Finite Group Databasebeta

← #34015938

Subgroups — #34015938

Order 18688.

1246 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626608C212yesmaximal, complemented
2#22625193C212yesmaximal, complemented
3#22625190C212yesmaximal, complemented
4#22625188C212yesmaximal, complemented
5#22625186C212yesmaximal, complemented
6#22625164C212yesmaximal, complemented
7#22625162C212yesmaximal, complemented
8C2×C4×#11924028C211yesmaximal, characteristic
9#17989609—22no—
10#17989608C2214yes—
11#17989606—22no—
12#17989603C2214yes—
13#17989591—22no—
14#17989558C2214yes—
15C4×#11924038—22no—
16#17989433C2214yes—
17#17989432C2214yes—
18#17989431C2214yes—
19#17989430C2214yes—
20C22×#11924028C411yescharacteristic
21C4×#11924028—22no—
22C4×#11924028—22no—
23C4×#11924028—22no—
24C4×#11924028—22no—
25C2×C4×Dic146C411yescharacteristic
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×D292C411yescharacteristic
28C2×C4×D292C2211yescharacteristic
29C2×C4×C22⋊D73C411yescharacteristic
30C2×C4×C22⋊D73C411yescharacteristic
31C2×C4×C22⋊D73C2211yescharacteristic
32C2×C4×C22⋊D73C2211yescharacteristic
33C2×#14556550C2211yescharacteristic
34C2×#14556548C411yescharacteristic
35C2×#14556548C2211yescharacteristic
36C2×C42×D73C411yescharacteristic
37C2×C42×D73C2211yescharacteristic
38C22×C42×C73C411yescharacteristic
39C2×#11924038—24no—
40C4⋊#10596833—24no—
41C4⋊#10596833—24no—
42#14556648—24no—
43C22⋊#10596833C2318yes—
44#14556646—24no—
45C4×#10596833—24no—
46C2×#11924028—22no—
47C2×#11924028—22no—
48C2×#11924028—24no—
49C2×#11924028—24no—
50C22×Dic146C2×C411yescharacteristic
51C22×D292C2×C411yescharacteristic
52C22×C22⋊D73C2×C411yescharacteristic
53C22×C22⋊D73C2×C411yescharacteristic
54C22×C4×D73C2×C411yescharacteristic
55C22×C4×D73C2×C411yescharacteristic
56C22×C4×D73C2×C411yescharacteristic
57C22×C4×D73C2×C411yescharacteristic
58C22×C4×D73C2×C411yescharacteristic
59C22×C4×D73C2311yescharacteristic
60C4×Dic146—22no—
61C4×Dic146—22no—
62C4×Dic146—22no—
63C4×Dic146—22no—
64C4×D292—22no—
65C4×D292—22no—
66C4×D292—22no—
67C4×D292—22no—
68C4×C22⋊D73—22no—
69C4×C22⋊D73—22no—
70C4×C22⋊D73—22no—
71C4×C22⋊D73—22no—
72C4×C22⋊D73—22no—
73C4×C22⋊D73—22no—
74C4×C22⋊D73—22no—
75C4×C22⋊D73—22no—
76#14556550—22no—
77#14556550—22no—
78#14556548—22no—
79#14556548—22no—
80#14556548—22no—
81#14556548—22no—
82C2×C4⋊Dic73C2×C411yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×#11924007C2×C411yescharacteristic
87C2×#11924007C2311yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2311yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2311yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2×C411yescharacteristic
96C2×C4×Dic73C2×C411yescharacteristic
97C2×C4×Dic73C2×C411yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C42×D73—21no—
101C42×D73—21no—
102C42×D73—21no—
103C42×D73—21no—
104C42×D73D412yes—
105C42×D73D412yes—
106C42×D73D412yes—
107C42×D73D412yes—
108C23×C4×C73C2×C411yescharacteristic
109C23×C4×C73C2×C411yescharacteristic
110C23×C4×C73C2×C411yescharacteristic
111C2×C42×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73—21no—
115C2×C42×C73C2×C411yescharacteristic
116C2×C42×C73C2×C411yescharacteristic
117C2×C42×C73C2×C411yescharacteristic
118C2×C42×C73C2×C411yescharacteristic
119#11924038—48no—
120C2×#10596833—28no—
121C23×D73C22×C411yescharacteristic
122C23×D73C22×C411yescharacteristic
123#11924028—216no—
124#11924028—216no—
125C2×Dic146—22no—
126C2×Dic146—22no—
127C2×Dic146—22no—
128C2×D292—22no—
129C2×D292—22no—
130C2×D292—22no—
131C2×C22⋊D73—22no—
132C2×C22⋊D73—22no—
133C2×C22⋊D73—22no—
134C2×C22⋊D73—22no—
135C2×C22⋊D73—22no—
136C2×C22⋊D73—22no—
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C22×Dic73C2411yescharacteristic
143C2×C4×D73—21no—
144C2×C4×D73—21no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—42no—
153C2×C4×D73—42no—
154C2×C4×D73—42no—
155C2×C4×D73—42no—
156C2×C4×D73C22⋊C412yes—
157C2×C4×D73C22⋊C412yes—
158C2×C4×D73C22⋊C412yes—
159C2×C4×D73C22⋊C412yes—
160C2×C4×D73M1614yescomplemented
161C2×C4×D73C2×D412yes—
162C2×C4×D73C2×D412yes—
163C4⋊Dic73—22no—
164C4⋊Dic73—22no—
165#11924007—22no—
166#11924007—22no—
167#11924007—22no—
168#11924007—22no—
169C22⋊Dic73—22no—
170C22⋊Dic73—22no—
171#11924005—22no—
172#11924005—22no—
173#11924005—22no—
174#11924005—22no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73C22⋊C412yes—
182C4×Dic73C22⋊C412yes—
183C4×Dic73C2×D412yes—
184C4×Dic73C2×D412yes—
185C4×Dic73C2×D412yes—
186C4×Dic73C2×D412yes—
187C24×C73C22×C411yescharacteristic
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—22no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—42no—
196C22×C4×C73—42no—
197C22×C4×C73M1614yescomplemented
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C42×C73—21no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—21no—
210C42×C73C22⋊C411yescharacteristic
211C42×C73C22⋊C411yescharacteristic
212C42×C73C22⋊C411yescharacteristic
213C42×C73C22⋊C411yescharacteristic
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—41no—
217C23×C73—41no—
218C23×C73C2×M1612yes—
219C23×C73C23×C411yescharacteristic
220C22×D73—21no—
221C22×D73—21no—
222C22×D73—21no—
223C22×D73—21no—
224C22×D73—41no—
225C22×D73—41no—
226C22×D73—41no—
227C22×D73—41no—
228C22×D73C2×C22⋊C412yes—
229C22×D73C2×M1612yes—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—24no—
233C2×C4×C73—24no—
234C2×C4×C73—22no—
235C2×C4×C73—22no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—42no—
239C2×C4×C73—42no—
240C2×C4×C73—42no—
241C2×C4×C73—42no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73C2×C22⋊C411yescharacteristic
245C2×C4×C73C2×C22⋊C411yescharacteristic
246C2×C4×C73C2×C22⋊C411yescharacteristic
247C2×C4×C73C2×C22⋊C411yescharacteristic
248C2×C4×C73C2×C22⋊C411yescharacteristic
249C2×C4×C73C2×C22⋊C411yescharacteristic
250C2×C4×C73C2×M1612yes—
251C2×C4×C73C2×M1612yes—
252C2×C4×C73C2×M1612yes—
253C22⋊D73—28no—
254C22⋊D73—28no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73C2×C22⋊C412yes—
266C2×Dic73C2×C22⋊C412yes—
267C2×Dic73C2×M1612yes—
268C2×Dic73C22×D412yes—
269D292—28no—
270C4×D73—24no—
271C4×D73—24no—
272C4×D73—24no—
273C4×D73—24no—
274C4×D73—24no—
275C4×D73—24no—
276C4×D73—42no—
277C4×D73—42no—
278C4×D73—42no—
279C4×D73—42no—
280C4×D73—42no—
281C4×D73—42no—
282Dic146—28no—
283#10596833—48no—
284C22×C73—21no—
285C22×C73—21no—
286C22×C73—22no—
287C22×C73—42no—
288C22×C73—42no—
289C22×C73—41no—
290C22×C73—41no—
291C22×C73C22×C22⋊C411yescharacteristic
292C22×C73C22×M1611yescharacteristic
293C22×C73C22×M1611yescharacteristic
294C2×D73—22no—
295C2×D73—22no—
296C2×D73—22no—
297C2×D73—22no—
298C2×D73—42no—
299C2×D73—42no—
300C2×D73—42no—
301C2×D73—41no—
302C2×D73—41no—
303C2×D73—42no—
304C4×C73—22no—
305C4×C73—21no—
306C4×C73—21no—
307C4×C73—41no—
308C4×C73—41no—
309C4×C73#40712yes—
310C4×C73#40712yes—
311C4×C73#41012yes—
312C4×C73#41312yes—
313Dic73—22no—
314Dic73—22no—
315Dic73—22no—
316Dic73—22no—
317Dic73—41no—
318Dic73—41no—
319#17361—731nomaximal, Sylow
320C2×C73—21no—
321C2×C73—21no—
322C2×C73—42no—
323C2×C73C2×#40711yescharacteristic
324C2×C73C2×#41011yescharacteristic
325C2×C73C2×#41311yescharacteristic
326D73—42no—
327D73—42no—
328C2×C4×#41—731no—
329#2920—732no—
330#1467—732no—
331#1466—732no—
332#1465—732no—
333#1465—732no—
334#1458—732no—
335#1458—732no—
336C73#1736111yescharacteristic, complemented, Sylow
337C22×#41—731no—
338C4×#41—1462no—
339C4×#41—1462no—
340C4×#41—1462no—
341C4×#41—1462no—
342C2×C4×Q8—731no—
343C2×C4×Q8—731no—
344C2×C4×D4—731no—
345C2×C4×D4—731no—
346C2×C4×D4—731no—
347C2×C4×D4—731no—
348C2×C4×D4—731no—
349C2×C4×D4—731no—
350C2×#117—731no—
351C2×#117—731no—
352C2×#117—731no—
353C22×C42—731no—
354C22×C42—731no—
355C22×C42#6440811yescharacteristic
356#432—734no—
357#432—1462no—
358#431—734no—
359#431—1462no—
360#423—1462no—
361#407—734no—
362C4×M16—1462no—
363#324—734no—
364#324—734no—
365#323—734no—
366#323—734no—
367C2×#41—1462no—
368C2×#41—1462no—
369C2×#41—1464no—
370C2×#41—1464no—
371C22×Q8—731no—
372C22×D4—731no—
373C22×D4—731no—
374C22×D4—731no—
375C23×C4—731no—
376C23×C4—731no—
377C23×C4—731no—
378C23×C4—731no—
379C23×C4—731no—
380C23×C4—731no—
381C23×C4C2×#6440811yescharacteristic
382C23×C4C2×#6440811yescharacteristic
383C23×C4C2×#6440811yescharacteristic
384C2×M16—1464no—
385C4×Q8—1462no—
386C4×Q8—1462no—
387C4×Q8—1462no—
388C4×Q8—1462no—
389C4×D4—1462no—
390C4×D4—1462no—
391C4×D4—1462no—
392C4×D4—1462no—
393C4×D4—1462no—
394C4×D4—1462no—
395C4×D4—1462no—
396C4×D4—1462no—
397C4×D4—1462no—
398C4×D4—1462no—
399C4×D4—1462no—
400C4×D4—1462no—
401#117—1462no—
402#117—1462no—
403#117—1462no—
404#117—1462no—
405#117—1462no—
406#117—1462no—
407C2×C4⋊C4—731no—
408C2×C4⋊C4—731no—
409C2×C4⋊C4—731no—
410C2×C4⋊C4—731no—
411C2×C4⋊C4—731no—
412C2×C4⋊C4—731no—
413C2×C22⋊C4—731no—
414C2×C22⋊C4—731no—
415C2×C22⋊C4—731no—
416C2×C22⋊C4—731no—
417C2×C22⋊C4—731no—
418C2×C22⋊C4—731no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—731no—
424C2×C42—731no—
425C2×C42—731no—
426C2×C42—732no—
427C2×C42—732no—
428C2×C42—732no—
429C2×C42—732no—
430C2×C42—731no—
431C2×C42—731no—
432C2×C42—731no—
433C2×C42—1461no—
434C2×C42—1461no—
435C2×C42—1461no—
436C2×C42—1461no—
437C2×C42C2×#6440811yescharacteristic
438C2×C42C2×#6440811yescharacteristic
439C2×C42C2×#6440811yescharacteristic
440C2×C42C2×#6440811yescharacteristic
441C4⋊C8—1464no—
442C4⋊C8—1464no—
443C22⋊C8—738no—
444C22⋊C8—1464no—
445#97—1464no—
446C4×C8—1464no—
447C24—731no—
448C24—731no—
449C24C22×#6440811yescharacteristic
450#41—14616no—
451#41—14616no—
452C2×Q8—1462no—
453C2×Q8—1462no—
454C2×Q8—1462no—
455C2×D4—1462no—
456C2×D4—1462no—
457C2×D4—1462no—
458C2×D4—1462no—
459C2×D4—1462no—
460C2×D4—1462no—
461C2×D4—1462no—
462C2×D4—1462no—
463C2×D4—1462no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—2922no—
474C22×C4—2922no—
475C22×C4—2922no—
476C22×C4—2922no—
477C22×C4—731no—
478C22×C4—731no—
479C22×C4—732no—
480C22×C4—732no—
481C22×C4—731no—
482C22×C4—731no—
483C22×C4—731no—
484C22×C4—731no—
485C22×C4—734no—
486C22×C4—732no—
487C22×C4—732no—
488C22×C4—732no—
489C22×C4—732no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1462no—
495C22×C4—1462no—
496C22×C4—1462no—
497C22×C4—1461no—
498C22×C4—1461no—
499C22×C4#1192403814yescomplemented
500C22×C4C22×#6440811yescharacteristic
501C22×C4C22×#6440811yescharacteristic
502C22×C4C22×#6440811yescharacteristic
503C22×C4C22×#6440811yescharacteristic
504C22×C4C22×#6440811yescharacteristic
505C22×C4C22×#6440811yescharacteristic
506M16—2928no—
507C2×C8—1468no—
508C4⋊C4—1462no—
509C4⋊C4—1462no—
510C4⋊C4—1462no—
511C4⋊C4—1462no—
512C4⋊C4—1462no—
513C4⋊C4—1462no—
514C22⋊C4—1462no—
515C22⋊C4—1462no—
516C22⋊C4—1462no—
517C22⋊C4—1462no—
518C22⋊C4—1462no—
519C22⋊C4—1462no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—732no—
527C42—732no—
528C42—732no—
529C42—732no—
530C42—732no—
531C42—732no—
532C42—1461no—
533C42—1461no—
534C42—1461no—
535C42—1461no—
536C42—1461no—
537C42—1461no—
538C42C22⋊#6440811yescharacteristic
539C42C22⋊#6440811yescharacteristic
540C42C22⋊#6440811yescharacteristic
541C42C22⋊#6440811yescharacteristic
542C23—21no—
543C23—21no—
544C23—41no—
545C23—41no—
546C23—2921no—
547C23—2921no—
548C23—2921no—
549C23—2921no—
550C23—732no—
551C23—732no—
552C23—1461no—
553C23—1461no—
554C23—1461no—
555C23—1461no—
556C23C2×#1192403812yes—
557C23C23×#6440811yescharacteristic
558Q8—1468no—
559D4—1468no—
560D4—1468no—
561D4—1468no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—2922no—
577C2×C4—2922no—
578C2×C4—2922no—
579C2×C4—2922no—
580C2×C4—2922no—
581C2×C4—2922no—
582C2×C4—2921no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—732no—
587C2×C4—732no—
588C2×C4—732no—
589C2×C4—732no—
590C2×C4—1461no—
591C2×C4—1461no—
592C2×C4—1461no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4—1461no—
596C2×C4—1464no—
597C2×C4—1464no—
598C2×C4—1464no—
599C2×C4—1464no—
600C2×C4—1464no—
601C2×C4—1464no—
602C2×C4C2×C22⋊#6440811yescharacteristic
603C2×C4C2×C22⋊#6440811yescharacteristic
604C2×C4C2×C22⋊#6440811yescharacteristic
605C2×C4C2×C22⋊#6440811yescharacteristic
606C2×C4C2×C22⋊#6440811yescharacteristic
607C2×C4C2×C22⋊#6440811yescharacteristic
608C2×C4D73⋊M1612yes—
609C2×C4C2×#1192403812yes—
610C2×C4C2×#1192403812yes—
611C8—2928no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—42no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—2922no—
620C22—2922no—
621C22—2922no—
622C22—2922no—
623C22—2921no—
624C22—2921no—
625C22—1462no—
626C22—1462no—
627C22—1462no—
628C22—1462no—
629C22C22×C22⋊#6440811yescharacteristic
630C22C2×D73⋊M1611yescharacteristic
631C22C22×#1192403811yescharacteristic
632C4—22no—
633C4—21no—
634C4—21no—
635C4—41no—
636C4—41no—
637C4—2921no—
638C4—2921no—
639C4—1462no—
640C4—1462no—
641C4—1462no—
642C4—1462no—
643C4#1798955812yes—
644C4#1798955812yes—
645C4#1798956612yes—
646C4#1798957312yes—
647C2—21no—
648C2—21no—
649C2—42no—
650C2—2922no—
651C2—2922no—
652C2C2×#1798955811yescharacteristic
653C2C2×#1798956611yescharacteristic
654C2C2×#1798957311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC22×C42×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC22×#11924028C4
cosocleC22×Dic73C24
hypercenterC22×C42#64408
hypocenterC73#17361
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #22626608C2semidirect
2. #22625193C2semidirect
3. #22625190C2semidirect
4. #22625188C2semidirect
5. #22625186C2semidirect
6. #22625164C2semidirect
7. #22625162C2semidirect
160. C2×C4×D73M16semidirect
197. C22×C4×C73M16semidirect
336. C73#17361semidirect
499. C22×C4#11924038semidirect

Maximal subgroups

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

subgroupindex
#226266082
#226251932
#226251902
#226251882
#226251862
#226251642
#226251622
C2×C4×#119240282
#1736173