Finite Group Databasebeta

← #33056060

Subgroups — #33056060

Order 18688.

596 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#22620015C211yesmaximal, characteristic
2#22619079C211yesmaximal, characteristic
3#22619010C211yesmaximal, characteristic, complemented
4#22608806C211yesmaximal, characteristic, complemented
5#22608805C211yesmaximal, characteristic, complemented
6#22608782C211yesmaximal, characteristic, complemented
7#22608773C211yesmaximal, characteristic, complemented
8#22608745C211yesmaximal, characteristic, complemented
9C8×#11924018C211yesmaximal, characteristic, complemented
10C8×#11924015C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608358C211yesmaximal, characteristic, complemented
13#22608338C211yesmaximal, characteristic
14#22608232C211yesmaximal, characteristic, complemented
15C73×#1579C211yesmaximal, characteristic, complemented
16#17989124C2211yescharacteristic
17C4×Q8×D73C2211yescharacteristic
18#17988916C411yescharacteristic
19#17988902C411yescharacteristic
20#17988893C411yescharacteristic
21#17988892C411yescharacteristic
22#17988812C411yescharacteristic
23#17988811C411yescharacteristic
24#17988741C411yescharacteristic
25#17988727C411yescharacteristic
26#17988718C2211yescharacteristic
27Q8×#10596831C2211yescharacteristic
28C8×Dic146—21no—
29C8×Dic146C2211yescharacteristic
30#17988711—21no—
31#17988711C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924017C2211yescharacteristic
34C4×#11924015C2211yescharacteristic
35#17988666—21no—
36#17988664C2211yescharacteristic
37#17988657—21no—
38C8×D292C2211yescharacteristic
39#17988646—21no—
40#17988639—21no—
41#17988639C2211yescharacteristic
42#17988638—21no—
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988638C2211yescharacteristic
46#17988612—21no—
47#17988609C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×Q8×D73C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×#11924011—21no—
73C2×C8×D73—21no—
74#14556586—21no—
75#14556582C2×C411yescharacteristic
76#14556580C2×C411yescharacteristic
77#14556576—21no—
78#14556567C2×C411yescharacteristic
79#14556566C2×C411yescharacteristic
80Q8×Dic73C2×C411yescharacteristic
81C4×Dic146—21no—
82C4×Dic146C2311yescharacteristic
83#14556556—21no—
84#14556556C2×C411yescharacteristic
85C4×D292—21no—
86C4×D292C2311yescharacteristic
87#14556548—21no—
88C4⋊C4×D73—21no—
89C4⋊C4×D73C2×C411yescharacteristic
90C42×D73—21no—
91C42×D73C2311yescharacteristic
92#14556524C2×C411yescharacteristic
93#14556523C2×C411yescharacteristic
94#14556522C2×C411yescharacteristic
95C4⋊#10596831—21no—
96C4⋊#10596831—21no—
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
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#14556515C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503C2×C411yescharacteristic
118#14556503C2×C411yescharacteristic
119#14556503D411yescharacteristic
120#14556503D411yescharacteristic
121#14556502—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
139C4×C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146Q8×D73—22no—
147Q8×D73—22no—
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—22no—
158#11924015—22no—
159#11924011—81no—
160#11924011—81no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C8×D73—81no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924005—21no—
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73C22×C411yescharacteristic
187C4×Dic73C2×D411yescharacteristic
188C4×Dic73#4111yescharacteristic
189C2×Q8×C73C22×C411yescharacteristic
190C2×Q8×C73C22×C411yescharacteristic
191Q16×C73—22no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73C22×C411yescharacteristic
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C2×D411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73C22×C411yescharacteristic
202C4⋊C4×C73C22×C411yescharacteristic
203C42×C73—21no—
204C42×C73—21no—
205C42×C73C2411yescharacteristic
206C22×D73—21no—
207C22×D73C4×D411yescharacteristic
208Q8×C73—21no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73#13112yes—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73C23×C411yescharacteristic
217C2×C4×C73C22×D411yescharacteristic
218C2×C4×C73C2×#4111yescharacteristic
219C2×Dic73—21no—
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73C4×D411yescharacteristic
223C2×Dic73C4×D411yescharacteristic
224C2×Dic73C4×D411yescharacteristic
225D292—21no—
226D292—21no—
227D292—81no—
228C4×D73—24no—
229C4×D73—21no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—41no—
234C4×D73—41no—
235C4×D73—41no—
236C4×D73—81no—
237Dic146—24no—
238Dic146—21no—
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×C73C2×C4×D411yescharacteristic
255C2×D73—21no—
256C2×D73—21no—
257C2×D73—21no—
258C2×D73—41no—
259C2×D73—41no—
260C2×D73—41no—
261C4×C73—22no—
262C4×C73—21no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73C2×#13111yescharacteristic
267C4×C73C2×#13111yescharacteristic
268C4×C73#57711yescharacteristic
269C4×C73#57811yescharacteristic
270Dic73—21no—
271Dic73—22no—
272Dic73—21no—
273Dic73—21no—
274Dic73—41no—
275Dic73—41no—
276#17919—731nomaximal, Sylow
277C2×C73#292911yescharacteristic
278C2×C73#294711yescharacteristic
279C2×C73#295711yescharacteristic
280D73—41no—
281D73—81no—
282#3108—731no—
283#2993—731no—
284#2982—731no—
285#1588—731no—
286#1587—731no—
287#1584—731no—
288#1583—731no—
289#1579D7311yescharacteristic, complemented
290SD16⋊C8—731no—
291C8×Q16—731no—
292C8×SD16—731no—
293#1574—731no—
294#1487—731no—
295#1482—731no—
296#1454—731no—
297C73#1791911yescharacteristic, complemented, Sylow
298#529—731no—
299C2×C4×Q8—731no—
300#483—731no—
301#480—731no—
302#479—731no—
303#479—731no—
304#464—731no—
305#464—731no—
306#451—731no—
307#448—731no—
308#446—731no—
309C8×Q8—731no—
310C8×Q8—731no—
311C8×Q8—731no—
312C8×Q8—1461no—
313C8×Q8—1461no—
314C8×Q8C2×D7311yescharacteristic
315C8×Q8C2×D7311yescharacteristic
316C4×Q16—731no—
317C4×Q16C2×D7311yescharacteristic
318C4×SD16—731no—
319C4×SD16—731no—
320#436—731no—
321#436—1461no—
322#435—1461no—
323C8×D4—731no—
324#433—1461no—
325#431—731no—
326#431—731no—
327#431—731no—
328#431—731no—
329#431—1461no—
330#431—1461no—
331#424—1461no—
332#423—731no—
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⋊C8C2×D7311yescharacteristic
342Q8⋊C8C2×D7311yescharacteristic
343D4⋊C8—731no—
344D4⋊C8—731no—
345#322—731no—
346#322—731no—
347#322C2×D7311yescharacteristic
348C82—731no—
349C22×Q8—731no—
350C2×Q16—731no—
351C2×Q16C4×D7311yescharacteristic
352C2×SD16—731no—
353C2×SD16—731no—
354C2×M16—1461no—
355C2×M16—1461no—
356C22×C8—1461no—
357#126—1461no—
358#125—731no—
359#124—731no—
360#123—1461no—
361C22⋊Q8—731no—
362#121—731no—
363C4×Q8—731no—
364C4×Q8—731no—
365C4×Q8—731no—
366C4×Q8—1461no—
367C4×Q8—1461no—
368C4×Q8C22×D7311yescharacteristic
369C4×Q8C22×D7311yescharacteristic
370C4×D4—731no—
371C4×D4—1461no—
372#117—1461no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—1461no—
375C2×C42—731no—
376C2×C42—1461no—
377#107—731no—
378#107C4×D7311yescharacteristic
379#106—731no—
380#106—731no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
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#103C4×D7311yescharacteristic
402#103C4×D7311yescharacteristic
403#102—731no—
404#102—731no—
405C22⋊C8—731no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—1461no—
414C4×C8—21no—
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×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426C2×Q8—731no—
427C2×Q8—1461no—
428C2×Q8—1462no—
429C2×Q8—1462no—
430C2×Q8C2×C4×D7311yescharacteristic
431C2×Q8C2×C4×D7311yescharacteristic
432C2×D4—731no—
433C2×D4—1461no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1461no—
440Q16—22no—
441Q16—1462no—
442SD16—1462no—
443SD16—1462no—
444M16—5841no—
445M16—5841no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
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—21no—
463C4⋊C4—731no—
464C4⋊C4—731no—
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—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C42—21no—
480C42—21no—
481C42—731no—
482C42—731no—
483C42—731no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42C23×D7311yescharacteristic
488C23—731no—
489C23—1461no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—732no—
494Q8—1464no—
495Q8—1461no—
496Q8#1455659712yes—
497D4—5841no—
498D4—1461no—
499D4—1461no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—2921no—
505C2×C4—2921no—
506C2×C4—2921no—
507C2×C4—5841no—
508C2×C4—731no—
509C2×C4—731no—
510C2×C4—731no—
511C2×C4—1464no—
512C2×C4—1461no—
513C2×C4—1461no—
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—2921no—
537C22—2921no—
538C22—2921no—
539C22—1461no—
540C22—1461no—
541C22—1461no—
542C22C4×D4×D7311yescharacteristic
543C4—21no—
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—2921no—
549C4—2921no—
550C4—1461no—
551C4—1461no—
552C4—1461no—
553C4—1462no—
554C4#131×D7311yescharacteristic
555C4C2×#1455659711yescharacteristic
556C4#1798939611yescharacteristic
557C4#1798940311yescharacteristic
558C2—2921no—
559C2—5841no—
560C2#2261862011yescharacteristic
561C2#2261877311yescharacteristic
562C2#2261884511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1579C2
socleC22×C73C2×C4×D4
prime radical#14556566C2×C4
cosocleC42×C73C24
hypercenter#1579D73
hypocenterC73#17919
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
3. #22619010C2semidirect
4. #22608806C2semidirect
5. #22608805C2semidirect
6. #22608782C2semidirect
7. #22608773C2semidirect
8. #22608745C2semidirect
9. C8×#11924018C2semidirect
10. C8×#11924015C2semidirect
11. #22608718C2semidirect
12. #22608358C2semidirect
14. #22608232C2semidirect
15. C73×#1579C2semidirect
289. #1579D73semidirect
297. C73#17919semidirect

Maximal subgroups

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

subgroupindex
#226200152
#226190792
#226190102
#226088062
#226088052
#226087822
#226087732
#226087452
C8×#119240182
C8×#119240152
#226087182
#226083582
#226083382
#226082322
C73×#15792
#1791973