Finite Group Databasebeta

← #33094239

Subgroups — #33094239

Order 18688.

702 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613231C211yesmaximal, characteristic
2#22610547C211yesmaximal, characteristic
3#22610546C211yesmaximal, characteristic
4#22610541C211yesmaximal, characteristic
5#22610498C211yesmaximal, characteristic, complemented
6#22610496C211yesmaximal, characteristic, complemented
7#22610493C211yesmaximal, characteristic, complemented
8#22610075C211yesmaximal, characteristic, complemented
9C8×#11924007C211yesmaximal, characteristic, complemented
10C8×#11924007C211yesmaximal, characteristic, complemented
11C8×C4⋊Dic73C211yesmaximal, characteristic, complemented
12C8×C22⋊Dic73C211yesmaximal, characteristic
13C8×C22⋊Dic73C211yesmaximal, characteristic
14#22609617C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C73C211yesmaximal, characteristic
16C2×C4⋊#10596831C2211yescharacteristic
17C2×#14556520C2211yescharacteristic
18C2×#14556520C2211yescharacteristic
19C2×C22⋊#10596831C2211yescharacteristic
20C2×C22⋊#10596831C2211yescharacteristic
21C2×#14556502C2211yescharacteristic
22C2×#14556501C2211yescharacteristic
23C2×#14556501C2211yescharacteristic
24C2×C8×Dic73C2211yescharacteristic
25C2×C8×Dic73C2211yescharacteristic
26C2×C8×Dic73C2211yescharacteristic
27C2×C8×Dic73C2211yescharacteristic
28C73⋊#401C411yescharacteristic
29#17988529C411yescharacteristic
30#17988528C411yescharacteristic
31#17988527C411yescharacteristic
32#17988515C411yescharacteristic
33#17988515C411yescharacteristic
34#17988512C411yescharacteristic
35#17988510C411yescharacteristic
36C4×#11924007C2211yescharacteristic
37C4×#11924007C2211yescharacteristic
38C4×C4⋊Dic73C2211yescharacteristic
39C4×C22⋊Dic73C2211yescharacteristic
40C4×C22⋊Dic73C2211yescharacteristic
41#17988433C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C23×C8×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C4×C8×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic
56C4×C22⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×#10596831C2311yescharacteristic
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C2×C4⋊Dic73C2×C411yescharacteristic
64C2×C4⋊Dic73C2×C411yescharacteristic
65C2×#11924007C2×C411yescharacteristic
66C2×#11924007C2×C411yescharacteristic
67C2×#11924007C2×C411yescharacteristic
68C2×#11924007C2×C411yescharacteristic
69C2×C22⋊Dic73C2×C411yescharacteristic
70C2×C22⋊Dic73C2×C411yescharacteristic
71C2×C22⋊Dic73C2×C411yescharacteristic
72C2×C22⋊Dic73C2×C411yescharacteristic
73C2×C4×Dic73C2311yescharacteristic
74C2×C4×Dic73C2311yescharacteristic
75C2×C4×Dic73C2311yescharacteristic
76C2×C4×Dic73C2311yescharacteristic
77C4⋊#10596831—22no—
78#14556520—22no—
79#14556520—22no—
80C22⋊#10596831—22no—
81C22⋊#10596831—22no—
82#14556502—22no—
83#14556501—22no—
84#14556501—22no—
85C8×Dic73—22no—
86C8×Dic73—22no—
87C8×Dic73—22no—
88C8×Dic73—22no—
89#14556498C2×C411yescharacteristic
90#14556498C2×C411yescharacteristic
91#14556498C2×C411yescharacteristic
92#14556498C2×C411yescharacteristic
93#14556498C2×C411yescharacteristic
94#14556498C2×C411yescharacteristic
95#14556498C2×C411yescharacteristic
96#14556498C2×C411yescharacteristic
97#14556498C2×C411yescharacteristic
98#14556498C2×C411yescharacteristic
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
103C23×C4×C73C2311yescharacteristic
104C22×C8×C73—22no—
105C22×C8×C73—22no—
106C22×C8×C73—22no—
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C2×C22⋊C4×C73C2×C411yescharacteristic
112C2×C22⋊C4×C73C2×C411yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C22⋊C8×C73—22no—
116C4×C8×C73—22no—
117C4×C8×C73—22no—
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120C22×Dic73C22×C411yescharacteristic
121C22×Dic73C22×C411yescharacteristic
122C22×Dic73C22×C411yescharacteristic
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831#4112yes—
139C2×#10596831#4112yes—
140C4⋊Dic73—22no—
141C4⋊Dic73—22no—
142#11924007—22no—
143#11924007—22no—
144#11924007—22no—
145#11924007—22no—
146C22⋊Dic73—22no—
147C22⋊Dic73—22no—
148C22⋊Dic73—22no—
149C22⋊Dic73—22no—
150C4×Dic73—21no—
151C4×Dic73—21no—
152C4×Dic73—21no—
153C4×Dic73—21no—
154C4×Dic73—21no—
155C4×Dic73—21no—
156C4×Dic73—21no—
157C4×Dic73—21no—
158C24×C73C22×C411yescharacteristic
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C2411yescharacteristic
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—44no—
180C2×C8×C73#4112yes—
181C2×C8×C73#4112yes—
182C2×C8×C73#4112yes—
183C2×C8×C73#4112yes—
184C22⋊C4×C73—22no—
185C22⋊C4×C73—22no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C23×C73—21no—
191C23×C73—21no—
192C23×C73—21no—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73#13112yes—
197C23×C73C23×C411yescharacteristic
198C2×C4×C73—21no—
199C2×C4×C73—21no—
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73#13112yes—
217C2×C4×C73C2×#4111yescharacteristic
218C2×C4×C73C2×#4111yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C2×C4×C73C2×#4111yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73#13112yes—
246C2×Dic73#13112yes—
247C8×C73—22no—
248C8×C73—41no—
249C8×C73—41no—
250C8×C73#12614yes—
251#10596831—22no—
252#10596831—22no—
253#10596831—41no—
254#10596831—41no—
255C22×C73—22no—
256C22×C73—22no—
257C22×C73—22no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73C4×#4111yescharacteristic
263C22×C73C4×#4111yescharacteristic
264C22×C73C4×#4111yescharacteristic
265C22×C73C2×#13111yescharacteristic
266C22×C73C2×#13111yescharacteristic
267C22×C73C2×#13111yescharacteristic
268C22×C73C2×#13111yescharacteristic
269C4×C73—22no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73C2×#12611yescharacteristic
275C4×C73#52911yescharacteristic
276C4×C73#52911yescharacteristic
277C4×C73#52911yescharacteristic
278Dic73—22no—
279Dic73—22no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284Dic73—41no—
285Dic73—41no—
286#21668—731nomaximal, Sylow
287C2×C73—42no—
288C2×C73C4×#12611yescharacteristic
289C2×C73#296611yescharacteristic
290C2×C73#296611yescharacteristic
291C2×C73#296611yescharacteristic
292C2×C73#296611yescharacteristic
293C2×C73#296611yescharacteristic
294C2×C73#296611yescharacteristic
295#2401—731no—
296#1924—731no—
297#1924—731no—
298#1924—731no—
299#1917—731no—
300#1917—731no—
301#1917—731no—
302#1840—731no—
303C8×C4⋊C4—731no—
304C8×C4⋊C4—731no—
305C8×C4⋊C4—731no—
306C8×C22⋊C4—731no—
307C8×C22⋊C4—731no—
308C8×C22⋊C4D7311yescharacteristic
309#1726—731no—
310C73#2166811yescharacteristic, complemented, Sylow
311C23×C8C2×D7311yescharacteristic
312C2×C4⋊C8—731no—
313C2×C4⋊C8—731no—
314C2×C4⋊C8—731no—
315C2×C22⋊C8—731no—
316C2×C22⋊C8—731no—
317C2×C22⋊C8C2×D7311yescharacteristic
318C2×#97—731no—
319C2×#97—731no—
320C2×#97—731no—
321C2×C4×C8—731no—
322C2×C4×C8—731no—
323C2×C4×C8—731no—
324C2×C4×C8—731no—
325C2×C4×C8C2×D7311yescharacteristic
326C2×C4×C8C2×D7311yescharacteristic
327#401—731no—
328#400—731no—
329#400—731no—
330#400—731no—
331#397—731no—
332#397—731no—
333#397—731no—
334#396—731no—
335C4×C4⋊C4—731no—
336C4×C4⋊C4—731no—
337C4×C4⋊C4—731no—
338C4×C22⋊C4—731no—
339C4×C22⋊C4—731no—
340C4×C22⋊C4C2×D7311yescharacteristic
341#376—731no—
342#336—731no—
343#336—731no—
344#336—731no—
345#336—731no—
346#336—731no—
347#336—731no—
348#336—731no—
349#336—731no—
350#336—731no—
351#336—731no—
352#336C2×D7311yescharacteristic
353#336C2×D7311yescharacteristic
354C23×C4C22×D7311yescharacteristic
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—731no—
359C22×C8—731no—
360C22×C8—731no—
361C22×C8—731no—
362C22×C8C22×D7311yescharacteristic
363C22×C8C22×D7311yescharacteristic
364C22×C8C22×D7311yescharacteristic
365C22×C8C22×D7311yescharacteristic
366C2×C4⋊C4—731no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C22⋊C4—731no—
373C2×C22⋊C4—731no—
374C2×C22⋊C4—731no—
375C2×C22⋊C4—731no—
376C2×C22⋊C4C4×D7311yescharacteristic
377C2×C22⋊C4C4×D7311yescharacteristic
378C2×C42—731no—
379C2×C42—731no—
380C2×C42—731no—
381C2×C42—731no—
382C2×C42C22×D7311yescharacteristic
383C2×C42C22×D7311yescharacteristic
384C4⋊C8—1462no—
385C4⋊C8—1462no—
386C4⋊C8—1462no—
387C22⋊C8—22no—
388C22⋊C8—1462no—
389C22⋊C8—1462no—
390#97—1462no—
391#97—1462no—
392#97—1462no—
393C4×C8—22no—
394C4×C8—22no—
395C4×C8—1462no—
396C4×C8—1462no—
397C4×C8—1462no—
398C4×C8—1462no—
399#95—731no—
400#95—731no—
401#95—731no—
402#95—731no—
403#95—731no—
404#95—731no—
405#95—731no—
406#95—731no—
407#95—731no—
408#95—731no—
409#95—731no—
410#95—731no—
411#95—731no—
412#95—731no—
413#95C4×D7311yescharacteristic
414#95C4×D7311yescharacteristic
415C24C2×C4×D7311yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—731no—
423C22×C4—731no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—731no—
427C22×C4—731no—
428C22×C4—731no—
429C22×C4—731no—
430C22×C4C2×C4×D7311yescharacteristic
431C22×C4C2×C4×D7311yescharacteristic
432C22×C4C2×C4×D7311yescharacteristic
433C22×C4C2×C4×D7311yescharacteristic
434C22×C4C2×C4×D7311yescharacteristic
435C22×C4C23×D7311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—44no—
445C2×C8—732no—
446C2×C8—732no—
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8#1192402712yes—
458C2×C8#1192402712yes—
459C2×C8#1192402812yes—
460C2×C8#1192402812yes—
461C4⋊C4—1462no—
462C4⋊C4—1462no—
463C4⋊C4—1462no—
464C4⋊C4—1462no—
465C4⋊C4—1462no—
466C4⋊C4—1462no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—1462no—
470C22⋊C4—1462no—
471C22⋊C4—1462no—
472C22⋊C4—1462no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—1461no—
478C42—1461no—
479C42—1461no—
480C42—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23#1455659712yes—
492C23C22×C4×D7311yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—732no—
512C2×C4—732no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4#1455659712yes—
536C2×C4#41×D7311yescharacteristic
537C2×C4#41×D7311yescharacteristic
538C2×C4C2×#1192402711yescharacteristic
539C2×C4C2×#1192402711yescharacteristic
540C2×C4C2×#1192402811yescharacteristic
541C2×C4C2×#1192402811yescharacteristic
542C8—22no—
543C8—41no—
544C8—41no—
545C8—2921no—
546C8—2921no—
547C8—1462no—
548C8—1462no—
549C8#1455658414yes—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C4×#1192402711yescharacteristic
558C22C4×#1192402711yescharacteristic
559C22C4×#1192402811yescharacteristic
560C22#131×D7311yescharacteristic
561C22#131×D7311yescharacteristic
562C22C2×#1455659711yescharacteristic
563C22C2×#1455659711yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—2921no—
570C4—2921no—
571C4—2921no—
572C4—2921no—
573C4—2921no—
574C4—2921no—
575C4—1462no—
576C4—1462no—
577C4C2×#1455658411yescharacteristic
578C4#1798911511yescharacteristic
579C4#1798911711yescharacteristic
580C4#1798911911yescharacteristic
581C2—42no—
582C2C4×#1455658411yescharacteristic
583C2#2261889911yescharacteristic
584C2#2261889911yescharacteristic
585C2#2261889911yescharacteristic
586C2#2261890211yescharacteristic
587C2#2261890311yescharacteristic
588C2#2261890611yescharacteristic
subgroupG/H
centerC22×C8C22×D73
commutator, socleC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC8×C22⋊C4×C73C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenterC8×C22⋊C4D73
hypocenterC73#21668
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C8 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #22610498C2semidirect
6. #22610496C2semidirect
7. #22610493C2semidirect
8. #22610075C2semidirect
9. C8×#11924007C2semidirect
10. C8×#11924007C2semidirect
11. C8×C4⋊Dic73C2semidirect
14. #22609617C2semidirect
310. C73#21668semidirect

Maximal subgroups

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

subgroupindex
#226132312
#226105472
#226105462
#226105412
#226104982
#226104962
#226104932
#226100752
C8×#119240072
C8×C4⋊Dic732
C8×C22⋊Dic732
#226096172
C8×C22⋊C4×C732
#2166873