Finite Group Databasebeta

← #33057134

Subgroups — #33057134

Order 18688.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619978C211yesmaximal, characteristic
2#22619087C211yesmaximal, characteristic, complemented
3#22618966C211yesmaximal, characteristic, complemented
4#22608824C211yesmaximal, characteristic, complemented
5#22608813C211yesmaximal, characteristic, complemented
6#22608812C211yesmaximal, characteristic, complemented
7#22608798C211yesmaximal, characteristic, complemented
8#22608792C211yesmaximal, characteristic, complemented
9#22608785C211yesmaximal, characteristic, complemented
10#22608734C211yesmaximal, characteristic, complemented
11#22608723C211yesmaximal, characteristic, complemented
12#22608714C211yesmaximal, characteristic, complemented
13#22608392C211yesmaximal, characteristic, complemented
14#22608214C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C73C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988922C411yescharacteristic
18#17988905C411yescharacteristic
19#17988887C411yescharacteristic
20#17988887C411yescharacteristic
21#17988802C411yescharacteristic
22#17988802C411yescharacteristic
23#17988738C411yescharacteristic
24#17988721C411yescharacteristic
25#17988714C2211yescharacteristic, complemented
26#17988711C2211yescharacteristic, complemented
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988665C2211yescharacteristic
32#17988665C2211yescharacteristic
33#17988664C2211yescharacteristic, complemented
34#17988659—21no—
35#17988659—21no—
36#17988658—21no—
37D4×#10596831C2211yescharacteristic
38D4×#10596831C2211yescharacteristic
39#17988652C2211yescharacteristic, complemented
40C8×C22⋊D73—21no—
41#17988647—21no—
42#17988644C2211yescharacteristic
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988612—21no—
46#17988551—21no—
47C2×C22⋊#10596831—21no—
48#17988339C2211yescharacteristic, complemented
49#17988339C2211yescharacteristic, complemented
50#17988337C2211yescharacteristic, complemented
51#17988337C2211yescharacteristic, complemented
52#17988319C2211yescharacteristic, complemented
53#17988319C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic, complemented
55#17988316C2211yescharacteristic, complemented
56#17988308C2211yescharacteristic, complemented
57#17988308C2211yescharacteristic, complemented
58C8×#10596831C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60C2×C4×D4×C73C2211yescharacteristic
61C2×C4⋊C8×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924016C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924012—21no—
73C2×#11924011—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76C2×C8×D73—21no—
77#14556585—21no—
78#14556583C2×C411yescharacteristic
79#14556579C2×C411yescharacteristic
80#14556574—21no—
81#14556570C2×C411yescharacteristic
82#14556565C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×D292C2311yescharacteristic
85C4×C22⋊D73—21no—
86#14556548—21no—
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2×C411yescharacteristic
93C4⋊#10596831D411yescharacteristic
94C4⋊#10596831D411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556514C2×C411yescharacteristic
100#14556514C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556512C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831—21no—
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831—21no—
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831C2×C411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115C22⋊#10596831D411yescharacteristic
116#14556503—21no—
117#14556503—21no—
118#14556502—21no—
119#14556501—21no—
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C22×D4×C73C2×C411yescharacteristic
126C23×C4×C73—21no—
127C22×C8×C73—21no—
128C22×C8×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73—21no—
131C4×D4×C73C2×C411yescharacteristic
132C4×D4×C73C2×C411yescharacteristic
133C4×D4×C73C2311yescharacteristic
134C4×D4×C73C2311yescharacteristic
135C2×C4⋊C4×C73C2×C411yescharacteristic
136C2×C22⋊C4×C73—21no—
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924016—22no—
149#11924016—41no—
150#11924013—22no—
151#11924013—41no—
152#11924012—81no—
153#11924012—81no—
154#11924011—81no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—81no—
158C2×#10596831—81no—
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C8×D73—81no—
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174C22⋊Dic73—21no—
175#11924005—21no—
176#11924005—21no—
177#11924005—21no—
178#11924005—21no—
179C4×Dic73—21no—
180C24×C73—21no—
181C2×D4×C73—22no—
182C2×D4×C73—21no—
183C2×D4×C73—41no—
184C2×D4×C73C22×C411yescharacteristic
185C2×D4×C73C22×C411yescharacteristic
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—81no—
192C22×C4×C73—81no—
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73#4111yescharacteristic
196C2×C8×C73—24no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—81no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73C22×C411yescharacteristic
204C4⋊C4×C73C22×C411yescharacteristic
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C22⋊C4×C73—21no—
209C42×C73C22×C411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—42no—
216C23×C73—42no—
217C23×C73—81no—
218C23×C73C4×D411yescharacteristic
219C22×D73—21no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—42no—
224D4×C73#13112yes—
225C2×C4×C73—22no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—81no—
237C2×C4×C73—81no—
238C2×C4×C73—81no—
239C2×C4×C73C4×D411yescharacteristic
240C2×C4×C73C4×D411yescharacteristic
241C2×C4×C73C4×D411yescharacteristic
242C2×C4×C73C23×C411yescharacteristic
243C2×C4×C73C22×D411yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C22⋊D73—42no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249D292—21no—
250D292—21no—
251C4×D73—41no—
252C4×D73—41no—
253Dic146—21no—
254Dic146—21no—
255C8×C73—22no—
256C8×C73—22no—
257C8×C73—41no—
258C8×C73—41no—
259#10596831—21no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—21no—
267#10596831—41no—
268#10596831—41no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73—22no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—84no—
278C22×C73#44312yes—
279C22×C73C2×C4×D411yescharacteristic
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—41no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—21no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73C2×#13111yescharacteristic
290C4×C73#56811yescharacteristic
291C4×C73#57611yescharacteristic
292C4×C73#57711yescharacteristic
293Dic73—41no—
294Dic73—41no—
295Dic73—41no—
296#18014—731nomaximal, Sylow
297C2×C73—22no—
298C2×C73—42no—
299C2×C73—81no—
300C2×C73#293311yescharacteristic
301C2×C73#294611yescharacteristic
302C2×C73C2×#44311yescharacteristic
303D73—81no—
304#3105—731no—
305#2994—731no—
306#2974—731no—
307#1590—731no—
308#1589—731no—
309#1588—731no—
310#1586—731no—
311#1586—731no—
312#1585—731no—
313C8×SD16—731no—
314C8×D8—731no—
315#1573—731no—
316#1494—731no—
317C2×D4⋊C8D7311yescharacteristic, complemented
318#1450—731no—
319C73#1801411yescharacteristic, complemented, Sylow
320#529—731no—
321C2×C4×D4C2×D7311yescharacteristic
322#484—731no—
323#481—731no—
324#478—731no—
325#478—731no—
326#463—731no—
327#463—731no—
328#450—731no—
329#447—731no—
330#446—731no—
331C8×Q8—731no—
332C4×SD16—731no—
333C4×SD16—731no—
334C4×D8—731no—
335C4×D8—731no—
336#436—731no—
337#436—731no—
338#436—731no—
339#435—1461no—
340#435—1461no—
341#435—1461no—
342C8×D4—731no—
343C8×D4—731no—
344C8×D4—731no—
345C8×D4—1461no—
346#433—1461no—
347#432—731no—
348#431—731no—
349#431—731no—
350#424—1461no—
351C2×C4⋊C8C2×D7311yescharacteristic
352#407—1461no—
353C2×C22⋊C8—1461no—
354C2×C4×C8C2×D7311yescharacteristic
355#335—731no—
356#335—731no—
357#334—731no—
358#334—731no—
359Q8⋊C8—731no—
360Q8⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8C2×D7311yescharacteristic
364D4⋊C8C2×D7311yescharacteristic
365D4⋊C8C2×D7311yescharacteristic
366D4⋊C8C2×D7311yescharacteristic
367#322—731no—
368#322—731no—
369C82—731no—
370C82—731no—
371C22×D4C4×D7311yescharacteristic
372C23×C4—21no—
373C2×SD16—731no—
374C2×SD16—731no—
375C2×D8—731no—
376C2×D8—731no—
377C2×M16—1461no—
378C2×M16—1461no—
379C2×M16—1461no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—1461no—
383C22×C8—1461no—
384C22×C8—1461no—
385#126—1461no—
386#125—731no—
387#124—731no—
388#123—1461no—
389C22⋊Q8—731no—
390#121—731no—
391C4×Q8—731no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—731no—
395C4×D4—1461no—
396C4×D4C4×D7311yescharacteristic
397C4×D4C4×D7311yescharacteristic
398C4×D4C22×D7311yescharacteristic
399C4×D4C22×D7311yescharacteristic
400#117—1461no—
401C2×C4⋊C4C4×D7311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C42C22×D7311yescharacteristic
404#107—731no—
405#107—731no—
406#106—731no—
407#106—731no—
408C4⋊C8—21no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—731no—
414C4⋊C8—731no—
415C4⋊C8—1461no—
416C4⋊C8—1461no—
417C4⋊C8C22×D7311yescharacteristic
418C4⋊C8C22×D7311yescharacteristic
419#103—731no—
420#103—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102—731no—
426#102—731no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—731no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437C22⋊C8—1461no—
438#97—1461no—
439#97—1461no—
440C4×C8—21no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—731no—
445C4×C8—1461no—
446C4×C8C22×D7311yescharacteristic
447C4×C8C22×D7311yescharacteristic
448C24—21no—
449C2×Q8—731no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—731no—
454C2×D4—1461no—
455C2×D4C2×C4×D7311yescharacteristic
456C2×D4C2×C4×D7311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—1461no—
465C22×C4C2×C4×D7311yescharacteristic
466C22×C4D4×D7311yescharacteristic
467C22×C4#1192402711yescharacteristic
468SD16—2921no—
469SD16—1462no—
470D8—2921no—
471D8—1462no—
472M16—5841no—
473M16—5841no—
474M16—5841no—
475C2×C8—24no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—81no—
481C2×C8—5841no—
482C2×C8—5841no—
483C2×C8—5841no—
484C2×C8—731no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—731no—
488C2×C8—731no—
489C2×C8—731no—
490C2×C8—731no—
491C2×C8—731no—
492C2×C8—1461no—
493C2×C8—1461no—
494C4⋊C4—21no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4C2×C4×D7311yescharacteristic
502C4⋊C4C2×C4×D7311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C22⋊C4—1461no—
511C22⋊C4—1461no—
512C42—1461no—
513C42C2×C4×D7311yescharacteristic
514C42D4×D7311yescharacteristic
515C42#1192402711yescharacteristic
516C42C23×D7311yescharacteristic
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—1461no—
523C23#1455655111yescharacteristic
524Q8—1461no—
525Q8—1461no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—2922no—
531D4—1461no—
532D4—1461no—
533D4#1455659712yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4#1455655111yescharacteristic
554C2×C4#1455655111yescharacteristic
555C2×C4#1455655111yescharacteristic
556C2×C4C22×C4×D7311yescharacteristic
557C2×C4C2×D4×D7311yescharacteristic
558C2×C4C2×#1192402711yescharacteristic
559C8—22no—
560C8—22no—
561C8—41no—
562C8—41no—
563C8—2921no—
564C8—2921no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C8—1461no—
572C8—1461no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—2921no—
583C22—2921no—
584C22—2921no—
585C22#1798870112yes—
586C22C2×#1455655111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—2921no—
594C4—2921no—
595C4—2921no—
596C4C2×#1455659711yescharacteristic
597C4#1798935311yescharacteristic
598C4#1798938811yescharacteristic
599C4#1798939311yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—5841no—
604C2#2261865211yescharacteristic
605C2#2261875711yescharacteristic
606C2C2×#1798870111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC2×D4⋊C8×C73C2
socleC22×C73C2×C4×D4
prime radical#17988721C4
cosocleC42×C73C24
hypercenterC2×D4⋊C8D73
hypocenterC73#18014
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #22619087C2semidirect
3. #22618966C2semidirect
4. #22608824C2semidirect
5. #22608813C2semidirect
6. #22608812C2semidirect
7. #22608798C2semidirect
8. #22608792C2semidirect
9. #22608785C2semidirect
10. #22608734C2semidirect
11. #22608723C2semidirect
12. #22608714C2semidirect
13. #22608392C2semidirect
14. #22608214C2semidirect
15. C2×D4⋊C8×C73C2semidirect
25. #17988714C22semidirect
26. #17988711C22semidirect
33. #17988664C22semidirect
39. #17988652C22semidirect
48. #17988339C22semidirect
49. #17988339C22semidirect
50. #17988337C22semidirect
51. #17988337C22semidirect
52. #17988319C22semidirect
53. #17988319C22semidirect
54. #17988316C22semidirect
55. #17988316C22semidirect
56. #17988308C22semidirect
57. #17988308C22semidirect
58. C8×#10596831C22semidirect
59. C8×#10596831C22semidirect
317. C2×D4⋊C8D73semidirect
319. C73#18014semidirect

Maximal subgroups

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

subgroupindex
#226199782
#226190872
#226189662
#226088242
#226088132
#226088122
#226087982
#226087922
#226087852
#226087342
#226087232
#226087142
#226083922
#226082142
C2×D4⋊C8×C732
#1801473