Finite Group Databasebeta

← #33085390

Subgroups — #33085390

Order 18688.

1462 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989066C211yesmaximal, characteristic
2C2×#17988559C212yesmaximal
3#22612548C212yesmaximal, complemented
4#22609919C211yesmaximal, characteristic, complemented
5#22609918C212yesmaximal, complemented
6#22609917C212yesmaximal, complemented
7#22609916C212yesmaximal, complemented
8#22609662C212yesmaximal, complemented
9C73×#1799C211yesmaximal, characteristic, complemented
10C22×#11924027C2211yescharacteristic
11#17989066—24no—
12#17989066—24no—
13C2×C4×Dic146C411yescharacteristic, complemented
14C2×#14556556C411yescharacteristic, complemented
15C2×D4×Dic73C2211yescharacteristic
16C2×C4×C22⋊D73C411yescharacteristic, complemented
17C2×C4×C22⋊D73C2211yescharacteristic
18C2×#14556551C411yescharacteristic, complemented
19C2×#14556551C2211yescharacteristic
20C2×#14556548C411yescharacteristic, complemented
21C2×#14556547C411yescharacteristic, complemented
22C2×#14556547C2214yes—
23C2×#14556547C2211yescharacteristic
24C22×#11924007C411yescharacteristic, complemented
25C22×#11924007C2211yescharacteristic
26C2×C4⋊C4×D73C411yescharacteristic, complemented
27#17988559—28no—
28C2×#14556506C2212yes—
29C2×#14556505C2214yes—
30#17988484—24no—
31#17988482—24no—
32#17988447C2212yes—
33#17988445C2214yes—
34#17988354C2212yes—
35#17988353C2214yes—
36C2×C4×D4×C73C2211yescharacteristic
37C2×#99×C73C2212yes—
38#380×C73C2212yes—
39#342×C73C2212yes—
40C2×#11924027—24no—
41C2×#11924027—24no—
42C2×#11924027D414yes—
43C2×#11924027Q814yes—
44C22×Dic146C2×C411yescharacteristic
45C22×C22⋊D73C2×C411yescharacteristic
46C22×C22⋊D73C2311yescharacteristic
47C23×Dic73C2×C411yescharacteristic
48C23×Dic73C2×C411yescharacteristic
49C23×Dic73C2311yescharacteristic
50C23×Dic73C2311yescharacteristic
51C22×C4×D73C2×C411yescharacteristic
52C22×C4×D73C2×C411yescharacteristic
53C22×C4×D73C2×C411yescharacteristic
54C4×Dic146—22no—
55C4×Dic146—22no—
56#14556556—24no—
57D4×Dic73—24no—
58C4×C22⋊D73—22no—
59C4×C22⋊D73—22no—
60C4×C22⋊D73—22no—
61C4×C22⋊D73—22no—
62#14556551—24no—
63#14556551—24no—
64#14556548—22no—
65#14556548—22no—
66#14556547—24no—
67#14556547—24no—
68#14556547—28no—
69#14556547—28no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×#11924007—22no—
73C2×#11924007—22no—
74C2×#11924007—24no—
75C2×#11924007—24no—
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×#11924007D414yes—
85C2×#11924007D414yes—
86C4⋊C4×D73—24no—
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2314yes—
89C2×C22⋊Dic73C2311yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×C4×Dic73—24no—
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2×C411yescharacteristic
96C2×C4×Dic73C2×C411yescharacteristic
97C2×C4×Dic73C2×C411yescharacteristic
98#14556506—24no—
99#14556505—28no—
100#14556498—24no—
101#14556498—22no—
102C22×D4×C73C2311yescharacteristic
103C23×C4×C73C2×C411yescharacteristic
104C23×C4×C73C2311yescharacteristic
105C4×D4×C73—22no—
106C4×D4×C73—22no—
107C2×C4⋊C4×C73—22no—
108C2×C4⋊C4×C73C2×C411yescharacteristic
109C2×C22⋊C4×C73C2×C411yescharacteristic
110C2×C22⋊C4×C73C2314yes—
111C2×C22⋊C4×C73C2311yescharacteristic
112C2×C42×C73C2×C411yescharacteristic
113#99×C73—24no—
114#95×C73—22no—
115C23×D73C22×C411yescharacteristic
116#11924027—216no—
117#11924027—216no—
118C2×Dic146—22no—
119C2×Dic146—22no—
120C2×Dic146C4⋊C414yescomplemented
121C2×C22⋊D73—22no—
122C2×C22⋊D73—22no—
123C2×C22⋊D73—22no—
124C2×C22⋊D73—22no—
125C2×C22⋊D73C4⋊C414yescomplemented
126C2×C22⋊D73C2×D412yes—
127C2×C22⋊D73C2×Q812yes—
128C22×Dic73—22no—
129C22×Dic73—22no—
130C22×Dic73—22no—
131C22×Dic73—24no—
132C22×Dic73—81no—
133C22×Dic73—81no—
134C22×Dic73C4⋊C414yescomplemented
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C22×Dic73C2×D414yes—
143C22×Dic73C2×D414yes—
144C22×Dic73C2×D412yes—
145C22×Dic73C2×Q812yes—
146C22×Dic73#4114yes—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—81no—
152C2×C4×D73—81no—
153C2×C4×D73C4⋊C414yescomplemented
154C4⋊Dic73—22no—
155C4⋊Dic73—82no—
156#11924007—21no—
157#11924007—21no—
158#11924007—22no—
159#11924007—22no—
160#11924007—22no—
161#11924007—48no—
162#11924007—84no—
163#11924007C22⋊C414yes—
164#11924007C22⋊C412yes—
165#11924007C22⋊C412yes—
166#11924007C22⋊C414yes—
167#11924007C22⋊C412yes—
168#11924007C22⋊C412yes—
169C22⋊Dic73—22no—
170C22⋊Dic73—22no—
171C22⋊Dic73—24no—
172C22⋊Dic73—24no—
173#11924005—21no—
174#11924005—21no—
175#11924005—22no—
176C4×Dic73—22no—
177C4×Dic73—22no—
178C4×Dic73—22no—
179C4×Dic73—22no—
180C4×Dic73—22no—
181C4×Dic73—48no—
182C24×C73C22×C411yescharacteristic
183C24×C73C2411yescharacteristic
184C2×D4×C73—22no—
185C2×D4×C73—22no—
186C2×D4×C73C2×D412yes—
187C2×D4×C73C2×Q812yes—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—24no—
191C22×C4×C73—81no—
192C22×C4×C73—81no—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C2×D412yes—
199C22×C4×C73C2×D412yes—
200C4⋊C4×C73—22no—
201C4⋊C4×C73—82no—
202C22⋊C4×C73—22no—
203C22⋊C4×C73—22no—
204C22⋊C4×C73—24no—
205C22⋊C4×C73—24no—
206C42×C73—21no—
207C42×C73—21no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—41no—
211C23×C73—41no—
212C23×C73—41no—
213C23×C73—41no—
214C23×C73C2×C4⋊C412yes—
215C23×C73C23×C411yescharacteristic
216C23×C73C22×D412yes—
217C23×C73C22×D411yescharacteristic
218C23×C73C22×Q811yescharacteristic
219C23×C73C2×#4112yes—
220C22×D73—21no—
221C22×D73—21no—
222C22×D73—41no—
223C22×D73—41no—
224C22×D73C2×C4⋊C412yes—
225D4×C73—24no—
226D4×C73—24no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—42no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—42no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—44no—
238C2×C4×C73—44no—
239C2×C4×C73—44no—
240C2×C4×C73—81no—
241C2×C4×C73—81no—
242C2×C4×C73C2×C22⋊C411yescharacteristic
243C2×C4×C73C2×C22⋊C411yescharacteristic
244C2×C4×C73C2×C22⋊C412yes—
245C2×C4×C73C2×C4⋊C412yes—
246C22⋊D73—24no—
247C22⋊D73—24no—
248C22⋊D73—28no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—28no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—44no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—44no—
260C2×Dic73—44no—
261C2×Dic73—44no—
262C2×Dic73—82no—
263C2×Dic73C2×C22⋊C412yes—
264C2×Dic73C2×C22⋊C412yes—
265C2×Dic73C2×C22⋊C412yes—
266C2×Dic73C2×C22⋊C412yes—
267C2×Dic73C2×C4⋊C412yes—
268C2×Dic73C2×C4⋊C412yes—
269C2×Dic73C2×C4⋊C412yes—
270C2×Dic73#11712yes—
271C2×Dic73#11712yes—
272C2×Dic73#12118yes—
273C2×Dic73C22⋊Q818yes—
274C4×D73—28no—
275C4×D73—82no—
276C4×D73—82no—
277Dic146—28no—
278C22×C73—22no—
279C22×C73—21no—
280C22×C73—22no—
281C22×C73—21no—
282C22×C73—22no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—42no—
286C22×C73—42no—
287C22×C73—42no—
288C22×C73—41no—
289C22×C73—41no—
290C22×C73C22×C22⋊C411yescharacteristic
291C22×C73C22×C4⋊C411yescharacteristic
292C22×C73C2×#11711yescharacteristic
293C22×C73C2×#12112yes—
294C22×C73C2×C22⋊Q812yes—
295C2×D73—22no—
296C2×D73—42no—
297C2×D73—41no—
298C2×D73—41no—
299C2×D73—42no—
300C4×C73—22no—
301C4×C73—21no—
302C4×C73—21no—
303C4×C73—22no—
304C4×C73—41no—
305C4×C73—41no—
306C4×C73—84no—
307Dic73—22no—
308Dic73—22no—
309Dic73—22no—
310Dic73—41no—
311Dic73—41no—
312Dic73—84no—
313Dic73#38014yes—
314Dic73#38014yes—
315#20634—731nomaximal, Sylow
316C2×C73—22no—
317C2×C73—21no—
318C2×C73—21no—
319C2×C73—22no—
320C2×C73—42no—
321C2×C73C2×#38011yescharacteristic
322C2×C73#288311yescharacteristic
323C2×C73#288411yescharacteristic
324D73—42no—
325C2×#520—731no—
326C2×#410—732no—
327#2316—732no—
328#1799—732no—
329#1799—732no—
330#1799—732no—
331#1799—731no—
332#1799D7311yescharacteristic, complemented
333#1740—732no—
334C73#2063411yescharacteristic, complemented, Sylow
335C22×#41—731no—
336#520—1464no—
337#520—1464no—
338C2×C4×Q8—731no—
339C2×C4×Q8—731no—
340C2×C4×D4—731no—
341C2×C4×D4—731no—
342C2×C4×D4—731no—
343C2×C4×D4—731no—
344C2×C4×D4—731no—
345C2×C4×D4C2×D7311yescharacteristic
346C2×#117—731no—
347C2×#117—731no—
348C2×#117—731no—
349C2×#117—734no—
350C22×C4⋊C4—731no—
351C22×C4⋊C4—731no—
352C22×C4⋊C4—731no—
353#410—1468no—
354C2×#99—732no—
355C2×#99—734no—
356C2×#99C2×D7312yes—
357#389—1464no—
358#389—1464no—
359#380—732no—
360#380—734no—
361#380C2×D7312yes—
362#342—734no—
363#342—732no—
364#342C2×D7312yes—
365C2×#41—734no—
366C2×#41—734no—
367C2×#41—1464no—
368C2×#41—1464no—
369C22×Q8—731no—
370C22×D4—731no—
371C22×D4—731no—
372C22×D4C22×D7311yescharacteristic
373C23×C4—731no—
374C23×C4—731no—
375C23×C4—731no—
376C23×C4—731no—
377C23×C4—731no—
378C23×C4—731no—
379C23×C4—731no—
380C23×C4C4×D7311yescharacteristic
381C23×C4C22×D7311yescharacteristic
382C4×Q8—1462no—
383C4×Q8—1462no—
384C4×Q8—1464no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—1464no—
388C4×D4—1464no—
389C4×D4—1462no—
390C4×D4—1462no—
391C4×D4—1464no—
392C4×D4—1462no—
393C4×D4—1462no—
394#117—1462no—
395#117—1462no—
396#117—1468no—
397#117—1468no—
398#117—1464no—
399#117—1464no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—734no—
406C2×C4⋊C4—734no—
407C2×C4⋊C4—731no—
408C2×C4⋊C4—731no—
409C2×C4⋊C4—731no—
410C2×C4⋊C4—731no—
411C2×C4⋊C4—731no—
412C2×C4⋊C4—1464no—
413C2×C4⋊C4—1464no—
414C2×C4⋊C4—1464no—
415C2×C4⋊C4—1462no—
416C2×C4⋊C4—1462no—
417C2×C4⋊C4—1462no—
418C2×C4⋊C4C4×D7311yescharacteristic
419C2×C22⋊C4—731no—
420C2×C22⋊C4—731no—
421C2×C22⋊C4—731no—
422C2×C22⋊C4—731no—
423C2×C22⋊C4—734no—
424C2×C22⋊C4C4×D7311yescharacteristic
425C2×C22⋊C4C22×D7314yes—
426C2×C22⋊C4C22×D7311yescharacteristic
427C2×C42—731no—
428C2×C42—731no—
429C2×C42—731no—
430C2×C42—731no—
431C2×C42—731no—
432C2×C42—1464no—
433C2×C42C4×D7311yescharacteristic
434#99—24no—
435#99—1468no—
436#99—1464no—
437#95—22no—
438#95—1464no—
439#95—1462no—
440C24—731no—
441C24C2×C4×D7311yescharacteristic
442C24C23×D7311yescharacteristic
443#41—14616no—
444#41—14616no—
445C2×Q8—734no—
446C2×Q8—1462no—
447C2×Q8—1462no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—734no—
451C2×D4—732no—
452C2×D4—732no—
453C2×D4—1462no—
454C2×D4—1462no—
455C2×D4—1462no—
456C2×D4—1462no—
457C2×D4D4×D7312yes—
458C2×D4Q8×D7312yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—5841no—
465C22×C4—5841no—
466C22×C4—5841no—
467C22×C4—5841no—
468C22×C4—731no—
469C22×C4—731no—
470C22×C4—734no—
471C22×C4—731no—
472C22×C4—731no—
473C22×C4—731no—
474C22×C4—731no—
475C22×C4—734no—
476C22×C4—732no—
477C22×C4—732no—
478C22×C4—734no—
479C22×C4—734no—
480C22×C4—731no—
481C22×C4—734no—
482C22×C4—1462no—
483C22×C4—1462no—
484C22×C4—1462no—
485C22×C4—1464no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1462no—
490C22×C4C2×C4×D7311yescharacteristic
491C22×C4C2×C4×D7311yescharacteristic
492C22×C4C2×C4×D7311yescharacteristic
493C22×C4C2×C4×D7311yescharacteristic
494C22×C4C2×C4×D7311yescharacteristic
495C22×C4D4×D7312yes—
496C22×C4D4×D7312yes—
497C4⋊C4—22no—
498C4⋊C4—82no—
499C4⋊C4—2928no—
500C4⋊C4—5844no—
501C4⋊C4—5842no—
502C4⋊C4—732no—
503C4⋊C4—732no—
504C4⋊C4—734no—
505C4⋊C4—732no—
506C4⋊C4—732no—
507C4⋊C4—734no—
508C4⋊C4—1462no—
509C4⋊C4—1462no—
510C4⋊C4—1462no—
511C4⋊C4—1462no—
512C4⋊C4—1461no—
513C4⋊C4—1461no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—1462no—
519C22⋊C4—1464no—
520C22⋊C4—1464no—
521C22⋊C4—1462no—
522C22⋊C4—1462no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C42—21no—
526C42—21no—
527C42—2928no—
528C42—1462no—
529C42—1462no—
530C42—1462no—
531C42—1462no—
532C42—1462no—
533C23—21no—
534C23—21no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—2921no—
540C23—2921no—
541C23—732no—
542C23—1461no—
543C23—1461no—
544C23C4⋊C4×D7312yes—
545C23C22×C4×D7311yescharacteristic
546C23C2×D4×D7312yes—
547C23C2×D4×D7311yescharacteristic
548C23C2×Q8×D7311yescharacteristic
549C23#41×D7312yes—
550Q8—1468no—
551D4—24no—
552D4—24no—
553D4—1468no—
554D4—1464no—
555D4—1464no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2924no—
574C2×C4—2924no—
575C2×C4—2924no—
576C2×C4—2924no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—5842no—
580C2×C4—5842no—
581C2×C4—5842no—
582C2×C4—732no—
583C2×C4—732no—
584C2×C4—732no—
585C2×C4—732no—
586C2×C4—732no—
587C2×C4—732no—
588C2×C4—738no—
589C2×C4—738no—
590C2×C4—732no—
591C2×C4—732no—
592C2×C4—732no—
593C2×C4—1468no—
594C2×C4—1461no—
595C2×C4—1461no—
596C2×C4—1468no—
597C2×C4—1461no—
598C2×C4—1461no—
599C2×C4C22⋊C4×D7311yescharacteristic
600C2×C4C22⋊C4×D7311yescharacteristic
601C2×C4C22⋊C4×D7312yes—
602C2×C4C4⋊C4×D7312yes—
603C22—22no—
604C22—21no—
605C22—22no—
606C22—21no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—41no—
614C22—41no—
615C22—2922no—
616C22—2922no—
617C22—2921no—
618C22—2921no—
619C22—1462no—
620C22C2×C22⋊C4×D7311yescharacteristic
621C22C2×C4⋊C4×D7311yescharacteristic
622C22#117×D7311yescharacteristic
623C22#121×D7312yes—
624C22C22⋊Q8×D7312yes—
625C4—21no—
626C4—21no—
627C4—22no—
628C4—22no—
629C4—41no—
630C4—41no—
631C4—84no—
632C4—2921no—
633C4—2921no—
634C4—5844no—
635C4—734no—
636C4—734no—
637C4—1462no—
638C4—1462no—
639C4—1462no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—22no—
644C2—42no—
645C2—2922no—
646C2#380×D7311yescharacteristic
647C2#2261838911yescharacteristic
648C2#2261839311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC73×#1799C2
socleC22×C73C22×C22⋊C4
prime radicalC22×#11924027C22
cosocleC24×C73C24
hypercenter#1799D73
hypocenterC73#20634
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #22612548C2semidirect
4. #22609919C2semidirect
5. #22609918C2semidirect
6. #22609917C2semidirect
7. #22609916C2semidirect
8. #22609662C2semidirect
9. C73×#1799C2semidirect
13. C2×C4×Dic146C4semidirect
14. C2×#14556556C4semidirect
16. C2×C4×C22⋊D73C4semidirect
18. C2×#14556551C4semidirect
20. C2×#14556548C4semidirect
21. C2×#14556547C4semidirect
24. C22×#11924007C4semidirect
26. C2×C4⋊C4×D73C4semidirect
120. C2×Dic146C4⋊C4semidirect
125. C2×C22⋊D73C4⋊C4semidirect
134. C22×Dic73C4⋊C4semidirect
153. C2×C4×D73C4⋊C4semidirect
332. #1799D73semidirect
334. C73#20634semidirect

Maximal subgroups

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

subgroupindex
C2×#179890662
C2×#179885592
#226125482
#226099192
#226099182
#226099172
#226099162
#226096622
C73×#17992
#2063473