Finite Group Databasebeta

← #33056084

Subgroups — #33056084

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619998C211yesmaximal, characteristic
2#22619038C211yesmaximal, characteristic
3#22619027C211yesmaximal, characteristic, complemented
4#22608800C211yesmaximal, characteristic, complemented
5#22608788C211yesmaximal, characteristic, complemented
6#22608783C211yesmaximal, characteristic, complemented
7#22608749C211yesmaximal, characteristic, complemented
8SD16⋊#10596831C211yesmaximal, characteristic, complemented
9#22608735C211yesmaximal, characteristic, complemented
10#22608734C211yesmaximal, characteristic, complemented
11#22608713C211yesmaximal, characteristic, complemented
12#22608362C211yesmaximal, characteristic
13#22608332C211yesmaximal, characteristic, complemented
14#22608232C211yesmaximal, characteristic, complemented
15C73×#1582C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×#11924027C2211yescharacteristic
18#17988931C411yescharacteristic
19#17988927C411yescharacteristic
20#17988871C411yescharacteristic
21#17988865C411yescharacteristic
22#17988796C411yescharacteristic
23#17988790C411yescharacteristic
24#17988750C411yescharacteristic
25#17988746C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988715—21no—
28#17988714—21no—
29Q8×#10596831C2211yescharacteristic
30C8×Dic146C2211yescharacteristic
31#17988711C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×Dic292C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924016C2211yescharacteristic
36D4×#10596831C2211yescharacteristic
37C8×C22⋊D73—21no—
38#17988650—21no—
39#17988649—21no—
40#17988647—21no—
41#17988643C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988637—21no—
46C2×#14556520—21no—
47C4⋊C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988317C2211yescharacteristic
56D4⋊#10596831C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924027C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C22×#10596831—21no—
72C2×C8×D73—21no—
73#14556590C2×C411yescharacteristic
74#14556589C2×C411yescharacteristic
75#14556581—21no—
76#14556571C2×C411yescharacteristic
77#14556569—21no—
78#14556567C2×C411yescharacteristic
79C4×Dic146—21no—
80C4×Dic146C2311yescharacteristic
81C4×Dic146C2311yescharacteristic
82#14556556C2×C411yescharacteristic
83D4×Dic73C2×C411yescharacteristic
84C4×C22⋊D73—21no—
85#14556551—21no—
86#14556549C2×C411yescharacteristic
87#14556548—21no—
88#14556547—21no—
89C2×C4×Dic73—21no—
90C42×D73C2311yescharacteristic
91#14556525C2×C411yescharacteristic
92#14556524C2×C411yescharacteristic
93#14556522C2×C411yescharacteristic
94C4⋊#10596831—21no—
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556514C2×C411yescharacteristic
112#14556512C2×C411yescharacteristic
113C22⋊#10596831—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503C2×C411yescharacteristic
117#14556503C2×C411yescharacteristic
118#14556503D411yescharacteristic
119#14556503D411yescharacteristic
120#14556501—21no—
121#14556501—21no—
122C4×#10596831—21no—
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×SD16×C73C2×C411yescharacteristic
130C22×C8×C73—21no—
131C4×Q8×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133#106×C73C2×C411yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924027—22no—
145#11924027—22no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C2×C22⋊D73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C2×C4×D73C22×C411yescharacteristic
153C2×C4×D73C2×D411yescharacteristic
154C2×C4×D73#4111yescharacteristic
155Dic292—22no—
156#11924018—22no—
157#11924016—22no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—81no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C8×D73—81no—
167C4⋊Dic73—21no—
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177C22⋊Dic73—21no—
178#11924005—21no—
179#11924005—21no—
180#11924005—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73C22×C411yescharacteristic
186C4×Dic73C2×D411yescharacteristic
187C4×Dic73#4111yescharacteristic
188C2×Q8×C73C22×C411yescharacteristic
189C2×D4×C73C22×C411yescharacteristic
190C22×C4×C73—21no—
191SD16×C73—22no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—81no—
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C4⋊C4×C73—21no—
201C4⋊C4×C73C22×C411yescharacteristic
202C4⋊C4×C73C22×C411yescharacteristic
203C22⋊C4×C73—21no—
204C42×C73—21no—
205C42×C73C2411yescharacteristic
206C23×C73—21no—
207C22×D73C4×D411yescharacteristic
208Q8×C73—21no—
209Q8×C73—21no—
210D4×C73—21no—
211D4×C73#13112yes—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C22⋊D73—24no—
221C2×Dic73—24no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—81no—
227C2×Dic73C4×D411yescharacteristic
228C2×Dic73C4×D411yescharacteristic
229C2×Dic73C4×D411yescharacteristic
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—21no—
234C4×D73—41no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—81no—
239Dic146#13112yes—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—41no—
245C8×C73—41no—
246C8×C73—41no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254C22×C73—22no—
255C22×C73—41no—
256C22×C73—41no—
257C22×C73C2×C4×D411yescharacteristic
258C2×D73—21no—
259C2×D73—21no—
260C2×D73—21no—
261C4×C73—21no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73C2×#13111yescharacteristic
266C4×C73C2×#13111yescharacteristic
267C4×C73#57711yescharacteristic
268C4×C73#57811yescharacteristic
269Dic73—22no—
270Dic73—21no—
271Dic73—21no—
272Dic73—21no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276#17921—731nomaximal, Sylow
277C2×C73—42no—
278C2×C73#292911yescharacteristic
279C2×C73#294711yescharacteristic
280C2×C73#295711yescharacteristic
281D73—41no—
282#3107—731no—
283#2988—731no—
284#2985—731no—
285#1587—731no—
286#1585—731no—
287#1584—731no—
288#1582D7311yescharacteristic, complemented
289#1579—731no—
290SD16⋊C8—731no—
291C8×Q16—731no—
292C8×SD16—731no—
293#1573—731no—
294#1488—731no—
295#1481—731no—
296#1454—731no—
297C73#1792111yescharacteristic, complemented, Sylow
298#533—731no—
299C4×#41—731no—
300#485—731no—
301#485—731no—
302#475—731no—
303#474—731no—
304#462—731no—
305#461—731no—
306#452—731no—
307#452—731no—
308#446—731no—
309#446—1461no—
310#446—1461no—
311#446C2×D7311yescharacteristic
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—731no—
315C8×Q8—731no—
316C4×Q16—731no—
317C4×Q16—731no—
318C4×SD16—731no—
319C4×SD16C2×D7311yescharacteristic
320C8×D4—731no—
321C8×D4—1461no—
322C8×D4—1461no—
323C8×D4C2×D7311yescharacteristic
324#433—1461no—
325#433—1461no—
326#432—731no—
327#431—731no—
328#431—731no—
329#431—731no—
330#431—1461no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—1461no—
333#335—731no—
334#335—731no—
335#334—731no—
336#334C2×D7311yescharacteristic
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8C2×D7311yescharacteristic
343D4⋊C8—731no—
344D4⋊C8C2×D7311yescharacteristic
345#322—731no—
346#322—731no—
347#322C2×D7311yescharacteristic
348C82—731no—
349C2×#41—731no—
350C2×Q16—731no—
351C2×Q16—731no—
352C2×SD16—731no—
353C2×SD16C4×D7311yescharacteristic
354C22×C8—21no—
355C22×C8—1461no—
356C22×C8—1461no—
357C4⋊Q8—731no—
358C4⋊Q8—731no—
359#125—1461no—
360C22⋊Q8—731no—
361C22⋊Q8—731no—
362C22⋊Q8—1461no—
363C4×Q8—731no—
364C4×Q8—731no—
365C4×Q8—731no—
366C4×Q8—1461no—
367C4×Q8C22×D7311yescharacteristic
368C4×D4—731no—
369C4×D4—1461no—
370C4×D4—1461no—
371C4×D4C22×D7311yescharacteristic
372#117—731no—
373#117—1461no—
374#117—1461no—
375C2×C42—731no—
376C2×C42—1461no—
377#107—731no—
378#107—731no—
379#106—731no—
380#106C4×D7311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—731no—
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8C22×D7311yescharacteristic
396C4⋊C8C22×D7311yescharacteristic
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103C4×D7311yescharacteristic
403#102—731no—
404#102C4×D7311yescharacteristic
405C22⋊C8—21no—
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—
415#97—1461no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—1461no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426#41—1462no—
427#41—1462no—
428C2×Q8—731no—
429C2×Q8—731no—
430C2×Q8—1461no—
431C2×Q8C2×C4×D7311yescharacteristic
432C2×D4—1461no—
433C2×D4C2×C4×D7311yescharacteristic
434C22×C4—21no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—1461no—
439C22×C4—1461no—
440Q16—1462no—
441Q16—1462no—
442SD16—22no—
443SD16—1462no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—5841no—
449C2×C8—5841no—
450C2×C8—731no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8C2×C4×D7311yescharacteristic
458C2×C8C2×C4×D7311yescharacteristic
459C2×C8D4×D7311yescharacteristic
460C2×C8D4×D7311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—731no—
463C4⋊C4—731no—
464C4⋊C4—1461no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4C2×C4×D7311yescharacteristic
473C4⋊C4C2×C4×D7311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C42—21no—
480C42—731no—
481C42—731no—
482C42—731no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42C23×D7311yescharacteristic
488C23—21no—
489C23—731no—
490Q8—21no—
491Q8—21no—
492Q8—5841no—
493Q8—732no—
494Q8—1461no—
495Q8—1461no—
496Q8—1461no—
497D4—21no—
498D4—1464no—
499D4#1455659912yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—2921no—
506C2×C4—5841no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—731no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1464no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4C22×C4×D7311yescharacteristic
520C2×C4C2×D4×D7311yescharacteristic
521C2×C4#41×D7311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—2921no—
530C8—2921no—
531C8—2921no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22—1461no—
540C22—1461no—
541C22—1461no—
542C22C4×D4×D7311yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—2921no—
548C4—2921no—
549C4—2921no—
550C4—1461no—
551C4—1461no—
552C4—1461no—
553C4—1462no—
554C4#131×D7311yescharacteristic
555C4C2×#1455659911yescharacteristic
556C4#1798939311yescharacteristic
557C4#1798940111yescharacteristic
558C2—42no—
559C2—2921no—
560C2#2261862211yescharacteristic
561C2#2261876711yescharacteristic
562C2#2261884511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1582C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924027C2×C4
cosocleC42×C73C24
hypercenter#1582D73
hypocenterC73#17921
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
3. #22619027C2semidirect
4. #22608800C2semidirect
5. #22608788C2semidirect
6. #22608783C2semidirect
7. #22608749C2semidirect
8. SD16⋊#10596831C2semidirect
9. #22608735C2semidirect
10. #22608734C2semidirect
11. #22608713C2semidirect
13. #22608332C2semidirect
14. #22608232C2semidirect
15. C73×#1582C2semidirect
288. #1582D73semidirect
297. C73#17921semidirect

Maximal subgroups

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

subgroupindex
#226199982
#226190382
#226190272
#226088002
#226087882
#226087832
#226087492
SD16⋊#105968312
#226087352
#226087342
#226087132
#226083622
#226083322
#226082322
C73×#15822
#1792173