Finite Group Databasebeta

← C2×#24918410 #36275594

Subgroups — C2×#24918410 #36275594

Order 21248.

2134 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128255C211yesmaximal, characteristic
2C2×C4⋊Q8×D83C211yesmaximal, characteristic
3#24918410C2116yesmaximal, direct product factor
4C2×#19128079C212yesmaximal, complemented
5C2×#19128050C212yesmaximal, complemented
6C2×#19127912C211yesmaximal, characteristic, complemented
7C2×#19127911C211yesmaximal, characteristic, complemented
8C2×#19127908C211yesmaximal, characteristic, complemented
9C2×#19127858C212yesmaximal
10C2×#19127855C212yesmaximal
11C2×#19127753C211yesmaximal, characteristic
12C2×#462×C83C211yesmaximal, characteristic, complemented
13C22×Q8×D83C2212yes—
14C22×Dic332C2212yes—
15C22×#13050580C2212yes—
16C22×#13050580C2212yes—
17#19128255—24no—
18#19128255C2218yes—
19C2×#14581792C2211yescharacteristic
20C2×#14581791—21no—
21C2×#14581791—21no—
22C2×#14581791C2211yescharacteristic
23C2×#14581790C2212yes—
24C2×#14581790C2211yescharacteristic
25C4⋊Q8×D83—24no—
26C4⋊Q8×D83C2218yes—
27C2×#14581782—21no—
28C2×#14581772C2211yescharacteristic
29C2×#14581770—21no—
30C2×#14581768C2211yescharacteristic
31C2×C4×Dic166—21no—
32C2×C4×Dic166C2211yescharacteristic
33C2×#14581749—21no—
34C2×C4⋊C4×D83—21no—
35C2×C4⋊C4×D83—21no—
36C2×C42×D83C2211yescharacteristic
37#19128079C22116yescomplemented
38#19128050C22116yescomplemented
39#19127912C2218yescomplemented
40#19127911C2218yescomplemented
41#19127908C2218yescomplemented
42#19127858C22116yes—
43#19127855C22116yes—
44#19127753C2218yes—
45C2×C4⋊(C83⋊C8)C2211yescharacteristic
46C2×#14581717C2212yes—
47C2×#14581716C2212yes—
48C2×#14581715C2212yes—
49C2×(C2×D83)⋊C8C2212yes—
50C2×C8×Dic83C2212yes—
51C22×Q16×C83C2212yes—
52C2×C4⋊Q8×C83C2211yescharacteristic
53C2×C4×Q8×C83C2211yescharacteristic
54#462×C83C2218yescomplemented
55C2×C4⋊C8×C83C2211yescharacteristic
56C2×#103×C83C2212yes—
57C22×Dic166—21no—
58C22×Dic166—22no—
59C22×Dic166C2311yescharacteristic
60C22×Dic166C2312yes—
61C2×Q8×D83—24no—
62C2×Q8×D83—44no—
63C2×Q8×D83—44no—
64C2×Q8×D83C2318yes—
65C22×C4×D83—22no—
66C22×C4×D83D411yescharacteristic
67C22×C4×D83D411yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C2×Dic332—44no—
70C2×Dic332C2318yes—
71C2×#13050580—44no—
72C2×#13050580—44no—
73C2×#13050580C2318yes—
74C2×#13050580C2318yes—
75C22×C83⋊C8C2312yes—
76#14581792—22no—
77#14581792C2314yes—
78#14581791—28no—
79#14581791—28no—
80#14581791—22no—
81#14581791C2314yes—
82#14581790—24no—
83#14581790—22no—
84#14581790C2314yes—
85#14581790C2318yes—
86#14581782—28no—
87#14581772—22no—
88#14581772C2314yes—
89#14581770—28no—
90#14581768—22no—
91#14581768C2314yes—
92C4×Dic166—28no—
93C4×Dic166—22no—
94C4×Dic166C2314yes—
95#14581749—28no—
96C2×C4⋊Dic83—21no—
97C2×C4⋊Dic83—21no—
98C2×C4⋊Dic83—21no—
99C2×C4⋊Dic83C2311yescharacteristic
100C2×Dic83⋊C4—22no—
101C2×Dic83⋊C4—22no—
102C2×Dic83⋊C4—21no—
103C2×Dic83⋊C4—21no—
104C2×Dic83⋊C4—21no—
105C2×Dic83⋊C4—21no—
106C2×Dic83⋊C4—21no—
107C4⋊C4×D83—28no—
108C4⋊C4×D83—28no—
109C2×(C2×D83)⋊C4—21no—
110C2×(C2×D83)⋊C4—21no—
111C2×C4×Dic83—21no—
112C2×C4×Dic83D411yescharacteristic
113C2×C4×Dic83D411yescharacteristic
114C2×C4×Dic83C2311yescharacteristic
115C42×D83D414yes—
116C42×D83C2314yes—
117C4⋊(C83⋊C8)C2314yes—
118#14581717C2318yes—
119#14581716C2318yes—
120#14581715C2318yes—
121(C2×D83)⋊C8C2318yes—
122C8×Dic83C2318yes—
123C22×Q8×C83C2311yescharacteristic
124C22×Q8×C83C2312yes—
125C2×Q16×C83—44no—
126C2×Q16×C83C2318yes—
127C22×C8×C83C2312yes—
128C4⋊Q8×C83—22no—
129C4⋊Q8×C83C2314yes—
130C4×Q8×C83—22no—
131C4×Q8×C83C2314yes—
132C2×C4⋊C4×C83—21no—
133C2×C4⋊C4×C83—21no—
134C2×C4⋊C4×C83—21no—
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C42×C83—21no—
137C2×C42×C83C2311yescharacteristic
138C4⋊C8×C83C2314yes—
139#103×C83C2318yes—
140C23×D83C2×D411yescharacteristic
141C2×Dic166—22no—
142C2×Dic166—24no—
143C2×Dic166—22no—
144C2×Dic166—24no—
145C2×Dic166—21no—
146C2×Dic166—22no—
147C2×Dic166—24no—
148C2×Dic166—28no—
149C2×Dic166—48no—
150C2×Dic166—44no—
151C2×Dic166C2412yes—
152C2×Dic166C2414yes—
153Q8×D83—48no—
154Q8×D83—48no—
155Q8×D83—416no—
156C22×Dic83—22no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83C2×D411yescharacteristic
160C22×Dic83C2×D411yescharacteristic
161C22×Dic83C2×D411yescharacteristic
162C2×C4×D83—22no—
163C2×C4×D83—22no—
164C2×C4×D83—24no—
165C2×C4×D83—28no—
166C2×C4×D83—48no—
167C2×C4×D83Q1618yescomplemented
168C2×C4×D83C2×D412yes—
169C2×C4×D83C2×D414yes—
170C2×C4×D83C2×D414yes—
171C2×C4×D83C2412yes—
172Dic332—48no—
173#13050580—48no—
174#13050580—48no—
175C2×C83⋊C8—24no—
176C2×C83⋊C8C2414yes—
177C4⋊Dic83—21no—
178C4⋊Dic83—24no—
179C4⋊Dic83—24no—
180C4⋊Dic83—24no—
181C4⋊Dic83C2412yes—
182Dic83⋊C4—24no—
183Dic83⋊C4—24no—
184Dic83⋊C4—24no—
185Dic83⋊C4—24no—
186Dic83⋊C4—24no—
187Dic83⋊C4—28no—
188Dic83⋊C4—28no—
189(C2×D83)⋊C4—24no—
190(C2×D83)⋊C4—24no—
191C4×Dic83—24no—
192C4×Dic83C2×D414yes—
193C4×Dic83C2×D412yes—
194C4×Dic83C2×D414yes—
195C4×Dic83C2412yes—
196C2×Q8×C83—21no—
197C2×Q8×C83—22no—
198C2×Q8×C83—22no—
199C2×Q8×C83—24no—
200C2×Q8×C83—24no—
201C2×Q8×C83—22no—
202C2×Q8×C83C2412yes—
203C2×Q8×C83C2414yes—
204C22×C4×C83—22no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83C2×D411yescharacteristic
208C22×C4×C83C2×D411yescharacteristic
209C22×C4×C83C2411yescharacteristic
210Q16×C83—48no—
211C2×C8×C83—24no—
212C2×C8×C83C2414yes—
213C4⋊C4×C83—24no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—24no—
216C4⋊C4×C83—24no—
217C4⋊C4×C83C2412yes—
218C42×C83—24no—
219C42×C83C2×D412yes—
220C42×C83C2412yes—
221C23×C83C22×D411yescharacteristic
222C22×D83—22no—
223C22×D83—22no—
224C22×D83C2×Q1614yes—
225C22×D83C22×D412yes—
226Q8×C83—22no—
227Q8×C83—24no—
228Q8×C83—22no—
229Q8×C83—24no—
230Q8×C83—42no—
231Q8×C83—44no—
232C2×C4×C83—22no—
233C2×C4×C83—22no—
234C2×C4×C83—22no—
235C2×C4×C83—24no—
236C2×C4×C83—42no—
237C2×C4×C83—44no—
238C2×C4×C83—42no—
239C2×C4×C83C2×Q1614yes—
240C2×C4×C83C22×D412yes—
241C2×C4×C83C22×D411yescharacteristic
242C2×C4×C83C22×D412yes—
243C2×C4×C83H(5,𝔽2)12yes—
244C2×C4×C83H(5,𝔽2)12yes—
245C2×C4×C83C2511yescharacteristic
246C2×Dic83—22no—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—24no—
250C2×Dic83—44no—
251C2×Dic83—42no—
252C2×Dic83—42no—
253C2×Dic83C2×Q1614yes—
254C2×Dic83#13714yes—
255C2×Dic83C22×D412yes—
256C2×Dic83C22×D412yes—
257C2×Dic83C22×D412yes—
258C4×D83—24no—
259C4×D83—22no—
260C4×D83—22no—
261C4×D83—28no—
262C4×D83—416no—
263C4×D83C2×Q16116yescomplemented
264Dic166—22no—
265Dic166—24no—
266Dic166—22no—
267Dic166—24no—
268Dic166—416no—
269Dic166—44no—
270Dic166—42no—
271Dic166—48no—
272C8×C83—24no—
273C83⋊C8—24no—
274C22×C83#53512yes—
275C22×C83C22×Q1612yes—
276C22×C83C2×#13712yes—
277C22×C83C23×D411yescharacteristic
278C2×D83—22no—
279C2×D83—28no—
280C2×D83—22no—
281C2×D83C22×Q1614yes—
282C4×C83—22no—
283C4×C83—44no—
284C4×C83—42no—
285C4×C83—42no—
286C4×C83#53512yes—
287C4×C83C22×Q1614yes—
288C4×C83C2×H(5,𝔽2)11yescharacteristic
289C4×C83C2×H(5,𝔽2)11yescharacteristic
290Dic83—22no—
291Dic83—44no—
292Dic83—42no—
293Dic83—42no—
294Dic83C22×Q1614yes—
295Dic83C2×#13714yes—
296C2×#3209—831nomaximal, Sylow
297C2×C83#320914yescomplemented
298C2×C83C2×#53511yescharacteristic
299C2×C83C23×Q1611yescharacteristic
300C2×C83C22×#13711yescharacteristic
301D83—24no—
302C2×#533—831no—
303C22×C4⋊Q8—831no—
304#3209—8316no—
305C2×#494—832no—
306C2×#487—832no—
307C2×#462—831no—
308C2×#462—831no—
309C2×#462—831no—
310C2×#462D8311yescharacteristic, complemented
311C2×#451—832no—
312C2×#451—832no—
313C2×#431—831no—
314C83C2×#320911yescharacteristic, complemented, Sylow
315C23×Q8—832no—
316C22×Q16—832no—
317C22×Q16—832no—
318C22×Q16—832no—
319C22×Q16C2×D8312yes—
320#533—838no—
321#533—1664no—
322C2×C4⋊Q8—831no—
323C2×C4⋊Q8—832no—
324C2×C4⋊Q8—831no—
325C2×C4⋊Q8—838no—
326C2×C4⋊Q8—831no—
327C2×C4⋊Q8—1661no—
328C2×C4⋊Q8—1661no—
329C2×C4⋊Q8—1664no—
330C2×C4⋊Q8C2×D8311yescharacteristic
331C2×#125—1661no—
332C2×C22⋊Q8—831no—
333C2×C22⋊Q8—831no—
334C2×C22⋊Q8—1661no—
335C2×C4×Q8—831no—
336C2×C4×Q8—1661no—
337C2×C4×Q8C2×D8311yescharacteristic
338C2×#117—1661no—
339C22×C4⋊C4—1661no—
340C22×C4⋊C4—1661no—
341C22×C42—831no—
342#494—8316no—
343#487—8316no—
344#462—838no—
345#462—838no—
346#462—838no—
347#462C2×D8318yescomplemented
348#451—8316no—
349#451—8316no—
350#431—838no—
351C2×C4⋊C8—831no—
352C2×C4⋊C8C2×D8311yescharacteristic
353C2×#103—832no—
354C2×#103—832no—
355C2×#103—832no—
356C2×#103C2×D8312yes—
357C2×C22⋊C8—832no—
358C2×C4×C8—832no—
359C22×Q8—3324no—
360C22×Q8—3324no—
361C22×Q8—838no—
362C22×Q8—831no—
363C22×Q8—832no—
364C22×Q8—1661no—
365C22×Q8—1662no—
366C22×Q8—1664no—
367C22×Q8C22×D8311yescharacteristic
368C22×Q8C22×D8312yes—
369C23×C4—831no—
370C23×C4—831no—
371C23×C4—831no—
372C23×C4—1662no—
373C2×Q16—44no—
374C2×Q16—3324no—
375C2×Q16—3324no—
376C2×Q16—3324no—
377C2×Q16—838no—
378C2×Q16—838no—
379C2×Q16—838no—
380C2×Q16C22×D8318yes—
381C22×C8—832no—
382C22×C8C22×D8312yes—
383C4⋊Q8—22no—
384C4⋊Q8—834no—
385C4⋊Q8—838no—
386C4⋊Q8—834no—
387C4⋊Q8—834no—
388C4⋊Q8—1668no—
389C4⋊Q8—1668no—
390C4⋊Q8—1662no—
391C4⋊Q8—1664no—
392C4⋊Q8—1662no—
393C4⋊Q8—1662no—
394C4⋊Q8C22×D8314yes—
395#125—1668no—
396C22⋊Q8—834no—
397C22⋊Q8—834no—
398C22⋊Q8—1668no—
399C22⋊Q8—1662no—
400C22⋊Q8—1662no—
401C4×Q8—22no—
402C4×Q8—834no—
403C4×Q8—1668no—
404C4×Q8—1662no—
405C4×Q8C22×D8314yes—
406#117—1668no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—831no—
411C2×C4⋊C4—1668no—
412C2×C4⋊C4—1668no—
413C2×C4⋊C4—1662no—
414C2×C4⋊C4—1662no—
415C2×C4⋊C4—1661no—
416C2×C4⋊C4—1661no—
417C2×C4⋊C4—1661no—
418C2×C4⋊C4—1661no—
419C2×C4⋊C4—1661no—
420C2×C4⋊C4—1661no—
421C2×C4⋊C4—1661no—
422C2×C4⋊C4—1661no—
423C2×C4⋊C4C22×D8311yescharacteristic
424C2×C22⋊C4—1661no—
425C2×C22⋊C4—1661no—
426C2×C42—21no—
427C2×C42—831no—
428C2×C42—831no—
429C2×C42—831no—
430C2×C42—834no—
431C2×C42—834no—
432C2×C42—1661no—
433C2×C42C22×D8311yescharacteristic
434C4⋊C8—834no—
435C4⋊C8C22×D8314yes—
436#103—838no—
437#103—838no—
438#103—838no—
439#103C22×D8318yes—
440C22⋊C8—838no—
441C4×C8—838no—
442C24—831no—
443C2×Q8—21no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—24no—
447C2×Q8—22no—
448C2×Q8—24no—
449C2×Q8—3324no—
450C2×Q8—3328no—
451C2×Q8—3328no—
452C2×Q8—3328no—
453C2×Q8—33216no—
454C2×Q8—834no—
455C2×Q8—832no—
456C2×Q8—1664no—
457C2×Q8—1668no—
458C2×Q8—1662no—
459C2×Q8—1664no—
460C2×Q8—1662no—
461C2×Q8—1664no—
462C2×Q8—1661no—
463C2×Q8—1662no—
464C2×Q8C23×D8314yes—
465C2×Q8C23×D8312yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—3328no—
470C22×C4—831no—
471C22×C4—831no—
472C22×C4—838no—
473C22×C4—834no—
474C22×C4—831no—
475C22×C4—834no—
476C22×C4—832no—
477C22×C4—832no—
478C22×C4—1668no—
479C22×C4—1664no—
480C22×C4—1661no—
481C22×C4—1661no—
482C22×C4—1662no—
483C22×C4—1662no—
484C22×C4—1662no—
485C22×C4D4×D8311yescharacteristic
486C22×C4D4×D8311yescharacteristic
487C22×C4C23×D8311yescharacteristic
488Q16—48no—
489Q16—3328no—
490Q16—3328no—
491Q16—3328no—
492C2×C8—24no—
493C2×C8—834no—
494C2×C8—1664no—
495C2×C8C23×D8314yes—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—832no—
501C4⋊C4—1668no—
502C4⋊C4—1668no—
503C4⋊C4—1664no—
504C4⋊C4—1664no—
505C4⋊C4—1664no—
506C4⋊C4—1664no—
507C4⋊C4—1664no—
508C4⋊C4—1661no—
509C4⋊C4—1664no—
510C4⋊C4—1664no—
511C4⋊C4—1664no—
512C4⋊C4C23×D8312yes—
513C22⋊C4—1664no—
514C22⋊C4—1664no—
515C42—24no—
516C42—834no—
517C42—834no—
518C42—832no—
519C42—832no—
520C42—1664no—
521C42D4×D8312yes—
522C42C23×D8312yes—
523C23—834no—
524C23—832no—
525C23—1662no—
526C23—1662no—
527C23C2×D4×D8311yescharacteristic
528Q8—22no—
529Q8—24no—
530Q8—22no—
531Q8—24no—
532Q8—44no—
533Q8—42no—
534Q8—3328no—
535Q8—33216no—
536Q8—3324no—
537Q8—3322no—
538Q8—1662no—
539Q8—1664no—
540Q8—1662no—
541Q8—1664no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—33216no—
550C2×C4—3322no—
551C2×C4—3324no—
552C2×C4—3322no—
553C2×C4—834no—
554C2×C4—834no—
555C2×C4—832no—
556C2×C4—832no—
557C2×C4—8316no—
558C2×C4—832no—
559C2×C4—1668no—
560C2×C4—1662no—
561C2×C4—1662no—
562C2×C4—1664no—
563C2×C4—1662no—
564C2×C4—1664no—
565C2×C4—1662no—
566C2×C4—1662no—
567C2×C4Q16×D8314yes—
568C2×C4C2×D4×D8312yes—
569C2×C4C2×D4×D8312yes—
570C2×C4C2×D4×D8311yescharacteristic
571C2×C4#1458183712yes—
572C2×C4#1458183812yes—
573C2×C4C24×D8311yescharacteristic
574C8—24no—
575C8—1664no—
576C22—834no—
577C22—1662no—
578C22—1668no—
579C22—1662no—
580C22#1912826712yes—
581C22C2×Q16×D8312yes—
582C22#137×D8312yes—
583C22C22×D4×D8311yescharacteristic
584C4—22no—
585C4—42no—
586C4—44no—
587C4—42no—
588C4—3322no—
589C4—3324no—
590C4—3322no—
591C4—834no—
592C4—834no—
593C4—1662no—
594C4#1912826712yes—
595C4C2×Q16×D8314yes—
596C4C2×#1458183711yescharacteristic
597C4C2×#1458183811yescharacteristic
598C2—1664no—
599C2#2491841014yesdirect product factor
600C2C2×#1912826711yescharacteristic
601C2C22×Q16×D8311yescharacteristic
602C2C2×#137×D8311yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#462×C83C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
hypercenterC2×#462D83
hypocenterC83C2×#3209
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #24918410C2direct (N × H)
4. C2×#19128079C2semidirect
5. C2×#19128050C2semidirect
6. C2×#19127912C2semidirect
7. C2×#19127911C2semidirect
8. C2×#19127908C2semidirect
12. C2×#462×C83C2semidirect
37. #19128079C22semidirect
38. #19128050C22semidirect
39. #19127912C22semidirect
40. #19127911C22semidirect
41. #19127908C22semidirect
54. #462×C83C22semidirect
167. C2×C4×D83Q16semidirect
263. C4×D83C2×Q16semidirect
297. C2×C83#3209semidirect
310. C2×#462D83semidirect
314. C83C2×#3209semidirect
347. #462C2×D83semidirect
599. C2#24918410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282552
C2×C4⋊Q8×D832
#249184102
C2×#191280792
C2×#191280502
C2×#191279122
C2×#191279112
C2×#191279082
C2×#191278582
C2×#191278552
C2×#191277532
C2×#462×C832
C2×#320983