Finite Group Databasebeta

← #33051894

Subgroups — #33051894

Order 18688.

1210 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989067C211yesmaximal, characteristic
2#22618959C212yesmaximal, complemented
3#22608274C212yesmaximal, complemented
4#22608266C212yesmaximal, complemented
5#22608265C211yesmaximal, characteristic, complemented
6#22608259C212yesmaximal, complemented
7#22608246C212yesmaximal, complemented
8#324×D73C212yesmaximal, complemented
9C73×#1464C211yesmaximal, characteristic, complemented
10C22×#11924028C411yescharacteristic
11#17989067—24no—
12#17989067—24no—
13C2×C4×Dic146C411yescharacteristic
14C2×C4×Dic146C2211yescharacteristic
15C2×C4×D292C411yescharacteristic
16C2×C4×D292C2211yescharacteristic
17C2×#14556551C411yescharacteristic
18C2×#14556551C411yescharacteristic
19C2×#14556551C2211yescharacteristic
20C2×#14556551C2211yescharacteristic
21C2×#14556549C411yescharacteristic
22C2×#14556549C411yescharacteristic
23C22×C4⋊Dic73C411yescharacteristic
24C2×C4⋊C4×D73C2211yescharacteristic
25C2×C4⋊C4×D73C2211yescharacteristic
26#17988660—24no—
27#17988657—24no—
28#17988644C2212yes—
29#17988549C2214yes—
30C22⋊C8×D73C2214yes—
31#17988313C2212yes—
32#17988312C2214yes—
33#17988312C2214yes—
34#17988311C2212yes—
35C2×#117×C73C2211yescharacteristic
36#432×C73C2212yes—
37#324×C73C2212yes—
38#323×C73C2212yes—
39C2×#11924028—22no—
40C2×#11924028—22no—
41C2×#11924028—24no—
42C2×#11924028—24no—
43C22×Dic146C2×C411yescharacteristic
44C22×D292C2×C411yescharacteristic
45C22×C22⋊D73C2×C411yescharacteristic
46C22×C22⋊D73C2×C411yescharacteristic
47C23×Dic73C2×C411yescharacteristic
48C23×Dic73C2×C411yescharacteristic
49C22×C4×D73C2×C411yescharacteristic
50C22×C4×D73C2×C411yescharacteristic
51C22×C4×D73C2×C411yescharacteristic
52C22×C4×D73C2×C411yescharacteristic
53C22×C4×D73C2311yescharacteristic
54C22×C4×D73C2311yescharacteristic
55C2×#11924011—24no—
56C2×C8×D73—24no—
57C4×Dic146—22no—
58C4×Dic146—22no—
59C4×Dic146—22no—
60C4×Dic146—22no—
61C4×D292—22no—
62C4×D292—22no—
63C4×D292D414yes—
64C4×D292D414yes—
65#14556551—24no—
66#14556551—24no—
67#14556551—24no—
68#14556551—24no—
69#14556549—24no—
70#14556549—24no—
71C2×C4⋊Dic73—22no—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73C2×C411yescharacteristic
74C2×C4⋊Dic73C2×C411yescharacteristic
75C2×C4⋊Dic73C2×C411yescharacteristic
76C2×C4⋊Dic73C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2311yescharacteristic
80C2×#11924007C2311yescharacteristic
81C4⋊C4×D73—24no—
82C4⋊C4×D73—24no—
83C2×#11924005C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×#11924005C2×C411yescharacteristic
87C2×C4×Dic73C2×C411yescharacteristic
88C2×C4×Dic73C2×C411yescharacteristic
89C2×C4×Dic73C2×C411yescharacteristic
90C2×C4×Dic73C2×C411yescharacteristic
91C4⋊#10596831—22no—
92C22⋊#10596831C2314yes—
93#14556503—24no—
94#14556503—24no—
95#14556502—22no—
96C23×C4×C73C2×C411yescharacteristic
97#117×C73—22no—
98#117×C73—22no—
99C2×C4⋊C4×C73C2×C411yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73C2×C411yescharacteristic
102C2×C22⋊C4×C73C2311yescharacteristic
103C2×C42×C73C2×C411yescharacteristic
104C2×C42×C73C2311yescharacteristic
105C4⋊C8×C73—22no—
106C22⋊C8×C73C2314yes—
107#97×C73—22no—
108C23×D73C22×C411yescharacteristic
109C23×D73C22×C411yescharacteristic
110#11924028—216no—
111#11924028—216no—
112C2×Dic146—21no—
113C2×Dic146—21no—
114C2×Dic146—22no—
115C2×Dic146—22no—
116C2×D292—22no—
117C2×D292—22no—
118C2×D292C22⋊C412yes—
119C2×D292C22⋊C412yes—
120C2×C22⋊D73—22no—
121C2×C22⋊D73—22no—
122C2×C22⋊D73—22no—
123C2×C22⋊D73—22no—
124C2×C22⋊D73—22no—
125C2×C22⋊D73M1614yescomplemented
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—81no—
129C22×Dic73—81no—
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—22no—
142C2×C4×D73—22no—
143C2×C4×D73—81no—
144C2×C4×D73—81no—
145C2×C4×D73—81no—
146C2×C4×D73—81no—
147C2×C4×D73M1614yescomplemented
148C2×C4×D73C2×D414yes—
149C2×C4×D73C2×D414yes—
150#11924011—84no—
151C2×#10596831—24no—
152C8×D73—84no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—22no—
156C4⋊Dic73—22no—
157C4⋊Dic73C22⋊C412yes—
158C4⋊Dic73C22⋊C412yes—
159#11924007—22no—
160#11924007—22no—
161#11924007—22no—
162#11924007—22no—
163#11924005—22no—
164#11924005—22no—
165#11924005C22⋊C414yes—
166#11924005C22⋊C414yes—
167C4×Dic73—22no—
168C4×Dic73—22no—
169C4×Dic73—22no—
170C4×Dic73—22no—
171C24×C73C22×C411yescharacteristic
172C22×C4×C73—22no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—22no—
176C22×C4×C73C22×C411yescharacteristic
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—
184C4⋊C4×C73—22no—
185C22⋊C4×C73—22no—
186C22⋊C4×C73—22no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73C2×D412yes—
190C42×C73C2×D412yes—
191C23×C73—21no—
192C23×C73—21no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73C2×M1612yes—
196C23×C73C23×C411yescharacteristic
197C22×D73—21no—
198C22×D73—21no—
199C22×D73—41no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—41no—
203C22×D73C2×C22⋊C412yes—
204C22×D73C2×C22⋊C412yes—
205C22×D73C2×M1612yes—
206C22×D73C2×M1612yes—
207C2×C4×C73—24no—
208C2×C4×C73—24no—
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—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73C2×C22⋊C411yescharacteristic
220C2×C4×C73C2×C22⋊C411yescharacteristic
221C2×C4×C73C2×C22⋊C412yes—
222C2×C4×C73C2×M1612yes—
223C2×C4×C73C22×D412yes—
224C22⋊D73—28no—
225C22⋊D73—28no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—41no—
233C2×Dic73—41no—
234C2×Dic73—41no—
235C2×Dic73—41no—
236C2×Dic73—82no—
237C2×Dic73—82no—
238C2×Dic73C2×C22⋊C412yes—
239C2×Dic73C2×C22⋊C412yes—
240C2×Dic73C2×M1612yes—
241C2×Dic73C2×M1612yes—
242D292—24no—
243D292—24no—
244C4×D73—28no—
245C4×D73—28no—
246C4×D73—44no—
247C4×D73—44no—
248C4×D73—82no—
249C4×D73—82no—
250Dic146—24no—
251Dic146—24no—
252C8×C73—44no—
253#10596831—44no—
254C22×C73—21no—
255C22×C73—21no—
256C22×C73—22no—
257C22×C73—42no—
258C22×C73—42no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73C22×C22⋊C411yescharacteristic
262C22×C73C22×M1611yescharacteristic
263C22×C73C22×M1611yescharacteristic
264C2×D73—22no—
265C2×D73—22no—
266C2×D73—22no—
267C2×D73—22no—
268C2×D73—22no—
269C2×D73—42no—
270C2×D73—42no—
271C2×D73—42no—
272C2×D73—42no—
273C2×D73#40714yes—
274C4×C73—21no—
275C4×C73—21no—
276C4×C73—22no—
277C4×C73—22no—
278C4×C73—22no—
279C4×C73—41no—
280C4×C73—41no—
281Dic73—22no—
282Dic73—22no—
283Dic73—22no—
284Dic73—22no—
285Dic73—41no—
286Dic73—41no—
287#17368—731nomaximal, Sylow
288C2×C73—21no—
289C2×C73—21no—
290C2×C73—42no—
291C2×C73C2×#40711yescharacteristic
292C2×C73#288311yescharacteristic
293C2×C73#288911yescharacteristic
294D73—24no—
295D73—42no—
296C2×#520—731no—
297#2973—732no—
298#1467—732no—
299#1465—732no—
300#1464—731no—
301#1464D7311yescharacteristic, complemented
302#1463—732no—
303#1459—732no—
304C2×#324—732no—
305C73#1736811yescharacteristic, complemented, Sylow
306C22×#41—731no—
307#520—1464no—
308#520—1464no—
309C2×C4×Q8—731no—
310C2×C4×Q8—731no—
311C2×C4×D4—731no—
312C2×C4×D4—731no—
313C2×C4×D4—731no—
314C2×C4×D4—731no—
315C2×C4×D4—731no—
316C2×C4×D4—731no—
317C2×#117—731no—
318C2×#117—731no—
319C2×#117C2×D7311yescharacteristic
320C22×C4⋊C4—731no—
321C22×C4⋊C4—731no—
322C22×C4⋊C4—731no—
323#435—1464no—
324#435—1464no—
325#432—732no—
326#432C2×D7312yes—
327#407—734no—
328C2×C22⋊C8—734no—
329#324—732no—
330#324—734no—
331#324—734no—
332#324C2×D7312yes—
333#323—732no—
334#323C2×D7312yes—
335C2×#41—1464no—
336C2×#41—1462no—
337C2×#41—1462no—
338C2×#41—1464no—
339C22×Q8—731no—
340C22×D4—731no—
341C22×D4—731no—
342C22×D4—731no—
343C23×C4—731no—
344C23×C4—731no—
345C23×C4—731no—
346C23×C4—731no—
347C23×C4—731no—
348C23×C4—731no—
349C23×C4—731no—
350C23×C4—731no—
351C23×C4C4×D7311yescharacteristic
352C2×M16—1464no—
353C22×C8—1464no—
354C4×Q8—1462no—
355C4×Q8—1462no—
356C4×Q8—1462no—
357C4×Q8—1462no—
358C4×D4—734no—
359C4×D4—734no—
360C4×D4—1462no—
361C4×D4—1462no—
362C4×D4—1464no—
363C4×D4—1464no—
364C4×D4—1464no—
365C4×D4—1464no—
366#117—22no—
367#117—22no—
368#117—1464no—
369#117—1464no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—1464no—
379C2×C4⋊C4—1464no—
380C2×C4⋊C4—1462no—
381C2×C4⋊C4—1462no—
382C2×C4⋊C4C4×D7311yescharacteristic
383C2×C4⋊C4C22×D7311yescharacteristic
384C2×C22⋊C4—731no—
385C2×C22⋊C4—731no—
386C2×C22⋊C4—731no—
387C2×C22⋊C4—731no—
388C2×C22⋊C4C4×D7311yescharacteristic
389C2×C22⋊C4C22×D7311yescharacteristic
390C2×C42—731no—
391C2×C42—731no—
392C2×C42—731no—
393C2×C42—731no—
394C2×C42C4×D7311yescharacteristic
395C2×C42C22×D7311yescharacteristic
396C4⋊C8—22no—
397C4⋊C8—1462no—
398C22⋊C8—734no—
399C22⋊C8—1464no—
400C22⋊C8—1464no—
401C22⋊C8C22×D7314yes—
402#97—22no—
403#97—1462no—
404C24—731no—
405C24—731no—
406C24C2×C4×D7311yescharacteristic
407#41—14616no—
408#41—14616no—
409C2×Q8—1462no—
410C2×Q8—1462no—
411C2×Q8—1461no—
412C2×Q8—1461no—
413C2×D4—734no—
414C2×D4—732no—
415C2×D4—732no—
416C2×D4—1462no—
417C2×D4—1462no—
418C2×D4—1462no—
419C2×D4—1462no—
420C2×D4—1462no—
421C2×D4—1462no—
422C2×D4—1462no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—5841no—
428C22×C4—5841no—
429C22×C4—5841no—
430C22×C4—5841no—
431C22×C4—5841no—
432C22×C4—5841no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—734no—
436C22×C4—734no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—734no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4C2×C4×D7311yescharacteristic
452C22×C4C2×C4×D7311yescharacteristic
453C22×C4C2×C4×D7311yescharacteristic
454C22×C4C2×C4×D7311yescharacteristic
455C22×C4C2×C4×D7311yescharacteristic
456C22×C4C23×D7311yescharacteristic
457M16—5844no—
458C2×C8—24no—
459C2×C8—5844no—
460C2×C8—1464no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—732no—
464C4⋊C4—732no—
465C4⋊C4—1462no—
466C4⋊C4—1462no—
467C4⋊C4—1462no—
468C4⋊C4—1462no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1462no—
472C4⋊C4—1462no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—734no—
476C22⋊C4—734no—
477C22⋊C4—1462no—
478C22⋊C4—1462no—
479C42—21no—
480C42—21no—
481C42—1462no—
482C42—1462no—
483C42—1462no—
484C42—1462no—
485C42D4×D7312yes—
486C42D4×D7312yes—
487C23—21no—
488C23—21no—
489C23—41no—
490C23—41no—
491C23—2921no—
492C23—2921no—
493C23—2921no—
494C23—2921no—
495C23—732no—
496C23—732no—
497C23—732no—
498C23—732no—
499C23—1461no—
500C23—1461no—
501C23M16×D7312yes—
502C23C22×C4×D7311yescharacteristic
503Q8—1464no—
504Q8—1464no—
505D4—1464no—
506D4—1464no—
507D4—1468no—
508D4—1468no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—2924no—
522C2×C4—2924no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—5842no—
528C2×C4—5842no—
529C2×C4—5842no—
530C2×C4—5842no—
531C2×C4—732no—
532C2×C4—732no—
533C2×C4—732no—
534C2×C4—732no—
535C2×C4—1468no—
536C2×C4—1468no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1461no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4C22⋊C4×D7311yescharacteristic
544C2×C4C22⋊C4×D7311yescharacteristic
545C2×C4C22⋊C4×D7312yes—
546C2×C4M16×D7312yes—
547C2×C4C2×D4×D7312yes—
548C8—44no—
549C8—2924no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—41no—
557C22—2922no—
558C22—2922no—
559C22—2922no—
560C22—2922no—
561C22—734no—
562C22—1462no—
563C22—1462no—
564C22—1462no—
565C22—1462no—
566C22—1462no—
567C22C2×C22⋊C4×D7311yescharacteristic
568C22C2×M16×D7311yescharacteristic
569C22C2×M16×D7311yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—21no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—2921no—
578C4—2921no—
579C4—1462no—
580C4—1462no—
581C4—1462no—
582C4—1462no—
583C2—21no—
584C2—21no—
585C2—42no—
586C2—2922no—
587C2—1464no—
588C2#407×D7311yescharacteristic
589C2#2261839011yescharacteristic
590C2#2261841211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1464C2
socleC22×C73C22×C22⋊C4
prime radicalC22×#11924028C4
cosocleC22×C4×C73C24
hypercenter#1464D73
hypocenterC73#17368
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #22618959C2semidirect
3. #22608274C2semidirect
4. #22608266C2semidirect
5. #22608265C2semidirect
6. #22608259C2semidirect
7. #22608246C2semidirect
8. #324×D73C2semidirect
9. C73×#1464C2semidirect
125. C2×C22⋊D73M16semidirect
147. C2×C4×D73M16semidirect
301. #1464D73semidirect
305. C73#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#179890672
#226189592
#226082742
#226082662
#226082652
#226082592
#226082462
#324×D732
C73×#14642
#1736873