Finite Group Databasebeta

← C2×#72213553 #72213591

Subgroups — C2×#72213553 #72213591

Order 2048.

8828 conjugacy classes of subgroups.

The subgroup lattice has 1549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72213553C218yesmaximal, direct product factor
2C2×#92827C214yesmaximal, complemented
3C2×#126586C212yesmaximal, complemented
4C22×#9644C211yesmaximal, characteristic
5C22×C4×#127C411yescharacteristic
6C2×#33418—22no—
7C22×#1842C411yescharacteristic
8C22×#1744C2211yescharacteristic
9C23×D4⋊C8—22no—
10C2×#9644—22no—
11C2×#9644—24no—
12C2×#9644C414yes—
13C2×#9644C412yes—
14C2×#9644C2214yes—
15C2×#9644C2212yes—
16#126586—24no—
17#126586C2218yescomplemented
18C2×#7143—22no—
19C2×#7143C2214yescomplemented
20#92827C22116yescomplemented
21C23×#127C811yescharacteristic
22C23×C4×D4—21no—
23C23×C4×D4—41no—
24C23×C4⋊C8—21no—
25C23×C4⋊C8—41no—
26C23×C4×C8D412yes—
27C2×C4×#127—21no—
28C2×C4×#127—22no—
29C2×C4×#127—21no—
30C2×C4×#127—22no—
31C2×C4×#127—41no—
32C2×C4×#127—42no—
33C2×C4×#127—41no—
34C2×C4×#127—42no—
35C2×C4×#127C812yes—
36C2×C4×#127C814yes—
37C2×C4×#127C2×C414yes—
38C2×C4×#127C2×C412yes—
39C22×#390—21no—
40C22×#390—41no—
41C22×#384C811yescharacteristic
42C22×C43C2×C411yescharacteristic
43#33418—28no—
44#33418—28no—
45#33418—44no—
46#33418—44no—
47C2×#2163—24no—
48C2×#2163—24no—
49C2×#2162—42no—
50C2×#2162—42no—
51C2×#2150—42no—
52C2×#2112—42no—
53C2×C4×M32—24no—
54C2×#1842—21no—
55C2×#1842—22no—
56C2×#1842—41no—
57C2×#1842—42no—
58C2×#1842C2×C414yes—
59C2×#1842C2×C412yes—
60C2×#1744—41no—
61C2×#1744—42no—
62C2×#1744C2×C411yescharacteristic
63C2×#1744C2×C412yes—
64C2×#1744D412yes—
65C2×#1744D414yes—
66C2×#1744C2311yescharacteristic
67C2×#1744C2312yes—
68C22×#336—41no—
69C22×D4⋊C8—24no—
70C22×D4⋊C8—28no—
71C22×D4⋊C8—24no—
72C22×D4⋊C8—28no—
73C22×D4⋊C8—42no—
74C22×D4⋊C8—42no—
75C22×D4⋊C8—44no—
76C22×D4⋊C8—42no—
77C22×D4⋊C8—42no—
78C22×D4⋊C8—44no—
79#9644—28no—
80#9644—24no—
81#9644—28no—
82#9644—24no—
83#9644C2×C418yes—
84#9644C2×C414yes—
85#9644C2314yes—
86#7143—28no—
87#7143—24no—
88#7143C2318yescomplemented
89C24×D4—21no—
90C24×D4—41no—
91C25×C4—41no—
92C24×C8—22no—
93C24×C8—41no—
94C22×#127—21no—
95C22×#127—22no—
96C22×#127—41no—
97C22×#127—42no—
98C22×#127—48no—
99C22×#127C2×C812yes—
100C22×#127C2×C814yes—
101C22×C4×D4—24no—
102C22×C4×D4—22no—
103C22×C4×D4—22no—
104C22×C4×D4—24no—
105C22×C4×D4—44no—
106C22×C4×D4—42no—
107C22×C4×D4—44no—
108C22×C4×D4—42no—
109C22×C4×D4—42no—
110C22×C4×D4—41no—
111C22×C4×D4—42no—
112C22×C4×D4—41no—
113C22×C4×D4—44no—
114C22×C4×D4—42no—
115C22×C4×D4—42no—
116C22×C4×D4—44no—
117C22×C4×D4—42no—
118C22×C4×D4—44no—
119C22×C4×D4—42no—
120C22×C4×D4—42no—
121C22×C4×D4—42no—
122C22×C4×D4—44no—
123C22×C4×D4—88no—
124C22×C4×D4—88no—
125C23×C4⋊C4—21no—
126C23×C4⋊C4—41no—
127C23×C22⋊C4—42no—
128C23×C22⋊C4—41no—
129C23×C42—21no—
130C23×C42—21no—
131C23×C42C22⋊C411yescharacteristic
132C23×C42C2×C811yescharacteristic
133C23×C42M1611yescharacteristic
134C22×M32—44no—
135C22×C4⋊C8—22no—
136C22×C4⋊C8—24no—
137C22×C4⋊C8—44no—
138C22×C4⋊C8—42no—
139C22×C4⋊C8—42no—
140C22×C4⋊C8—41no—
141C22×C4⋊C8—44no—
142C22×C4⋊C8—42no—
143C22×C4⋊C8—42no—
144C22×C4⋊C8—44no—
145C22×C4⋊C8—42no—
146C22×C4⋊C8—88no—
147C22×C4×C8—22no—
148C22×C4×C8—24no—
149C22×C4×C8—22no—
150C22×C4×C8—22no—
151C22×C4×C8—24no—
152C22×C4×C8C22⋊C412yes—
153C22×C4×C8C22⋊C414yes—
154C22×C4×C8D812yes—
155C22×C4×C8D812yes—
156C22×C4×C8D814yes—
157C22×C4×C8SD1612yes—
158C22×C4×C8SD1612yes—
159C22×C4×C8SD1614yes—
160C22×C4×C8C2×D412yes—
161C22×C4×C8C2×D414yes—
162C4×#127—24no—
163C4×#127—24no—
164C4×#127—24no—
165C4×#127—24no—
166C4×#127—22no—
167C4×#127—24no—
168C4×#127—22no—
169C4×#127—44no—
170C4×#127—44no—
171C4×#127—44no—
172C4×#127—42no—
173C4×#127—44no—
174C4×#127—42no—
175C4×#127—44no—
176C4×#127—44no—
177C4×#127—44no—
178C4×#127—44no—
179C4×#127—44no—
180C4×#127—42no—
181C4×#127—44no—
182C4×#127—42no—
183C4×#127C2×C818yes—
184C4×#127C2×C814yes—
185C4×#127C22×C414yes—
186C2×#390—22no—
187C2×#390—24no—
188C2×#390—22no—
189C2×#390—24no—
190C2×#390—44no—
191C2×#390—42no—
192C2×#390—44no—
193C2×#390—42no—
194C2×#390—44no—
195C2×#390—42no—
196C2×#390—42no—
197C2×#390—44no—
198C2×#390—42no—
199C2×#390—44no—
200C2×#384—21no—
201C2×#384—22no—
202C2×#384—42no—
203C2×#384—41no—
204C2×#384C2×C812yes—
205C2×#384C2×C814yes—
206C2×C43—22no—
207C2×C43—21no—
208C2×C43—22no—
209C2×C43—21no—
210C2×C43C22⋊C411yescharacteristic
211C2×C43C22⋊C412yes—
212C2×C43C2×C812yes—
213C2×C43C2×C811yescharacteristic
214C2×C43M1612yes—
215C2×C43M1611yescharacteristic
216C2×C43C22×C411yescharacteristic
217C2×C43C22×C412yes—
218#2163—216no—
219#2163—28no—
220#2163—28no—
221#2163—48no—
222#2163—44no—
223#2163—44no—
224#2162—48no—
225#2162—48no—
226#2162—48no—
227#2162—48no—
228#2150—48no—
229#2150—48no—
230C2×C4⋊C16—44no—
231C2×C4⋊C16—44no—
232#2112—48no—
233#2112—48no—
234C2×C22⋊C16—44no—
235C2×C22⋊C16—44no—
236C4×M32—216no—
237C4×M32—48no—
238C2×#346—28no—
239C2×C4×C16—44no—
240#1842—24no—
241#1842—22no—
242#1842—44no—
243#1842—42no—
244#1842—42no—
245#1842—44no—
246#1842C22×C414yes—
247#1744—42no—
248#1744—41no—
249#1744—44no—
250#1744—42no—
251#1744—42no—
252#1744—41no—
253#1744C22⋊C414yes—
254#1744C22⋊C412yes—
255#1744C22×C411yescharacteristic
256#1744C22×C412yes—
257#1744C2×D414yes—
258#1744C2×D412yes—
259#1744C2411yescharacteristic
260C2×#336—41no—
261C2×#336—42no—
262C2×#336—42no—
263C2×#336—44no—
264C2×#336—41no—
265C2×#336—42no—
266C2×D4⋊C8—28no—
267C2×D4⋊C8—216no—
268C2×D4⋊C8—28no—
269C2×D4⋊C8—48no—
270C2×D4⋊C8—44no—
271C2×D4⋊C8—44no—
272C2×D4⋊C8—48no—
273C2×D4⋊C8—48no—
274C2×D4⋊C8—48no—
275C2×D4⋊C8—48no—
276C2×D4⋊C8—44no—
277C2×D4⋊C8—48no—
278C2×D4⋊C8—48no—
279C2×D4⋊C8—44no—
280C2×D4⋊C8—44no—
281C2×D4⋊C8—48no—
282C2×D4⋊C8—44no—
283C2×D4⋊C8—48no—
284C26—41no—
285C23×D4—28no—
286C23×D4—22no—
287C23×D4—24no—
288C23×D4—48no—
289C23×D4—42no—
290C23×D4—44no—
291C23×D4—44no—
292C23×D4—44no—
293C23×D4—42no—
294C23×D4—416no—
295C23×D4—42no—
296C23×D4—41no—
297C23×D4—44no—
298C23×D4—42no—
299C23×D4—42no—
300C23×D4—88no—
301C23×D4—88no—
302C24×C4—21no—
303C24×C4—21no—
304C24×C4—41no—
305C24×C4—44no—
306C24×C4—42no—
307C24×C4—44no—
308C24×C4—42no—
309C24×C4—88no—
310C24×C4—88no—
311C24×C4—82no—
312C24×C4—81no—
313C24×C4—81no—
314C24×C4—82no—
315C24×C4—81no—
316C24×C4—81no—
317C24×C4C22⋊C811yescharacteristic
318C24×C4#9911yescharacteristic
319C24×C4#10011yescharacteristic
320C23×C8—22no—
321C23×C8—22no—
322C23×C8—22no—
323C23×C8—24no—
324C23×C8—22no—
325C23×C8—24no—
326C23×C8—22no—
327C23×C8—24no—
328C23×C8—22no—
329C23×C8—24no—
330C23×C8—44no—
331C23×C8—42no—
332C23×C8—88no—
333C23×C8—88no—
334C23×C8—82no—
335C23×C8—81no—
336C23×C8—81no—
337C2×#127—22no—
338C2×#127—24no—
339C2×#127—44no—
340C2×#127—42no—
341C2×#127—42no—
342C2×#127—44no—
343C2×#127—48no—
344C2×#127—48no—
345C2×#127—416no—
346C2×#127—48no—
347C2×#127—432no—
348C2×#127—48no—
349C2×#127—416no—
350C2×#127C22×C814yes—
351C2×C4×D4—24no—
352C2×C4×D4—24no—
353C2×C4×D4—28no—
354C2×C4×D4—48no—
355C2×C4×D4—44no—
356C2×C4×D4—48no—
357C2×C4×D4—48no—
358C2×C4×D4—48no—
359C2×C4×D4—44no—
360C2×C4×D4—48no—
361C2×C4×D4—44no—
362C2×C4×D4—48no—
363C2×C4×D4—44no—
364C2×C4×D4—44no—
365C2×C4×D4—44no—
366C2×C4×D4—44no—
367C2×C4×D4—44no—
368C2×C4×D4—48no—
369C2×C4×D4—48no—
370C2×C4×D4—48no—
371C2×C4×D4—48no—
372C2×C4×D4—48no—
373C2×C4×D4—44no—
374C2×C4×D4—42no—
375C2×C4×D4—44no—
376C2×C4×D4—42no—
377C2×C4×D4—44no—
378C2×C4×D4—48no—
379C2×C4×D4—44no—
380C2×C4×D4—44no—
381C2×C4×D4—48no—
382C2×C4×D4—44no—
383C2×C4×D4—48no—
384C2×C4×D4—48no—
385C2×C4×D4—44no—
386C2×C4×D4—816no—
387C2×C4×D4—88no—
388C2×C4×D4—88no—
389C2×C4×D4—816no—
390C2×C4×D4—816no—
391C2×C4×D4—88no—
392C2×C4×D4—832no—
393C2×C4×D4—816no—
394C2×C4×D4—832no—
395C2×C4×D4—816no—
396C2×C4×D4—88no—
397C2×C4×D4—816no—
398C2×C4×D4—84no—
399C2×C4×D4—84no—
400C2×C4×D4—82no—
401C2×C4×D4—84no—
402C2×C4×D4—84no—
403C2×C4×D4—84no—
404C2×C4×D4—82no—
405C2×C4×D4—84no—
406C2×C4×D4—82no—
407C2×C4×D4—84no—
408C2×C4×D4—82no—
409C2×C4×D4—84no—
410C2×C4×D4—82no—
411C2×C4×D4—82no—
412C2×C4×D4—84no—
413C22×C4⋊C4—22no—
414C22×C4⋊C4—24no—
415C22×C4⋊C4—44no—
416C22×C4⋊C4—42no—
417C22×C4⋊C4—42no—
418C22×C4⋊C4—44no—
419C22×C4⋊C4—42no—
420C22×C4⋊C4—44no—
421C22×C4⋊C4—42no—
422C22×C4⋊C4—42no—
423C22×C4⋊C4—41no—
424C22×C4⋊C4—88no—
425C22×C22⋊C4—48no—
426C22×C22⋊C4—44no—
427C22×C22⋊C4—48no—
428C22×C22⋊C4—44no—
429C22×C22⋊C4—44no—
430C22×C22⋊C4—42no—
431C22×C22⋊C4—44no—
432C22×C22⋊C4—42no—
433C22×C22⋊C4—816no—
434C22×C22⋊C4—82no—
435C22×C22⋊C4—84no—
436C22×C22⋊C4—82no—
437C22×C42—28no—
438C22×C42—28no—
439C22×C42—22no—
440C22×C42—21no—
441C22×C42—22no—
442C22×C42—21no—
443C22×C42—22no—
444C22×C42—21no—
445C22×C42—22no—
446C22×C42—21no—
447C22×C42—22no—
448C22×C42—21no—
449C22×C42—22no—
450C22×C42—21no—
451C22×C42—22no—
452C22×C42—21no—
453C22×C42—22no—
454C22×C42—21no—
455C22×C42—22no—
456C22×C42—21no—
457C22×C42—22no—
458C22×C42—21no—
459C22×C42—44no—
460C22×C42—44no—
461C22×C42—84no—
462C22×C42C22⋊C811yescharacteristic
463C22×C42C22⋊C812yes—
464C22×C42C22⋊C811yescharacteristic
465C22×C42C22⋊C812yes—
466C22×C42C22⋊C812yes—
467C22×C42C22⋊C811yescharacteristic
468C22×C42#9912yes—
469C22×C42#9911yescharacteristic
470C22×C42#10012yes—
471C22×C42#10011yescharacteristic
472C22×C42#10212yes—
473C22×C42#10214yes—
474C22×C42#10212yes—
475C22×C42#10412yes—
476C22×C42#10414yes—
477C22×C42#10412yes—
478C22×C42C2×C22⋊C411yescharacteristic
479C22×C42C2×C22⋊C412yes—
480C22×C42C22×C811yescharacteristic
481C22×C42C22×C812yes—
482C22×C42C2×M1611yescharacteristic
483C22×C42C2×M1612yes—
484C2×M32—416no—
485C2×M32—816no—
486C22×C16—48no—
487C2×C4⋊C8—24no—
488C2×C4⋊C8—48no—
489C2×C4⋊C8—44no—
490C2×C4⋊C8—44no—
491C2×C4⋊C8—48no—
492C2×C4⋊C8—44no—
493C2×C4⋊C8—48no—
494C2×C4⋊C8—44no—
495C2×C4⋊C8—42no—
496C2×C4⋊C8—44no—
497C2×C4⋊C8—816no—
498C2×C4⋊C8—88no—
499C2×C4⋊C8—816no—
500C2×C4⋊C8—88no—
501C2×C4⋊C8—84no—
502C2×C4⋊C8—82no—
503C2×C4⋊C8—82no—
504C2×C4⋊C8—84no—
505C2×C4×C8—22no—
506C2×C4×C8—24no—
507C2×C4×C8—22no—
508C2×C4×C8—24no—
509C2×C4×C8—24no—
510C2×C4×C8—24no—
511C2×C4×C8—24no—
512C2×C4×C8—22no—
513C2×C4×C8—24no—
514C2×C4×C8—24no—
515C2×C4×C8—24no—
516C2×C4×C8—24no—
517C2×C4×C8—24no—
518C2×C4×C8—22no—
519C2×C4×C8—24no—
520C2×C4×C8—22no—
521C2×C4×C8—24no—
522C2×C4×C8—22no—
523C2×C4×C8—22no—
524C2×C4×C8—24no—
525C2×C4×C8—24no—
526C2×C4×C8—22no—
527C2×C4×C8—22no—
528C2×C4×C8—24no—
529C2×C4×C8—24no—
530C2×C4×C8—22no—
531C2×C4×C8#10214yes—
532C2×C4×C8#10212yes—
533C2×C4×C8#10212yes—
534C2×C4×C8#10214yes—
535C2×C4×C8#10214yes—
536C2×C4×C8#10214yes—
537C2×C4×C8#10214yes—
538C2×C4×C8C2×C22⋊C412yes—
539C2×C4×C8C2×C22⋊C414yes—
540C2×C4×C8C2×D812yes—
541C2×C4×C8C2×D814yes—
542C2×C4×C8C2×D814yes—
543C2×C4×C8C2×D812yes—
544C2×C4×C8C2×SD1612yes—
545C2×C4×C8C2×SD1614yes—
546C2×C4×C8C2×SD1612yes—
547C2×C4×C8C2×SD1614yes—
548C2×C4×C8C22×D412yes—
549#390—24no—
550#390—28no—
551#390—24no—
552#390—48no—
553#390—44no—
554#390—48no—
555#390—48no—
556#390—48no—
557#390—48no—
558#390—44no—
559#390—44no—
560#390—48no—
561#390—44no—
562#390—48no—
563#390—44no—
564#390—48no—
565#390—44no—
566#384—24no—
567#384—22no—
568#384—42no—
569#384—44no—
570#384—42no—
571#384—44no—
572#384C22×C814yes—
573C43—22no—
574C43—22no—
575C43—22no—
576C43—22no—
577C43—22no—
578C43—22no—
579C43—21no—
580C43—22no—
581C43—21no—
582C43—22no—
583C43—21no—
584C43—22no—
585C43—21no—
586C43—22no—
587C43C22⋊C812yes—
588C43C22⋊C812yes—
589C43C22⋊C812yes—
590C43C2×C22⋊C412yes—
591C43C2×C22⋊C411yescharacteristic
592C43C22×C811yescharacteristic
593C43C22×C812yes—
594C43C2×M1611yescharacteristic
595C43C2×M1612yes—
596C43C23×C411yescharacteristic
597C4⋊C16—416no—
598C4⋊C16—48no—
599C4⋊C16—48no—
600C22⋊C16—48no—
601C22⋊C16—48no—
602C22⋊C16—416no—
603#346—216no—
604#346—48no—
605C4×C16—416no—
606#336—44no—
607#336—42no—
608#336—41no—
609#336—42no—
610#336—42no—
611#336—44no—
612#336—41no—
613D4⋊C8—48no—
614D4⋊C8—48no—
615D4⋊C8—48no—
616D4⋊C8—416no—
617D4⋊C8—416no—
618D4⋊C8—48no—
619C25—48no—
620C25—44no—
621C25—42no—
622C25—88no—
623C25—84no—
624C25—88no—
625C25—82no—
626C25—81no—
627C25—81no—
628C25#32311yescharacteristic
629C22×D4—28no—
630C22×D4—216no—
631C22×D4—24no—
632C22×D4—48no—
633C22×D4—416no—
634C22×D4—432no—
635C22×D4—416no—
636C22×D4—416no—
637C22×D4—44no—
638C22×D4—48no—
639C22×D4—44no—
640C22×D4—44no—
641C22×D4—416no—
642C22×D4—48no—
643C22×D4—48no—
644C22×D4—432no—
645C22×D4—432no—
646C22×D4—48no—
647C22×D4—416no—
648C22×D4—48no—
649C22×D4—42no—
650C22×D4—44no—
651C22×D4—44no—
652C22×D4—44no—
653C22×D4—48no—
654C22×D4—48no—
655C22×D4—88no—
656C22×D4—816no—
657C22×D4—816no—
658C22×D4—88no—
659C22×D4—88no—
660C22×D4—816no—
661C22×D4—88no—
662C22×D4—88no—
663C22×D4—88no—
664C22×D4—816no—
665C22×D4—816no—
666C22×D4—88no—
667C22×D4—8128no—
668C22×D4—84no—
669C22×D4—84no—
670C22×D4—84no—
671C22×D4—82no—
672C22×D4—82no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—24no—
677C23×C4—28no—
678C23×C4—28no—
679C23×C4—22no—
680C23×C4—21no—
681C23×C4—22no—
682C23×C4—21no—
683C23×C4—22no—
684C23×C4—21no—
685C23×C4—22no—
686C23×C4—21no—
687C23×C4—44no—
688C23×C4—44no—
689C23×C4—44no—
690C23×C4—44no—
691C23×C4—44no—
692C23×C4—44no—
693C23×C4—42no—
694C23×C4—44no—
695C23×C4—44no—
696C23×C4—48no—
697C23×C4—816no—
698C23×C4—88no—
699C23×C4—816no—
700C23×C4—88no—
701C23×C4—832no—
702C23×C4—816no—
703C23×C4—88no—
704C23×C4—82no—
705C23×C4—81no—
706C23×C4—81no—
707C23×C4—82no—
708C23×C4—84no—
709C23×C4—84no—
710C23×C4—82no—
711C23×C4—82no—
712C23×C4—84no—
713C23×C4—84no—
714C23×C4—82no—
715C23×C4—84no—
716C23×C4—84no—
717C23×C4—84no—
718C23×C4—84no—
719C23×C4—82no—
720C23×C4—84no—
721C23×C4—82no—
722C23×C4—168no—
723C23×C4—168no—
724C23×C4—164no—
725C23×C4—168no—
726C23×C4—164no—
727C23×C4—1616no—
728C23×C4—168no—
729C23×C4—164no—
730C23×C4—164no—
731C23×C4#32312yes—
732C23×C4#32312yes—
733C23×C4#32311yescharacteristic
734C23×C4#32312yes—
735C23×C4#32311yescharacteristic
736C23×C4#32311yescharacteristic
737C23×C4D4⋊C814yes—
738C23×C4D4⋊C812yes—
739C23×C4D4⋊C812yes—
740C23×C4#32712yes—
741C23×C4#32714yes—
742C23×C4#32712yes—
743C23×C4#32911yescharacteristic
744C23×C4#32912yes—
745C23×C4#32911yescharacteristic
746C23×C4#33112yes—
747C23×C4#33111yescharacteristic
748C23×C4#33111yescharacteristic
749C23×C4C2×C22⋊C811yescharacteristic
750C23×C4C2×C22⋊C812yes—
751C23×C4C2×#9912yes—
752C23×C4C2×#9911yescharacteristic
753C23×C4C2×#10012yes—
754C23×C4C2×#10011yescharacteristic
755C22×C8—22no—
756C22×C8—24no—
757C22×C8—22no—
758C22×C8—24no—
759C22×C8—22no—
760C22×C8—24no—
761C22×C8—22no—
762C22×C8—24no—
763C22×C8—22no—
764C22×C8—22no—
765C22×C8—24no—
766C22×C8—24no—
767C22×C8—22no—
768C22×C8—24no—
769C22×C8—24no—
770C22×C8—24no—
771C22×C8—22no—
772C22×C8—24no—
773C22×C8—48no—
774C22×C8—48no—
775C22×C8—44no—
776C22×C8—84no—
777C22×C8—84no—
778C22×C8—88no—
779C22×C8—88no—
780C22×C8—84no—
781C22×C8—88no—
782C22×C8—84no—
783C22×C8—88no—
784C22×C8—816no—
785C22×C8—88no—
786C22×C8—82no—
787C22×C8—84no—
788C22×C8—82no—
789C22×C8—84no—
790C22×C8—168no—
791C22×C8—164no—
792C22×C8—164no—
793#127—48no—
794#127—48no—
795#127—416no—
796#127—416no—
797#127—416no—
798#127—416no—
799#127—416no—
800#127—432no—
801C4×D4—48no—
802C4×D4—48no—
803C4×D4—416no—
804C4×D4—48no—
805C4×D4—48no—
806C4×D4—416no—
807C4×D4—816no—
808C4×D4—88no—
809C4×D4—88no—
810C4×D4—832no—
811C4×D4—832no—
812C4×D4—832no—
813C4×D4—816no—
814C4×D4—832no—
815C4×D4—816no—
816C4×D4—88no—
817C4×D4—816no—
818C4×D4—832no—
819C4×D4—88no—
820C4×D4—84no—
821C4×D4—88no—
822C4×D4—84no—
823C4×D4—84no—
824C4×D4—88no—
825C4×D4—88no—
826C4×D4—84no—
827C4×D4—88no—
828C4×D4—88no—
829C4×D4—88no—
830C4×D4—88no—
831C4×D4—88no—
832C4×D4—88no—
833C4×D4—88no—
834C2×C4⋊C4—24no—
835C2×C4⋊C4—44no—
836C2×C4⋊C4—44no—
837C2×C4⋊C4—48no—
838C2×C4⋊C4—48no—
839C2×C4⋊C4—44no—
840C2×C4⋊C4—48no—
841C2×C4⋊C4—44no—
842C2×C4⋊C4—42no—
843C2×C4⋊C4—44no—
844C2×C4⋊C4—816no—
845C2×C4⋊C4—88no—
846C2×C4⋊C4—816no—
847C2×C4⋊C4—88no—
848C2×C4⋊C4—84no—
849C2×C4⋊C4—84no—
850C2×C4⋊C4—82no—
851C2×C4⋊C4—82no—
852C2×C22⋊C4—48no—
853C2×C22⋊C4—416no—
854C2×C22⋊C4—48no—
855C2×C22⋊C4—44no—
856C2×C22⋊C4—48no—
857C2×C22⋊C4—44no—
858C2×C22⋊C4—832no—
859C2×C22⋊C4—816no—
860C2×C22⋊C4—832no—
861C2×C22⋊C4—816no—
862C2×C22⋊C4—88no—
863C2×C22⋊C4—84no—
864C2×C22⋊C4—84no—
865C2×C22⋊C4—88no—
866C2×C22⋊C4—88no—
867C2×C22⋊C4—84no—
868C2×C22⋊C4—84no—
869C2×C22⋊C4—88no—
870C2×C42—28no—
871C2×C42—24no—
872C2×C42—28no—
873C2×C42—24no—
874C2×C42—28no—
875C2×C42—24no—
876C2×C42—28no—
877C2×C42—24no—
878C2×C42—216no—
879C2×C42—28no—
880C2×C42—216no—
881C2×C42—28no—
882C2×C42—22no—
883C2×C42—21no—
884C2×C42—21no—
885C2×C42—22no—
886C2×C42—22no—
887C2×C42—22no—
888C2×C42—21no—
889C2×C42—22no—
890C2×C42—21no—
891C2×C42—22no—
892C2×C42—21no—
893C2×C42—22no—
894C2×C42—21no—
895C2×C42—22no—
896C2×C42—21no—
897C2×C42—22no—
898C2×C42—21no—
899C2×C42—22no—
900C2×C42—22no—
901C2×C42—21no—
902C2×C42—21no—
903C2×C42—22no—
904C2×C42—22no—
905C2×C42—22no—
906C2×C42—22no—
907C2×C42—21no—
908C2×C42—22no—
909C2×C42—21no—
910C2×C42—42no—
911C2×C42—42no—
912C2×C42—42no—
913C2×C42—42no—
914C2×C42—48no—
915C2×C42—48no—
916C2×C42—44no—
917C2×C42—44no—
918C2×C42—44no—
919C2×C42—44no—
920C2×C42—44no—
921C2×C42—44no—
922C2×C42—84no—
923C2×C42—82no—
924C2×C42—84no—
925C2×C42—82no—
926C2×C42—84no—
927C2×C42—82no—
928C2×C42—84no—
929C2×C42—82no—
930C2×C42#32312yes—
931C2×C42#32312yes—
932C2×C42#32312yes—
933C2×C42D4⋊C812yes—
934C2×C42D4⋊C814yes—
935C2×C42D4⋊C814yes—
936C2×C42D4⋊C814yes—
937C2×C42D4⋊C814yes—
938C2×C42D4⋊C814yes—
939C2×C42D4⋊C812yes—
940C2×C42#32714yes—
941C2×C42#32714yes—
942C2×C42#32712yes—
943C2×C42#32714yes—
944C2×C42#32714yes—
945C2×C42#32714yes—
946C2×C42#32712yes—
947C2×C42#32914yes—
948C2×C42#32912yes—
949C2×C42#32914yes—
950C2×C42#32912yes—
951C2×C42#33114yes—
952C2×C42#33112yes—
953C2×C42#33112yes—
954C2×C42#33114yes—
955C2×C42C2×C22⋊C812yes—
956C2×C42C2×C22⋊C811yescharacteristic
957C2×C42C2×C22⋊C812yes—
958C2×C42C2×C22⋊C811yescharacteristic
959C2×C42C2×C22⋊C811yescharacteristic
960C2×C42C2×C22⋊C812yes—
961C2×C42C2×#9911yescharacteristic
962C2×C42C2×#9912yes—
963C2×C42C2×#10011yescharacteristic
964C2×C42C2×#10012yes—
965C2×C42C2×#10214yes—
966C2×C42C2×#10212yes—
967C2×C42C2×#10212yes—
968C2×C42C2×#10214yes—
969C2×C42C2×#10412yes—
970C2×C42C2×#10414yes—
971C2×C42C2×#10414yes—
972C2×C42C2×#10412yes—
973C2×C42C22×C22⋊C411yescharacteristic
974C2×C42C23×C811yescharacteristic
975C2×C42C22×M1611yescharacteristic
976M32—832no—
977C2×C16—416no—
978C2×C16—816no—
979C4⋊C8—48no—
980C4⋊C8—88no—
981C4⋊C8—816no—
982C4⋊C8—88no—
983C4⋊C8—84no—
984C4⋊C8—88no—
985C4×C8—22no—
986C4×C8—22no—
987C4×C8—24no—
988C4×C8—24no—
989C4×C8—22no—
990C4×C8—24no—
991C4×C8—22no—
992C4×C8—24no—
993C4×C8—24no—
994C4×C8—24no—
995C4×C8—24no—
996C4×C8—22no—
997C4×C8—22no—
998C4×C8—24no—
999C4×C8—24no—
1000C4×C8—24no—
1001C4×C8—22no—
1002C4×C8—22no—
1003C4×C8C2×#10212yes—
1004C4×C8C2×#10214yes—
1005C4×C8C2×#10214yes—
1006C4×C8C2×#10212yes—
1007C4×C8C22×D812yes—
1008C4×C8C22×SD1612yes—
1009C24—22no—
1010C24—22no—
1011C24—24no—
1012C24—24no—
1013C24—416no—
1014C24—48no—
1015C24—44no—
1016C24—816no—
1017C24—88no—
1018C24—88no—
1019C24—816no—
1020C24—88no—
1021C24—88no—
1022C24—864no—
1023C24—816no—
1024C24—88no—
1025C24—84no—
1026C24—84no—
1027C24—82no—
1028C24—82no—
1029C24—84no—
1030C24—168no—
1031C24—164no—
1032C24—1632no—
1033C24—168no—
1034C24—164no—
1035C24—164no—
1036C24—164no—
1037C24#127012yes—
1038C24#127011yescharacteristic
1039C24#127011yescharacteristic
1040C24C2×#32312yes—
1041C24C2×#32311yescharacteristic
1042C2×D4—28no—
1043C2×D4—48no—
1044C2×D4—416no—
1045C2×D4—416no—
1046C2×D4—432no—
1047C2×D4—432no—
1048C2×D4—44no—
1049C2×D4—48no—
1050C2×D4—48no—
1051C2×D4—48no—
1052C2×D4—432no—
1053C2×D4—416no—
1054C2×D4—48no—
1055C2×D4—416no—
1056C2×D4—88no—
1057C2×D4—816no—
1058C2×D4—88no—
1059C2×D4—84no—
1060C2×D4—88no—
1061C2×D4—88no—
1062C2×D4—816no—
1063C2×D4—816no—
1064C2×D4—832no—
1065C2×D4—832no—
1066C2×D4—88no—
1067C2×D4—816no—
1068C2×D4—88no—
1069C2×D4—832no—
1070C2×D4—8128no—
1071C2×D4—8128no—
1072C2×D4—832no—
1073C2×D4—864no—
1074C2×D4—84no—
1075C2×D4—88no—
1076C2×D4—88no—
1077C2×D4—816no—
1078C2×D4—816no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—24no—
1082C22×C4—28no—
1083C22×C4—24no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—22no—
1087C22×C4—24no—
1088C22×C4—22no—
1089C22×C4—24no—
1090C22×C4—22no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—216no—
1096C22×C4—28no—
1097C22×C4—28no—
1098C22×C4—28no—
1099C22×C4—24no—
1100C22×C4—28no—
1101C22×C4—24no—
1102C22×C4—28no—
1103C22×C4—24no—
1104C22×C4—28no—
1105C22×C4—24no—
1106C22×C4—28no—
1107C22×C4—24no—
1108C22×C4—28no—
1109C22×C4—24no—
1110C22×C4—21no—
1111C22×C4—21no—
1112C22×C4—22no—
1113C22×C4—21no—
1114C22×C4—22no—
1115C22×C4—21no—
1116C22×C4—44no—
1117C22×C4—42no—
1118C22×C4—44no—
1119C22×C4—42no—
1120C22×C4—48no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—42no—
1130C22×C4—44no—
1131C22×C4—42no—
1132C22×C4—44no—
1133C22×C4—42no—
1134C22×C4—432no—
1135C22×C4—432no—
1136C22×C4—42no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—44no—
1141C22×C4—816no—
1142C22×C4—832no—
1143C22×C4—88no—
1144C22×C4—88no—
1145C22×C4—816no—
1146C22×C4—88no—
1147C22×C4—82no—
1148C22×C4—84no—
1149C22×C4—84no—
1150C22×C4—82no—
1151C22×C4—84no—
1152C22×C4—84no—
1153C22×C4—88no—
1154C22×C4—84no—
1155C22×C4—88no—
1156C22×C4—84no—
1157C22×C4—1616no—
1158C22×C4—168no—
1159C22×C4—1616no—
1160C22×C4—168no—
1161C22×C4—168no—
1162C22×C4—1616no—
1163C22×C4—1616no—
1164C22×C4—1616no—
1165C22×C4—1616no—
1166C22×C4—164no—
1167C22×C4—168no—
1168C22×C4—164no—
1169C22×C4—168no—
1170C22×C4—168no—
1171C22×C4—164no—
1172C22×C4—164no—
1173C22×C4—168no—
1174C22×C4—164no—
1175C22×C4—168no—
1176C22×C4—164no—
1177C22×C4—1616no—
1178C22×C4—168no—
1179C22×C4#127012yes—
1180C22×C4#127011yescharacteristic
1181C22×C4#127012yes—
1182C22×C4#127012yes—
1183C22×C4#127012yes—
1184C22×C4#127014yes—
1185C22×C4#127012yes—
1186C22×C4#127014yes—
1187C22×C4#127014yes—
1188C22×C4#127012yes—
1189C22×C4#127014yes—
1190C22×C4#127012yes—
1191C22×C4#127012yes—
1192C22×C4#127012yes—
1193C22×C4#127011yescharacteristic
1194C22×C4#132014yes—
1195C22×C4#132114yes—
1196C22×C4#135714yes—
1197C22×C4#135914yes—
1198C22×C4C2×#32311yescharacteristic
1199C22×C4C2×#32312yes—
1200C22×C4C2×#32311yescharacteristic
1201C22×C4C2×#32312yes—
1202C22×C4C2×#32311yescharacteristic
1203C22×C4C2×#32312yes—
1204C22×C4C2×D4⋊C812yes—
1205C22×C4C2×D4⋊C812yes—
1206C22×C4C2×D4⋊C814yes—
1207C22×C4C2×D4⋊C814yes—
1208C22×C4C2×#32714yes—
1209C22×C4C2×#32712yes—
1210C22×C4C2×#32712yes—
1211C22×C4C2×#32714yes—
1212C22×C4C2×#32912yes—
1213C22×C4C2×#32911yescharacteristic
1214C22×C4C2×#32911yescharacteristic
1215C22×C4C2×#32912yes—
1216C22×C4C2×#33111yescharacteristic
1217C22×C4C2×#33112yes—
1218C22×C4C2×#33111yescharacteristic
1219C22×C4C2×#33112yes—
1220C22×C4C22×C22⋊C811yescharacteristic
1221C22×C4C22×#9911yescharacteristic
1222C22×C4C22×#10011yescharacteristic
1223C2×C8—22no—
1224C2×C8—22no—
1225C2×C8—24no—
1226C2×C8—22no—
1227C2×C8—22no—
1228C2×C8—24no—
1229C2×C8—44no—
1230C2×C8—48no—
1231C2×C8—48no—
1232C2×C8—44no—
1233C2×C8—48no—
1234C2×C8—44no—
1235C2×C8—48no—
1236C2×C8—44no—
1237C2×C8—82no—
1238C2×C8—84no—
1239C2×C8—82no—
1240C2×C8—82no—
1241C2×C8—84no—
1242C2×C8—84no—
1243C2×C8—84no—
1244C2×C8—84no—
1245C2×C8—82no—
1246C2×C8—84no—
1247C2×C8—88no—
1248C2×C8—84no—
1249C2×C8—164no—
1250C2×C8—168no—
1251C2×C8—168no—
1252C2×C8—164no—
1253C4⋊C4—48no—
1254C4⋊C4—88no—
1255C4⋊C4—88no—
1256C4⋊C4—816no—
1257C4⋊C4—84no—
1258C4⋊C4—88no—
1259C22⋊C4—816no—
1260C22⋊C4—816no—
1261C22⋊C4—832no—
1262C22⋊C4—88no—
1263C22⋊C4—88no—
1264C22⋊C4—816no—
1265C42—22no—
1266C42—24no—
1267C42—22no—
1268C42—28no—
1269C42—28no—
1270C42—28no—
1271C42—24no—
1272C42—28no—
1273C42—24no—
1274C42—28no—
1275C42—22no—
1276C42—24no—
1277C42—22no—
1278C42—41no—
1279C42—41no—
1280C42—42no—
1281C42—41no—
1282C42—42no—
1283C42—41no—
1284C42—42no—
1285C42—42no—
1286C42—42no—
1287C42—42no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42—44no—
1292C42—82no—
1293C42—81no—
1294C42—81no—
1295C42—82no—
1296C42—82no—
1297C42—82no—
1298C42—82no—
1299C42—81no—
1300C42—82no—
1301C42—81no—
1302C42#127014yes—
1303C42#127014yes—
1304C42#127014yes—
1305C42#127014yes—
1306C42#127014yes—
1307C42#127014yes—
1308C42C2×D4⋊C814yes—
1309C42C2×D4⋊C812yes—
1310C42C2×D4⋊C812yes—
1311C42C2×D4⋊C814yes—
1312C42C2×#32712yes—
1313C42C2×#32712yes—
1314C42C2×#32714yes—
1315C42C2×#32714yes—
1316C42C2×#32912yes—
1317C42C2×#32914yes—
1318C42C2×#33112yes—
1319C42C2×#33114yes—
1320C42C22×#10212yes—
1321C42C22×#10412yes—
1322C16—816no—
1323C23—216no—
1324C23—216no—
1325C23—22no—
1326C23—22no—
1327C23—24no—
1328C23—22no—
1329C23—22no—
1330C23—24no—
1331C23—22no—
1332C23—24no—
1333C23—22no—
1334C23—24no—
1335C23—22no—
1336C23—24no—
1337C23—22no—
1338C23—48no—
1339C23—88no—
1340C23—816no—
1341C23—816no—
1342C23—864no—
1343C23—832no—
1344C23—88no—
1345C23—84no—
1346C23—88no—
1347C23—88no—
1348C23—84no—
1349C23—164no—
1350C23—168no—
1351C23—1632no—
1352C23—1664no—
1353C23—1616no—
1354C23—1632no—
1355C23—1632no—
1356C23—164no—
1357C23—168no—
1358C23—168no—
1359C23—164no—
1360C23—168no—
1361C23—164no—
1362C23#710714yes—
1363C23#711514yes—
1364C23C2×#127011yescharacteristic
1365C23C2×#127012yes—
1366C23C2×#127012yes—
1367C23C2×#127011yescharacteristic
1368C23C2×#132012yes—
1369C23C2×#132112yes—
1370C23C22×#32311yescharacteristic
1371D4—416no—
1372D4—88no—
1373D4—816no—
1374D4—816no—
1375D4—816no—
1376D4—864no—
1377D4—832no—
1378D4—832no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—28no—
1390C2×C4—24no—
1391C2×C4—28no—
1392C2×C4—24no—
1393C2×C4—28no—
1394C2×C4—28no—
1395C2×C4—28no—
1396C2×C4—28no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—41no—
1417C2×C4—42no—
1418C2×C4—41no—
1419C2×C4—42no—
1420C2×C4—44no—
1421C2×C4—42no—
1422C2×C4—44no—
1423C2×C4—41no—
1424C2×C4—42no—
1425C2×C4—41no—
1426C2×C4—41no—
1427C2×C4—42no—
1428C2×C4—41no—
1429C2×C4—416no—
1430C2×C4—416no—
1431C2×C4—48no—
1432C2×C4—48no—
1433C2×C4—416no—
1434C2×C4—416no—
1435C2×C4—48no—
1436C2×C4—48no—
1437C2×C4—41no—
1438C2×C4—42no—
1439C2×C4—41no—
1440C2×C4—41no—
1441C2×C4—42no—
1442C2×C4—41no—
1443C2×C4—88no—
1444C2×C4—84no—
1445C2×C4—1616no—
1446C2×C4—168no—
1447C2×C4—168no—
1448C2×C4—164no—
1449C2×C4—168no—
1450C2×C4—168no—
1451C2×C4—164no—
1452C2×C4—168no—
1453C2×C4—1616no—
1454C2×C4—164no—
1455C2×C4—164no—
1456C2×C4#710518yes—
1457C2×C4#710518yes—
1458C2×C4#710718yes—
1459C2×C4#710714yes—
1460C2×C4C2×#127012yes—
1461C2×C4C2×#127014yes—
1462C2×C4C2×#127012yes—
1463C2×C4C2×#127011yescharacteristic
1464C2×C4C2×#127012yes—
1465C2×C4C2×#127014yes—
1466C2×C4C2×#127011yescharacteristic
1467C2×C4C2×#127012yes—
1468C2×C4C2×#132014yes—
1469C2×C4C2×#132114yes—
1470C2×C4C2×#135714yes—
1471C2×C4C2×#135712yes—
1472C2×C4C2×#135914yes—
1473C2×C4C2×#135912yes—
1474C2×C4C22×D4⋊C812yes—
1475C2×C4C22×#32712yes—
1476C2×C4C22×#32911yescharacteristic
1477C2×C4C22×#33111yescharacteristic
1478C8—42no—
1479C8—42no—
1480C8—42no—
1481C8—44no—
1482C8—44no—
1483C8—42no—
1484C8—164no—
1485C22—28no—
1486C22—28no—
1487C22—216no—
1488C22—24no—
1489C22—24no—
1490C22—28no—
1491C22—28no—
1492C22—21no—
1493C22—21no—
1494C22—22no—
1495C22—21no—
1496C22—21no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—816no—
1501C22—88no—
1502C22—168no—
1503C22—1616no—
1504C22—1632no—
1505C22—1632no—
1506C22—1616no—
1507C22—164no—
1508C22—164no—
1509C22C2×#710512yes—
1510C22C2×#710512yes—
1511C22C2×#710714yes—
1512C22C2×#710712yes—
1513C22C2×#711514yes—
1514C22C2×#711512yes—
1515C22C22×#127011yescharacteristic
1516C22C22×#132011yescharacteristic
1517C22C22×#132111yescharacteristic
1518C4—22no—
1519C4—24no—
1520C4—22no—
1521C4—22no—
1522C4—21no—
1523C4—21no—
1524C4—22no—
1525C4—22no—
1526C4—42no—
1527C4—42no—
1528C4—44no—
1529C4—42no—
1530C4—42no—
1531C4—44no—
1532C4—164no—
1533C4C2×#710518yes—
1534C4C2×#710712yes—
1535C4C2×#710714yes—
1536C4C22×#135711yescharacteristic
1537C4C22×#135911yescharacteristic
1538C2—21no—
1539C2—21no—
1540C2—22no—
1541C2—24no—
1542C2—24no—
1543C2—168no—
1544C2C22×#711511yescharacteristic
1545C2#7221355314yesdirect product factor
1546C2C22×#710711yescharacteristic
1547C2C22×#710511yescharacteristic
subgroupG/H
centerC22×C4#1270
commutatorC2×C42C23×C8
Frattini, cosocle#1744C24
socleC23C2×#1270
prime radicalC23×#127C8
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ C22×#1744 ◁ G
LECSG ▷ #1744 ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72213553C2direct (N × H)
2. C2×#92827C2semidirect
3. C2×#126586C2semidirect
17. #126586C22semidirect
19. C2×#7143C22semidirect
20. #92827C22semidirect
88. #7143C23semidirect
1545. C2#72213553direct (N × H)

Maximal subgroups

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

subgroupindex
#722135532
C2×#928272
C2×#1265862
C22×#96442