Finite Group Databasebeta

← C2×#22610358 #33087652

Subgroups — C2×#22610358 #33087652

Order 18688.

2438 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D73C211yesmaximal, characteristic, complemented
2C22×#14556566C211yesmaximal, characteristic
3C22×#14556513C211yesmaximal, characteristic, complemented
4C22×#14556511C211yesmaximal, characteristic, complemented
5C2×#17988444C211yesmaximal, characteristic, complemented
6#22610358C218yesmaximal, direct product factor
7C2×#17988349C211yesmaximal, characteristic, complemented
8C2×#340×C73C211yesmaximal, characteristic, complemented
9C23×D292—21no—
10C23×D292C2211yescharacteristic
11C23×C4×D73C2211yescharacteristic
12C23×#10596831C2211yescharacteristic
13C22×C8×D73—24no—
14C22×C8×D73—24no—
15C22×C8×D73—24no—
16C22×C8×D73C2214yescomplemented
17C2×#14556566—24no—
18C2×#14556566—22no—
19C2×#14556566C418yescomplemented
20C2×#14556566C2214yes—
21C22×C4⋊Dic73C2211yescharacteristic
22C22×#11924005—21no—
23C22×#11924005—21no—
24C2×#14556513—24no—
25C2×#14556513C2214yescomplemented
26C2×#14556511—24no—
27C2×#14556511C2214yescomplemented
28#17988444—22no—
29#17988444C2214yescomplemented
30C2×#14556498—21no—
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×C414yes—
49C22×D292C2312yes—
50C23×Dic73—21no—
51C23×Dic73D411yescharacteristic
52C22×C4×D73—22no—
53C22×C4×D73—22no—
54C22×C4×D73—22no—
55C22×C4×D73—22no—
56C22×C4×D73C2×C414yes—
57C22×C4×D73D412yes—
58C22×C4×D73D414yes—
59C22×C4×D73C2312yes—
60C22×#10596831—22no—
61C22×#10596831—22no—
62C22×#10596831D414yescomplemented
63C22×#10596831C2312yes—
64C2×C8×D73—232no—
65C2×C8×D73—28no—
66C2×C8×D73—28no—
67C2×C8×D73—28no—
68#14556566—216no—
69#14556566—28no—
70#14556566C2×C4116yescomplemented
71C2×C4⋊Dic73—22no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73C2312yes—
75C2×#11924005—28no—
76C2×#11924005—24no—
77C2×#11924005—24no—
78C2×#11924005—44no—
79#14556513—28no—
80#14556511—28no—
81#14556498—24no—
82C23×C4×C73—21no—
83C23×C4×C73—21no—
84C23×C4×C73C2311yescharacteristic
85C22×C8×C73—22no—
86C22×C8×C73—22no—
87C22×C8×C73D414yescomplemented
88C22×C8×C73C2312yes—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73C2×C414yes—
95C2×C4⋊C4×C73C2312yes—
96C2×C4⋊C4×C73C2312yes—
97C23×D73—22no—
98C23×D73—22no—
99C23×D73—22no—
100C23×D73—22no—
101C23×D73—24no—
102C23×D73—22no—
103C23×D73—42no—
104C23×D73—42no—
105C23×D73—42no—
106C23×D73—42no—
107C23×D73—42no—
108C23×D73—42no—
109C23×D73C22⋊C414yes—
110C23×D73D814yes—
111C23×D73SD1614yes—
112C23×D73C2×D412yes—
113C2×D292—28no—
114C2×D292—28no—
115C2×D292—22no—
116C2×D292—22no—
117C2×D292—22no—
118C2×D292—22no—
119C2×D292—216no—
120C2×D292—24no—
121C2×D292—22no—
122C2×D292—432no—
123C2×D292—48no—
124C2×D292—48no—
125C2×D292—44no—
126C2×D292—42no—
127C2×D292—42no—
128C2×D292—44no—
129C2×D292C22×C414yes—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—22no—
133C22×Dic73—42no—
134C22×Dic73—42no—
135C22×Dic73—42no—
136C22×Dic73C22⋊C414yes—
137C22×Dic73C2×D412yes—
138C2×C4×D73—28no—
139C2×C4×D73—28no—
140C2×C4×D73—28no—
141C2×C4×D73—24no—
142C2×C4×D73—24no—
143C2×C4×D73—28no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73C22⋊C418yes—
149C2×C4×D73C22×C414yes—
150C2×C4×D73C2×D414yes—
151C2×#10596831—28no—
152C2×#10596831—22no—
153C2×#10596831—22no—
154C2×#10596831C2×D414yescomplemented
155C8×D73—232no—
156C4⋊Dic73—22no—
157C4⋊Dic73—22no—
158C4⋊Dic73—42no—
159#11924005—216no—
160#11924005—48no—
161C24×C73C2×D411yescharacteristic
162C22×C4×C73—24no—
163C22×C4×C73—22no—
164C22×C4×C73—22no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73C22×C412yes—
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D412yes—
173C22×C4×C73C2×D412yes—
174C22×C4×C73C2×D412yes—
175C22×C4×C73#4112yes—
176C22×C4×C73#4112yes—
177C22×C4×C73C2411yescharacteristic
178C2×C8×C73—28no—
179C2×C8×C73—22no—
180C2×C8×C73—22no—
181C2×C8×C73C2×D414yescomplemented
182C4⋊C4×C73—24no—
183C4⋊C4×C73—22no—
184C4⋊C4×C73—22no—
185C4⋊C4×C73—22no—
186C4⋊C4×C73—42no—
187C4⋊C4×C73C22×C414yes—
188C23×C73C2×C22⋊C412yes—
189C23×C73#12112yes—
190C23×C73#12112yes—
191C23×C73C2×D812yes—
192C23×C73C2×SD1612yes—
193C23×C73#13512yes—
194C23×C73#13512yes—
195C23×C73C22×D411yescharacteristic
196C22×D73—22no—
197C22×D73—22no—
198C22×D73—22no—
199C22×D73—22no—
200C22×D73—28no—
201C22×D73—28no—
202C22×D73—28no—
203C22×D73—28no—
204C22×D73—28no—
205C22×D73—28no—
206C22×D73—24no—
207C22×D73—42no—
208C22×D73—42no—
209C22×D73—42no—
210C22×D73—42no—
211C22×D73—42no—
212C22×D73—42no—
213C22×D73—48no—
214C22×D73—48no—
215C22×D73—48no—
216C22×D73—84no—
217C22×D73—84no—
218C22×D73—84no—
219C22×D73—84no—
220C22×D73#102116yescomplemented
221C22×D73C2×C22⋊C414yes—
222C22×D73C2×D814yes—
223C22×D73C2×SD1614yes—
224C2×C4×C73—24no—
225C2×C4×C73—42no—
226C2×C4×C73—42no—
227C2×C4×C73—48no—
228C2×C4×C73—42no—
229C2×C4×C73—42no—
230C2×C4×C73—42no—
231C2×C4×C73—84no—
232C2×C4×C73C2×C22⋊C412yes—
233C2×C4×C73C4×D414yes—
234C2×C4×C73C4×D414yes—
235C2×C4×C73#12014yes—
236C2×C4×C73#12112yes—
237C2×C4×C73#12112yes—
238C2×C4×C73#12314yes—
239C2×C4×C73C23×C411yescharacteristic
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73C22×D411yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—28no—
248C2×Dic73—42no—
249C2×Dic73—42no—
250C2×Dic73—42no—
251C2×Dic73—84no—
252C2×Dic73C2×C22⋊C414yes—
253D292—24no—
254D292—24no—
255D292—432no—
256D292—42no—
257D292—42no—
258D292—48no—
259C4×D73—24no—
260C4×D73—24no—
261C4×D73—24no—
262C4×D73—24no—
263C4×D73—216no—
264C8×C73—24no—
265#10596831—24no—
266C22×C73#38614yes—
267C22×C73C2×#10214yes—
268C22×C73#41614yes—
269C22×C73#46514yes—
270C22×C73#46514yes—
271C22×C73#46614yes—
272C22×C73#46614yes—
273C22×C73C22×C22⋊C411yescharacteristic
274C22×C73C2×#12111yescharacteristic
275C22×C73C2×#12111yescharacteristic
276C22×C73C22×D811yescharacteristic
277C22×C73C22×SD1611yescharacteristic
278C22×C73C2×#13511yescharacteristic
279C22×C73C2×#13511yescharacteristic
280C2×D73—24no—
281C2×D73—232no—
282C2×D73—24no—
283C2×D73—24no—
284C2×D73—24no—
285C2×D73—24no—
286C2×D73—24no—
287C2×D73—44no—
288C2×D73—44no—
289C2×D73—44no—
290C2×D73—816no—
291C2×D73—82no—
292C2×D73—82no—
293C2×D73—82no—
294C2×D73—82no—
295C2×D73C2×#10218yescomplemented
296C4×C73—44no—
297C4×C73—82no—
298C4×C73#38614yes—
299C4×C73C2×C4×D411yescharacteristic
300C4×C73C2×C4×D411yescharacteristic
301C4×C73C2×#12011yescharacteristic
302C4×C73C2×#12311yescharacteristic
303Dic73—24no—
304Dic73—82no—
305C2×#1893—731nomaximal, Sylow
306C2×C73#189318yescomplemented
307C2×C73C2×#38611yescharacteristic
308C2×C73C22×#10211yescharacteristic
309C2×C73C2×#41611yescharacteristic
310C2×C73C2×#46511yescharacteristic
311C2×C73C2×#46511yescharacteristic
312C2×C73C2×#46611yescharacteristic
313C2×C73C2×#46611yescharacteristic
314D73—28no—
315D73—84no—
316C24×C8—731no—
317C22×#121—731no—
318C22×#102—731no—
319C22×#102—731no—
320C2×#380—731no—
321#1893—738no—
322C2×#340—731no—
323C2×#340D7311yescharacteristic, complemented
324C73C2×#189311yescharacteristic, complemented, Sylow
325C23×D4—731no—
326C23×D4—1461no—
327C24×C4—731no—
328C23×C8—731no—
329C23×C8—734no—
330C23×C8—1464no—
331C23×C8—1464no—
332C23×C8—1464no—
333C23×C8C2×D7311yescharacteristic
334C2×#121—738no—
335C2×#121—734no—
336C2×#121—1464no—
337C2×#121—1462no—
338C22×C4⋊C4—731no—
339C22×C4⋊C4C2×D7311yescharacteristic
340C22×C4⋊C4C2×D7311yescharacteristic
341C22×C22⋊C4—1461no—
342C22×C22⋊C4—1461no—
343C2×#102—734no—
344C2×#102—734no—
345C2×#102—1464no—
346C2×#102—1464no—
347#380—734no—
348#380—1462no—
349C2×#95—1461no—
350#340—734no—
351#340C2×D7314yescomplemented
352C25—731no—
353C25—1461no—
354C22×D4—2924no—
355C22×D4—2924no—
356C22×D4—734no—
357C22×D4—732no—
358C22×D4—1468no—
359C22×D4—1464no—
360C22×D4—1461no—
361C22×D4—1462no—
362C22×D4—1462no—
363C22×D4—1462no—
364C22×D4—1462no—
365C22×D4—1462no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—731no—
369C23×C4—734no—
370C23×C4—734no—
371C23×C4—732no—
372C23×C4—732no—
373C23×C4—1461no—
374C23×C4—1462no—
375C23×C4—1462no—
376C23×C4—1462no—
377C23×C4—1462no—
378C23×C4C22×D7311yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—734no—
382C22×C8—732no—
383C22×C8—1468no—
384C22×C8—1468no—
385C22×C8—14632no—
386C22×C8—1462no—
387C22×C8—1462no—
388C22×C8—1468no—
389C22×C8D29214yescomplemented
390C22×C8C22×D7312yes—
391#121—7316no—
392#121—14616no—
393#121—1468no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—732no—
400C2×C4⋊C4—1461no—
401C2×C4⋊C4—1462no—
402C2×C4⋊C4—1462no—
403C2×C4⋊C4C4×D7314yes—
404C2×C4⋊C4C22×D7312yes—
405C2×C4⋊C4C22×D7312yes—
406C2×C22⋊C4—2924no—
407C2×C22⋊C4—1464no—
408C2×C22⋊C4—1468no—
409C2×C22⋊C4—1464no—
410#102—1468no—
411#102—1468no—
412#95—1464no—
413C24—2922no—
414C24—2922no—
415C24—2922no—
416C24—2922no—
417C24—2922no—
418C24—2922no—
419C24—734no—
420C24—734no—
421C24—734no—
422C24—732no—
423C24—1464no—
424C24—1462no—
425C24—1462no—
426C24—1462no—
427C24—1462no—
428C24—1462no—
429C24D4×D7311yescharacteristic
430C2×D4—29232no—
431C2×D4—2928no—
432C2×D4—2928no—
433C2×D4—2924no—
434C2×D4—2922no—
435C2×D4—2922no—
436C2×D4—2924no—
437C2×D4—734no—
438C2×D4—14616no—
439C2×D4—1464no—
440C2×D4—1468no—
441C2×D4—1468no—
442C2×D4—1462no—
443C2×D4—1462no—
444C2×D4—1462no—
445C2×D4—1462no—
446C2×D4—1462no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—2922no—
456C22×C4—2922no—
457C22×C4—2922no—
458C22×C4—734no—
459C22×C4—732no—
460C22×C4—738no—
461C22×C4—734no—
462C22×C4—734no—
463C22×C4—1462no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4—1468no—
467C22×C4—1468no—
468C22×C4—1468no—
469C22×C4—1464no—
470C22×C4—1464no—
471C22×C4—1468no—
472C22×C4—1462no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4C2×C4×D7312yes—
477C22×C4D4×D7311yescharacteristic
478C22×C4D4×D7312yes—
479C22×C4D4×D7312yes—
480C22×C4C2×D29212yes—
481C22×C4#1192402812yes—
482C22×C4#1192402912yes—
483C22×C4C23×D7311yescharacteristic
484C2×C8—28no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—734no—
488C2×C8—14632no—
489C2×C8—1468no—
490C2×C8—1462no—
491C2×C8—1462no—
492C2×C8C2×D29214yescomplemented
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—42no—
498C4⋊C4—2922no—
499C4⋊C4—1462no—
500C4⋊C4—1462no—
501C4⋊C4C2×C4×D7314yes—
502C22⋊C4—2928no—
503C22⋊C4—14616no—
504C23—2928no—
505C23—2922no—
506C23—2922no—
507C23—2928no—
508C23—2928no—
509C23—2922no—
510C23—2922no—
511C23—2922no—
512C23—2922no—
513C23—5844no—
514C23—5844no—
515C23—5844no—
516C23—5844no—
517C23—734no—
518C23—7316no—
519C23—734no—
520C23—734no—
521C23—1464no—
522C23—1468no—
523C23—1468no—
524C23—1468no—
525C23—1468no—
526C23—1462no—
527C23—1468no—
528C23—1462no—
529C23—1468no—
530C23—1462no—
531C23—1462no—
532C23C22⋊C4×D7312yes—
533C23#1455656412yes—
534C23#1455656612yes—
535C23D8×D7312yes—
536C23SD16×D7312yes—
537C23#1455661212yes—
538C23#1455661412yes—
539C23C2×D4×D7311yescharacteristic
540D4—29232no—
541D4—2928no—
542D4—2922no—
543D4—2922no—
544D4—1464no—
545D4—1464no—
546C2×C4—24no—
547C2×C4—48no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—84no—
554C2×C4—2922no—
555C2×C4—2922no—
556C2×C4—2922no—
557C2×C4—5844no—
558C2×C4—734no—
559C2×C4—1468no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4—14616no—
563C2×C4—1464no—
564C2×C4—1464no—
565C2×C4—1464no—
566C2×C4—1464no—
567C2×C4C22⋊C4×D7312yes—
568C2×C4#1455655314yes—
569C2×C4C4×D29214yes—
570C2×C4#1455656114yes—
571C2×C4#1455656412yes—
572C2×C4#1455656612yes—
573C2×C4#1455657614yes—
574C2×C4C22×C4×D7311yescharacteristic
575C2×C4C2×D4×D7311yescharacteristic
576C2×C4C2×D4×D7311yescharacteristic
577C2×C4C22×D29211yescharacteristic
578C2×C4C2×#1192402811yescharacteristic
579C2×C4C2×#1192402911yescharacteristic
580C8—24no—
581C8—1464no—
582C22—2924no—
583C22—2924no—
584C22—2924no—
585C22—5842no—
586C22—5842no—
587C22—5842no—
588C22—5842no—
589C22—58416no—
590C22—738no—
591C22—1464no—
592C22—1464no—
593C22—1464no—
594C22—1464no—
595C22—1464no—
596C22—1464no—
597C22—14632no—
598C22#1798846514yes—
599C22#102×D7314yes—
600C22#1798858214yes—
601C22#1798881714yes—
602C22#1798881914yes—
603C22#1798882214yes—
604C22#1798882414yes—
605C22C2×C22⋊C4×D7311yescharacteristic
606C22C2×#1455656411yescharacteristic
607C22C2×#1455656611yescharacteristic
608C22C2×D8×D7311yescharacteristic
609C22C2×SD16×D7311yescharacteristic
610C22C2×#1455661211yescharacteristic
611C22C2×#1455661411yescharacteristic
612C4—44no—
613C4—82no—
614C4—5842no—
615C4—1464no—
616C4#1798846514yes—
617C4C2×#1455655311yescharacteristic
618C4C2×C4×D29211yescharacteristic
619C4C2×#1455656111yescharacteristic
620C4C2×#1455657611yescharacteristic
621C2—5844no—
622C2—1468no—
623C2#2261035818yesdirect product factor
624C2C2×#1798846511yescharacteristic
625C2C2×#102×D7311yescharacteristic
626C2C2×#1798858211yescharacteristic
627C2C2×#1798881711yescharacteristic
628C2C2×#1798881911yescharacteristic
629C2C2×#1798882211yescharacteristic
630C2C2×#1798882411yescharacteristic
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×#1893
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
1. C23×C8×D73C2semidirect
3. C22×#14556513C2semidirect
4. C22×#14556511C2semidirect
5. C2×#17988444C2semidirect
6. #22610358C2direct (N × H)
7. C2×#17988349C2semidirect
8. C2×#340×C73C2semidirect
16. C22×C8×D73C22semidirect
19. C2×#14556566C4semidirect
25. C2×#14556513C22semidirect
27. C2×#14556511C22semidirect
29. #17988444C22semidirect
31. #17988349C22semidirect
35. #340×C73C22semidirect
62. C22×#10596831D4semidirect
70. #14556566C2×C4semidirect
87. C22×C8×C73D4semidirect
154. C2×#10596831C2×D4semidirect
181. C2×C8×C73C2×D4semidirect
220. C22×D73#102semidirect
295. C2×D73C2×#102semidirect
306. C2×C73#1893semidirect
323. C2×#340D73semidirect
324. C73C2×#1893semidirect
351. #340C2×D73semidirect
389. C22×C8D292semidirect
492. C2×C8C2×D292semidirect
623. C2#22610358direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D732
C22×#145565662
C22×#145565132
C22×#145565112
C2×#179884442
#226103582
C2×#179883492
C2×#340×C732
C2×#189373