Finite Group Databasebeta

← #33057352

Subgroups — #33057352

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619963C211yesmaximal, characteristic
2#22619018C211yesmaximal, characteristic, complemented
3#22618997C211yesmaximal, characteristic
4#22608835C211yesmaximal, characteristic, complemented
5#22608823C211yesmaximal, characteristic, complemented
6#22608811C211yesmaximal, characteristic, complemented
7#22608790C211yesmaximal, characteristic, complemented
8#22608776C211yesmaximal, characteristic, complemented
9#22608769C211yesmaximal, characteristic, complemented
10#22608745C211yesmaximal, characteristic, complemented
11C8×#11924017C211yesmaximal, characteristic, complemented
12#22608711C211yesmaximal, characteristic, complemented
13#22608401C211yesmaximal, characteristic
14#22608327C211yesmaximal, characteristic, complemented
15C73×#1454C211yesmaximal, characteristic, complemented
16#17989137C2211yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18#17988906C411yescharacteristic
19#17988906C411yescharacteristic
20#17988873C411yescharacteristic
21#17988873C411yescharacteristic
22#17988788C411yescharacteristic
23#17988788C411yescharacteristic
24#17988728C411yescharacteristic
25#17988728C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988717C2211yescharacteristic
28#17988716—21no—
29#17988716—21no—
30C8×Dic146C2211yescharacteristic
31C8×Dic146C2211yescharacteristic
32C4×#11924017C2211yescharacteristic
33C4×#11924017C2211yescharacteristic
34C4×#11924017C2211yescharacteristic
35C4×#11924017C2211yescharacteristic
36#17988666C2211yescharacteristic
37#17988666C2211yescharacteristic
38#17988664—21no—
39C8×D292C2211yescharacteristic
40C8×D292C2211yescharacteristic
41#17988652—21no—
42#17988644C2211yescharacteristic
43#17988641—21no—
44#17988640C2211yescharacteristic
45#17988637—21no—
46#17988552—21no—
47#17988552—21no—
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988338C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988316C2211yescharacteristic
57#17988316C2211yescharacteristic
58#17988316C2211yescharacteristic
59#17988316C2211yescharacteristic
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic
64#322×C73C2211yescharacteristic
65#322×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#11924028—21no—
68C22×Dic146C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×#11924017C2×C411yescharacteristic
72C2×#11924017C2×C411yescharacteristic
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77#14556591C2×C411yescharacteristic
78#14556588C2×C411yescharacteristic
79#14556579—21no—
80#14556565—21no—
81#14556565C2×C411yescharacteristic
82#14556565C2×C411yescharacteristic
83C4×Dic146—21no—
84C4×Dic146—21no—
85C4×Dic146C2×C411yescharacteristic
86C4×Dic146C2×C411yescharacteristic
87C4×Dic146C2311yescharacteristic
88C4×Dic146C2311yescharacteristic
89C4×D292—21no—
90C4×D292C2311yescharacteristic
91C4×D292C2311yescharacteristic
92C2×C4⋊Dic73C2×C411yescharacteristic
93C2×#11924007—21no—
94C2×C4×Dic73—21no—
95#14556523C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97#14556523C2×C411yescharacteristic
98#14556523C2×C411yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115C22⋊#10596831—21no—
116C22⋊#10596831—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556502—21no—
122#14556501—21no—
123#14556501—21no—
124C4×#10596831—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—21no—
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C22⋊C8×C73—21no—
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73C2×C411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137C22⋊C8×C73D411yescharacteristic
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—81no—
145#11924028—81no—
146C2×Dic146—22no—
147C2×Dic146—21no—
148C2×Dic146—21no—
149C2×Dic146—41no—
150C2×Dic146C22×C411yescharacteristic
151C2×Dic146C22×C411yescharacteristic
152C2×D292—21no—
153C2×D292—21no—
154C2×D292C22×C411yescharacteristic
155C2×D292C22×C411yescharacteristic
156C2×C22⋊D73—21no—
157C2×C22⋊D73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162#11924017—22no—
163#11924017—22no—
164#11924017—41no—
165#11924017—41no—
166#11924011—81no—
167#11924011—81no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C8×D73—81no—
173C8×D73—81no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73C22×C411yescharacteristic
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179C4⋊Dic73C22×C411yescharacteristic
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183#11924007—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73#4111yescharacteristic
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73C4×D411yescharacteristic
210C22×D73—21no—
211C22×D73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—41no—
217C2×C4×C73C4×D411yescharacteristic
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C22⋊D73—81no—
224C22⋊D73—81no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—42no—
232C2×Dic73—42no—
233D292—21no—
234D292—21no—
235D292—21no—
236D292—21no—
237D292—42no—
238D292—81no—
239C4×D73—41no—
240C4×D73—41no—
241C4×D73—41no—
242C4×D73—41no—
243Dic146—21no—
244Dic146—21no—
245Dic146—21no—
246Dic146—42no—
247Dic146—81no—
248Dic146#13112yes—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73—21no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—41no—
258C8×C73—41no—
259#10596831—41no—
260#10596831—41no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—21no—
266C22×C73C2×C4×D411yescharacteristic
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C2×D73—41no—
271C2×D73—41no—
272C2×D73—41no—
273C4×C73—21no—
274C4×C73—21no—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73C2×#13111yescharacteristic
278C4×C73#56811yescharacteristic
279C4×C73#57711yescharacteristic
280C4×C73#57711yescharacteristic
281Dic73—22no—
282Dic73—41no—
283Dic73—41no—
284Dic73—41no—
285Dic73—41no—
286Dic73—41no—
287#18030—731nomaximal, Sylow
288C2×C73—41no—
289C2×C73#293311yescharacteristic
290C2×C73#294911yescharacteristic
291C2×C73#295511yescharacteristic
292D73—81no—
293D73—81no—
294#3103—731no—
295#2984—731no—
296#2979—731no—
297#1592—731no—
298#1590—731no—
299#1588—731no—
300#1585—731no—
301#1583—731no—
302#1582—731no—
303SD16⋊C8—731no—
304C8×SD16—731no—
305#1572—731no—
306#1496—731no—
307#1479—731no—
308#1454D7311yescharacteristic, complemented
309C73#1803011yescharacteristic, complemented, Sylow
310#532—731no—
311C2×C4×Q8—731no—
312#481—731no—
313#481—731no—
314#475—731no—
315#475—731no—
316#460—731no—
317#460—731no—
318#448—731no—
319#448—731no—
320#446—731no—
321#446—731no—
322#446—1461no—
323#446—1461no—
324C8×Q8—731no—
325C8×Q8—731no—
326C4×SD16—731no—
327C4×SD16—731no—
328C4×SD16—731no—
329C4×SD16—731no—
330#436—731no—
331#436—731no—
332#436—1461no—
333C8×D4—731no—
334C8×D4—731no—
335C8×D4—1461no—
336#432—731no—
337#432—1461no—
338#431—731no—
339#431—1461no—
340#431C2×D7311yescharacteristic
341#431C2×D7311yescharacteristic
342#431C2×D7311yescharacteristic
343#408—1461no—
344#408—1461no—
345#335—731no—
346#335—731no—
347#334—731no—
348#334—731no—
349Q8⋊C8—731no—
350Q8⋊C8—731no—
351Q8⋊C8—731no—
352Q8⋊C8—731no—
353D4⋊C8—731no—
354D4⋊C8—731no—
355D4⋊C8—731no—
356D4⋊C8—731no—
357#322C2×D7311yescharacteristic
358#322C2×D7311yescharacteristic
359#322C2×D7311yescharacteristic
360C82C2×D7311yescharacteristic
361C2×#41—1461no—
362C22×Q8—731no—
363C2×SD16—731no—
364C2×SD16—731no—
365C2×SD16—731no—
366C2×SD16—731no—
367C2×M16—1461no—
368C2×M16—1461no—
369C22×C8—1461no—
370C22×C8—1461no—
371C4⋊Q8—731no—
372#127—731no—
373#124—1461no—
374#121—731no—
375#121—731no—
376#121—1461no—
377C4×Q8—731no—
378C4×Q8—731no—
379C4×Q8—731no—
380C4×Q8—731no—
381C4×Q8—1461no—
382C4×Q8—1461no—
383C4×D4—731no—
384C4×D4—731no—
385C4×D4—1461no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—1461no—
388C2×C42—1461no—
389C2×C42C22×D7311yescharacteristic
390#106—731no—
391#106—731no—
392#106—731no—
393#106—731no—
394C4⋊C8—21no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8C4×D7311yescharacteristic
404C4⋊C8C4×D7311yescharacteristic
405C4⋊C8D29211yescharacteristic
406C4⋊C8D29211yescharacteristic
407#103—731no—
408#103—731no—
409#103—731no—
410#103—731no—
411#102—731no—
412#102—731no—
413#102—731no—
414#102—731no—
415C22⋊C8—21no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420C22⋊C8—1461no—
421C22⋊C8—1461no—
422C22⋊C8C4×D7311yescharacteristic
423C22⋊C8C4×D7311yescharacteristic
424C22⋊C8D29211yescharacteristic
425C22⋊C8D29211yescharacteristic
426#97—1461no—
427#97—1461no—
428#97—1461no—
429C4×C8—1461no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435C4×C8C22×D7311yescharacteristic
436C4×C8C22×D7311yescharacteristic
437C4×C8C22×D7311yescharacteristic
438#41—5841no—
439#41—5841no—
440C2×Q8—2921no—
441C2×Q8—731no—
442C2×Q8—731no—
443C2×Q8—1462no—
444C2×Q8—1461no—
445C2×Q8—1461no—
446C2×D4—731no—
447C2×D4—731no—
448C2×D4—1461no—
449C2×D4—1461no—
450C2×D4—1461no—
451C2×D4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4C2×C4×D7311yescharacteristic
457C22×C4C2×D29211yescharacteristic
458C22×C4#1192402811yescharacteristic
459SD16—2921no—
460SD16—2921no—
461SD16—1462no—
462SD16—1462no—
463M16—5841no—
464M16—5841no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—5841no—
468C2×C8—5841no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8C2×C4×D7311yescharacteristic
474C2×C8C2×C4×D7311yescharacteristic
475C2×C8C2×C4×D7311yescharacteristic
476C2×C8C2×C4×D7311yescharacteristic
477C2×C8C2×D29211yescharacteristic
478C2×C8C2×D29211yescharacteristic
479C2×C8C2×D29211yescharacteristic
480C2×C8C2×D29211yescharacteristic
481C4⋊C4—731no—
482C4⋊C4—731no—
483C4⋊C4—731no—
484C4⋊C4—731no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4—1461no—
491C22⋊C4—1461no—
492C22⋊C4—1461no—
493C22⋊C4—1461no—
494C22⋊C4—1461no—
495C42—1461no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C42C2×C4×D7311yescharacteristic
500C42C2×D29211yescharacteristic
501C42#1192402811yescharacteristic
502C42C23×D7311yescharacteristic
503C23—1461no—
504C23—1461no—
505C23C4×D29211yescharacteristic
506Q8—2922no—
507Q8—5841no—
508Q8—732no—
509Q8—1461no—
510Q8—1461no—
511Q8—1461no—
512D4—2922no—
513D4—5841no—
514D4—5841no—
515D4—5841no—
516D4—1461no—
517D4—1461no—
518D4—1461no—
519D4—1461no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—2922no—
526C2×C4—2922no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—2921no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4C4×D29211yescharacteristic
538C2×C4C4×D29211yescharacteristic
539C2×C4C4×D29211yescharacteristic
540C2×C4C22×C4×D7311yescharacteristic
541C2×C4C22×D29211yescharacteristic
542C2×C4C2×#1192402811yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—2921no—
554C8—2921no—
555C8—2921no—
556C8—2921no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—2921no—
561C22—2921no—
562C22—2921no—
563C22—2921no—
564C22—2921no—
565C22—2921no—
566C22C2×C4×D29211yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—2921no—
572C4—2921no—
573C4—2921no—
574C4—2921no—
575C4—2921no—
576C4—1462no—
577C4#131×D7311yescharacteristic
578C4#1798935211yescharacteristic
579C4#1798939911yescharacteristic
580C4#1798939911yescharacteristic
581C2—41no—
582C2—5841no—
583C2—5841no—
584C2#2261865911yescharacteristic
585C2#2261879211yescharacteristic
586C2#2261883511yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1454C2
socleC22×C73C2×C4×D4
prime radical#17989137C22
cosocleC42×C73C24
hypercenter#1454D73
hypocenterC73#18030
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #22619018C2semidirect
4. #22608835C2semidirect
5. #22608823C2semidirect
6. #22608811C2semidirect
7. #22608790C2semidirect
8. #22608776C2semidirect
9. #22608769C2semidirect
10. #22608745C2semidirect
11. C8×#11924017C2semidirect
12. #22608711C2semidirect
14. #22608327C2semidirect
15. C73×#1454C2semidirect
308. #1454D73semidirect
309. C73#18030semidirect

Maximal subgroups

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

subgroupindex
#226199632
#226190182
#226189972
#226088352
#226088232
#226088112
#226087902
#226087762
#226087692
#226087452
C8×#119240172
#226087112
#226084012
#226083272
C73×#14542
#1803073