Finite Group Databasebeta

← C2×#22610247 #33087183

Subgroups — C2×#22610247 #33087183

Order 18688.

2614 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556566C211yesmaximal, characteristic
2C22×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3C22×#14556513C211yesmaximal, characteristic, complemented
4C22×#14556511C211yesmaximal, characteristic, complemented
5C22×#14556503C211yesmaximal, characteristic, complemented
6#22610247C218yesmaximal, direct product factor
7C2×#17988349C211yesmaximal, characteristic, complemented
8C2×#340×C73C211yesmaximal, characteristic, complemented
9C23×D292—21no—
10C23×D292C2211yescharacteristic
11C23×C4×D73—21no—
12C23×C4×D73C2211yescharacteristic
13C23×#10596831C2211yescharacteristic
14C2×#14556566—24no—
15C2×#14556566—22no—
16C2×#14556566C418yescomplemented
17C2×#14556566C2214yes—
18C22×C4⋊Dic73C2211yescharacteristic
19C22×#11924007—21no—
20C2×C4⋊C4×D73—22no—
21C2×C4⋊C4×D73—24no—
22C2×C4⋊C4×D73—24no—
23C2×C4⋊C4×D73C2214yescomplemented
24C22×#11924005—21no—
25C2×#14556513—24no—
26C2×#14556513C2214yescomplemented
27C2×#14556511—24no—
28C2×#14556511C2214yescomplemented
29C2×#14556503—24no—
30C2×#14556503C2214yescomplemented
31#17988349C2214yescomplemented
32C23×C8×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35#340×C73C2214yescomplemented
36C24×D73—21no—
37C24×D73D411yescharacteristic
38C22×D292—28no—
39C22×D292—24no—
40C22×D292—22no—
41C22×D292—22no—
42C22×D292—21no—
43C22×D292—22no—
44C22×D292—22no—
45C22×D292—22no—
46C22×D292—44no—
47C22×D292—44no—
48C22×D292C2×C414yescomplemented
49C22×D292C2312yes—
50C23×Dic73—21no—
51C23×Dic73D411yescharacteristic
52C22×C4×D73—28no—
53C22×C4×D73—24no—
54C22×C4×D73—22no—
55C22×C4×D73—22no—
56C22×C4×D73—22no—
57C22×C4×D73—22no—
58C22×C4×D73—44no—
59C22×C4×D73—44no—
60C22×C4×D73C2×C414yes—
61C22×C4×D73D412yes—
62C22×C4×D73D414yes—
63C22×C4×D73C2312yes—
64C22×#10596831—22no—
65C22×#10596831—22no—
66C22×#10596831—22no—
67C22×#10596831C2312yes—
68#14556566—216no—
69#14556566—28no—
70#14556566C2×C4116yescomplemented
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73D414yescomplemented
74C2×C4⋊Dic73C2312yes—
75C2×#11924007—28no—
76C2×#11924007—24no—
77C4⋊C4×D73—216no—
78C4⋊C4×D73—28no—
79C4⋊C4×D73—28no—
80C2×#11924005—28no—
81C2×#11924005—24no—
82#14556513—28no—
83#14556511—28no—
84#14556503—28no—
85C23×C4×C73—21no—
86C23×C4×C73—21no—
87C23×C4×C73C2311yescharacteristic
88C22×C8×C73—22no—
89C22×C8×C73—22no—
90C22×C8×C73—22no—
91C22×C8×C73C2312yes—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73C2×C414yescomplemented
97C2×C4⋊C4×C73D414yescomplemented
98C2×C4⋊C4×C73C2312yes—
99C2×C4⋊C4×C73C2312yes—
100C23×D73—22no—
101C23×D73—22no—
102C23×D73—22no—
103C23×D73—22no—
104C23×D73—24no—
105C23×D73—22no—
106C23×D73—42no—
107C23×D73—42no—
108C23×D73—42no—
109C23×D73—42no—
110C23×D73—42no—
111C23×D73—42no—
112C23×D73C22⋊C414yes—
113C23×D73D814yes—
114C23×D73SD1614yes—
115C23×D73C2×D412yes—
116C2×D292—28no—
117C2×D292—28no—
118C2×D292—22no—
119C2×D292—22no—
120C2×D292—22no—
121C2×D292—22no—
122C2×D292—216no—
123C2×D292—24no—
124C2×D292—22no—
125C2×D292—432no—
126C2×D292—48no—
127C2×D292—48no—
128C2×D292—42no—
129C2×D292—44no—
130C2×D292—44no—
131C2×D292—42no—
132C2×D292C22×C414yescomplemented
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—24no—
136C22×Dic73—22no—
137C22×Dic73—42no—
138C22×Dic73—42no—
139C22×Dic73C22⋊C414yes—
140C22×Dic73C2×D412yes—
141C2×C4×D73—28no—
142C2×C4×D73—28no—
143C2×C4×D73—24no—
144C2×C4×D73—28no—
145C2×C4×D73—28no—
146C2×C4×D73—24no—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—216no—
152C2×C4×D73—48no—
153C2×C4×D73—432no—
154C2×C4×D73—48no—
155C2×C4×D73C22⋊C418yes—
156C2×C4×D73C22×C414yes—
157C2×C4×D73C2×D414yes—
158C2×#10596831—22no—
159C2×#10596831—22no—
160C2×#10596831—22no—
161C2×#10596831—44no—
162C4⋊Dic73—24no—
163C4⋊Dic73—22no—
164C4⋊Dic73C2×D414yescomplemented
165#11924007—216no—
166#11924005—216no—
167C24×C73C2×D411yescharacteristic
168C22×C4×C73—24no—
169C22×C4×C73—24no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73—42no—
173C22×C4×C73—42no—
174C22×C4×C73—42no—
175C22×C4×C73—42no—
176C22×C4×C73C22×C412yes—
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D412yes—
179C22×C4×C73C2×D412yes—
180C22×C4×C73C2×D412yes—
181C22×C4×C73#4112yes—
182C22×C4×C73#4112yes—
183C22×C4×C73C2411yescharacteristic
184C2×C8×C73—22no—
185C2×C8×C73—22no—
186C2×C8×C73—22no—
187C2×C8×C73—44no—
188C4⋊C4×C73—24no—
189C4⋊C4×C73—24no—
190C4⋊C4×C73—22no—
191C4⋊C4×C73—22no—
192C4⋊C4×C73C22×C414yescomplemented
193C4⋊C4×C73C2×D414yescomplemented
194C23×C73C2×C22⋊C412yes—
195C23×C73#12012yes—
196C23×C73#12312yes—
197C23×C73C2×D812yes—
198C23×C73C2×SD1612yes—
199C23×C73AGL(1,ℤ/8)12yes—
200C23×C73#13712yes—
201C23×C73C22×D411yescharacteristic
202C22×D73—22no—
203C22×D73—22no—
204C22×D73—22no—
205C22×D73—22no—
206C22×D73—28no—
207C22×D73—28no—
208C22×D73—28no—
209C22×D73—28no—
210C22×D73—28no—
211C22×D73—28no—
212C22×D73—24no—
213C22×D73—42no—
214C22×D73—42no—
215C22×D73—42no—
216C22×D73—42no—
217C22×D73—42no—
218C22×D73—42no—
219C22×D73—48no—
220C22×D73—48no—
221C22×D73—48no—
222C22×D73—84no—
223C22×D73—84no—
224C22×D73—84no—
225C22×D73—84no—
226C22×D73#102116yescomplemented
227C22×D73C2×C22⋊C414yes—
228C22×D73C2×D814yes—
229C22×D73C2×SD1614yes—
230C2×C4×C73—24no—
231C2×C4×C73—24no—
232C2×C4×C73—42no—
233C2×C4×C73—42no—
234C2×C4×C73—42no—
235C2×C4×C73—42no—
236C2×C4×C73—48no—
237C2×C4×C73—48no—
238C2×C4×C73C2×C22⋊C412yes—
239C2×C4×C73C4×D414yes—
240C2×C4×C73C4×D414yes—
241C2×C4×C73#12012yes—
242C2×C4×C73#12114yes—
243C2×C4×C73#12114yes—
244C2×C4×C73#12312yes—
245C2×C4×C73C23×C411yescharacteristic
246C2×C4×C73C22×D411yescharacteristic
247C2×C4×C73C22×D411yescharacteristic
248C2×C4×C73C22×D411yescharacteristic
249C2×C4×C73C2×#4111yescharacteristic
250C2×C4×C73C2×#4111yescharacteristic
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—28no—
254C2×Dic73—24no—
255C2×Dic73—42no—
256C2×Dic73—42no—
257C2×Dic73—48no—
258C2×Dic73C2×C22⋊C414yes—
259D292—24no—
260D292—24no—
261D292—432no—
262D292—42no—
263D292—42no—
264D292—48no—
265C4×D73—24no—
266C4×D73—24no—
267C4×D73—24no—
268C4×D73—24no—
269C4×D73—216no—
270C4×D73—432no—
271C8×C73—42no—
272#10596831—42no—
273C22×C73#38614yes—
274C22×C73C2×#10214yes—
275C22×C73#41714yes—
276C22×C73#44714yes—
277C22×C73#44814yes—
278C22×C73#48014yes—
279C22×C73#48114yes—
280C22×C73C22×C22⋊C411yescharacteristic
281C22×C73C2×#12011yescharacteristic
282C22×C73C2×#12311yescharacteristic
283C22×C73C22×D811yescharacteristic
284C22×C73C22×SD1611yescharacteristic
285C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C73C2×#13711yescharacteristic
287C2×D73—24no—
288C2×D73—24no—
289C2×D73—24no—
290C2×D73—232no—
291C2×D73—24no—
292C2×D73—24no—
293C2×D73—24no—
294C2×D73—44no—
295C2×D73—44no—
296C2×D73—44no—
297C2×D73—82no—
298C2×D73—82no—
299C2×D73—816no—
300C2×D73—82no—
301C2×D73—82no—
302C2×D73C2×#10218yescomplemented
303C4×C73—44no—
304C4×C73—44no—
305C4×C73#38614yes—
306C4×C73C2×C4×D411yescharacteristic
307C4×C73C2×C4×D411yescharacteristic
308C4×C73C2×#12111yescharacteristic
309C4×C73C2×#12111yescharacteristic
310Dic73—24no—
311Dic73—44no—
312C2×#1874—731nomaximal, Sylow
313C2×C73#187418yescomplemented
314C2×C73C2×#38611yescharacteristic
315C2×C73C22×#10211yescharacteristic
316C2×C73C2×#41711yescharacteristic
317C2×C73C2×#44711yescharacteristic
318C2×C73C2×#44811yescharacteristic
319C2×C73C2×#48011yescharacteristic
320C2×C73C2×#48111yescharacteristic
321D73—28no—
322D73—84no—
323C22×#121—731no—
324C23×C4⋊C4—731no—
325C22×#102—731no—
326C22×#102—731no—
327C22×C22⋊C8—731no—
328#1874—738no—
329C2×#340—731no—
330C2×#340D7311yescharacteristic, complemented
331C73C2×#187411yescharacteristic, complemented, Sylow
332C23×D4—731no—
333C23×D4—1461no—
334C24×C4—731no—
335C24×C4—1461no—
336C23×C8—731no—
337C23×C8C2×D7311yescharacteristic
338C2×#121—738no—
339C2×#121—734no—
340C2×#121—1462no—
341C2×#121—1464no—
342C22×C4⋊C4—731no—
343C22×C4⋊C4—734no—
344C22×C4⋊C4—1464no—
345C22×C4⋊C4—1462no—
346C22×C4⋊C4—1461no—
347C22×C4⋊C4—1464no—
348C22×C4⋊C4C2×D7311yescharacteristic
349C22×C4⋊C4C2×D7311yescharacteristic
350C22×C22⋊C4—1461no—
351C2×#102—734no—
352C2×#102—734no—
353C2×#102—1464no—
354C2×#102—1464no—
355C2×C22⋊C8—734no—
356C2×C22⋊C8—1464no—
357#340—734no—
358#340C2×D7314yescomplemented
359C25—731no—
360C25—1461no—
361C22×D4—2924no—
362C22×D4—2924no—
363C22×D4—734no—
364C22×D4—732no—
365C22×D4—1468no—
366C22×D4—1464no—
367C22×D4—1461no—
368C22×D4—1462no—
369C22×D4—1462no—
370C22×D4—1462no—
371C22×D4—1462no—
372C22×D4—1462no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—2924no—
376C23×C4—2924no—
377C23×C4—731no—
378C23×C4—734no—
379C23×C4—732no—
380C23×C4—734no—
381C23×C4—732no—
382C23×C4—1464no—
383C23×C4—1468no—
384C23×C4—1461no—
385C23×C4—1462no—
386C23×C4—1462no—
387C23×C4—1462no—
388C23×C4—1462no—
389C23×C4C22×D7311yescharacteristic
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—732no—
394C22×C8—1462no—
395C22×C8—1462no—
396C22×C8—1462no—
397C22×C8C22×D7312yes—
398#121—7316no—
399#121—14616no—
400#121—1468no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—734no—
406C2×C4⋊C4—732no—
407C2×C4⋊C4—1468no—
408C2×C4⋊C4—14616no—
409C2×C4⋊C4—1464no—
410C2×C4⋊C4—1468no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4—1462no—
413C2×C4⋊C4—1468no—
414C2×C4⋊C4C4×D7314yescomplemented
415C2×C4⋊C4D29214yescomplemented
416C2×C4⋊C4C22×D7312yes—
417C2×C4⋊C4C22×D7312yes—
418C2×C22⋊C4—1468no—
419C2×C22⋊C4—1464no—
420#102—1468no—
421#102—1468no—
422C22⋊C8—1468no—
423C24—2922no—
424C24—2922no—
425C24—2922no—
426C24—2922no—
427C24—2922no—
428C24—2922no—
429C24—734no—
430C24—734no—
431C24—734no—
432C24—732no—
433C24—1464no—
434C24—1462no—
435C24—1462no—
436C24—1462no—
437C24—1462no—
438C24—1462no—
439C24D4×D7311yescharacteristic
440C2×D4—29232no—
441C2×D4—2928no—
442C2×D4—2928no—
443C2×D4—2922no—
444C2×D4—2924no—
445C2×D4—2924no—
446C2×D4—2922no—
447C2×D4—734no—
448C2×D4—14616no—
449C2×D4—1464no—
450C2×D4—1468no—
451C2×D4—1468no—
452C2×D4—1462no—
453C2×D4—1462no—
454C2×D4—1462no—
455C2×D4—1462no—
456C2×D4—1462no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—2928no—
466C22×C4—29232no—
467C22×C4—2928no—
468C22×C4—2922no—
469C22×C4—2922no—
470C22×C4—734no—
471C22×C4—732no—
472C22×C4—738no—
473C22×C4—734no—
474C22×C4—734no—
475C22×C4—14616no—
476C22×C4—1464no—
477C22×C4—1462no—
478C22×C4—1462no—
479C22×C4—1462no—
480C22×C4—1468no—
481C22×C4—1468no—
482C22×C4—1464no—
483C22×C4—1468no—
484C22×C4—1468no—
485C22×C4—1464no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1462no—
490C22×C4C2×C4×D7312yes—
491C22×C4D4×D7311yescharacteristic
492C22×C4D4×D7312yes—
493C22×C4D4×D7312yes—
494C22×C4C2×D29212yes—
495C22×C4#1192402812yes—
496C22×C4#1192402912yes—
497C22×C4C23×D7311yescharacteristic
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—44no—
502C2×C8—2924no—
503C2×C8—1462no—
504C2×C8—1462no—
505C2×C8—1462no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—734no—
511C4⋊C4—14616no—
512C4⋊C4—1464no—
513C4⋊C4—1462no—
514C4⋊C4C2×C4×D7314yescomplemented
515C4⋊C4C2×D29214yescomplemented
516C22⋊C4—14616no—
517C23—2922no—
518C23—2928no—
519C23—2922no—
520C23—2928no—
521C23—2922no—
522C23—2928no—
523C23—2922no—
524C23—2922no—
525C23—2922no—
526C23—5844no—
527C23—5844no—
528C23—5844no—
529C23—5844no—
530C23—734no—
531C23—7316no—
532C23—734no—
533C23—734no—
534C23—1464no—
535C23—1462no—
536C23—1468no—
537C23—1468no—
538C23—1468no—
539C23—1468no—
540C23—1468no—
541C23—1462no—
542C23—1462no—
543C23—1468no—
544C23—1462no—
545C23C22⋊C4×D7312yes—
546C23#1455656112yes—
547C23#1455657612yes—
548C23D8×D7312yes—
549C23SD16×D7312yes—
550C23#1455661812yes—
551C23#1455662312yes—
552C23C2×D4×D7311yescharacteristic
553D4—29232no—
554D4—2928no—
555D4—2922no—
556D4—2922no—
557D4—1464no—
558D4—1464no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—29232no—
568C2×C4—2928no—
569C2×C4—2922no—
570C2×C4—2922no—
571C2×C4—734no—
572C2×C4—1464no—
573C2×C4—1468no—
574C2×C4—1462no—
575C2×C4—1462no—
576C2×C4—14616no—
577C2×C4—1464no—
578C2×C4—1464no—
579C2×C4—1464no—
580C2×C4—1464no—
581C2×C4C22⋊C4×D7312yes—
582C2×C4#1455655314yes—
583C2×C4C4×D29214yes—
584C2×C4#1455656112yes—
585C2×C4#1455656414yes—
586C2×C4#1455656614yes—
587C2×C4#1455657612yes—
588C2×C4C22×C4×D7311yescharacteristic
589C2×C4C2×D4×D7311yescharacteristic
590C2×C4C2×D4×D7311yescharacteristic
591C2×C4C22×D29211yescharacteristic
592C2×C4C2×#1192402811yescharacteristic
593C2×C4C2×#1192402911yescharacteristic
594C8—42no—
595C8—2922no—
596C22—2924no—
597C22—2924no—
598C22—2924no—
599C22—58416no—
600C22—5842no—
601C22—5842no—
602C22—5842no—
603C22—5842no—
604C22—738no—
605C22—14632no—
606C22—1464no—
607C22—1464no—
608C22—1464no—
609C22—1464no—
610C22—1464no—
611C22—1464no—
612C22#1798846514yes—
613C22#102×D7314yes—
614C22#1798858714yes—
615C22#1798872214yes—
616C22#1798872714yes—
617C22#1798890214yes—
618C22#1798890714yes—
619C22C2×C22⋊C4×D7311yescharacteristic
620C22C2×#1455656111yescharacteristic
621C22C2×#1455657611yescharacteristic
622C22C2×D8×D7311yescharacteristic
623C22C2×SD16×D7311yescharacteristic
624C22C2×#1455661811yescharacteristic
625C22C2×#1455662311yescharacteristic
626C4—44no—
627C4—44no—
628C4—2924no—
629C4—1464no—
630C4#1798846514yes—
631C4C2×#1455655311yescharacteristic
632C4C2×C4×D29211yescharacteristic
633C4C2×#1455656411yescharacteristic
634C4C2×#1455656611yescharacteristic
635C2—5844no—
636C2—1468no—
637C2#2261024718yesdirect product factor
638C2C2×#1798846511yescharacteristic
639C2C2×#102×D7311yescharacteristic
640C2C2×#1798858711yescharacteristic
641C2C2×#1798872211yescharacteristic
642C2C2×#1798872711yescharacteristic
643C2C2×#1798890211yescharacteristic
644C2C2×#1798890711yescharacteristic
subgroupG/H
centerC24D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#340×C73C2
socleC24×C73C2×D4
prime radicalC22×#14556566C2
cosocleC22×C4×C73C24
hypercenterC2×#340D73
hypocenterC73C2×#1874
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D73C2semidirect
3. C22×#14556513C2semidirect
4. C22×#14556511C2semidirect
5. C22×#14556503C2semidirect
6. #22610247C2direct (N × H)
7. C2×#17988349C2semidirect
8. C2×#340×C73C2semidirect
16. C2×#14556566C4semidirect
23. C2×C4⋊C4×D73C22semidirect
26. C2×#14556513C22semidirect
28. C2×#14556511C22semidirect
30. C2×#14556503C22semidirect
31. #17988349C22semidirect
35. #340×C73C22semidirect
48. C22×D292C2×C4semidirect
70. #14556566C2×C4semidirect
73. C2×C4⋊Dic73D4semidirect
96. C2×C4⋊C4×C73C2×C4semidirect
97. C2×C4⋊C4×C73D4semidirect
132. C2×D292C22×C4semidirect
164. C4⋊Dic73C2×D4semidirect
192. C4⋊C4×C73C22×C4semidirect
193. C4⋊C4×C73C2×D4semidirect
226. C22×D73#102semidirect
302. C2×D73C2×#102semidirect
313. C2×C73#1874semidirect
330. C2×#340D73semidirect
331. C73C2×#1874semidirect
358. #340C2×D73semidirect
414. C2×C4⋊C4C4×D73semidirect
415. C2×C4⋊C4D292semidirect
514. C4⋊C4C2×C4×D73semidirect
515. C4⋊C4C2×D292semidirect
637. C2#22610247direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565662
C22×C4⋊C4×D732
C22×#145565132
C22×#145565112
C22×#145565032
#226102472
C2×#179883492
C2×#340×C732
C2×#187473