Finite Group Databasebeta

← #33056087

Subgroups — #33056087

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#22620003C211yesmaximal, characteristic
2#22619040C211yesmaximal, characteristic
3#22619028C211yesmaximal, characteristic, complemented
4#22608801C211yesmaximal, characteristic, complemented
5#22608787C211yesmaximal, characteristic, complemented
6#22608780C211yesmaximal, characteristic, complemented
7#22608766C211yesmaximal, characteristic, complemented
8#22608749C211yesmaximal, characteristic, complemented
9#22608742C211yesmaximal, characteristic, complemented
10#22608737C211yesmaximal, characteristic, complemented
11#22608730C211yesmaximal, characteristic, complemented
12#22608363C211yesmaximal, characteristic
13#22608333C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1573C211yesmaximal, characteristic, complemented
16#17989144C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988929C411yescharacteristic
19#17988929C411yescharacteristic
20#17988873C411yescharacteristic
21#17988868C411yescharacteristic
22#17988798C411yescharacteristic
23#17988793C411yescharacteristic
24#17988751C411yescharacteristic
25#17988751C411yescharacteristic
26#17988715—21no—
27#17988715—21no—
28#17988714C2211yescharacteristic
29#17988714C2211yescharacteristic
30#17988711C2211yescharacteristic
31#17988711C2211yescharacteristic
32#17988711C2211yescharacteristic
33#17988711C2211yescharacteristic
34C4×Dic292C2211yescharacteristic
35C4×Dic292C2211yescharacteristic
36C4×#11924017C2211yescharacteristic
37C4×#11924017C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988652C2211yescharacteristic
40C8×C22⋊D73—21no—
41C8×C22⋊D73—21no—
42#17988645—21no—
43#17988645—21no—
44#17988640C2211yescharacteristic
45#17988640C2211yescharacteristic
46#17988639—21no—
47C4⋊C8×D73—21no—
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988317C2211yescharacteristic
51#17988317C2211yescharacteristic
52#17988317C2211yescharacteristic
53#17988317C2211yescharacteristic
54#17988314C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#432×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62C2×C4⋊C8×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×Dic292C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×#11924017C2×C411yescharacteristic
72C2×C8×D73—21no—
73C2×C8×D73—21no—
74#14556591C2×C411yescharacteristic
75#14556591C2×C411yescharacteristic
76#14556583—21no—
77#14556570—21no—
78#14556570C2×C411yescharacteristic
79#14556570C2×C411yescharacteristic
80C4×Dic146—21no—
81C4×Dic146C2×C411yescharacteristic
82C4×Dic146C2311yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×Dic146C2311yescharacteristic
85C4×D292C2×C411yescharacteristic
86C4×D292C2311yescharacteristic
87C4×C22⋊D73—21no—
88C4×C22⋊D73—21no—
89#14556550—21no—
90#14556550C2×C411yescharacteristic
91#14556548—21no—
92C42×D73—21no—
93#14556525C2×C411yescharacteristic
94#14556525C2×C411yescharacteristic
95#14556523C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97C4⋊#10596831—21no—
98C4⋊#10596831D411yescharacteristic
99C4⋊#10596831D411yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556516C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556516C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114C22⋊#10596831—21no—
115C22⋊#10596831D411yescharacteristic
116C22⋊#10596831D411yescharacteristic
117#14556503—21no—
118#14556503—21no—
119#14556501—21no—
120#14556501—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C8×Dic73—21no—
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C22×C8×C73—21no—
130C2×C42×C73C2311yescharacteristic
131C4⋊C8×C73—21no—
132C4⋊C8×C73C2×C411yescharacteristic
133C4⋊C8×C73C2×C411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138C22⋊C8×C73—21no—
139C22⋊C8×C73C2×C411yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—22no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C2×Dic146C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155Dic292—22no—
156Dic292—22no—
157#11924017—22no—
158#11924017—22no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831C2×D411yescharacteristic
162C2×#10596831C2×D411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C8×D73—81no—
166C8×D73—81no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182C22⋊Dic73—21no—
183#11924005—21no—
184#11924005—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73#4111yescharacteristic
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—81no—
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C22×C411yescharacteristic
202C42×C73C22×C411yescharacteristic
203C42×C73C2×D411yescharacteristic
204C42×C73#4111yescharacteristic
205C42×C73C2411yescharacteristic
206C23×C73C4×D411yescharacteristic
207C22×D73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—41no—
213C2×C4×C73C4×D411yescharacteristic
214C2×C4×C73C4×D411yescharacteristic
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C23×C411yescharacteristic
217C2×C4×C73C22×D411yescharacteristic
218C2×C4×C73C2×#4111yescharacteristic
219C22⋊D73—24no—
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227D292—21no—
228D292#13112yes—
229C4×D73—24no—
230C4×D73—41no—
231C4×D73—41no—
232C4×D73—81no—
233Dic146—21no—
234Dic146—21no—
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—
247C8×C73—41no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—41no—
253#10596831—41no—
254C22×C73—21no—
255C22×C73—21no—
256C22×C73—21no—
257C22×C73C2×C4×D411yescharacteristic
258C2×D73—22no—
259C2×D73—41no—
260C2×D73—41no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73C2×#13111yescharacteristic
266C4×C73C2×#13111yescharacteristic
267C4×C73#57711yescharacteristic
268C4×C73#57811yescharacteristic
269Dic73—22no—
270Dic73—41no—
271Dic73—41no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276#17921—731nomaximal, Sylow
277C2×C73—41no—
278C2×C73#292911yescharacteristic
279C2×C73#294711yescharacteristic
280C2×C73#295711yescharacteristic
281D73—42no—
282#3107—731no—
283#2988—731no—
284#2985—731no—
285#1587—731no—
286#1585—731no—
287#1584—731no—
288#1582—731no—
289#1579—731no—
290SD16⋊C8—731no—
291C8×Q16—731no—
292C8×SD16—731no—
293#1573D7311yescharacteristic, complemented
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—731no—
310#446—1461no—
311#446—1461no—
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—731no—
315C8×Q8—731no—
316C4×Q16—731no—
317C4×Q16—731no—
318C4×SD16—731no—
319C4×SD16—731no—
320C8×D4—731no—
321C8×D4—731no—
322C8×D4—1461no—
323C8×D4—1461no—
324#433—1461no—
325#433—1461no—
326#432C2×D7311yescharacteristic
327#431—731no—
328#431—731no—
329#431—1461no—
330#431C2×D7311yescharacteristic
331C2×C4⋊C8—1461no—
332C2×C4⋊C8C2×D7311yescharacteristic
333#335C2×D7311yescharacteristic
334#335C2×D7311yescharacteristic
335#334C2×D7311yescharacteristic
336#334C2×D7311yescharacteristic
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343D4⋊C8—731no—
344D4⋊C8—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C82—731no—
349C2×#41—731no—
350C2×Q16—731no—
351C2×Q16—731no—
352C2×SD16—731no—
353C2×SD16—731no—
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—731no—
367C4×Q8—1461no—
368C4×D4—731no—
369C4×D4—731no—
370C4×D4—1461no—
371C4×D4—1461no—
372#117—731no—
373#117—1461no—
374#117—1461no—
375C2×C42—1461no—
376C2×C42C22×D7311yescharacteristic
377#107—731no—
378#107—731no—
379#106—731no—
380#106—731no—
381C4⋊C8—21no—
382C4⋊C8—731no—
383C4⋊C8—731no—
384C4⋊C8—1461no—
385C4⋊C8—1461no—
386C4⋊C8—1461no—
387C4⋊C8—1461no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8C4×D7311yescharacteristic
392C4⋊C8C4×D7311yescharacteristic
393C4⋊C8C22×D7311yescharacteristic
394C4⋊C8C22×D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396C4⋊C8C22×D7311yescharacteristic
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#102—731no—
404#102—731no—
405C22⋊C8—21no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—1461no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8C4×D7311yescharacteristic
412C22⋊C8C4×D7311yescharacteristic
413#97—21no—
414#97—1461no—
415#97—1461no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426#41—1462no—
427#41—1462no—
428C2×Q8—731no—
429C2×Q8—731no—
430C2×Q8—731no—
431C2×Q8—1461no—
432C2×D4—731no—
433C2×D4—1461no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4C2×C4×D7311yescharacteristic
438C22×C4D4×D7311yescharacteristic
439C22×C4#1192402911yescharacteristic
440Q16—1462no—
441Q16—1462no—
442SD16—1462no—
443SD16—1462no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—5841no—
450C2×C8—5841no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8C2×C4×D7311yescharacteristic
458C2×C8C2×C4×D7311yescharacteristic
459C2×C8C2×C4×D7311yescharacteristic
460C2×C8C2×C4×D7311yescharacteristic
461C4⋊C4—731no—
462C4⋊C4—731no—
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⋊C4—1461no—
473C4⋊C4—1461no—
474C22⋊C4—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C42—1461no—
480C42—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42C2×C4×D7311yescharacteristic
485C42D4×D7311yescharacteristic
486C42#1192402911yescharacteristic
487C42C23×D7311yescharacteristic
488C23—1461no—
489C23#1455655311yescharacteristic
490Q8—5841no—
491Q8—732no—
492Q8—1461no—
493Q8—1461no—
494Q8—1461no—
495Q8—1461no—
496Q8—1461no—
497D4—732no—
498D4—1464no—
499D4—1461no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—2921no—
506C2×C4—2921no—
507C2×C4—5841no—
508C2×C4—1464no—
509C2×C4—1461no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4#1455655311yescharacteristic
517C2×C4#1455655311yescharacteristic
518C2×C4#1455655311yescharacteristic
519C2×C4C22×C4×D7311yescharacteristic
520C2×C4C2×D4×D7311yescharacteristic
521C2×C4C2×#1192402911yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—2921no—
531C8—2921no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—2921no—
540C22—2921no—
541C22—1462no—
542C22C2×#1455655311yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—2921no—
548C4—2921no—
549C4—2921no—
550C4—2921no—
551C4—2921no—
552C4—2921no—
553C4—1462no—
554C4#131×D7311yescharacteristic
555C4#131×D7311yescharacteristic
556C4#1798939711yescharacteristic
557C4#1798940311yescharacteristic
558C2—41no—
559C2—2922no—
560C2#2261862411yescharacteristic
561C2#2261877211yescharacteristic
562C2#2261884711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1573C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C2×C4
cosocleC42×C73C24
hypercenter#1573D73
hypocenterC73#17921
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #22619028C2semidirect
4. #22608801C2semidirect
5. #22608787C2semidirect
6. #22608780C2semidirect
7. #22608766C2semidirect
8. #22608749C2semidirect
9. #22608742C2semidirect
10. #22608737C2semidirect
11. #22608730C2semidirect
13. #22608333C2semidirect
14. #22608231C2semidirect
15. C73×#1573C2semidirect
293. #1573D73semidirect
297. C73#17921semidirect

Maximal subgroups

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

subgroupindex
#226200032
#226190402
#226190282
#226088012
#226087872
#226087802
#226087662
#226087492
#226087422
#226087372
#226087302
#226083632
#226083332
#226082312
C73×#15732
#1792173