Finite Group Databasebeta

← #33094273

Subgroups — #33094273

Order 18688.

676 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#22613232C211yesmaximal, characteristic
2#22610545C211yesmaximal, characteristic
3#22610537C211yesmaximal, characteristic
4#22610536C211yesmaximal, characteristic
5#22610496C211yesmaximal, characteristic, complemented
6#22610491C211yesmaximal, characteristic, complemented
7#22610075C211yesmaximal, characteristic, complemented
8#22609806C211yesmaximal, characteristic, complemented
9#22609797C211yesmaximal, characteristic, complemented
10#22609796C211yesmaximal, characteristic, complemented
11#22609713C211yesmaximal, characteristic
12#22609713C211yesmaximal, characteristic
13#22609711C211yesmaximal, characteristic
14#22609617C211yesmaximal, characteristic, complemented
15C73×#1916C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C2×C4⋊#10596831C2211yescharacteristic
18C2×#14556520C2211yescharacteristic
19C2×#14556503C2211yescharacteristic
20C2×#14556503C2211yescharacteristic
21C2×#14556503C2211yescharacteristic
22C2×#14556502C2211yescharacteristic
23C2×#14556502C2211yescharacteristic
24C2×#14556501C2211yescharacteristic
25C2×#14556501C2211yescharacteristic
26C2×C4×#10596831C2211yescharacteristic
27C2×C8×Dic73C2211yescharacteristic
28C2×C8×Dic73C2211yescharacteristic
29C2×C8×Dic73C2211yescharacteristic
30C73⋊#401C411yescharacteristic
31#17988529C411yescharacteristic
32#17988526C411yescharacteristic
33#17988525C411yescharacteristic
34#17988516C411yescharacteristic
35#17988514C411yescharacteristic
36#17988513C411yescharacteristic
37#17988509C411yescharacteristic
38C4×#11924007C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×#11924005C2211yescharacteristic
41C4×#11924005C2211yescharacteristic
42C4×#11924005C2211yescharacteristic
43#17988433C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C4×C8×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×C4×D73C2311yescharacteristic
60C2×#11924011—22no—
61C2×#11924011—22no—
62C2×#11924011—22no—
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C2×C4⋊Dic73C2×C411yescharacteristic
68C2×C4⋊Dic73C2×C411yescharacteristic
69C2×#11924007C2×C411yescharacteristic
70C2×#11924007C2×C411yescharacteristic
71C2×#11924005C2×C411yescharacteristic
72C2×#11924005C2×C411yescharacteristic
73C2×#11924005C2×C411yescharacteristic
74C2×#11924005C2×C411yescharacteristic
75C2×#11924005C2×C411yescharacteristic
76C2×#11924005C2×C411yescharacteristic
77C2×C4×Dic73C2311yescharacteristic
78C2×C4×Dic73C2311yescharacteristic
79C2×C4×Dic73C2311yescharacteristic
80C4⋊#10596831—22no—
81#14556520—22no—
82#14556503—22no—
83#14556503—22no—
84#14556503—22no—
85#14556502—22no—
86#14556502—22no—
87#14556501—22no—
88#14556501—22no—
89C4×#10596831—22no—
90C8×Dic73—22no—
91C8×Dic73—22no—
92C8×Dic73—22no—
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
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2×C411yescharacteristic
112C2×C4⋊C4×C73C2×C411yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116C4⋊C8×C73—22no—
117C4×C8×C73—22no—
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120C23×D73C22×C411yescharacteristic
121C22×Dic73C22×C411yescharacteristic
122C22×Dic73C22×C411yescharacteristic
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C2×C4×D73—21no—
129C2×C4×D73—21no—
130C2×C4×D73—21no—
131C2×C4×D73—21no—
132C2×C4×D73—21no—
133C2×C4×D73—21no—
134#11924011—44no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831#4112yes—
144C2×#10596831#4112yes—
145C2×#10596831#4112yes—
146C2×#10596831#4112yes—
147C4⋊Dic73—22no—
148C4⋊Dic73—22no—
149#11924007—22no—
150#11924007—41no—
151#11924005—22no—
152#11924005—22no—
153#11924005—41no—
154#11924005—41no—
155#11924005—41no—
156#11924005—41no—
157C4×Dic73—21no—
158C4×Dic73—21no—
159C4×Dic73—21no—
160C4×Dic73—21no—
161C4×Dic73—21no—
162C4×Dic73—21no—
163C22×C4×C73C22×C411yescharacteristic
164C22×C4×C73C22×C411yescharacteristic
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C2411yescharacteristic
170C2×C8×C73—21no—
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—21no—
180C2×C8×C73#4112yes—
181C2×C8×C73#4112yes—
182C4⋊C4×C73—22no—
183C4⋊C4×C73—41no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C23×C73C23×C411yescharacteristic
191C22×D73—21no—
192C22×D73—21no—
193C22×D73—21no—
194C22×D73—21no—
195C22×D73—21no—
196C22×D73—21no—
197C22×D73—21no—
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—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73#13112yes—
216C2×C4×C73C2×#4111yescharacteristic
217C2×C4×C73C2×#4111yescharacteristic
218C2×C4×C73C2×#4111yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C2×C4×C73C2×#4111yescharacteristic
222C2×Dic73—21no—
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#13112yes—
243C4×D73—41no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247C8×C73—22no—
248C8×C73—22no—
249C8×C73—41no—
250C8×C73—41no—
251#10596831—22no—
252#10596831—41no—
253#10596831—41no—
254#10596831#12614yes—
255C22×C73C4×#4111yescharacteristic
256C22×C73C4×#4111yescharacteristic
257C22×C73C4×#4111yescharacteristic
258C22×C73C2×#13111yescharacteristic
259C22×C73C2×#13111yescharacteristic
260C22×C73#56811yescharacteristic
261C22×C73#56811yescharacteristic
262C2×D73—41no—
263C2×D73—41no—
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C4×C73—22no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73C2×#12611yescharacteristic
276C4×C73#52911yescharacteristic
277C4×C73#52911yescharacteristic
278C4×C73#52911yescharacteristic
279Dic73—22no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284Dic73—41no—
285Dic73—41no—
286#21671—731nomaximal, Sylow
287C2×C73C4×#12611yescharacteristic
288C2×C73#296611yescharacteristic
289C2×C73#296711yescharacteristic
290C2×C73#296811yescharacteristic
291C2×C73#296911yescharacteristic
292C2×C73#296911yescharacteristic
293C2×C73#296911yescharacteristic
294D73—81no—
295#2401—731no—
296#1924—731no—
297#1923—731no—
298#1923—731no—
299#1917—731no—
300#1916—731no—
301#1916D7311yescharacteristic, complemented
302#1840—731no—
303#1771—731no—
304#1770—731no—
305C8×C4⋊C4—731no—
306#1753—731no—
307#1753—731no—
308#1753—731no—
309#1726—731no—
310C73#2167111yescharacteristic, complemented, Sylow
311C22×M16—731no—
312C2×C4⋊C8—731no—
313C2×C4⋊C8—731no—
314C2×C4⋊C8C2×D7311yescharacteristic
315C2×C22⋊C8—731no—
316C2×C22⋊C8—731no—
317C2×C22⋊C8—731no—
318C2×#97—731no—
319C2×#97—731no—
320C2×#97—731no—
321C2×#97—731no—
322C2×C4×C8—731no—
323C2×C4×C8—731no—
324C2×C4×C8—731no—
325C2×C4×C8—731no—
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⋊C4C2×D7311yescharacteristic
338C4×C22⋊C4—731no—
339C4×C22⋊C4—731no—
340C4×C22⋊C4—731no—
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#336C2×D7311yescharacteristic
351#336C2×D7311yescharacteristic
352#336C2×D7311yescharacteristic
353#336C2×D7311yescharacteristic
354C23×C4—731no—
355C2×M16—1462no—
356C2×M16—1462no—
357C2×M16—1462no—
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⋊C4C4×D7311yescharacteristic
371C2×C4⋊C4C4×D7311yescharacteristic
372C2×C22⋊C4—731no—
373C2×C22⋊C4—731no—
374C2×C22⋊C4—731no—
375C2×C22⋊C4—731no—
376C2×C22⋊C4—731no—
377C2×C22⋊C4—731no—
378C2×C42—731no—
379C2×C42—731no—
380C2×C42—731no—
381C2×C42C22×D7311yescharacteristic
382C2×C42C22×D7311yescharacteristic
383C2×C42C22×D7311yescharacteristic
384C4⋊C8—22no—
385C4⋊C8—1462no—
386C4⋊C8—1462no—
387C22⋊C8—1462no—
388C22⋊C8—1462no—
389C22⋊C8—1462no—
390#97—1462no—
391#97—1462no—
392#97—1462no—
393#97—1462no—
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
415C24—731no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—731no—
419C22×C4—731no—
420C22×C4—731no—
421C22×C4—731no—
422C22×C4—731no—
423C22×C4—1461no—
424C22×C4—1461no—
425C22×C4—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4C2×C4×D7311yescharacteristic
430C22×C4C2×C4×D7311yescharacteristic
431C22×C4C2×C4×D7311yescharacteristic
432C22×C4C2×C4×D7311yescharacteristic
433C22×C4C2×C4×D7311yescharacteristic
434C22×C4C2×C4×D7311yescharacteristic
435C22×C4C23×D7311yescharacteristic
436M16—2924no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—732no—
448C2×C8—732no—
449C2×C8—732no—
450C2×C8—732no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8#1192402712yes—
460C2×C8#1192402912yes—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—2921no—
464C4⋊C4—1462no—
465C4⋊C4—1462no—
466C4⋊C4—1462no—
467C22⋊C4—2921no—
468C22⋊C4—2921no—
469C22⋊C4—2921no—
470C22⋊C4—2921no—
471C22⋊C4—1462no—
472C22⋊C4—1462no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—1461no—
480C42—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C23—1461no—
486C23—1461no—
487C23—1461no—
488C23—1461no—
489C23—1461no—
490C23—1461no—
491C23—1461no—
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—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—2921no—
511C2×C4—2921no—
512C2×C4—2921no—
513C2×C4—2921no—
514C2×C4—732no—
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×C4#41×D7311yescharacteristic
539C2×C4#41×D7311yescharacteristic
540C2×C4C2×#1192402711yescharacteristic
541C2×C4C2×#1192402911yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C8—2921no—
547C8—2921no—
548C8—734no—
549C8—1462no—
550C22—2921no—
551C22—2921no—
552C22—2921no—
553C22—2921no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22C4×#1192402711yescharacteristic
558C22#1798905511yescharacteristic
559C22C4×#1192402911yescharacteristic
560C22#131×D7311yescharacteristic
561C22C2×#1455659711yescharacteristic
562C22#1798935211yescharacteristic
563C22#1798935311yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—2921no—
571C4—2921no—
572C4—2921no—
573C4—2921no—
574C4—2921no—
575C4—2921no—
576C4—1462no—
577C4#126×D7311yescharacteristic
578C4#1798911411yescharacteristic
579C4#1798912211yescharacteristic
580C4#1798912311yescharacteristic
581C2—5841no—
582C2#2261248111yescharacteristic
583C2#2261889911yescharacteristic
584C2#2261891311yescharacteristic
585C2#2261892411yescharacteristic
586C2#2261892911yescharacteristic
587C2#2261893311yescharacteristic
588C2#2261893411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1916C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1916D73
hypocenterC73#21671
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
5. #22610496C2semidirect
6. #22610491C2semidirect
7. #22610075C2semidirect
8. #22609806C2semidirect
9. #22609797C2semidirect
10. #22609796C2semidirect
14. #22609617C2semidirect
15. C73×#1916C2semidirect
301. #1916D73semidirect
310. C73#21671semidirect

Maximal subgroups

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

subgroupindex
#226132322
#226105452
#226105372
#226105362
#226104962
#226104912
#226100752
#226098062
#226097972
#226097962
#226097132
#226097112
#226096172
C73×#19162
#2167173