Finite Group Databasebeta

← #33057202

Subgroups — #33057202

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620000C211yesmaximal, characteristic
2#22619062C211yesmaximal, characteristic
3#22619029C211yesmaximal, characteristic, complemented
4#22608821C211yesmaximal, characteristic, complemented
5#22608820C211yesmaximal, characteristic, complemented
6#22608811C211yesmaximal, characteristic, complemented
7#22608806C211yesmaximal, characteristic, complemented
8#22608799C211yesmaximal, characteristic, complemented
9Q16×#10596831C211yesmaximal, characteristic, complemented
10C8×#11924018C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608384C211yesmaximal, characteristic, complemented
13#22608312C211yesmaximal, characteristic
14#22608216C211yesmaximal, characteristic, complemented
15C73×#1587C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×#11924029C2211yescharacteristic
18#17988930C411yescharacteristic
19#17988926C411yescharacteristic
20#17988870C411yescharacteristic
21#17988866C411yescharacteristic
22#17988795C411yescharacteristic
23#17988791C411yescharacteristic
24#17988752C411yescharacteristic
25#17988748C411yescharacteristic
26#17988715—21no—
27#17988714C2211yescharacteristic
28Q8×#10596831C2211yescharacteristic
29Q8×#10596831C2211yescharacteristic
30C8×Dic146C2211yescharacteristic
31#17988711—21no—
32C4×#11924018C2211yescharacteristic
33C4×#11924017C2211yescharacteristic
34C4×#11924015C2211yescharacteristic
35#17988666—21no—
36#17988666C2211yescharacteristic
37#17988664—21no—
38#17988664C2211yescharacteristic
39#17988649—21no—
40#17988647—21no—
41#17988639C2211yescharacteristic
42#17988638—21no—
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988609—21no—
46#17988609C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988308C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×#11924011—21no—
73C2×#11924011—21no—
74C2×C8×D73—21no—
75#14556590C2×C411yescharacteristic
76#14556589C2×C411yescharacteristic
77#14556581—21no—
78#14556571C2×C411yescharacteristic
79#14556569—21no—
80#14556567C2×C411yescharacteristic
81Q8×Dic73C2×C411yescharacteristic
82C4×Dic146—21no—
83C4×Dic146C2311yescharacteristic
84C4×D292—21no—
85C4×D292C2311yescharacteristic
86#14556553—21no—
87#14556553C2×C411yescharacteristic
88#14556549—21no—
89#14556549C2×C411yescharacteristic
90#14556548—21no—
91C42×D73—21no—
92C42×D73C2311yescharacteristic
93#14556524C2×C411yescharacteristic
94#14556523C2×C411yescharacteristic
95#14556522C2×C411yescharacteristic
96C4⋊#10596831—21no—
97C4⋊#10596831—21no—
98C4⋊#10596831C2311yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503C2×C411yescharacteristic
117#14556503C2×C411yescharacteristic
118#14556503D411yescharacteristic
119#14556503D411yescharacteristic
120#14556501—21no—
121C4×#10596831—21no—
122C4×#10596831—21no—
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×Q16×C73C2×C411yescharacteristic
130C4×Q8×C73C2311yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132#107×C73C2×C411yescharacteristic
133C4⋊C8×C73—21no—
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#103×C73C2×C411yescharacteristic
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924029—22no—
145#11924029—41no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73C22×C411yescharacteristic
154C2×C4×D73C2×D411yescharacteristic
155C2×C4×D73#4111yescharacteristic
156#11924018—22no—
157#11924017—41no—
158#11924015—41no—
159#11924011—81no—
160#11924011—81no—
161#11924011—81no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C8×D73—24no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73C22×C411yescharacteristic
188C4×Dic73C2×D411yescharacteristic
189C4×Dic73#4111yescharacteristic
190C2×Q8×C73C22×C411yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192Q16×C73—22no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C42×C73—21no—
205C42×C73—21no—
206C42×C73C2411yescharacteristic
207C22×D73—21no—
208C22×D73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73#13112yes—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73C4×D411yescharacteristic
224C2×Dic73C4×D411yescharacteristic
225C2×Dic73C4×D411yescharacteristic
226D292—21no—
227D292—21no—
228D292—42no—
229C4×D73—21no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—22no—
234C4×D73—42no—
235C4×D73—41no—
236C4×D73—41no—
237C4×D73—42no—
238Dic146—21no—
239Dic146—21no—
240Dic146—42no—
241C8×C73—22no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—41no—
247C8×C73—41no—
248#10596831—22no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—41no—
254#10596831—41no—
255C22×C73C2×C4×D411yescharacteristic
256C2×D73—21no—
257C2×D73—21no—
258C2×D73—21no—
259C2×D73—41no—
260C2×D73—41no—
261C2×D73—41no—
262C4×C73—22no—
263C4×C73—21no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73C2×#13111yescharacteristic
268C4×C73#56811yescharacteristic
269C4×C73#57711yescharacteristic
270C4×C73#57811yescharacteristic
271Dic73—21no—
272Dic73—21no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276Dic73#44312yes—
277#18019—731nomaximal, Sylow
278C2×C73#293311yescharacteristic
279C2×C73#294711yescharacteristic
280C2×C73C2×#44311yescharacteristic
281D73—41no—
282D73—81no—
283#3107—731no—
284#2991—731no—
285#2986—731no—
286#1590—731no—
287#1590—731no—
288#1588—731no—
289#1588—731no—
290#1587—731no—
291#1587D7311yescharacteristic, complemented
292C8×Q16—731no—
293C8×Q16—731no—
294#1574—731no—
295#1493—731no—
296#1476—731no—
297#1450—731no—
298C73#1801911yescharacteristic, complemented, Sylow
299#533—731no—
300C4×#41—731no—
301#485—731no—
302#485—731no—
303#475—731no—
304#474—731no—
305#462—731no—
306#461—731no—
307#452—731no—
308#452—731no—
309#446—731no—
310#446—1461no—
311#446C2×D7311yescharacteristic
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—731no—
315C8×Q8—1461no—
316C8×Q8C2×D7311yescharacteristic
317C4×Q16—731no—
318C4×Q16C2×D7311yescharacteristic
319C4×SD16—731no—
320C4×SD16—731no—
321#436—731no—
322#436—731no—
323#436—1461no—
324#436—1461no—
325#433—1461no—
326#433—1461no—
327#431—731no—
328#431—731no—
329#431—731no—
330#431—1461no—
331#423—731no—
332#423—1461no—
333C2×C4×C8—731no—
334#335—731no—
335#335—731no—
336#334—731no—
337#334C2×D7311yescharacteristic
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8C2×D7311yescharacteristic
343Q8⋊C8C2×D7311yescharacteristic
344D4⋊C8—731no—
345D4⋊C8—731no—
346#322—731no—
347#322C2×D7311yescharacteristic
348C82—731no—
349C82—731no—
350C2×#41—731no—
351C2×Q16—731no—
352C2×Q16C4×D7311yescharacteristic
353C2×SD16—731no—
354C2×SD16—731no—
355C2×M16—1461no—
356C2×M16—1461no—
357C2×M16—1461no—
358C22×C8—1461no—
359C4⋊Q8—731no—
360C4⋊Q8—731no—
361#125—1461no—
362C22⋊Q8—731no—
363C22⋊Q8—731no—
364C22⋊Q8—1461no—
365C4×Q8—731no—
366C4×Q8—731no—
367C4×Q8—1461no—
368C4×Q8C22×D7311yescharacteristic
369C4×Q8C22×D7311yescharacteristic
370C4×D4—731no—
371C4×D4—731no—
372C4×D4—1461no—
373C4×D4—1461no—
374#117—731no—
375#117—1461no—
376#117—1461no—
377C2×C42—731no—
378C2×C42—1461no—
379#107—731no—
380#107C4×D7311yescharacteristic
381#106—731no—
382#106—731no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8C22×D7311yescharacteristic
397C4⋊C8C22×D7311yescharacteristic
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103C4×D7311yescharacteristic
403#103C4×D7311yescharacteristic
404#102—731no—
405#102—731no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—731no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—21no—
414#97—1461no—
415C4×C8—21no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—1461no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426C4×C8C22×D7311yescharacteristic
427#41—2921no—
428#41—1462no—
429C2×Q8—731no—
430C2×Q8—1461no—
431C2×Q8C2×C4×D7311yescharacteristic
432C2×Q8C2×C4×D7311yescharacteristic
433C2×D4—731no—
434C2×D4—1461no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4—1461no—
441Q16—22no—
442Q16—1462no—
443SD16—2921no—
444SD16—2921no—
445M16—5841no—
446M16—5841no—
447M16—5841no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—1464no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8C2×C4×D7311yescharacteristic
460C2×C8C2×C4×D7311yescharacteristic
461C2×C8D4×D7311yescharacteristic
462C2×C8D4×D7311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—731no—
466C4⋊C4—731no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4C2×C4×D7311yescharacteristic
475C4⋊C4C2×C4×D7311yescharacteristic
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—21no—
483C42—731no—
484C42—731no—
485C42—731no—
486C42—1461no—
487C42—1461no—
488C42—1461no—
489C42C23×D7311yescharacteristic
490C23—731no—
491C23—1461no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—2922no—
496Q8—1461no—
497Q8—1461no—
498Q8#1455659912yes—
499D4—2922no—
500D4—1461no—
501D4—1461no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—2922no—
507C2×C4—2922no—
508C2×C4—2921no—
509C2×C4—2921no—
510C2×C4—731no—
511C2×C4—731no—
512C2×C4—731no—
513C2×C4—1462no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4C22×C4×D7311yescharacteristic
522C2×C4C2×D4×D7311yescharacteristic
523C2×C4#41×D7311yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—2921no—
532C8—2921no—
533C8—1462no—
534C8—1461no—
535C8—1461no—
536C8—1461no—
537C8—1461no—
538C22—2921no—
539C22—2921no—
540C22—2921no—
541C22—1461no—
542C22—1461no—
543C22—1461no—
544C22C4×D4×D7311yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—2921no—
551C4—2921no—
552C4—2921no—
553C4—732no—
554C4—1461no—
555C4—1461no—
556C4C2×#1455659911yescharacteristic
557C4#1798935211yescharacteristic
558C4#1798939611yescharacteristic
559C4#1798940311yescharacteristic
560C2—2921no—
561C2—5841no—
562C2#2261865711yescharacteristic
563C2#2261877311yescharacteristic
564C2#443×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1587C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924029C2×C4
cosocleC42×C73C24
hypercenter#1587D73
hypocenterC73#18019
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
3. #22619029C2semidirect
4. #22608821C2semidirect
5. #22608820C2semidirect
6. #22608811C2semidirect
7. #22608806C2semidirect
8. #22608799C2semidirect
9. Q16×#10596831C2semidirect
10. C8×#11924018C2semidirect
11. #22608718C2semidirect
12. #22608384C2semidirect
14. #22608216C2semidirect
15. C73×#1587C2semidirect
291. #1587D73semidirect
298. C73#18019semidirect

Maximal subgroups

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

subgroupindex
#226200002
#226190622
#226190292
#226088212
#226088202
#226088112
#226088062
#226087992
Q16×#105968312
C8×#119240182
#226087182
#226083842
#226083122
#226082162
C73×#15872
#1801973