Finite Group Databasebeta

← #33055231

Subgroups — #33055231

Order 18688.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618893C211yesmaximal, characteristic
2#22618592C211yesmaximal, characteristic
3#22618496C211yesmaximal, characteristic
4#22608719C211yesmaximal, characteristic, complemented
5#22608718C211yesmaximal, characteristic, complemented
6#22608715C211yesmaximal, characteristic, complemented
7#22608714C211yesmaximal, characteristic, complemented
8#22608704C211yesmaximal, characteristic, complemented
9#22608700C211yesmaximal, characteristic, complemented
10#22608698C211yesmaximal, characteristic, complemented
11#22608697C211yesmaximal, characteristic, complemented
12#22608688C211yesmaximal, characteristic, complemented
13#22608680C211yesmaximal, characteristic, complemented
14#334×D73C211yesmaximal, characteristic, complemented
15C73×#1565C211yesmaximal, characteristic, complemented
16C2×#14556597—21no—
17C4×#11924028C2211yescharacteristic
18#17988715C411yescharacteristic
19#17988715C411yescharacteristic
20#17988663C411yescharacteristic
21#17988663C411yescharacteristic
22#17988660C411yescharacteristic
23#17988660C411yescharacteristic
24#17988656C411yescharacteristic
25#17988656C411yescharacteristic
26#17988646—21no—
27#17988645—21no—
28#17988644C2211yescharacteristic
29#17988643C2211yescharacteristic
30#17988640C2211yescharacteristic
31#17988639C2211yescharacteristic
32#17988638C2211yescharacteristic
33#17988638C2211yescharacteristic
34#17988613—21no—
35#17988612—21no—
36#17988612—21no—
37#17988611C2211yescharacteristic
38#17988609C2211yescharacteristic
39#17988609C2211yescharacteristic
40#17988609C2211yescharacteristic
41C4⋊C8×D73C2211yescharacteristic
42C4⋊C8×D73C2211yescharacteristic
43C4⋊C8×D73C2211yescharacteristic
44#17988552—21no—
45#17988541—21no—
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988339C2211yescharacteristic
51#17988339C2211yescharacteristic
52#17988339C2211yescharacteristic
53#17988339C2211yescharacteristic
54#17988338C2211yescharacteristic
55#17988338C2211yescharacteristic
56#17988337C2211yescharacteristic
57#17988337C2211yescharacteristic
58#17988337C2211yescharacteristic
59#17988337C2211yescharacteristic
60#431×C73C2211yescharacteristic
61C2×C4⋊C8×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028D411yescharacteristic
68#14556597—44no—
69C2×#11924012—21no—
70C2×#11924011—21no—
71C2×#11924011—21no—
72C2×#11924011—21no—
73C2×#11924011C2×C411yescharacteristic
74C2×#11924011C2×C411yescharacteristic
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73C2×C411yescharacteristic
79C2×C8×D73C2×C411yescharacteristic
80C4×Dic146C2×C411yescharacteristic
81C4×Dic146Q811yescharacteristic
82C4×D292C2×C411yescharacteristic
83C4×D292Q811yescharacteristic
84C4×C22⋊D73C2×C411yescharacteristic
85C4×C22⋊D73C2×C411yescharacteristic
86C4×C22⋊D73Q811yescharacteristic
87C4×C22⋊D73Q811yescharacteristic
88#14556550D411yescharacteristic
89#14556548D411yescharacteristic
90#14556548D411yescharacteristic
91C42×D73C2311yescharacteristic
92C42×D73C2311yescharacteristic
93C4⋊#10596831—21no—
94C4⋊#10596831C2×C411yescharacteristic
95C4⋊#10596831C2×C411yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520C2×C411yescharacteristic
107#14556520C2×C411yescharacteristic
108#14556520C2×C411yescharacteristic
109#14556520C2×C411yescharacteristic
110C22⋊#10596831—21no—
111C22⋊#10596831C2×C411yescharacteristic
112C22⋊#10596831C2×C411yescharacteristic
113#14556503—21no—
114#14556503—21no—
115#14556503C2×C411yescharacteristic
116#14556503C2×C411yescharacteristic
117#14556503C2×C411yescharacteristic
118#14556503C2×C411yescharacteristic
119#14556502—21no—
120#14556501—21no—
121#14556501C2×C411yescharacteristic
122#14556501C2×C411yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C8×Dic73—21no—
126C8×Dic73C2×C411yescharacteristic
127C8×Dic73C2×C411yescharacteristic
128C2×M16×C73C2×C411yescharacteristic
129C2×M16×C73C2×C411yescharacteristic
130C22×C8×C73—21no—
131C2×C42×C73C2311yescharacteristic
132C4⋊C8×C73—21no—
133C4⋊C8×C73C2311yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C22⋊C8×C73—21no—
138#97×C73C2×C411yescharacteristic
139#97×C73C2×C411yescharacteristic
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143#11924028—22no—
144#11924028—22no—
145C2×Dic146C4⋊C411yescharacteristic
146C2×D292C4⋊C411yescharacteristic
147C2×C22⋊D73C4⋊C411yescharacteristic
148C2×C22⋊D73C4⋊C411yescharacteristic
149C2×C4×D73C22×C411yescharacteristic
150C2×C4×D73C22×C411yescharacteristic
151C2×C4×D73C2×D411yescharacteristic
152C2×C4×D73C2×D411yescharacteristic
153C2×C4×D73C2×Q811yescharacteristic
154C2×C4×D73C2×Q811yescharacteristic
155#11924012—42no—
156#11924011—22no—
157#11924011—41no—
158#11924011—42no—
159#11924011—42no—
160#11924011—42no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C22×C411yescharacteristic
169C8×D73—22no—
170C8×D73—41no—
171C8×D73—42no—
172C8×D73—42no—
173C8×D73—42no—
174C4⋊Dic73C4⋊C411yescharacteristic
175C4⋊Dic73C4⋊C411yescharacteristic
176#11924007C4⋊C411yescharacteristic
177#11924007C4⋊C411yescharacteristic
178#11924007C4⋊C411yescharacteristic
179#11924007C4⋊C411yescharacteristic
180C22⋊Dic73C4⋊C411yescharacteristic
181C22⋊Dic73C4⋊C411yescharacteristic
182#11924005C4⋊C411yescharacteristic
183#11924005C4⋊C411yescharacteristic
184#11924005C4⋊C411yescharacteristic
185#11924005C4⋊C411yescharacteristic
186C4×Dic73C22×C411yescharacteristic
187C4×Dic73C22×C411yescharacteristic
188C4×Dic73C2×D411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C4×Dic73C2×Q811yescharacteristic
191C4×Dic73C2×Q811yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×Q811yescharacteristic
195M16×C73—22no—
196M16×C73—41no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—42no—
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C42×C73C22×C411yescharacteristic
207C42×C73C2×D411yescharacteristic
208C42×C73C2×Q811yescharacteristic
209C42×C73C2411yescharacteristic
210C23×C73C2×C4⋊C411yescharacteristic
211C22×D73C2×C4⋊C411yescharacteristic
212C22×D73C2×C4⋊C411yescharacteristic
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—41no—
218C2×C4×C73C2×C4⋊C411yescharacteristic
219C2×C4×C73C2×C4⋊C411yescharacteristic
220C2×C4×C73C2×C4⋊C411yescharacteristic
221C2×C4×C73C23×C411yescharacteristic
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C73C22×Q811yescharacteristic
224C22⋊D73—22no—
225C22⋊D73—22no—
226C2×Dic73C2×C4⋊C411yescharacteristic
227C2×Dic73C2×C4⋊C411yescharacteristic
228C2×Dic73C2×C4⋊C411yescharacteristic
229C2×Dic73C2×C4⋊C411yescharacteristic
230C2×Dic73C2×C4⋊C411yescharacteristic
231C2×Dic73C2×C4⋊C411yescharacteristic
232D292—22no—
233C4×D73—21no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—21no—
238C4×D73—21no—
239C4×D73—41no—
240C4×D73—41no—
241C4×D73AGL(1,ℤ/8)12yes—
242C4×D73#13712yes—
243Dic146—22no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73#13112yescomplemented
252#10596831—21no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73C22×C4⋊C411yescharacteristic
264C2×D73—21no—
265C2×D73—21no—
266C2×D73—21no—
267C2×D73—21no—
268C2×D73—21no—
269C2×D73#42812yes—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73C2×#13111yescharacteristic
275C4×C73#56811yescharacteristic
276C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C73C2×#13711yescharacteristic
278Dic73—21no—
279Dic73—21no—
280Dic73—21no—
281Dic73—21no—
282Dic73—21no—
283Dic73#42812yes—
284#17830—731nomaximal, Sylow
285C2×C73—41no—
286C2×C73#290611yescharacteristic
287C2×C73C2×#42811yescharacteristic
288C2×C73#291611yescharacteristic
289D73—22no—
290D73—41no—
291#2965—731no—
292#2925—731no—
293#2906—731no—
294#1574—731no—
295#1574—731no—
296#1573—731no—
297#1573—731no—
298#1571—731no—
299#1570—731no—
300#1569—731no—
301#1569—731no—
302#1567—731no—
303#1565—731no—
304#1565D7311yescharacteristic, complemented
305C2×#334—731no—
306C73#1783011yescharacteristic, complemented, Sylow
307C2×#131—1461no—
308C4×#41—731no—
309#446—731no—
310#446—731no—
311#436—731no—
312#436—731no—
313#435—731no—
314#435—731no—
315#435—731no—
316#435—731no—
317#433—1461no—
318#433—1461no—
319#432—731no—
320#432—731no—
321#431—731no—
322#431—731no—
323#431—731no—
324#431—731no—
325#431C2×D7311yescharacteristic
326#424—1461no—
327#424—1461no—
328#424—1461no—
329#423—731no—
330#423—731no—
331#423—731no—
332#423—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8C2×D7311yescharacteristic
337#408—1461no—
338#405—1461no—
339C4×M16—731no—
340C4×M16C2×D7311yescharacteristic
341C2×C4×C8—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345#335—731no—
346#335—731no—
347#335—731no—
348#335C2×D7311yescharacteristic
349#335C2×D7311yescharacteristic
350#334—731no—
351#334—731no—
352#334—731no—
353#334—731no—
354#334—731no—
355#334—731no—
356#334C2×D7311yescharacteristic
357#334C2×D7311yescharacteristic
358C2×#41—731no—
359#131—2924no—
360C2×M16—731no—
361C2×M16—731no—
362C2×M16—1461no—
363C2×M16—1461no—
364C2×M16—1461no—
365C2×M16—1461no—
366C2×M16C4×D7311yescharacteristic
367C2×M16C4×D7311yescharacteristic
368C22×C8—21no—
369C22×C8—731no—
370C22×C8—731no—
371C22×C8—1461no—
372C22×C8—1461no—
373C22×C8—1461no—
374C4×Q8—731no—
375C4×Q8—731no—
376C4×D4—731no—
377C4×D4—731no—
378C4×D4—731no—
379C4×D4—731no—
380C4×D4—731no—
381C4×D4—731no—
382#117—731no—
383#117—731no—
384#117—731no—
385C2×C42—731no—
386C2×C42—731no—
387C2×C42C22×D7311yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—731no—
393C4⋊C8—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8—1461no—
406C4⋊C8C22×D7311yescharacteristic
407C4⋊C8C22×D7311yescharacteristic
408C4⋊C8C22×D7311yescharacteristic
409C4⋊C8C22×D7311yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—731no—
412C22⋊C8—731no—
413C22⋊C8—731no—
414C22⋊C8—731no—
415C22⋊C8—731no—
416C22⋊C8—731no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419C22⋊C8—1461no—
420#97—731no—
421#97—731no—
422#97—1461no—
423#97—1461no—
424#97C4×D7311yescharacteristic
425#97C4×D7311yescharacteristic
426C4×C8—21no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434#41—1462no—
435#41—1462no—
436C2×Q8—731no—
437C2×D4—731no—
438C2×D4—731no—
439C2×D4—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4C2×C4×D7311yescharacteristic
447C22×C4D4×D7311yescharacteristic
448C22×C4Q8×D7311yescharacteristic
449M16—22no—
450M16—41no—
451M16—2921no—
452M16—2922no—
453M16—2922no—
454M16—2922no—
455M16—2922no—
456M16—1462no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—2921no—
463C2×C8—2922no—
464C2×C8—2922no—
465C2×C8—2922no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—731no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1462no—
475C2×C8C2×C4×D7311yescharacteristic
476C2×C8C2×C4×D7311yescharacteristic
477C2×C8C2×C4×D7311yescharacteristic
478C2×C8C2×C4×D7311yescharacteristic
479C4⋊C4—731no—
480C4⋊C4—731no—
481C4⋊C4—731no—
482C4⋊C4—731no—
483C4⋊C4—731no—
484C4⋊C4—731no—
485C22⋊C4—731no—
486C22⋊C4—731no—
487C22⋊C4—731no—
488C22⋊C4—731no—
489C22⋊C4—731no—
490C22⋊C4—731no—
491C42—731no—
492C42—731no—
493C42—731no—
494C42—731no—
495C42—731no—
496C42—731no—
497C42C2×C4×D7311yescharacteristic
498C42D4×D7311yescharacteristic
499C42Q8×D7311yescharacteristic
500C42C23×D7311yescharacteristic
501C23—731no—
502C23—731no—
503C23C4⋊C4×D7311yescharacteristic
504Q8—1462no—
505D4—1462no—
506D4—1462no—
507D4—1462no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—2921no—
514C2×C4—2921no—
515C2×C4—731no—
516C2×C4—732no—
517C2×C4—732no—
518C2×C4—731no—
519C2×C4—731no—
520C2×C4—731no—
521C2×C4—731no—
522C2×C4—731no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4C4⋊C4×D7311yescharacteristic
530C2×C4C4⋊C4×D7311yescharacteristic
531C2×C4C4⋊C4×D7311yescharacteristic
532C2×C4C22×C4×D7311yescharacteristic
533C2×C4C2×D4×D7311yescharacteristic
534C2×C4C2×Q8×D7311yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—2921no—
543C8—2921no—
544C8—2921no—
545C8—2921no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C8—1461no—
550C8#1455659712yescomplemented
551C22—21no—
552C22—21no—
553C22—21no—
554C22—732no—
555C22—1461no—
556C22—1461no—
557C22—1461no—
558C22—1461no—
559C22—1461no—
560C22C2×C4⋊C4×D7311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—732no—
566C4—1461no—
567C4—1461no—
568C4—1461no—
569C4—1461no—
570C4—1461no—
571C4C2×#1455659711yescharacteristic
572C4#1798935311yescharacteristic
573C4AGL(1,ℤ/8)×D7311yescharacteristic
574C4#137×D7311yescharacteristic
575C2—41no—
576C2—2921no—
577C2—1462no—
578C2#2261849611yescharacteristic
579C2#428×D7311yescharacteristic
580C2#2261854111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1565C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924028D4
cosocleC42×C73C24
hypercenter#1565D73
hypocenterC73#17830
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
4. #22608719C2semidirect
5. #22608718C2semidirect
6. #22608715C2semidirect
7. #22608714C2semidirect
8. #22608704C2semidirect
9. #22608700C2semidirect
10. #22608698C2semidirect
11. #22608697C2semidirect
12. #22608688C2semidirect
13. #22608680C2semidirect
14. #334×D73C2semidirect
15. C73×#1565C2semidirect
251. C8×C73#131semidirect
304. #1565D73semidirect
306. C73#17830semidirect
550. C8#14556597semidirect

Maximal subgroups

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

subgroupindex
#226188932
#226185922
#226184962
#226087192
#226087182
#226087152
#226087142
#226087042
#226087002
#226086982
#226086972
#226086882
#226086802
#334×D732
C73×#15652
#1783073