Finite Group Databasebeta

← #34020032

Subgroups — #34020032

Order 18688.

1834 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D73⋊#99C212yesmaximal
2#22626367C212yesmaximal, complemented
3#22625678C212yesmaximal, complemented
4C4×#14556650C212yesmaximal, complemented
5#22625676C212yesmaximal, complemented
6C4×#14556649C212yesmaximal, complemented
7C2×#17989465C212yesmaximal, complemented
8C2×#17989059C211yesmaximal, characteristic
9C22×C22⋊#64408C2214yes—
10C2×#14556650C2214yes—
11D73⋊#99C4116yescomplemented
12C2×#14556649C2214yes—
13C22⋊C4×#64408—28no—
14C4×C22⋊#64408C2214yescomplemented
15C4×C22⋊#64408C2214yescomplemented
16#17989465C2214yescomplemented
17#17989465C2214yescomplemented
18C22×D4×D73C2211yescharacteristic
19#17989059—28no—
20C2×C4×D292C2211yescharacteristic
21C2×D4×Dic73C411yescharacteristic, complemented
22C2×#14556553C2211yescharacteristic
23C2×C4×C22⋊D73C411yescharacteristic, complemented
24C2×C4×C22⋊D73C2211yescharacteristic
25C2×#14556551C411yescharacteristic, complemented
26C2×#14556551C2211yescharacteristic
27C2×#14556549C411yescharacteristic, complemented
28C2×#14556548C411yescharacteristic, complemented
29C22×#11924005C411yescharacteristic, complemented
30C22×#11924005C2211yescharacteristic
31C2×C22⋊C4×D73C411yescharacteristic, complemented
32C2×C22⋊C4×D73C2211yescharacteristic
33C2×C4×D4×C73C411yescharacteristic, complemented
34C23×#64408—24no—
35C2×C22⋊#64408—24no—
36C2×C22⋊#64408—28no—
37C2×C22⋊#64408C2×C4116yescomplemented
38C2×C22⋊#64408C2318yes—
39C2×C4×#64408—24no—
40C2×C4×#64408—24no—
41#14556650C2×C4116yescomplemented
42#14556649C2×C4116yescomplemented
43(C2×#64408)⋊C4—24no—
44(C2×#64408)⋊C4—24no—
45C24×D73C2×C411yescharacteristic
46C24×D73C2311yescharacteristic
47C22×D292C2311yescharacteristic
48C22×C22⋊D73C2×C411yescharacteristic
49C22×C22⋊D73C2311yescharacteristic
50C2×D4×D73—24no—
51C2×D4×D73—24no—
52C2×D4×D73C2×C418yes—
53C23×Dic73C2×C411yescharacteristic
54C23×Dic73C2×C411yescharacteristic, complemented
55C22×C4×D73C2×C411yescharacteristic
56C22×C4×D73C2×C411yescharacteristic, complemented
57C22×C4×D73C2×C411yescharacteristic, complemented
58C22×C4×D73C2311yescharacteristic
59C22×C4×D73C2311yescharacteristic
60C4×D292—24no—
61D4×Dic73—24no—
62#14556553—24no—
63C4×C22⋊D73—24no—
64C4×C22⋊D73—24no—
65#14556551—24no—
66#14556551—24no—
67#14556549—24no—
68#14556548—24no—
69C2×C4⋊Dic73C2×C411yescharacteristic, complemented
70C2×#11924007C2×C411yescharacteristic, complemented
71C2×#11924007C2×C411yescharacteristic, complemented
72C2×C22⋊Dic73C2×C411yescharacteristic
73C2×C22⋊Dic73C2×C411yescharacteristic, complemented
74C2×#11924005—24no—
75C2×#11924005—24no—
76C2×#11924005C2×C411yescharacteristic
77C2×#11924005C2×C411yescharacteristic
78C2×#11924005C2×C411yescharacteristic
79C2×#11924005C2×C411yescharacteristic
80C2×#11924005C2×C411yescharacteristic, complemented
81C2×#11924005C2×C411yescharacteristic, complemented
82C2×#11924005C2311yescharacteristic
83C2×#11924005C2311yescharacteristic
84C22⋊C4×D73—24no—
85C22⋊C4×D73D418yes—
86C2×C4×Dic73C2×C411yescharacteristic, complemented
87C2×C4×Dic73C2×C411yescharacteristic, complemented
88C2×C4×Dic73C2×C411yescharacteristic, complemented
89C22×D4×C73C2×C411yescharacteristic
90C23×C4×C73C2×C411yescharacteristic
91C23×C4×C73C2×C411yescharacteristic, complemented
92C4×D4×C73—24no—
93C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
94C2×C22⋊C4×C73C2×C411yescharacteristic
95C2×C22⋊C4×C73C2×C411yescharacteristic, complemented
96C2×C42×C73C2×C411yescharacteristic, complemented
97C22×#64408—28no—
98C22×#64408—216no—
99C22×#64408—84no—
100C22×#64408—84no—
101C22⋊#64408—216no—
102C22⋊#64408—28no—
103C22⋊#64408C22×C4116yes—
104C4×#64408—84no—
105C4×#64408—84no—
106C23×D73—22no—
107C23×D73—22no—
108C23×D73—81no—
109C23×D73—81no—
110C23×D73—81no—
111C23×D73—81no—
112C23×D73C4214yescomplemented
113C23×D73C22×C411yescharacteristic
114C23×D73C22×C411yescharacteristic
115C23×D73C22×C414yes—
116C23×D73C2×D414yes—
117C23×D73#4114yes—
118C23×D73C2411yescharacteristic
119C2×D292—22no—
120C2×D292—22no—
121C2×D292C22×C414yes—
122C2×C22⋊D73—22no—
123C2×C22⋊D73—22no—
124C2×C22⋊D73—22no—
125C2×C22⋊D73—22no—
126C2×C22⋊D73C4214yescomplemented
127C2×C22⋊D73C22×C414yes—
128D4×D73—216no—
129D4×D73—216no—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—81no—
133C22×Dic73—81no—
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—81no—
144C2×C4×D73—81no—
145C2×C4×D73—81no—
146C2×C4×D73—81no—
147C2×C4×D73C4214yescomplemented
148C2×C4×D73C2×D414yes—
149C2×C4×D73C2×D414yes—
150C4⋊Dic73—22no—
151#11924007—22no—
152#11924007—22no—
153C22⋊Dic73—22no—
154C22⋊Dic73C22⋊C414yes—
155#11924005—22no—
156#11924005—22no—
157#11924005—22no—
158#11924005—22no—
159#11924005—22no—
160#11924005—22no—
161#11924005C22⋊C414yes—
162#11924005C22⋊C414yes—
163C4×Dic73—22no—
164C4×Dic73—22no—
165C4×Dic73—22no—
166C24×C73C22×C411yescharacteristic
167C24×C73C22×C411yescharacteristic
168C2×D4×C73—22no—
169C2×D4×C73—22no—
170C2×D4×C73C4214yescomplemented
171C22×C4×C73—22no—
172C22×C4×C73—22no—
173C22×C4×C73—81no—
174C22×C4×C73—81no—
175C22×C4×C73C22×C411yescharacteristic
176C22×C4×C73C22×C411yescharacteristic
177C22×C4×C73C22×C411yescharacteristic
178C22×C4×C73C22×C411yescharacteristic
179C22×C4×C73C22×C411yescharacteristic
180C4⋊C4×C73—22no—
181C22⋊C4×C73—22no—
182C22⋊C4×C73C22⋊C414yes—
183C42×C73—22no—
184C23×C73—21no—
185C23×C73—21no—
186C23×C73—41no—
187C23×C73—41no—
188C23×C73—41no—
189C23×C73—41no—
190C23×C73C2×C4212yes—
191C23×C73C2×C4212yes—
192C23×C73C2×C22⋊C412yes—
193C23×C73#11712yes—
194C23×C73C23×C411yescharacteristic
195C22×D73—21no—
196C22×D73—21no—
197C22×D73—28no—
198C22×D73—41no—
199C22×D73—41no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—44no—
203C22×D73—44no—
204C22×D73—41no—
205C22×D73—41no—
206C22×D73—82no—
207C22×D73—82no—
208C22×D73—84no—
209C22×D73—84no—
210C22×D73—84no—
211C22×D73—84no—
212C22×D73C2×C4212yes—
213C22×D73C2×C4212yes—
214C22×D73C2×C22⋊C412yes—
215C22×D73#11712yes—
216C22×D73C4×D418yes—
217C22×D73C4×D418yes—
218C22×D73C23×C412yes—
219C22×D73C22×D412yes—
220C22×D73C2×#4112yes—
221C2×#64408—216no—
222C2×#64408—48no—
223C2×#64408—48no—
224C2×#64408—816no—
225D4×C73—28no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—82no—
235C2×C4×C73—82no—
236C2×C4×C73C2×C4212yes—
237C2×C4×C73C2×C22⋊C412yes—
238C2×C4×C73C2×C22⋊C412yes—
239C22⋊D73—28no—
240C22⋊D73—28no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—82no—
250C2×Dic73—82no—
251C2×Dic73C2×C4212yes—
252C2×Dic73C2×C22⋊C412yes—
253C2×Dic73C2×C22⋊C412yes—
254D292—28no—
255C4×D73—28no—
256C4×D73—44no—
257C4×D73—44no—
258C4×D73—82no—
259C4×D73—82no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—22no—
263C22×C73—22no—
264C22×C73—22no—
265C22×C73—42no—
266C22×C73—42no—
267C22×C73—42no—
268C22×C73—42no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73C4×C22⋊C414yes—
272C22×C73C22×C4211yescharacteristic
273C22×C73C22×C22⋊C411yescharacteristic
274C22×C73C2×#11711yescharacteristic
275C2×D73—22no—
276C2×D73—22no—
277C2×D73—22no—
278C2×D73—22no—
279C2×D73—22no—
280C2×D73—48no—
281C2×D73—42no—
282C2×D73—42no—
283C2×D73—48no—
284C2×D73—42no—
285C2×D73—42no—
286C2×D73—42no—
287C2×D73—41no—
288C2×D73—41no—
289C2×D73—42no—
290C2×D73—88no—
291C2×D73C4×C22⋊C414yes—
292C2×D73C2×C4×D414yes—
293#64408—416no—
294C4×C73—22no—
295C4×C73—22no—
296C4×C73—22no—
297C4×C73—41no—
298C4×C73—41no—
299Dic73—22no—
300Dic73—22no—
301Dic73—22no—
302Dic73—41no—
303Dic73—41no—
304#20392—731nomaximal, Sylow
305C2×C73—21no—
306C2×C73—21no—
307C2×C73—24no—
308C2×C73—42no—
309C2×C73C2×C4×C22⋊C411yescharacteristic
310C2×C73#288311yescharacteristic
311C2×C73#288311yescharacteristic
312D73—24no—
313D73—24no—
314D73—42no—
315C2×#518—731no—
316C22×#99—732no—
317#2273—732no—
318C4×#99—732no—
319C4×#99—732no—
320C4×#99—732no—
321C4×#99—732no—
322C2×#342—732no—
323C73#2039211yescharacteristic, complemented, Sylow
324C23×D4—731no—
325#518—1468no—
326C2×C4×D4—731no—
327C2×C4×D4—731no—
328C2×C4×D4—731no—
329C2×C4×D4—731no—
330C2×C4×D4—731no—
331C2×C4×D4—731no—
332C2×C4×D4—731no—
333C2×C4×D4#6440811yescharacteristic, complemented
334C2×#117—731no—
335C2×#117—731no—
336C22×C22⋊C4—731no—
337C22×C22⋊C4—734no—
338C22×C22⋊C4—731no—
339C22×C22⋊C4—731no—
340C22×C22⋊C4—731no—
341C2×#99—734no—
342C2×#99—7316no—
343C2×#99—734no—
344C4×C22⋊C4—734no—
345C4×C22⋊C4—734no—
346C4×C22⋊C4—1468no—
347#342—734no—
348#342—734no—
349C25—731no—
350C25—731no—
351C22×D4—731no—
352C22×D4—731no—
353C22×D4—738no—
354C22×D4—731no—
355C22×D4—1464no—
356C22×D4—1464no—
357C22×D4C2×#6440811yescharacteristic
358C23×C4—731no—
359C23×C4—731no—
360C23×C4—731no—
361C23×C4—731no—
362C23×C4—731no—
363C23×C4—731no—
364C23×C4—731no—
365C23×C4—1464no—
366C23×C4C2×#6440811yescharacteristic
367C23×C4C2×#6440811yescharacteristic, complemented
368C4×D4—24no—
369C4×D4—1464no—
370C4×D4—1464no—
371C4×D4—1464no—
372C4×D4—1464no—
373C4×D4—1464no—
374C4×D4—1464no—
375C4×D4—1464no—
376#117—1464no—
377#117—1464no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4C2×#6440811yescharacteristic, complemented
382C2×C22⋊C4—731no—
383C2×C22⋊C4—731no—
384C2×C22⋊C4—731no—
385C2×C22⋊C4—738no—
386C2×C22⋊C4—738no—
387C2×C22⋊C4—7316no—
388C2×C22⋊C4—731no—
389C2×C22⋊C4—731no—
390C2×C22⋊C4—731no—
391C2×C22⋊C4—731no—
392C2×C22⋊C4—731no—
393C2×C22⋊C4—731no—
394C2×C22⋊C4—731no—
395C2×C22⋊C4—1464no—
396C2×C22⋊C4—1464no—
397C2×C22⋊C4—1464no—
398C2×C22⋊C4—1464no—
399C2×C22⋊C4—1468no—
400C2×C22⋊C4C2×#6440811yescharacteristic
401C2×C22⋊C4C2×#6440811yescharacteristic, complemented
402C2×C42—731no—
403C2×C42—731no—
404C2×C42—731no—
405C2×C42—1464no—
406C2×C42—1464no—
407C2×C42C2×#6440811yescharacteristic, complemented
408#99—7316no—
409#99—7316no—
410#95—1464no—
411#95—1464no—
412C24—5841no—
413C24—5841no—
414C24—5841no—
415C24—5841no—
416C24—731no—
417C24—731no—
418C24—734no—
419C24—731no—
420C24—734no—
421C24—734no—
422C24—734no—
423C24—1462no—
424C24—1462no—
425C24C22×#6440811yescharacteristic
426C24C22×#6440811yescharacteristic
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—734no—
430C2×D4—734no—
431C2×D4—734no—
432C2×D4—1462no—
433C2×D4—1462no—
434C2×D4—14616no—
435C2×D4—14616no—
436C2×D4—1462no—
437C2×D4—1462no—
438C2×D4—1462no—
439C2×D4—1462no—
440C2×D4C4×#6440814yescomplemented
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—81no—
444C22×C4—81no—
445C22×C4—5841no—
446C22×C4—5841no—
447C22×C4—5841no—
448C22×C4—5841no—
449C22×C4—5844no—
450C22×C4—5844no—
451C22×C4—5841no—
452C22×C4—5841no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—734no—
456C22×C4—734no—
457C22×C4—731no—
458C22×C4—731no—
459C22×C4—731no—
460C22×C4—734no—
461C22×C4—1462no—
462C22×C4—1462no—
463C22×C4—1462no—
464C22×C4—1468no—
465C22×C4—1462no—
466C22×C4—14616no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4C22×#6440811yescharacteristic
470C22×C4C22×#6440811yescharacteristic
471C22×C4C22×#6440811yescharacteristic
472C22×C4C22×#6440811yescharacteristic
473C22×C4C22×#6440811yescharacteristic
474C4⋊C4—22no—
475C4⋊C4—1462no—
476C4⋊C4—1462no—
477C4⋊C4—1462no—
478C22⋊C4—22no—
479C22⋊C4—734no—
480C22⋊C4—734no—
481C22⋊C4—734no—
482C22⋊C4—7316no—
483C22⋊C4—1462no—
484C22⋊C4—1462no—
485C22⋊C4—1462no—
486C22⋊C4—1462no—
487C22⋊C4—1462no—
488C22⋊C4—1462no—
489C22⋊C4—1468no—
490C22⋊C4—14616no—
491C22⋊C4—1462no—
492C22⋊C4C22⋊#6440814yes—
493C42—22no—
494C42—5844no—
495C42—5844no—
496C42—1462no—
497C42—1462no—
498C42—1462no—
499C23—21no—
500C23—21no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—2921no—
506C23—2921no—
507C23—2921no—
508C23—2924no—
509C23—2921no—
510C23—2924no—
511C23—2921no—
512C23—2921no—
513C23—5844no—
514C23—5844no—
515C23—5844no—
516C23—5844no—
517C23—5842no—
518C23—5842no—
519C23—732no—
520C23—732no—
521C23—732no—
522C23—732no—
523C23—738no—
524C23—738no—
525C23—732no—
526C23—732no—
527C23—732no—
528C23—1468no—
529C23—1461no—
530C23—1461no—
531C23C2×C4×#6440812yes—
532C23C2×C4×#6440812yes—
533C23C2×C22⋊#6440812yes—
534C23#1455667012yes—
535C23C23×#6440811yescharacteristic
536D4—28no—
537D4—1468no—
538D4—1468no—
539D4—1468no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—2924no—
551C2×C4—2924no—
552C2×C4—2928no—
553C2×C4—2928no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—5842no—
559C2×C4—5842no—
560C2×C4—5842no—
561C2×C4—58416no—
562C2×C4—5842no—
563C2×C4—732no—
564C2×C4—732no—
565C2×C4—732no—
566C2×C4—1468no—
567C2×C4—14616no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4C2×C4×#6440812yes—
573C2×C4C2×C22⋊#6440812yes—
574C2×C4C2×C22⋊#6440812yes—
575C22—21no—
576C22—22no—
577C22—21no—
578C22—22no—
579C22—22no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—2922no—
587C22—2922no—
588C22—2928no—
589C22—2922no—
590C22—2922no—
591C22—2922no—
592C22—2922no—
593C22—2928no—
594C22—2921no—
595C22—2921no—
596C22—5848no—
597C22—734no—
598C22—734no—
599C22—1462no—
600C22—1462no—
601C22—1462no—
602C22—1462no—
603C22—1462no—
604C22C4×C22⋊#6440814yes—
605C22C22×C4×#6440811yescharacteristic
606C22C22×C22⋊#6440811yescharacteristic
607C22C2×#1455667011yescharacteristic
608C4—22no—
609C4—22no—
610C4—22no—
611C4—41no—
612C4—41no—
613C4—29216no—
614C4—2921no—
615C4—2921no—
616C4—1462no—
617C4—1462no—
618C4—1462no—
619C2—21no—
620C2—21no—
621C2—24no—
622C2—42no—
623C2—2922no—
624C2—1464no—
625C2—1464no—
626C2C2×C4×C22⋊#6440811yescharacteristic
627C2#2262653011yescharacteristic
628C2#2262653111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#64408
commutatorC22×C73C22×C42
FrattiniC23C23×#64408
FittingC2×C4×D4×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC22×D4×D73C22
cosocleC23×D73C24
hypercenterC2×C4×D4#64408
hypocenterC73#20392
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #22626367C2semidirect
3. #22625678C2semidirect
4. C4×#14556650C2semidirect
5. #22625676C2semidirect
6. C4×#14556649C2semidirect
7. C2×#17989465C2semidirect
11. D73⋊#99C4semidirect
14. C4×C22⋊#64408C22semidirect
15. C4×C22⋊#64408C22semidirect
16. #17989465C22semidirect
17. #17989465C22semidirect
21. C2×D4×Dic73C4semidirect
23. C2×C4×C22⋊D73C4semidirect
25. C2×#14556551C4semidirect
27. C2×#14556549C4semidirect
28. C2×#14556548C4semidirect
29. C22×#11924005C4semidirect
31. C2×C22⋊C4×D73C4semidirect
33. C2×C4×D4×C73C4semidirect
37. C2×C22⋊#64408C2×C4semidirect
41. #14556650C2×C4semidirect
42. #14556649C2×C4semidirect
54. C23×Dic73C2×C4semidirect
56. C22×C4×D73C2×C4semidirect
57. C22×C4×D73C2×C4semidirect
69. C2×C4⋊Dic73C2×C4semidirect
70. C2×#11924007C2×C4semidirect
71. C2×#11924007C2×C4semidirect
73. C2×C22⋊Dic73C2×C4semidirect
80. C2×#11924005C2×C4semidirect
81. C2×#11924005C2×C4semidirect
86. C2×C4×Dic73C2×C4semidirect
87. C2×C4×Dic73C2×C4semidirect
88. C2×C4×Dic73C2×C4semidirect
91. C23×C4×C73C2×C4semidirect
93. C2×C4⋊C4×C73C2×C4semidirect
95. C2×C22⋊C4×C73C2×C4semidirect
96. C2×C42×C73C2×C4semidirect
112. C23×D73C42semidirect
126. C2×C22⋊D73C42semidirect
147. C2×C4×D73C42semidirect
170. C2×D4×C73C42semidirect
323. C73#20392semidirect
333. C2×C4×D4#64408semidirect
367. C23×C4C2×#64408semidirect
381. C2×C4⋊C4C2×#64408semidirect
401. C2×C22⋊C4C2×#64408semidirect
407. C2×C42C2×#64408semidirect
440. C2×D4C4×#64408semidirect

Maximal subgroups

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

subgroupindex
C2×D73⋊#992
#226263672
#226256782
C4×#145566502
#226256762
C4×#145566492
C2×#179894652
C2×#179890592
#2039273