Finite Group Databasebeta

← #33057395

Subgroups — #33057395

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619091C211yesmaximal, characteristic, complemented
2#22619063C211yesmaximal, characteristic, complemented
3#22608834C211yesmaximal, characteristic, complemented
4#22608816C211yesmaximal, characteristic, complemented
5#22608810C211yesmaximal, characteristic, complemented
6#22608810C211yesmaximal, characteristic, complemented
7#22608782C211yesmaximal, characteristic, complemented
8#22608761C211yesmaximal, characteristic, complemented
9SD16⋊#10596831C211yesmaximal, characteristic, complemented
10Q16×#10596831C211yesmaximal, characteristic, complemented
11#22608706C211yesmaximal, characteristic, complemented
12#22608396C211yesmaximal, characteristic, complemented
13#22608318C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#3102C211yesmaximal, characteristic
16#17988718C2211yescharacteristic
17Q8×#10596831C2211yescharacteristic
18Q8×#10596831C2211yescharacteristic
19Q8×#10596831C2211yescharacteristic
20#17988665—21no—
21#17988665—21no—
22#17988665C2211yescharacteristic
23#17988665C2211yescharacteristic
24#17988665C2211yescharacteristic
25#17988659—21no—
26D4×#10596831—21no—
27D4×#10596831C2211yescharacteristic
28#17988648—21no—
29#17988640—21no—
30#17988640C2211yescharacteristic
31#17988640C2211yescharacteristic
32#17988614—21no—
33#17988611—21no—
34#17988611C2211yescharacteristic
35C2×C4⋊#10596831C2211yescharacteristic
36#17988340C2211yescharacteristic
37#17988340C2211yescharacteristic
38#17988340C2211yescharacteristic
39#17988340C2211yescharacteristic
40Q8⋊#10596831C2211yescharacteristic
41Q8⋊#10596831C2211yescharacteristic
42Q8⋊#10596831C2211yescharacteristic
43Q8⋊#10596831C2211yescharacteristic
44D4⋊#10596831C2211yescharacteristic
45D4⋊#10596831C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48#17988309C2211yescharacteristic
49#17988309C2211yescharacteristic
50#17988308C2211yescharacteristic
51C8×#10596831C2211yescharacteristic
52#529×C73C2211yescharacteristic
53C4×#41×C73C2211yescharacteristic
54#485×C73C411yescharacteristic
55#482×C73C411yescharacteristic
56#479×C73C411yescharacteristic
57#478×C73C411yescharacteristic
58#464×C73C411yescharacteristic
59#463×C73C411yescharacteristic
60#452×C73C411yescharacteristic
61#449×C73C411yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63C4×SD16×C73C2211yescharacteristic
64C4×SD16×C73C2211yescharacteristic
65C4×D8×C73C2211yescharacteristic
66#431×C73C2211yescharacteristic
67C2×#11924012—21no—
68C2×#11924012—21no—
69C2×#11924012—21no—
70C2×#11924012—21no—
71C22×#10596831—21no—
72C22×#10596831—21no—
73C4⋊#10596831—21no—
74C4⋊#10596831—21no—
75C4⋊#10596831—21no—
76C4⋊#10596831—21no—
77C4⋊#10596831—21no—
78C4⋊#10596831—21no—
79C4⋊#10596831—21no—
80C4⋊#10596831D411yescharacteristic
81C4⋊#10596831D411yescharacteristic
82C4⋊#10596831C2311yescharacteristic
83C4⋊#10596831C2311yescharacteristic
84C4⋊#10596831C2311yescharacteristic
85C4⋊#10596831C2311yescharacteristic
86C22⋊#10596831—21no—
87C22⋊#10596831—21no—
88C22⋊#10596831—21no—
89C22⋊#10596831—21no—
90C22⋊#10596831—21no—
91C22⋊#10596831D411yescharacteristic
92C22⋊#10596831D411yescharacteristic
93#14556502—21no—
94C4×#10596831—21no—
95C4×#10596831—21no—
96C4×#10596831—21no—
97C4×#10596831C2311yescharacteristic
98C4×#10596831C2311yescharacteristic
99C4×#10596831C2311yescharacteristic
100C4×#10596831C2311yescharacteristic
101C2×#41×C73C2×C411yescharacteristic
102C2×Q16×C73C2×C411yescharacteristic
103C2×SD16×C73C2×C411yescharacteristic
104C2×SD16×C73C2×C411yescharacteristic
105C2×D8×C73C2×C411yescharacteristic
106#126×C73—21no—
107#125×C73C2×C411yescharacteristic
108#124×C73C2×C411yescharacteristic
109#123×C73—21no—
110C22⋊Q8×C73C2×C411yescharacteristic
111#121×C73C2×C411yescharacteristic
112C4×Q8×C73C2×C411yescharacteristic
113C4×Q8×C73C2311yescharacteristic
114C4×Q8×C73C2311yescharacteristic
115C4×D4×C73—21no—
116C4×D4×C73—21no—
117C4×D4×C73—21no—
118C4×D4×C73C2×C411yescharacteristic
119C4×D4×C73C2311yescharacteristic
120C4×D4×C73C2311yescharacteristic
121#117×C73—21no—
122#117×C73—21no—
123#117×C73C2×C411yescharacteristic
124C2×C42×C73—21no—
125C2×C42×C73C2311yescharacteristic
126#107×C73C2×C411yescharacteristic
127#107×C73C2×C411yescharacteristic
128#106×C73C2×C411yescharacteristic
129#106×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73C2×C411yescharacteristic
132#103×C73C2×C411yescharacteristic
133#103×C73C2×C411yescharacteristic
134#103×C73C2×C411yescharacteristic
135#103×C73C2×C411yescharacteristic
136#102×C73C2×C411yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141C22⋊C8×C73C2×C411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924012—81no—
145#11924012—81no—
146#11924012—81no—
147#11924012—81no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—81no—
155C2×#10596831—81no—
156C2×#10596831C2×D411yescharacteristic
157C2×#10596831C2×D411yescharacteristic
158C2×#10596831C2×D411yescharacteristic
159C2×#10596831C2×D411yescharacteristic
160#41×C73—22no—
161#41×C73—41no—
162C2×Q8×C73C22×C411yescharacteristic
163C2×Q8×C73C22×C411yescharacteristic
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73C22×C411yescharacteristic
167C2×D4×C73C22×C411yescharacteristic
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73C22×C411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73#4111yescharacteristic
175Q16×C73—22no—
176SD16×C73—22no—
177SD16×C73—41no—
178D8×C73—41no—
179C2×C8×C73C22×C411yescharacteristic
180C2×C8×C73C22×C411yescharacteristic
181C2×C8×C73C22×C411yescharacteristic
182C2×C8×C73C22×C411yescharacteristic
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73C22×C411yescharacteristic
190C4⋊C4×C73C22×C411yescharacteristic
191C4⋊C4×C73C22×C411yescharacteristic
192C4⋊C4×C73C22×C411yescharacteristic
193C22⋊C4×C73—21no—
194C22⋊C4×C73—21no—
195C22⋊C4×C73—21no—
196C22⋊C4×C73—21no—
197C22⋊C4×C73—21no—
198C22⋊C4×C73—21no—
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C23×C73—21no—
211C23×C73C4×D411yescharacteristic
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73#13112yes—
216D4×C73—21no—
217D4×C73—21no—
218D4×C73—21no—
219D4×C73—21no—
220D4×C73—42no—
221D4×C73—42no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—41no—
233C2×C4×C73—42no—
234C2×C4×C73—42no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73C4×D411yescharacteristic
240C2×C4×C73C4×D411yescharacteristic
241C2×C4×C73C4×D411yescharacteristic
242C2×C4×C73C23×C411yescharacteristic
243C2×C4×C73C22×D411yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—41no—
254#10596831—41no—
255#10596831—41no—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73C2×C4×D411yescharacteristic
269C4×C73—21no—
270C4×C73—22no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73C2×#13111yescharacteristic
280C4×C73#56811yescharacteristic
281C4×C73#57611yescharacteristic
282C4×C73#57811yescharacteristic
283#18033—731nomaximal, Sylow
284C2×C73—41no—
285C2×C73—81no—
286C2×C73—81no—
287C2×C73#293311yescharacteristic
288C2×C73#295111yescharacteristic
289C2×C73#295511yescharacteristic
290#3102D7311yescharacteristic
291#2994—731no—
292#2991—731no—
293#1592—731no—
294#1589—731no—
295#1588—731no—
296#1588—731no—
297#1584—731no—
298#1581—731no—
299SD16⋊C8—731no—
300C8×Q16—731no—
301#1571—731no—
302#1495—731no—
303#1477—731no—
304#1454—731no—
305C73#1803311yescharacteristic, complemented, Sylow
306#529C2×D7311yescharacteristic
307C4×#41C2×D7311yescharacteristic
308#485Dic7311yescharacteristic
309#482Dic7311yescharacteristic
310#479Dic7311yescharacteristic
311#478Dic7311yescharacteristic
312#464Dic7311yescharacteristic
313#463Dic7311yescharacteristic
314#452Dic7311yescharacteristic
315#449Dic7311yescharacteristic
316#446—731no—
317C8×Q8—731no—
318C8×Q8—731no—
319C8×Q8—731no—
320C4×Q16C2×D7311yescharacteristic
321C4×SD16C2×D7311yescharacteristic
322C4×SD16C2×D7311yescharacteristic
323C4×D8C2×D7311yescharacteristic
324#436—731no—
325#436—731no—
326#436—731no—
327#436—1461no—
328#436—1461no—
329#435—1461no—
330C8×D4—731no—
331C8×D4—1461no—
332#433—1461no—
333#431—731no—
334#431—731no—
335#431—1461no—
336#431C2×D7311yescharacteristic
337#424—1461no—
338#423—731no—
339#423—1461no—
340C2×C4⋊C8—731no—
341#335—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353#322—731no—
354#322—731no—
355#322—731no—
356C82—731no—
357C2×#41C2×Dic7311yescharacteristic
358C2×Q16C2×Dic7311yescharacteristic
359C2×SD16C2×Dic7311yescharacteristic
360C2×SD16C2×Dic7311yescharacteristic
361C2×D8C2×Dic7311yescharacteristic
362C2×M16—1461no—
363C2×M16—1461no—
364C2×M16—1461no—
365C2×M16—1461no—
366C22×C8—1461no—
367C22×C8—1461no—
368#126—21no—
369#125C2×Dic7311yescharacteristic
370#124C2×Dic7311yescharacteristic
371#123—21no—
372C22⋊Q8C2×Dic7311yescharacteristic
373#121C2×Dic7311yescharacteristic
374C4×Q8C2×Dic7311yescharacteristic
375C4×Q8C22×D7311yescharacteristic
376C4×Q8C22×D7311yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×Dic7311yescharacteristic
381C4×D4C22×D7311yescharacteristic
382C4×D4C22×D7311yescharacteristic
383#117—21no—
384#117—21no—
385#117C2×Dic7311yescharacteristic
386C2×C42—21no—
387C2×C42C22×D7311yescharacteristic
388#107C2×Dic7311yescharacteristic
389#107C2×Dic7311yescharacteristic
390#106C2×Dic7311yescharacteristic
391#106C2×Dic7311yescharacteristic
392C4⋊C8—731no—
393C4⋊C8—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8C2×Dic7311yescharacteristic
406C4⋊C8C2×Dic7311yescharacteristic
407#103C2×Dic7311yescharacteristic
408#103C2×Dic7311yescharacteristic
409#103C2×Dic7311yescharacteristic
410#103C2×Dic7311yescharacteristic
411#102C2×Dic7311yescharacteristic
412#102C2×Dic7311yescharacteristic
413#102C2×Dic7311yescharacteristic
414#102C2×Dic7311yescharacteristic
415C22⋊C8—731no—
416C22⋊C8—731no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8C2×Dic7311yescharacteristic
423C22⋊C8C2×Dic7311yescharacteristic
424#97—1461no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—1461no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434#41—22no—
435#41—41no—
436C2×Q8C22×Dic7311yescharacteristic
437C2×Q8C22×Dic7311yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×Dic7311yescharacteristic
441C2×D4C22×Dic7311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4C22×Dic7311yescharacteristic
447C22×C4D4×D7311yescharacteristic
448C22×C4#1192402711yescharacteristic
449Q16—22no—
450SD16—22no—
451SD16—41no—
452D8—41no—
453M16—5841no—
454M16—5841no—
455M16—5841no—
456M16—5841no—
457C2×C8—5841no—
458C2×C8—5841no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—731no—
462C2×C8—731no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8C22×Dic7311yescharacteristic
470C2×C8C22×Dic7311yescharacteristic
471C2×C8C22×Dic7311yescharacteristic
472C2×C8C22×Dic7311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C22×Dic7311yescharacteristic
480C4⋊C4C22×Dic7311yescharacteristic
481C4⋊C4C22×Dic7311yescharacteristic
482C4⋊C4C22×Dic7311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42C22×Dic7311yescharacteristic
496C42D4×D7311yescharacteristic
497C42#1192402711yescharacteristic
498C42C23×D7311yescharacteristic
499C23—21no—
500C23—21no—
501C23D4×Dic7311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8#1455659812yes—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—42no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4D4×Dic7311yescharacteristic
530C2×C4D4×Dic7311yescharacteristic
531C2×C4D4×Dic7311yescharacteristic
532C2×C4C23×Dic7311yescharacteristic
533C2×C4C2×D4×D7311yescharacteristic
534C2×C4C2×#1192402711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—2921no—
540C8—2921no—
541C8—2921no—
542C8—2921no—
543C8—2921no—
544C8—2921no—
545C8—1461no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C2×D4×Dic7311yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4C2×#1455659811yescharacteristic
570C4#1798935411yescharacteristic
571C4#1798938911yescharacteristic
572C4#1798940111yescharacteristic
573C2—41no—
574C2—81no—
575C2—81no—
576C2#2261865811yescharacteristic
577C2#2261880711yescharacteristic
578C2#2261883411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#3102C2
socleC22×C73C2×C4×D4
prime radical#449×C73C4
cosocleC42×C73C24
hypercenter#3102D73
hypocenterC73#18033
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #22619091C2semidirect
2. #22619063C2semidirect
3. #22608834C2semidirect
4. #22608816C2semidirect
5. #22608810C2semidirect
6. #22608810C2semidirect
7. #22608782C2semidirect
8. #22608761C2semidirect
9. SD16⋊#10596831C2semidirect
10. Q16×#10596831C2semidirect
11. #22608706C2semidirect
12. #22608396C2semidirect
13. #22608318C2semidirect
14. #22608231C2semidirect
305. C73#18033semidirect

Maximal subgroups

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

subgroupindex
#226190912
#226190632
#226088342
#226088162
#226088102
#226087822
#226087612
SD16⋊#105968312
Q16×#105968312
#226087062
#226083962
#226083182
#226082312
C73×#31022
#1803373