Finite Group Databasebeta

← C4×#17988514 #33007804

Subgroups — C4×#17988514 #33007804

Order 18688.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988514C211yesmaximal, characteristic
2C2×C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
3C2×C4×#11924005C212yesmaximal
4C2×C4×#11924005C211yesmaximal, characteristic
5#22608200C211yesmaximal, characteristic, complemented
6#22608191C212yesmaximal, complemented
7#22608188C211yesmaximal, characteristic, complemented
8#22608179C212yesmaximal
9#22608177C211yesmaximal, characteristic
10C4×#14556498C212yesmaximal, complemented
11C4×#95×C73C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2211yescharacteristic
15C22×#11924005C2212yes—
16C22×#11924005C2211yescharacteristic
17C22×#11924005C2211yescharacteristic
18C22×#11924005C2212yes—
19C22×C4×Dic73C2211yescharacteristic
20C22×C4×Dic73C2212yes—
21#17988514C418yesdirect product factor
22C4×C4⋊Dic73—24no—
23C4×#11924005—28no—
24C4×#11924005—24no—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2211yescharacteristic
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C22×C42×C73C2212yes—
35C22×C42×C73C2211yescharacteristic
36C2×#95×C73C2211yescharacteristic
37C2×#95×C73C2212yes—
38C2×#95×C73C2211yescharacteristic
39C24×D73C2311yescharacteristic
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2312yes—
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2312yes—
45C22×C4×D73—22no—
46C22×C4×D73—24no—
47C22×C4×D73—24no—
48C22×C4×D73—22no—
49C22×C4×D73D414yes—
50C2×C4⋊Dic73—24no—
51C2×C4⋊Dic73—22no—
52C2×C4⋊Dic73—22no—
53C2×C4⋊Dic73—22no—
54C2×C4⋊Dic73C2×C414yescomplemented
55C2×#11924005—24no—
56C2×#11924005—24no—
57C2×#11924005—22no—
58C2×#11924005—24no—
59C2×#11924005—22no—
60C2×#11924005—24no—
61C2×#11924005—22no—
62C2×#11924005—22no—
63C2×#11924005—24no—
64C2×#11924005—22no—
65C2×#11924005C2×C418yes—
66C2×#11924005C2×C414yes—
67C2×C4×Dic73—24no—
68C2×C4×Dic73—22no—
69C2×C4×Dic73—24no—
70C2×C4×Dic73—24no—
71C2×C4×Dic73—24no—
72#14556498—24no—
73#14556498—24no—
74#14556498—24no—
75#14556498—24no—
76#14556498—22no—
77#14556498—22no—
78#14556498—24no—
79#14556498—24no—
80#14556498C2×C418yescomplemented
81C23×C4×C73C2312yes—
82C23×C4×C73C2311yescharacteristic
83C23×C4×C73C2312yes—
84C23×C4×C73C2311yescharacteristic
85C23×C4×C73C2311yescharacteristic
86C2×C42×C73—24no—
87C2×C42×C73—24no—
88C2×C42×C73—24no—
89C2×C42×C73—24no—
90C2×C42×C73D414yes—
91#95×C73—24no—
92#95×C73—22no—
93#95×C73C2×C414yescomplemented
94C23×D73—21no—
95C23×D73—22no—
96C23×D73—21no—
97C23×D73—21no—
98C23×D73—22no—
99C23×D73—22no—
100C23×D73—22no—
101C23×D73—21no—
102C23×D73C22×C412yes—
103C23×D73C2×D412yes—
104C23×D73#4112yes—
105C22×Dic73—21no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—21no—
109C22×Dic73—21no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—21no—
129C22×Dic73C22×C412yes—
130C22×Dic73C22×C414yes—
131C22×Dic73C2×D412yes—
132C22×Dic73#4112yes—
133C22×Dic73#4114yes—
134C2×C4×D73—28no—
135C2×C4×D73—216no—
136C2×C4×D73—44no—
137C2×C4×D73—44no—
138C2×C4×D73—48no—
139C4⋊Dic73—28no—
140C4⋊Dic73—28no—
141#11924005—28no—
142#11924005—216no—
143#11924005—216no—
144#11924005—28no—
145C4×Dic73—48no—
146C4×Dic73—44no—
147C24×C73C2411yescharacteristic
148C22×C4×C73—22no—
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—22no—
152C22×C4×C73—22no—
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73—22no—
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—22no—
166C22×C4×C73C22×C414yes—
167C22×C4×C73C22×C412yes—
168C22×C4×C73C2×D412yes—
169C22×C4×C73C2×D412yes—
170C22×C4×C73C2×D412yes—
171C22×C4×C73C2×D412yes—
172C22×C4×C73#4114yes—
173C22×C4×C73#4114yes—
174C22×C4×C73#4112yes—
175C22×C4×C73#4114yes—
176C22×C4×C73#4112yes—
177C42×C73—28no—
178C42×C73—48no—
179C23×C73C23×C411yescharacteristic
180C23×C73C22×D411yescharacteristic
181C23×C73C22×D411yescharacteristic
182C23×C73C2×#4111yescharacteristic
183C23×C73C2×#4112yes—
184C23×C73C2×#4111yescharacteristic
185C23×C73C2×#4112yes—
186C23×C73C2×#4111yescharacteristic
187C23×C73C2×#4112yes—
188C23×C73C2×#4112yes—
189C23×C73C2×#4111yescharacteristic
190C22×D73—22no—
191C22×D73—24no—
192C22×D73—24no—
193C22×D73—22no—
194C22×D73—22no—
195C22×D73—24no—
196C22×D73—24no—
197C22×D73—22no—
198C22×D73—22no—
199C22×D73—24no—
200C22×D73—24no—
201C22×D73—22no—
202C22×D73—41no—
203C22×D73—41no—
204C22×D73—41no—
205C22×D73—42no—
206C22×D73—42no—
207C22×D73—42no—
208C22×D73—42no—
209C22×D73—42no—
210C22×D73—42no—
211C22×D73—41no—
212C22×D73C4×D414yes—
213C2×C4×C73—24no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—24no—
217C2×C4×C73—24no—
218C2×C4×C73—24no—
219C2×C4×C73—24no—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—24no—
223C2×C4×C73—24no—
224C2×C4×C73—24no—
225C2×C4×C73—22no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73—42no—
229C2×C4×C73—42no—
230C2×C4×C73—42no—
231C2×C4×C73—42no—
232C2×C4×C73—42no—
233C2×C4×C73—42no—
234C2×C4×C73—42no—
235C2×C4×C73—42no—
236C2×C4×C73C4×D414yes—
237C2×C4×C73#12114yes—
238C2×C4×C73#12318yes—
239C2×C4×C73#12314yes—
240C2×C4×C73#12414yes—
241C2×C4×C73#12618yes—
242C2×Dic73—24no—
243C2×Dic73—22no—
244C2×Dic73—24no—
245C2×Dic73—24no—
246C2×Dic73—24no—
247C2×Dic73—22no—
248C2×Dic73—24no—
249C2×Dic73—24no—
250C2×Dic73—22no—
251C2×Dic73—24no—
252C2×Dic73—24no—
253C2×Dic73—24no—
254C2×Dic73—42no—
255C2×Dic73—42no—
256C2×Dic73—41no—
257C2×Dic73—42no—
258C2×Dic73—41no—
259C2×Dic73—42no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—42no—
264C2×Dic73—42no—
265C2×Dic73—42no—
266C2×Dic73—42no—
267C2×Dic73—42no—
268C2×Dic73—42no—
269C2×Dic73—42no—
270C2×Dic73—41no—
271C4×D73—416no—
272C22×C73C2×C4×D411yescharacteristic
273C22×C73C2×C4×D411yescharacteristic
274C22×C73C4×#4112yes—
275C22×C73C4×#4112yes—
276C22×C73C4×#4111yescharacteristic
277C22×C73C2×#12111yescharacteristic
278C22×C73C2×#12312yes—
279C22×C73C2×#12311yescharacteristic
280C22×C73#52512yes—
281C22×C73#52511yescharacteristic
282C22×C73#52511yescharacteristic
283C22×C73C2×#12411yescharacteristic
284C22×C73C2×#12612yes—
285C22×C73#52912yes—
286C22×C73#52912yes—
287C22×C73#52911yescharacteristic
288C22×C73#52912yes—
289C22×C73#52912yes—
290C22×C73#52912yes—
291C22×C73#52912yes—
292C22×C73#52912yes—
293C22×C73#53211yescharacteristic
294C22×C73#53211yescharacteristic
295C2×D73—24no—
296C2×D73—28no—
297C2×D73—44no—
298C2×D73—42no—
299C2×D73—42no—
300C2×D73—42no—
301C2×D73—44no—
302C2×D73—42no—
303C2×D73—44no—
304C2×D73—42no—
305C2×D73—42no—
306C4×C73—24no—
307C4×C73—42no—
308C4×C73—44no—
309C4×C73—44no—
310C4×C73#39718yescomplemented
311Dic73—42no—
312Dic73—44no—
313Dic73—42no—
314Dic73—44no—
315Dic73—42no—
316C4×#397—731nomaximal, Sylow
317C2×C73C4×#12111yescharacteristic
318C2×C73C4×#12312yes—
319C2×C73C4×#12311yescharacteristic
320C2×C73C4×#12411yescharacteristic
321C2×C73C4×#12612yes—
322C2×C73C2×#39711yescharacteristic
323C2×C73#239211yescharacteristic
324C2×C73#239511yescharacteristic
325C2×C73#239512yes—
326C2×C73#239811yescharacteristic
327C2×C73#240112yes—
328D73—44no—
329C2×#397—731no—
330C2×C4×C4⋊C4—731no—
331C2×C4×C22⋊C4—731no—
332C2×C4×C22⋊C4—732no—
333#1445—731no—
334#1443—732no—
335#1442—731no—
336#1440—732no—
337#1439—731no—
338C4×#95—732no—
339C4×#95D7311yescharacteristic, complemented
340C73C4×#39711yescharacteristic, complemented, Sylow
341C24×C4—731no—
342C22×C4⋊C4—731no—
343C22×C4⋊C4—731no—
344C22×C22⋊C4—731no—
345C22×C22⋊C4—732no—
346C22×C22⋊C4—732no—
347C22×C22⋊C4—731no—
348C22×C42—731no—
349C22×C42—732no—
350C22×C42C2×D7312yes—
351C22×C42C2×D7311yescharacteristic
352#397—738no—
353C4×C4⋊C4—1464no—
354C4×C22⋊C4—1468no—
355C4×C22⋊C4—1464no—
356C2×#95—732no—
357C2×#95—732no—
358C2×#95—732no—
359C2×#95—732no—
360C2×#95—732no—
361C2×#95—732no—
362C2×#95—731no—
363C2×#95—731no—
364C2×#95—732no—
365C2×#95C2×D7311yescharacteristic
366C2×#95C2×D7312yes—
367C2×#95C2×D7311yescharacteristic
368C25—731no—
369C23×C4—732no—
370C23×C4—732no—
371C23×C4—731no—
372C23×C4—731no—
373C23×C4—731no—
374C23×C4—734no—
375C23×C4—1462no—
376C23×C4—1464no—
377C23×C4—1464no—
378C23×C4—1462no—
379C23×C4C22×D7312yes—
380C23×C4C22×D7311yescharacteristic
381C23×C4C22×D7312yes—
382C23×C4C22×D7311yescharacteristic
383C23×C4C22×D7311yescharacteristic
384C2×C4⋊C4—734no—
385C2×C4⋊C4—1464no—
386C2×C4⋊C4—1462no—
387C2×C4⋊C4—1462no—
388C2×C4⋊C4—1462no—
389C2×C22⋊C4—738no—
390C2×C22⋊C4—734no—
391C2×C22⋊C4—1462no—
392C2×C22⋊C4—1464no—
393C2×C22⋊C4—1464no—
394C2×C22⋊C4—1464no—
395C2×C22⋊C4—1464no—
396C2×C22⋊C4—1462no—
397C2×C22⋊C4—1462no—
398C2×C22⋊C4—1462no—
399C2×C22⋊C4—1464no—
400C2×C22⋊C4—1462no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—1464no—
406C2×C42—1462no—
407C2×C42—1464no—
408C2×C42—1464no—
409C2×C42—1464no—
410C2×C42D29214yes—
411#95—24no—
412#95—22no—
413#95—738no—
414#95—1464no—
415#95—1464no—
416#95—1464no—
417#95—1464no—
418#95—1462no—
419#95—1462no—
420#95—1464no—
421#95—1464no—
422#95C4×D7314yescomplemented
423C24—732no—
424C24—732no—
425C24—732no—
426C24—1461no—
427C24—1462no—
428C24—1461no—
429C24—1462no—
430C24—1461no—
431C24—1462no—
432C24—1462no—
433C24—1461no—
434C24C23×D7311yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—2924no—
454C22×C4—2924no—
455C22×C4—2928no—
456C22×C4—732no—
457C22×C4—734no—
458C22×C4—732no—
459C22×C4—732no—
460C22×C4—734no—
461C22×C4—1462no—
462C22×C4—1462no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1462no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1462no—
471C22×C4—1461no—
472C22×C4—1462no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1462no—
477C22×C4—1462no—
478C22×C4—1461no—
479C22×C4—1462no—
480C22×C4—1462no—
481C22×C4—1462no—
482C22×C4—1462no—
483C22×C4—1462no—
484C22×C4—1461no—
485C22×C4—1468no—
486C22×C4—14616no—
487C22×C4C2×C4×D7314yes—
488C22×C4C2×C4×D7312yes—
489C22×C4D4×D7312yes—
490C22×C4C2×D29212yes—
491C22×C4C2×D29212yes—
492C22×C4C2×D29212yes—
493C22×C4#1192402714yes—
494C22×C4#1192402814yes—
495C22×C4#1192402812yes—
496C22×C4#1192402814yes—
497C22×C4#1192402912yes—
498C4⋊C4—1468no—
499C4⋊C4—1468no—
500C22⋊C4—14616no—
501C22⋊C4—14616no—
502C22⋊C4—1468no—
503C22⋊C4—1468no—
504C42—28no—
505C42—48no—
506C42—2928no—
507C42—2924no—
508C23—2922no—
509C23—2922no—
510C23—2921no—
511C23—2921no—
512C23—2921no—
513C23—2921no—
514C23—2922no—
515C23—2922no—
516C23—2922no—
517C23—2922no—
518C23—734no—
519C23—1462no—
520C23—1462no—
521C23—1462no—
522C23—1464no—
523C23—1464no—
524C23—1462no—
525C23—1462no—
526C23—1464no—
527C23—1464no—
528C23—1462no—
529C23—1464no—
530C23—1464no—
531C23C22×C4×D7311yescharacteristic
532C23C2×D4×D7311yescharacteristic
533C23C22×D29211yescharacteristic
534C23#41×D7311yescharacteristic
535C23#41×D7312yes—
536C23#41×D7311yescharacteristic
537C23C2×#1192402712yes—
538C23C2×#1192402811yescharacteristic
539C23C2×#1192402812yes—
540C23C2×#1192402812yes—
541C23C2×#1192402911yescharacteristic
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—2922no—
566C2×C4—2922no—
567C2×C4—2922no—
568C2×C4—2922no—
569C2×C4—2922no—
570C2×C4—2921no—
571C2×C4—2922no—
572C2×C4—2922no—
573C2×C4—2921no—
574C2×C4—2922no—
575C2×C4—2922no—
576C2×C4—2921no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2922no—
581C2×C4—2922no—
582C2×C4—29216no—
583C2×C4—1464no—
584C2×C4—1464no—
585C2×C4—1462no—
586C2×C4—1464no—
587C2×C4—1464no—
588C2×C4—1464no—
589C2×C4—1462no—
590C2×C4—1464no—
591C2×C4—1464no—
592C2×C4—1462no—
593C2×C4—1464no—
594C2×C4—1464no—
595C2×C4C4×D29214yes—
596C2×C4#1455656614yes—
597C2×C4#1455657318yes—
598C2×C4#1455657514yes—
599C2×C4#1455657914yes—
600C2×C4#1455658618yes—
601C22—2924no—
602C22—2922no—
603C22—2922no—
604C22—2922no—
605C22—2924no—
606C22—2922no—
607C22—2922no—
608C22—2924no—
609C22—2922no—
610C22—1464no—
611C22—1468no—
612C22C4×D4×D7311yescharacteristic
613C22C2×C4×D29211yescharacteristic
614C22C4×#1192402712yes—
615C22C4×#1192402812yes—
616C22C4×#1192402911yescharacteristic
617C22C2×#1455656611yescharacteristic
618C22C2×#1455657312yes—
619C22C2×#1455657511yescharacteristic
620C22#1798909612yes—
621C22#1798909911yescharacteristic
622C22#1798909911yescharacteristic
623C22C2×#1455657911yescharacteristic
624C22C2×#1455658612yes—
625C22#1798911512yes—
626C22#1798911512yes—
627C22#1798911712yes—
628C22#1798911712yes—
629C22#1798911912yes—
630C22#1798912112yes—
631C22#1798912412yes—
632C22#1798912411yescharacteristic
633C22#1798913411yescharacteristic
634C22#1798913711yescharacteristic
635C4—24no—
636C4—42no—
637C4—44no—
638C4—44no—
639C4—2922no—
640C4—2924no—
641C4—2924no—
642C4—2922no—
643C4—2922no—
644C4#1798851418yesdirect product factor
645C2—2924no—
646C2C4×#1455656611yescharacteristic
647C2C4×#1455657312yes—
648C2C4×#1455657511yescharacteristic
649C2C4×#1455657911yescharacteristic
650C2C4×#1455658612yes—
651C2C2×#1798851411yescharacteristic
652C2#2261317111yescharacteristic
653C2#2261319111yescharacteristic
654C2#2261319212yes—
655C2#2261321711yescharacteristic
656C2#2261323212yes—
subgroupG/H
centerC23×C4C22×D73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC4×#95×C73C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenterC4×#95D73
hypocenterC73C4×#397
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic73C2semidirect
5. #22608200C2semidirect
6. #22608191C2semidirect
7. #22608188C2semidirect
10. C4×#14556498C2semidirect
11. C4×#95×C73C2semidirect
21. #17988514C4direct (N × H)
54. C2×C4⋊Dic73C2×C4semidirect
80. #14556498C2×C4semidirect
93. #95×C73C2×C4semidirect
310. C4×C73#397semidirect
339. C4×#95D73semidirect
340. C73C4×#397semidirect
422. #95C4×D73semidirect
644. C4#17988514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179885142
C2×C4×C4⋊Dic732
C2×C4×#119240052
#226082002
#226081912
#226081882
#226081792
#226081772
C4×#145564982
C4×#95×C732
C4×#39773