Finite Group Databasebeta

← #33055652

Subgroups — #33055652

Order 18688.

726 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618969C211yesmaximal, characteristic, complemented
2#22618952C211yesmaximal, characteristic, complemented
3C4×D8×D73C211yesmaximal, characteristic
4#22608797C211yesmaximal, characteristic, complemented
5#22608796C211yesmaximal, characteristic, complemented
6#22608794C211yesmaximal, characteristic, complemented
7#22608763C211yesmaximal, characteristic, complemented
8#22608760C211yesmaximal, characteristic, complemented
9#22608758C211yesmaximal, characteristic, complemented
10#22608757C211yesmaximal, characteristic, complemented
11#22608676C211yesmaximal, characteristic, complemented
12#22608320C211yesmaximal, characteristic, complemented
13#22608320C211yesmaximal, characteristic, complemented
14#22608222C211yesmaximal, characteristic, complemented
15C73×#1586C211yesmaximal, characteristic, complemented
16C2×D8×D73C411yescharacteristic
17C4×D4×D73C2211yescharacteristic
18C4×D4×D73C2211yescharacteristic
19C4×D584C2211yescharacteristic
20D8×Dic73C411yescharacteristic
21#17988669C411yescharacteristic
22C4×#11924013C2211yescharacteristic
23C4×#11924013C2211yescharacteristic
24#17988667C411yescharacteristic
25#17988667C411yescharacteristic
26#17988666C2211yescharacteristic, complemented
27#17988665C2211yescharacteristic, complemented
28#17988664C2211yescharacteristic, complemented
29#17988663—21no—
30#17988662—21no—
31C8×D292C2211yescharacteristic, complemented
32D4×#10596831C2211yescharacteristic, complemented
33#17988652C2211yescharacteristic, complemented
34C8×C22⋊D73—21no—
35#17988650—21no—
36#17988639C2211yescharacteristic
37#17988639C2211yescharacteristic
38#17988638C2211yescharacteristic
39#17988638C2211yescharacteristic
40#107×D73C411yescharacteristic
41#102×D73C411yescharacteristic
42#102×D73C411yescharacteristic
43#17988550—21no—
44#17988549—21no—
45C2×#14556503—21no—
46C22⋊C8×D73—21no—
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic, complemented
49#17988339C2211yescharacteristic, complemented
50#17988338C2211yescharacteristic, complemented
51#17988316C2211yescharacteristic, complemented
52#17988316C2211yescharacteristic, complemented
53D4⋊#10596831C2211yescharacteristic, complemented
54D4⋊#10596831C2211yescharacteristic, complemented
55#17988314C2211yescharacteristic, complemented
56#17988314C2211yescharacteristic, complemented
57#17988309C2211yescharacteristic, complemented
58#17988309C2211yescharacteristic, complemented
59#17988308C2211yescharacteristic, complemented
60C4×D8×C73C2211yescharacteristic
61#436×C73C2211yescharacteristic, complemented
62C8×D4×C73C2211yescharacteristic, complemented
63#334×C73C2211yescharacteristic, complemented
64D4⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic, complemented
66#322×C73C2211yescharacteristic, complemented
67C2×D4×D73C2×C411yescharacteristic
68C2×D4×D73C2×C411yescharacteristic
69C22×C4×D73—21no—
70C22×C4×D73—21no—
71C2×D584C2×C411yescharacteristic
72C2×#11924013C2×C411yescharacteristic
73C2×#11924013C2×C411yescharacteristic
74D8×D73—24no—
75C2×#11924012—21no—
76C2×#11924011—21no—
77C2×#11924011—21no—
78C22×#10596831—21no—
79C2×C8×D73—21no—
80C2×C8×D73—21no—
81C2×C8×D73C2×C411yescharacteristic
82C2×C8×D73C2×C411yescharacteristic
83C4×D292C2311yescharacteristic
84C4×D292C2311yescharacteristic
85D4×Dic73C2×C411yescharacteristic
86D4×Dic73C2×C411yescharacteristic
87#14556553C2×C411yescharacteristic
88#14556553C2×C411yescharacteristic
89C4×C22⋊D73—21no—
90C4×C22⋊D73—21no—
91#14556551—21no—
92#14556551—21no—
93C4⋊C4×D73C2×C411yescharacteristic
94C4⋊C4×D73C2×C411yescharacteristic
95C22⋊C4×D73—21no—
96C22⋊C4×D73—21no—
97C42×D73C2311yescharacteristic
98#14556525C2×C411yescharacteristic
99#14556524C2×C411yescharacteristic
100#14556524C2×C411yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103#14556520—21no—
104#14556520D411yescharacteristic
105#14556520D411yescharacteristic
106#14556513C2×C411yescharacteristic
107#14556513C2×C411yescharacteristic
108#14556512C2×C411yescharacteristic
109#14556512C2×C411yescharacteristic
110#14556511C2×C411yescharacteristic
111#14556511C2×C411yescharacteristic
112C22⋊#10596831—21no—
113C22⋊#10596831—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556503D411yescharacteristic
122#14556503D411yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73C2×C411yescharacteristic
129C8×Dic73C2×C411yescharacteristic
130C2×D8×C73C2×C411yescharacteristic
131C2×M16×C73—21no—
132C22×C8×C73—21no—
133C4×D4×C73C2311yescharacteristic
134C4×D4×C73C2311yescharacteristic
135#107×C73C2×C411yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138#102×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73—21no—
141C22⋊C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145C23×D73—21no—
146C23×D73—21no—
147C2×D292C22×C411yescharacteristic
148C2×D292C22×C411yescharacteristic
149C2×C22⋊D73—21no—
150C2×C22⋊D73—21no—
151D4×D73—22no—
152D4×D73—22no—
153D4×D73—22no—
154D4×D73M1614yescomplemented
155C22×Dic73—21no—
156C22×Dic73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—81no—
164C2×C4×D73—81no—
165C2×C4×D73—81no—
166C2×C4×D73—81no—
167C2×C4×D73C22×C411yescharacteristic
168C2×C4×D73C2×D411yescharacteristic
169C2×C4×D73#4111yescharacteristic
170D584—22no—
171#11924013—22no—
172#11924013—22no—
173#11924012—81no—
174#11924011—81no—
175#11924011—81no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—81no—
180C2×#10596831C22×C411yescharacteristic
181C2×#10596831C22×C411yescharacteristic
182C2×#10596831C2×D411yescharacteristic
183C2×#10596831C2×D411yescharacteristic
184C8×D73—22no—
185C8×D73—22no—
186C8×D73—81no—
187C8×D73—81no—
188C4⋊Dic73C22×C411yescharacteristic
189C4⋊Dic73C22×C411yescharacteristic
190#11924007—21no—
191#11924007—21no—
192C22⋊Dic73—21no—
193C22⋊Dic73—21no—
194#11924005—21no—
195#11924005—21no—
196#11924005—21no—
197#11924005—21no—
198C4×Dic73C22×C411yescharacteristic
199C4×Dic73C2×D411yescharacteristic
200C4×Dic73#4111yescharacteristic
201C2×D4×C73C22×C411yescharacteristic
202C2×D4×C73C22×C411yescharacteristic
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205D8×C73—22no—
206M16×C73—81no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—81no—
211C2×C8×C73C22×C411yescharacteristic
212C2×C8×C73C22×C411yescharacteristic
213C2×C8×C73C2×D411yescharacteristic
214C2×C8×C73C2×D411yescharacteristic
215C4⋊C4×C73C22×C411yescharacteristic
216C4⋊C4×C73C22×C411yescharacteristic
217C22⋊C4×C73—21no—
218C22⋊C4×C73—21no—
219C42×C73C2411yescharacteristic
220C23×C73—21no—
221C23×C73—21no—
222C22×D73—21no—
223C22×D73—24no—
224C22×D73—21no—
225C22×D73—42no—
226C22×D73—81no—
227C22×D73—81no—
228C22×D73—81no—
229C22×D73—81no—
230C22×D73C4×D411yescharacteristic
231D4×C73—21no—
232D4×C73—21no—
233D4×C73—21no—
234D4×C73C2×M1612yes—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73C23×C411yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C22⋊D73—24no—
245C22⋊D73—42no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—81no—
249C2×Dic73—81no—
250C2×Dic73C4×D411yescharacteristic
251C2×Dic73C4×D411yescharacteristic
252C2×Dic73C4×D411yescharacteristic
253D292—21no—
254D292—21no—
255D292—21no—
256D292C2×M1612yes—
257C4×D73—21no—
258C4×D73—21no—
259C4×D73—41no—
260C4×D73—41no—
261C4×D73—41no—
262C4×D73—41no—
263C4×D73—41no—
264C4×D73—81no—
265C4×D73—81no—
266C4×D73—81no—
267C4×D73—81no—
268C4×D73C2×M1612yes—
269C4×D73#13112yes—
270C8×C73—21no—
271C8×C73—21no—
272C8×C73—21no—
273C8×C73—21no—
274C8×C73—41no—
275C8×C73—41no—
276C8×C73—41no—
277#10596831—21no—
278#10596831—21no—
279#10596831—21no—
280#10596831—21no—
281#10596831—41no—
282#10596831—41no—
283#10596831—41no—
284C22×C73—22no—
285C22×C73—41no—
286C22×C73—41no—
287C22×C73—41no—
288C22×C73—41no—
289C22×C73—41no—
290C22×C73C2×C4×D411yescharacteristic
291C2×D73—21no—
292C2×D73—21no—
293C2×D73—22no—
294C2×D73—41no—
295C2×D73—41no—
296C2×D73—41no—
297C2×D73—41no—
298C2×D73—41no—
299C2×D73—84no—
300C2×D73—84no—
301C2×D73#43512yes—
302C4×C73—21no—
303C4×C73—41no—
304C4×C73—41no—
305C4×C73C22×M1611yescharacteristic
306C4×C73C2×#13111yescharacteristic
307C4×C73#57611yescharacteristic
308C4×C73#57611yescharacteristic
309Dic73—21no—
310Dic73—21no—
311Dic73—41no—
312Dic73—41no—
313Dic73#43512yes—
314#17877—731nomaximal, Sylow
315C2×C73—42no—
316C2×C73—81no—
317C2×C73C2×#43511yescharacteristic
318C2×C73#294811yescharacteristic
319C2×C73#295711yescharacteristic
320D73—22no—
321D73—42no—
322D73—81no—
323#2975—731no—
324#2972—731no—
325C2×C4×D8—731no—
326#1586—731no—
327#1586—731no—
328#1586—731no—
329#1586D7311yescharacteristic, complemented
330#1581—731no—
331#1581—731no—
332#1581—731no—
333#1581—731no—
334#1564—731no—
335#1478—731no—
336#1478—731no—
337#1452—731no—
338C73#1787711yescharacteristic, complemented, Sylow
339C22×D8—731no—
340C2×C4×D4—731no—
341C2×C4×D4—731no—
342C4×D8—731no—
343C4×D8—731no—
344C4×D8—731no—
345C4×D8—731no—
346C4×D8—731no—
347C4×D8—731no—
348C4×D8—731no—
349C4×D8C2×D7311yescharacteristic
350#436—731no—
351#436—731no—
352#436—731no—
353#436—1461no—
354#436—1461no—
355#436C2×D7311yescharacteristic, complemented
356C8×D4—731no—
357C8×D4—731no—
358C8×D4—731no—
359C8×D4—1461no—
360C8×D4—1461no—
361C8×D4C2×D7311yescharacteristic, complemented
362#431—731no—
363#431—731no—
364#431—731no—
365#431—731no—
366C2×#107—731no—
367C2×#102—731no—
368C2×#102—731no—
369#407—1461no—
370#407—1461no—
371C2×C22⋊C8—1461no—
372C2×C22⋊C8—1461no—
373C2×C4×C8—731no—
374#335—731no—
375#335—731no—
376#334—731no—
377#334C2×D7311yescharacteristic, complemented
378D4⋊C8—731no—
379D4⋊C8—731no—
380D4⋊C8—731no—
381D4⋊C8—731no—
382D4⋊C8—731no—
383D4⋊C8—731no—
384D4⋊C8C2×D7311yescharacteristic, complemented
385D4⋊C8C2×D7311yescharacteristic, complemented
386#322—731no—
387#322—731no—
388#322—731no—
389#322C2×D7311yescharacteristic, complemented
390C22×D4—731no—
391C22×D4—731no—
392C23×C4—1461no—
393C23×C4—1461no—
394C2×D8—731no—
395C2×D8—731no—
396C2×D8—731no—
397C2×D8—1464no—
398C2×D8C4×D7311yescharacteristic
399C2×M16—21no—
400C2×M16—1461no—
401C2×M16—1461no—
402C2×M16—1461no—
403C22×C8—21no—
404C22×C8—731no—
405C22×C8—731no—
406C22×C8—1461no—
407C22×C8—1461no—
408C22×C8—1461no—
409C4×D4—731no—
410C4×D4—731no—
411C4×D4—731no—
412C4×D4—731no—
413C4×D4—731no—
414C4×D4—731no—
415C4×D4—1461no—
416C4×D4—1461no—
417C4×D4—1461no—
418C4×D4—1461no—
419C4×D4C22×D7311yescharacteristic
420C4×D4C22×D7311yescharacteristic
421C2×C4⋊C4—731no—
422C2×C4⋊C4—731no—
423C2×C22⋊C4—1461no—
424C2×C22⋊C4—1461no—
425C2×C42—731no—
426#107—731no—
427#107—731no—
428#107—731no—
429#107C4×D7311yescharacteristic
430C4⋊C8—731no—
431C4⋊C8—731no—
432C4⋊C8—731no—
433C4⋊C8—731no—
434C4⋊C8—1461no—
435C4⋊C8C22×D7311yescharacteristic
436C4⋊C8C22×D7311yescharacteristic
437#102—731no—
438#102—731no—
439#102—731no—
440#102—731no—
441#102—731no—
442#102—731no—
443#102C4×D7311yescharacteristic
444#102C4×D7311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—731no—
448C22⋊C8—731no—
449C22⋊C8—1461no—
450C22⋊C8—1461no—
451C22⋊C8—1461no—
452C22⋊C8—1461no—
453C22⋊C8—1461no—
454C22⋊C8—1461no—
455C22⋊C8—1461no—
456C22⋊C8—1461no—
457C22⋊C8—1461no—
458C4×C8—731no—
459C4×C8—731no—
460C4×C8—731no—
461C4×C8—731no—
462C4×C8—731no—
463C4×C8—1461no—
464C4×C8—1461no—
465C4×C8C22×D7311yescharacteristic
466C4×C8C22×D7311yescharacteristic
467C4×C8C22×D7311yescharacteristic
468C24—1461no—
469C24—1461no—
470C2×D4—734no—
471C2×D4—731no—
472C2×D4—731no—
473C2×D4—1462no—
474C2×D4—1462no—
475C2×D4—1462no—
476C2×D4—1461no—
477C2×D4—1461no—
478C2×D4C2×C4×D7311yescharacteristic
479C2×D4C2×C4×D7311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—5841no—
483C22×C4—5841no—
484C22×C4—5841no—
485C22×C4—5841no—
486C22×C4—731no—
487C22×C4—731no—
488C22×C4—731no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1461no—
495C22×C4—1461no—
496C22×C4—1461no—
497D8—22no—
498D8—1462no—
499D8—1462no—
500D8—1462no—
501M16—81no—
502M16—5841no—
503M16—5841no—
504M16—5841no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—5841no—
510C2×C8—5841no—
511C2×C8—5841no—
512C2×C8—731no—
513C2×C8—731no—
514C2×C8—731no—
515C2×C8—731no—
516C2×C8—1462no—
517C2×C8—1462no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8C2×C4×D7311yescharacteristic
522C2×C8C2×C4×D7311yescharacteristic
523C2×C8D4×D7311yescharacteristic
524C2×C8D4×D7311yescharacteristic
525C4⋊C4—731no—
526C4⋊C4—731no—
527C4⋊C4—1461no—
528C4⋊C4—1461no—
529C4⋊C4C2×C4×D7311yescharacteristic
530C4⋊C4C2×C4×D7311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—1461no—
534C22⋊C4—1461no—
535C22⋊C4—1461no—
536C22⋊C4—1461no—
537C22⋊C4—1461no—
538C22⋊C4—1461no—
539C42—731no—
540C42—731no—
541C42—731no—
542C42C23×D7311yescharacteristic
543C23—21no—
544C23—21no—
545C23—2922no—
546C23—5841no—
547C23—5841no—
548C23—5841no—
549C23—5841no—
550C23—731no—
551C23—1464no—
552C23—1461no—
553C23—1461no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—2922no—
558D4—732no—
559D4—1464no—
560D4—1461no—
561D4—1461no—
562D4—1461no—
563D4M16×D7312yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—2921no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—5841no—
576C2×C4—5841no—
577C2×C4—5841no—
578C2×C4—5841no—
579C2×C4—5841no—
580C2×C4—5841no—
581C2×C4—731no—
582C2×C4—732no—
583C2×C4—732no—
584C2×C4—731no—
585C2×C4—731no—
586C2×C4—1461no—
587C2×C4—1461no—
588C2×C4—1461no—
589C2×C4—1461no—
590C2×C4C22×C4×D7311yescharacteristic
591C2×C4C2×D4×D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—2921no—
601C8—2921no—
602C8—2921no—
603C8—1461no—
604C8—1461no—
605C8—1461no—
606C8—1461no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—2921no—
614C22—2921no—
615C22—2921no—
616C22—2921no—
617C22—2921no—
618C22—5844no—
619C22—5844no—
620C22—732no—
621C22—1462no—
622C22—1461no—
623C22—1461no—
624C22C4×D4×D7311yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—2921no—
629C4—2921no—
630C4—732no—
631C4—1461no—
632C4—1461no—
633C4C2×M16×D7311yescharacteristic
634C4#131×D7311yescharacteristic
635C4#1798939111yescharacteristic
636C4#1798939111yescharacteristic
637C2—42no—
638C2—81no—
639C2—2922no—
640C2—5841no—
641C2—1462no—
642C2#435×D7311yescharacteristic
643C2#2261878011yescharacteristic
644C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1586C2
socleC22×C73C2×C4×D4
prime radicalC2×D8×D73C4
cosocleC42×C73C24
hypercenter#1586D73
hypocenterC73#17877
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
1. #22618969C2semidirect
2. #22618952C2semidirect
4. #22608797C2semidirect
5. #22608796C2semidirect
6. #22608794C2semidirect
7. #22608763C2semidirect
8. #22608760C2semidirect
9. #22608758C2semidirect
10. #22608757C2semidirect
11. #22608676C2semidirect
12. #22608320C2semidirect
13. #22608320C2semidirect
14. #22608222C2semidirect
15. C73×#1586C2semidirect
26. #17988666C22semidirect
27. #17988665C22semidirect
28. #17988664C22semidirect
31. C8×D292C22semidirect
32. D4×#10596831C22semidirect
33. #17988652C22semidirect
48. #17988339C22semidirect
49. #17988339C22semidirect
50. #17988338C22semidirect
51. #17988316C22semidirect
52. #17988316C22semidirect
53. D4⋊#10596831C22semidirect
54. D4⋊#10596831C22semidirect
55. #17988314C22semidirect
56. #17988314C22semidirect
57. #17988309C22semidirect
58. #17988309C22semidirect
59. #17988308C22semidirect
61. #436×C73C22semidirect
62. C8×D4×C73C22semidirect
63. #334×C73C22semidirect
64. D4⋊C8×C73C22semidirect
65. D4⋊C8×C73C22semidirect
66. #322×C73C22semidirect
154. D4×D73M16semidirect
329. #1586D73semidirect
338. C73#17877semidirect
355. #436C2×D73semidirect
361. C8×D4C2×D73semidirect
377. #334C2×D73semidirect
384. D4⋊C8C2×D73semidirect
385. D4⋊C8C2×D73semidirect
389. #322C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226189692
#226189522
C4×D8×D732
#226087972
#226087962
#226087942
#226087632
#226087602
#226087582
#226087572
#226086762
#226083202
#226082222
C73×#15862
#1787773