82no—
947C22—82no—
948C22—84no—
949C22—816no—
950C22#289612yes—
951C22C23×C22⋊C411yescharacteristic
952C4—22no—
953C4—22no—
954C4—21no—
955C4—22no—
956C4—22no—
957C4—22no—
958C4—22no—
959C4—21no—
960C4—21no—
961C4—22no—
962C4—22no—
963C4—22no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4#289612yes—
971C4C2×#56812yes—
972C4C2×#57512yes—
973C2—22no—
974C2—42no—
975C2—42no—
976C2—42no—
977C2—44no—
978C2—82no—
979C2#6006411yescharacteristic
980C2C2×#289611yescharacteristic
981C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radicalC2×#3475C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60277C2semidirect
3. #60125C2semidirect
4. #17513C2semidirect
5. #17492C2semidirect
6. #17491C2semidirect
7. #17487C2semidirect
8. #17451C2semidirect
9. #17448C2semidirect
10. #17443C2semidirect
43. #2965C22semidirect
45. #2925C22semidirect
50. #2920C22semidirect
51. #2920C22semidirect
52. C2×#431C22semidirect
53. C2×#423C22semidirect
56. #1497C22semidirect
57. #1495C22semidirect
58. #1494C22semidirect
59. #1490C22semidirect
60. #1489C22semidirect
61. #1488C22semidirect
62. #1487C22semidirect
63. #1487C22semidirect
66. #1485C22semidirect
67. #1483C22semidirect
68. #1482C22semidirect
69. #1478C22semidirect
70. #1477C22semidirect
71. #1476C22semidirect
245. #432C23semidirect
253. #431C23semidirect
254. #431C23semidirect
255. #431C23semidirect
261. #423C23semidirect
264. C2×C4⋊C8C23semidirect
275. C4×M16C23semidirect
276. C2×C4×C8C23semidirect
277. Q8⋊C8C23semidirect
278. Q8⋊C8C23semidirect

Maximal subgroups

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

subgroupindex
C2×#34752
#602772
#601252
#175132
#174922
#174912
#174872
#174512
#174482
#174432