Finite Group Databasebeta

← #33056812

Subgroups — #33056812

Order 18688.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620537C211yesmaximal, characteristic
2#22619076C211yesmaximal, characteristic
3#22619028C211yesmaximal, characteristic, complemented
4#22608808C211yesmaximal, characteristic, complemented
5#22608801C211yesmaximal, characteristic, complemented
6#22608801C211yesmaximal, characteristic, complemented
7#22608787C211yesmaximal, characteristic, complemented
8#22608780C211yesmaximal, characteristic, complemented
9#22608780C211yesmaximal, characteristic, complemented
10#22608773C211yesmaximal, characteristic, complemented
11#22608766C211yesmaximal, characteristic, complemented
12#22608389C211yesmaximal, characteristic
13#22608385C211yesmaximal, characteristic, complemented
14#22608218C211yesmaximal, characteristic, complemented
15C73×#1569C211yesmaximal, characteristic, complemented
16#17989144C2211yescharacteristic
17#17989121C2211yescharacteristic
18#17988996C411yescharacteristic
19#17988981C411yescharacteristic
20#17988956C411yescharacteristic
21#17988947C411yescharacteristic
22#17988845C411yescharacteristic
23#17988845C411yescharacteristic
24#17988833C411yescharacteristic
25#17988833C411yescharacteristic
26#17988715—21no—
27#17988715—21no—
28#17988714C2211yescharacteristic
29#17988714C2211yescharacteristic
30#17988714C2211yescharacteristic
31#17988711C2211yescharacteristic
32#17988711C2211yescharacteristic
33#17988711C2211yescharacteristic
34C4×Dic292C2211yescharacteristic
35C4×Dic292C2211yescharacteristic
36C4×#11924017C2211yescharacteristic
37C4×#11924017C2211yescharacteristic
38#17988664C2211yescharacteristic
39#17988663—21no—
40#17988656—21no—
41#17988652C2211yescharacteristic
42#17988647—21no—
43#17988645—21no—
44#17988645—21no—
45#17988640C2211yescharacteristic
46#17988612—21no—
47C2×C4×#10596831C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988317C2211yescharacteristic
51#17988317C2211yescharacteristic
52#17988317C2211yescharacteristic
53#17988317C2211yescharacteristic
54#17988314C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60#432×C73C2211yescharacteristic
61#423×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×Dic292C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—21no—
73C2×C8×D73—21no—
74#14556591C2×C411yescharacteristic
75#14556591C2×C411yescharacteristic
76#14556585—21no—
77#14556583—21no—
78#14556583C2×C411yescharacteristic
79#14556579C2×C411yescharacteristic
80#14556574—21no—
81#14556570—21no—
82#14556570C2×C411yescharacteristic
83#14556570C2×C411yescharacteristic
84#14556570C2×C411yescharacteristic
85#14556565C2×C411yescharacteristic
86C4×Dic146—21no—
87C4×Dic146C2311yescharacteristic
88C4×Dic146C2311yescharacteristic
89C4×Dic146C2311yescharacteristic
90C4×D292C2311yescharacteristic
91C4×C22⋊D73—21no—
92#14556550—21no—
93#14556548—21no—
94#14556525C2×C411yescharacteristic
95#14556525C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97#14556523C2×C411yescharacteristic
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⋊#10596831D411yescharacteristic
115C22⋊#10596831D411yescharacteristic
116#14556503—21no—
117#14556503—21no—
118#14556501—21no—
119#14556501—21no—
120#14556501—21no—
121C4×#10596831—21no—
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×M16×C73—21no—
130C2×M16×C73C2×C411yescharacteristic
131C2×M16×C73C2×C411yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C4⋊C8×C73—21no—
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138C22⋊C8×C73—21no—
139#97×C73—21no—
140#97×C73C2×C411yescharacteristic
141#97×C73C2×C411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×D292C22×C411yescharacteristic
149C2×C22⋊D73—21no—
150C2×C4×D73—21no—
151Dic292—41no—
152Dic292—41no—
153#11924017—41no—
154#11924017—41no—
155#11924011—81no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—42no—
159C2×#10596831C2×D411yescharacteristic
160C2×#10596831C2×D411yescharacteristic
161C2×#10596831C2×D411yescharacteristic
162C2×#10596831C2×D411yescharacteristic
163C8×D73—81no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73C22×C411yescharacteristic
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170C4⋊Dic73C22×C411yescharacteristic
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179C22⋊Dic73—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73#4111yescharacteristic
192M16×C73—41no—
193M16×C73—41no—
194M16×C73—81no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C22×C411yescharacteristic
203C42×C73C22×C411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73C4×D411yescharacteristic
208C22×D73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—41no—
214C2×C4×C73C4×D411yescharacteristic
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C22⋊D73—81no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228D292—21no—
229D292—21no—
230C4×D73—41no—
231C4×D73—41no—
232Dic146—21no—
233Dic146—21no—
234Dic146—21no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—81no—
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—41no—
244C8×C73—41no—
245C8×C73—41no—
246C8×C73—41no—
247#10596831—22no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—41no—
253C22×C73—21no—
254C22×C73—21no—
255C22×C73—21no—
256C22×C73C2×C4×D411yescharacteristic
257C2×D73—41no—
258C2×D73—41no—
259C2×D73—41no—
260C4×C73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—21no—
264C4×C73#56811yescharacteristic
265C4×C73#56811yescharacteristic
266C4×C73#57711yescharacteristic
267C4×C73#57811yescharacteristic
268Dic73—41no—
269Dic73—41no—
270Dic73—41no—
271Dic73—41no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275#17988—731nomaximal, Sylow
276C2×C73—41no—
277C2×C73#293211yescharacteristic
278C2×C73#294711yescharacteristic
279C2×C73#295611yescharacteristic
280D73—81no—
281#3172—731no—
282#2993—731no—
283#2985—731no—
284#1588—731no—
285#1587—731no—
286#1587—731no—
287#1585—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582—731no—
292#1569D7311yescharacteristic, complemented
293#1494—731no—
294#1493—731no—
295#1451—731no—
296C73#1798811yescharacteristic, complemented, Sylow
297#533—731no—
298#529—731no—
299#501—731no—
300#497—731no—
301#491—731no—
302#489—731no—
303#470—731no—
304#470—731no—
305#468—731no—
306#468—731no—
307#446—731no—
308#446—731no—
309#446—731no—
310#446—1461no—
311#446—1461no—
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—731no—
315C4×Q16—731no—
316C4×Q16—731no—
317C4×SD16—731no—
318C4×SD16—731no—
319#436—731no—
320#436—1461no—
321#435—1461no—
322C8×D4—731no—
323#433—1461no—
324#433—1461no—
325#433—1461no—
326#432C2×D7311yescharacteristic
327#431—731no—
328#424—1461no—
329#423C2×D7311yescharacteristic
330C4×M16C2×D7311yescharacteristic
331C2×C4×C8—731no—
332#335C2×D7311yescharacteristic
333#335C2×D7311yescharacteristic
334#334C2×D7311yescharacteristic
335#334C2×D7311yescharacteristic
336Q8⋊C8—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342D4⋊C8—731no—
343D4⋊C8—731no—
344#322—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C2×Q16—731no—
349C2×Q16—731no—
350C2×SD16—731no—
351C2×SD16—731no—
352C2×M16—21no—
353C2×M16—1461no—
354C2×M16C4×D7311yescharacteristic
355C2×M16C4×D7311yescharacteristic
356C22×C8—1461no—
357C22×C8—1461no—
358C4⋊Q8—731no—
359C4⋊Q8—731no—
360#126—1461no—
361#125—731no—
362#125—1461no—
363#124—731no—
364#123—1461no—
365C22⋊Q8—731no—
366C22⋊Q8—731no—
367C22⋊Q8—731no—
368C22⋊Q8—1461no—
369#121—731no—
370C4×Q8—731no—
371C4×Q8—731no—
372C4×Q8—731no—
373C4×Q8—1461no—
374C4×D4—731no—
375C4×D4—1461no—
376#117—1461no—
377#117—1461no—
378C2×C42C22×D7311yescharacteristic
379#107—731no—
380#107—731no—
381#106—731no—
382#106—731no—
383C4⋊C8—21no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—1461no—
387C4⋊C8—1461no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8C22×D7311yescharacteristic
393C4⋊C8C22×D7311yescharacteristic
394C4⋊C8C22×D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396#103—731no—
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#102—731no—
403#102—731no—
404C22⋊C8—21no—
405C22⋊C8—731no—
406C22⋊C8—731no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409#97—21no—
410#97—1461no—
411#97—1461no—
412#97—1461no—
413#97C4×D7311yescharacteristic
414#97C4×D7311yescharacteristic
415C4×C8—731no—
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
425C2×Q8—731no—
426C2×Q8—731no—
427C2×Q8—731no—
428C2×Q8—1461no—
429C2×D4—731no—
430C2×D4—1461no—
431C22×C4—1461no—
432C22×C4C2×C4×D7311yescharacteristic
433C22×C4D4×D7311yescharacteristic
434C22×C4#1192402911yescharacteristic
435Q16—2921no—
436Q16—2921no—
437SD16—2921no—
438SD16—2921no—
439M16—41no—
440M16—41no—
441M16—81no—
442M16—5841no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—2922no—
448C2×C8—5841no—
449C2×C8—731no—
450C2×C8—731no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8C2×C4×D7311yescharacteristic
456C2×C8C2×C4×D7311yescharacteristic
457C2×C8C2×C4×D7311yescharacteristic
458C2×C8C2×C4×D7311yescharacteristic
459C4⋊C4—731no—
460C4⋊C4—731no—
461C4⋊C4—731no—
462C4⋊C4—731no—
463C4⋊C4—1461no—
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⋊C4—1461no—
473C4⋊C4—1461no—
474C22⋊C4—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42C2×C4×D7311yescharacteristic
485C42D4×D7311yescharacteristic
486C42#1192402911yescharacteristic
487C42C23×D7311yescharacteristic
488C23—1461no—
489C23#1455655311yescharacteristic
490Q8—5841no—
491Q8—1461no—
492Q8—1461no—
493Q8—1461no—
494Q8—1461no—
495Q8—1461no—
496Q8—1461no—
497D4—5841no—
498D4—1461no—
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—1461no—
508C2×C4—1461no—
509C2×C4—1461no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4#1455655311yescharacteristic
515C2×C4#1455655311yescharacteristic
516C2×C4#1455655311yescharacteristic
517C2×C4C22×C4×D7311yescharacteristic
518C2×C4C2×D4×D7311yescharacteristic
519C2×C4C2×#1192402911yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—2921no—
529C8—1462no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—2921no—
538C22—2921no—
539C22—2921no—
540C22C2×#1455655311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—2921no—
546C4—2921no—
547C4—2921no—
548C4—2921no—
549C4—2921no—
550C4—2921no—
551C4—2921no—
552C4#1798935311yescharacteristic
553C4#1798935311yescharacteristic
554C4#1798939711yescharacteristic
555C4#1798940311yescharacteristic
556C2—41no—
557C2—5841no—
558C2#2261864811yescharacteristic
559C2#2261877211yescharacteristic
560C2#2261884011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1569C2
socleC22×C73C2×C4×D4
prime radical#14556565C2×C4
cosocleC42×C73C24
hypercenter#1569D73
hypocenterC73#17988
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #22619028C2semidirect
4. #22608808C2semidirect
5. #22608801C2semidirect
6. #22608801C2semidirect
7. #22608787C2semidirect
8. #22608780C2semidirect
9. #22608780C2semidirect
10. #22608773C2semidirect
11. #22608766C2semidirect
13. #22608385C2semidirect
14. #22608218C2semidirect
15. C73×#1569C2semidirect
292. #1569D73semidirect
296. C73#17988semidirect

Maximal subgroups

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

subgroupindex
#226205372
#226190762
#226190282
#226088082
#226088012
#226087872
#226087802
#226087732
#226087662
#226083892
#226083852
#226082182
C73×#15692
#1798873