Finite Group Databasebeta

← #33051921

Subgroups — #33051921

Order 18688.

1174 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989066C211yesmaximal, characteristic
2#22619015C212yesmaximal, complemented
3#22608272C211yesmaximal, characteristic, complemented
4#22608270C212yesmaximal, complemented
5#22608263C212yesmaximal, complemented
6#22608262C212yesmaximal, complemented
7#22608250C212yesmaximal, complemented
8#22608242C212yesmaximal, complemented
9C73×#1466C211yesmaximal, characteristic, complemented
10C22×#11924027C411yescharacteristic
11#17989066—24no—
12#17989066—24no—
13C2×C4×Dic146C2211yescharacteristic
14C2×#14556556C411yescharacteristic
15C2×D4×Dic73C411yescharacteristic
16C2×C4×C22⋊D73C411yescharacteristic
17C2×C4×C22⋊D73C411yescharacteristic
18C2×#14556551C2211yescharacteristic
19C2×#14556551C2211yescharacteristic
20C2×#14556548C2211yescharacteristic
21C2×#14556547C2211yescharacteristic
22C2×#14556547C2211yescharacteristic
23C22×#11924007C411yescharacteristic
24C22×#11924007C411yescharacteristic
25C2×C4⋊C4×D73C411yescharacteristic
26#17988716—24no—
27#17988715—24no—
28#17988644C2212yes—
29#17988641C2214yes—
30#17988637C2214yes—
31#17988312C2214yes—
32#17988311C2212yes—
33#17988311C2212yes—
34#17988310C2214yes—
35C2×C4×D4×C73C2211yescharacteristic
36#432×C73C2212yes—
37#323×C73C2212yes—
38#323×C73C2212yes—
39C2×#11924027—24no—
40C2×#11924027—24no—
41C2×#11924027—24no—
42C22×Dic146C2×C411yescharacteristic
43C22×C22⋊D73C2×C411yescharacteristic
44C22×C22⋊D73C2×C411yescharacteristic
45C23×Dic73C2×C411yescharacteristic
46C23×Dic73C2×C411yescharacteristic
47C23×Dic73C2×C411yescharacteristic
48C23×Dic73C2×C411yescharacteristic
49C22×C4×D73C2×C411yescharacteristic
50C22×C4×D73C2×C411yescharacteristic
51C22×C4×D73C2×C411yescharacteristic
52C4×Dic146D414yes—
53C4×Dic146D414yes—
54#14556556—24no—
55D4×Dic73—24no—
56C4×C22⋊D73—22no—
57C4×C22⋊D73—22no—
58C4×C22⋊D73—22no—
59C4×C22⋊D73—22no—
60#14556551—24no—
61#14556551—24no—
62#14556548—22no—
63#14556548—22no—
64#14556547—24no—
65#14556547—24no—
66C2×C4⋊Dic73C2×C411yescharacteristic
67C2×#11924007—22no—
68C2×#11924007—22no—
69C2×#11924007—22no—
70C2×#11924007—22no—
71C2×#11924007C2×C411yescharacteristic
72C2×#11924007C2×C411yescharacteristic
73C2×#11924007C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2311yescharacteristic
79C4⋊C4×D73—24no—
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2311yescharacteristic
84C2×C4×Dic73C2×C411yescharacteristic
85C2×C4×Dic73C2×C411yescharacteristic
86C2×C4×Dic73C2×C411yescharacteristic
87C2×C4×Dic73C2311yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C4⋊#10596831—22no—
90#14556520—24no—
91#14556520—24no—
92C22⋊#10596831C2314yes—
93#14556502—22no—
94#14556501—24no—
95C8×Dic73—24no—
96C22×D4×C73C2×C411yescharacteristic
97C23×C4×C73C2×C411yescharacteristic
98C23×C4×C73C2×C411yescharacteristic
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C22⋊C4×C73C2311yescharacteristic
103C2×C22⋊C4×C73C2311yescharacteristic
104C2×C42×C73C2311yescharacteristic
105C4⋊C8×C73—22no—
106C22⋊C8×C73C2314yes—
107#97×C73—22no—
108C23×D73C22×C411yescharacteristic
109#11924027—232no—
110C2×Dic146—22no—
111C2×Dic146—22no—
112C2×Dic146C22⋊C414yes—
113C2×C22⋊D73—22no—
114C2×C22⋊D73—22no—
115C2×C22⋊D73—22no—
116C2×C22⋊D73—22no—
117C2×C22⋊D73—22no—
118C2×C22⋊D73M1614yes—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—81no—
127C22×Dic73—81no—
128C22×Dic73M1614yes—
129C22×Dic73C22×C411yescharacteristic
130C22×Dic73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—81no—
142C2×C4×D73—81no—
143C2×#10596831—24no—
144C4⋊Dic73C22⋊C414yes—
145#11924007—21no—
146#11924007—21no—
147#11924007—22no—
148#11924007—22no—
149#11924007—22no—
150#11924007—22no—
151#11924007—22no—
152#11924007C22⋊C412yes—
153#11924007C22⋊C412yes—
154#11924007C22⋊C412yes—
155#11924007C22⋊C412yes—
156C22⋊Dic73—22no—
157C22⋊Dic73—22no—
158#11924005—21no—
159#11924005—21no—
160#11924005—22no—
161C4×Dic73—22no—
162C4×Dic73—22no—
163C4×Dic73—22no—
164C4×Dic73C2×D414yes—
165C4×Dic73C2×D414yes—
166C24×C73C22×C411yescharacteristic
167C24×C73C22×C411yescharacteristic
168C2×D4×C73—22no—
169C2×D4×C73—22no—
170C2×D4×C73—22no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—81no—
176C22×C4×C73—81no—
177C22×C4×C73C22×C411yescharacteristic
178C22×C4×C73C22×C411yescharacteristic
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C22×C411yescharacteristic
181C22×C4×C73C2411yescharacteristic
182C2×C8×C73—24no—
183C4⋊C4×C73—22no—
184C22⋊C4×C73—22no—
185C22⋊C4×C73—22no—
186C42×C73C2×D412yes—
187C42×C73C2×D412yes—
188C23×C73—21no—
189C23×C73—21no—
190C23×C73—21no—
191C23×C73—21no—
192C23×C73—41no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73—41no—
196C23×C73C2×M1612yes—
197C23×C73C2×M1612yes—
198C23×C73C23×C411yescharacteristic
199C22×D73—21no—
200C22×D73—21no—
201C22×D73—41no—
202C22×D73—41no—
203C22×D73C2×M1612yes—
204D4×C73—28no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—81no—
214C2×C4×C73—81no—
215C2×C4×C73—81no—
216C2×C4×C73—81no—
217C2×C4×C73C2×C22⋊C412yes—
218C2×C4×C73C2×C22⋊C411yescharacteristic
219C2×C4×C73C2×C22⋊C411yescharacteristic
220C2×C4×C73C22×D412yes—
221C22⋊D73—28no—
222C22⋊D73—28no—
223C2×Dic73—28no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—28no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—41no—
232C2×Dic73—41no—
233C2×Dic73—41no—
234C2×Dic73—41no—
235C2×Dic73—82no—
236C2×Dic73—82no—
237C2×Dic73C2×C22⋊C412yes—
238C2×Dic73C2×C22⋊C412yes—
239C2×Dic73C2×C22⋊C412yes—
240C2×Dic73C2×C22⋊C412yes—
241C2×Dic73C2×M1612yes—
242C2×Dic73C2×M1612yes—
243C2×Dic73C2×M1612yes—
244C4×D73—28no—
245C4×D73—82no—
246C4×D73—82no—
247Dic146—28no—
248C8×C73—44no—
249#10596831—44no—
250C22×C73—21no—
251C22×C73—21no—
252C22×C73—22no—
253C22×C73—22no—
254C22×C73—42no—
255C22×C73—42no—
256C22×C73—42no—
257C22×C73—42no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73C22×C22⋊C411yescharacteristic
263C22×C73C22×M1611yescharacteristic
264C22×C73C22×M1611yescharacteristic
265C2×D73—22no—
266C2×D73—42no—
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—42no—
270C4×C73—22no—
271C4×C73—22no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—41no—
275C4×C73—41no—
276Dic73—22no—
277Dic73—22no—
278Dic73—22no—
279Dic73—22no—
280Dic73—41no—
281Dic73—41no—
282Dic73#40714yes—
283#17372—731nomaximal, Sylow
284C2×C73—21no—
285C2×C73—21no—
286C2×C73—42no—
287C2×C73—42no—
288C2×C73C2×#40711yescharacteristic
289C2×C73#288411yescharacteristic
290C2×C73#288811yescharacteristic
291D73—42no—
292C2×#520—731no—
293#2983—732no—
294#1466—732no—
295#1466—731no—
296#1466D7311yescharacteristic, complemented
297#1464—732no—
298#1464—732no—
299#1460—732no—
300#1458—732no—
301C73#1737211yescharacteristic, complemented, Sylow
302C22×#41—731no—
303#520—1464no—
304#520—1464no—
305C2×C4×Q8—731no—
306C2×C4×Q8—731no—
307C2×C4×D4—731no—
308C2×C4×D4—731no—
309C2×C4×D4—731no—
310C2×C4×D4—731no—
311C2×C4×D4—731no—
312C2×C4×D4C2×D7311yescharacteristic
313C2×#117—731no—
314C2×#117—731no—
315C2×#117—731no—
316C22×C4⋊C4—731no—
317C22×C4⋊C4—731no—
318C22×C4⋊C4—731no—
319#446—1464no—
320#446—1464no—
321#432—732no—
322#432—734no—
323#432C2×D7312yes—
324#431—734no—
325#324—734no—
326#323—732no—
327#323—732no—
328#323—734no—
329#323C2×D7312yes—
330#323C2×D7312yes—
331C2×#41—1464no—
332C2×#41—1464no—
333C2×#41—1464no—
334C22×Q8—731no—
335C22×D4—731no—
336C22×D4—731no—
337C22×D4C4×D7311yescharacteristic
338C23×C4—731no—
339C23×C4—731no—
340C23×C4—731no—
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—731no—
344C23×C4—731no—
345C23×C4C4×D7311yescharacteristic
346C23×C4C4×D7311yescharacteristic
347C4×Q8—734no—
348C4×Q8—734no—
349C4×Q8—1464no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—1464no—
353C4×D4—1464no—
354C4×D4—1462no—
355C4×D4—1462no—
356C4×D4—1462no—
357C4×D4—1462no—
358C4×D4—1464no—
359#117—1464no—
360#117—1464no—
361#117—1462no—
362#117—1462no—
363C2×C4⋊C4—731no—
364C2×C4⋊C4—731no—
365C2×C4⋊C4—731no—
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×C4⋊C4—1464no—
373C2×C4⋊C4—1462no—
374C2×C4⋊C4—1462no—
375C2×C4⋊C4—1462no—
376C2×C4⋊C4—1462no—
377C2×C4⋊C4C4×D7311yescharacteristic
378C2×C22⋊C4—731no—
379C2×C22⋊C4—731no—
380C2×C22⋊C4—731no—
381C2×C22⋊C4—731no—
382C2×C22⋊C4C22×D7311yescharacteristic
383C2×C22⋊C4C22×D7311yescharacteristic
384C2×C42—731no—
385C2×C42—731no—
386C2×C42—731no—
387C2×C42—731no—
388C2×C42—731no—
389C2×C42C22×D7311yescharacteristic
390C4⋊C8—22no—
391C4⋊C8—1464no—
392C4⋊C8—1464no—
393C4⋊C8—1462no—
394C22⋊C8—734no—
395C22⋊C8C22×D7314yes—
396#97—22no—
397#97—1464no—
398#97—1462no—
399C4×C8—1464no—
400C24—731no—
401C24C2×C4×D7311yescharacteristic
402C24C2×C4×D7311yescharacteristic
403#41—14632no—
404C2×Q8—734no—
405C2×Q8—1462no—
406C2×Q8—1462no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—734no—
411C2×D4—1462no—
412C2×D4—1462no—
413C2×D4—1462no—
414C2×D4—1462no—
415C2×D4—1462no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4—5841no—
423C22×C4—5841no—
424C22×C4—5841no—
425C22×C4—5841no—
426C22×C4—731no—
427C22×C4—731no—
428C22×C4—731no—
429C22×C4—731no—
430C22×C4—731no—
431C22×C4—734no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—1462no—
435C22×C4—1462no—
436C22×C4—1462no—
437C22×C4—1462no—
438C22×C4—1462no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1462no—
446C22×C4C2×C4×D7311yescharacteristic
447C22×C4C2×C4×D7311yescharacteristic
448C22×C4C2×C4×D7311yescharacteristic
449C22×C4C2×C4×D7311yescharacteristic
450C22×C4C23×D7311yescharacteristic
451C2×C8—24no—
452C2×C8—1464no—
453C4⋊C4—22no—
454C4⋊C4—732no—
455C4⋊C4—732no—
456C4⋊C4—732no—
457C4⋊C4—732no—
458C4⋊C4—734no—
459C4⋊C4—1462no—
460C4⋊C4—1462no—
461C4⋊C4—1462no—
462C4⋊C4—1462no—
463C4⋊C4—1461no—
464C4⋊C4—1461no—
465C4⋊C4—1462no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—1462no—
469C22⋊C4—1462no—
470C22⋊C4—1461no—
471C22⋊C4—1461no—
472C22⋊C4—1462no—
473C42—734no—
474C42—734no—
475C42—1462no—
476C42—1462no—
477C42—1462no—
478C42D4×D7312yes—
479C42D4×D7312yes—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—2921no—
489C23—2921no—
490C23—732no—
491C23—1461no—
492C23—1461no—
493C23M16×D7312yes—
494C23M16×D7312yes—
495C23C22×C4×D7311yescharacteristic
496Q8—1468no—
497D4—28no—
498D4—1468no—
499D4—1468no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—2921no—
513C2×C4—2921no—
514C2×C4—2921no—
515C2×C4—2921no—
516C2×C4—5842no—
517C2×C4—5842no—
518C2×C4—5842no—
519C2×C4—5842no—
520C2×C4—732no—
521C2×C4—732no—
522C2×C4—732no—
523C2×C4—732no—
524C2×C4—732no—
525C2×C4—732no—
526C2×C4—732no—
527C2×C4—1468no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1468no—
531C2×C4—1468no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4C22⋊C4×D7312yes—
537C2×C4C22⋊C4×D7311yescharacteristic
538C2×C4C22⋊C4×D7311yescharacteristic
539C2×C4C2×D4×D7312yes—
540C8—44no—
541C8—2924no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—2922no—
555C22—2922no—
556C22—2921no—
557C22—2921no—
558C22—1462no—
559C22C2×C22⋊C4×D7311yescharacteristic
560C22C2×M16×D7311yescharacteristic
561C22C2×M16×D7311yescharacteristic
562C4—22no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—2921no—
569C4—2921no—
570C4—734no—
571C4—1462no—
572C4—1462no—
573C4—1462no—
574C4—1462no—
575C2—21no—
576C2—21no—
577C2—42no—
578C2—42no—
579C2—2922no—
580C2#407×D7311yescharacteristic
581C2#2261839311yescharacteristic
582C2#2261840711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1466C2
socleC22×C73C22×C22⋊C4
prime radicalC22×#11924027C4
cosocleC22×C4×C73C24
hypercenter#1466D73
hypocenterC73#17372
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #22619015C2semidirect
3. #22608272C2semidirect
4. #22608270C2semidirect
5. #22608263C2semidirect
6. #22608262C2semidirect
7. #22608250C2semidirect
8. #22608242C2semidirect
9. C73×#1466C2semidirect
296. #1466D73semidirect
301. C73#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#179890662
#226190152
#226082722
#226082702
#226082632
#226082622
#226082502
#226082422
C73×#14662
#1737273