Finite Group Databasebeta

← #33056076

Subgroups — #33056076

Order 18688.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619042C211yesmaximal, characteristic, complemented
2#22619007C211yesmaximal, characteristic, complemented
3#22608810C211yesmaximal, characteristic, complemented
4#22608796C211yesmaximal, characteristic, complemented
5#22608775C211yesmaximal, characteristic, complemented
6#22608761C211yesmaximal, characteristic, complemented
7#22608755C211yesmaximal, characteristic, complemented
8SD16⋊#10596831C211yesmaximal, characteristic, complemented
9SD16×#10596831C211yesmaximal, characteristic, complemented
10D8×#10596831C211yesmaximal, characteristic, complemented
11#22608716C211yesmaximal, characteristic, complemented
12#22608365C211yesmaximal, characteristic, complemented
13#22608330C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#3106C211yesmaximal, characteristic
16Q8×#10596831C2211yescharacteristic
17Q8×#10596831C2211yescharacteristic
18#17988665C2211yescharacteristic
19#17988665C2211yescharacteristic
20#17988659—21no—
21#17988659—21no—
22D4×#10596831—21no—
23D4×#10596831—21no—
24D4×#10596831C2211yescharacteristic
25D4×#10596831C2211yescharacteristic
26D4×#10596831C2211yescharacteristic
27D4×#10596831C2211yescharacteristic
28#17988644C2211yescharacteristic
29#17988640—21no—
30#17988640C2211yescharacteristic
31#17988640C2211yescharacteristic
32C2×C4⋊#10596831—21no—
33C2×C4⋊#10596831C2211yescharacteristic
34#17988554—21no—
35#17988554—21no—
36#17988340C2211yescharacteristic
37#17988340C2211yescharacteristic
38#17988338C2211yescharacteristic
39#17988338C2211yescharacteristic
40Q8⋊#10596831C2211yescharacteristic
41Q8⋊#10596831C2211yescharacteristic
42D4⋊#10596831C2211yescharacteristic
43D4⋊#10596831C2211yescharacteristic
44D4⋊#10596831C2211yescharacteristic
45D4⋊#10596831C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48#17988309C2211yescharacteristic
49#17988309C2211yescharacteristic
50#17988308C2211yescharacteristic
51C8×#10596831C2211yescharacteristic
52#532×C73C2211yescharacteristic
53C4×#41×C73C2211yescharacteristic
54#482×C73C411yescharacteristic
55#482×C73C411yescharacteristic
56#477×C73C411yescharacteristic
57#476×C73C411yescharacteristic
58#460×C73C411yescharacteristic
59#459×C73C411yescharacteristic
60#449×C73C411yescharacteristic
61#449×C73C411yescharacteristic
62C4×SD16×C73C2211yescharacteristic
63C4×SD16×C73C2211yescharacteristic
64C4×D8×C73C2211yescharacteristic
65C4×D8×C73C2211yescharacteristic
66#431×C73C2211yescharacteristic
67C2×#11924012—21no—
68C2×#11924012—21no—
69C22×#10596831—21no—
70C22×#10596831—21no—
71C22×#10596831—21no—
72C22×#10596831—21no—
73C22×#10596831—21no—
74C4⋊#10596831—21no—
75C4⋊#10596831—21no—
76C4⋊#10596831—21no—
77C4⋊#10596831—21no—
78C4⋊#10596831D411yescharacteristic
79C4⋊#10596831D411yescharacteristic
80C4⋊#10596831C2311yescharacteristic
81C4⋊#10596831C2311yescharacteristic
82C4⋊#10596831C2311yescharacteristic
83C4⋊#10596831C2311yescharacteristic
84C22⋊#10596831—21no—
85C22⋊#10596831—21no—
86C22⋊#10596831—21no—
87C22⋊#10596831—21no—
88C22⋊#10596831—21no—
89C22⋊#10596831—21no—
90C22⋊#10596831—21no—
91C22⋊#10596831—21no—
92C22⋊#10596831D411yescharacteristic
93C22⋊#10596831D411yescharacteristic
94#14556502—21no—
95C4×#10596831—21no—
96C4×#10596831—21no—
97C4×#10596831C2311yescharacteristic
98C4×#10596831C2311yescharacteristic
99C4×#10596831C2311yescharacteristic
100C4×#10596831C2311yescharacteristic
101C2×#41×C73—21no—
102C2×#41×C73C2×C411yescharacteristic
103C2×SD16×C73C2×C411yescharacteristic
104C2×SD16×C73C2×C411yescharacteristic
105C2×D8×C73C2×C411yescharacteristic
106C2×D8×C73C2×C411yescharacteristic
107C4⋊Q8×C73C2×C411yescharacteristic
108#127×C73C2×C411yescharacteristic
109#124×C73—21no—
110#121×C73—21no—
111#121×C73C2×C411yescharacteristic
112#121×C73C2×C411yescharacteristic
113C4×Q8×C73C2×C411yescharacteristic
114C4×Q8×C73C2311yescharacteristic
115C4×D4×C73—21no—
116C4×D4×C73—21no—
117C4×D4×C73—21no—
118C4×D4×C73C2×C411yescharacteristic
119C4×D4×C73C2311yescharacteristic
120C4×D4×C73C2311yescharacteristic
121C4×D4×C73C2311yescharacteristic
122#117×C73—21no—
123#117×C73C2×C411yescharacteristic
124C2×C42×C73—21no—
125C2×C42×C73C2311yescharacteristic
126#107×C73C2×C411yescharacteristic
127#107×C73C2×C411yescharacteristic
128#106×C73C2×C411yescharacteristic
129#106×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73C2×C411yescharacteristic
132#103×C73C2×C411yescharacteristic
133#103×C73C2×C411yescharacteristic
134#102×C73C2×C411yescharacteristic
135#102×C73C2×C411yescharacteristic
136#102×C73C2×C411yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141C22⋊C8×C73C2×C411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924012—81no—
145#11924012—81no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—81no—
153C2×#10596831—81no—
154C2×#10596831—81no—
155C2×#10596831—81no—
156C2×#10596831—81no—
157C2×#10596831C2×D411yescharacteristic
158C2×#10596831C2×D411yescharacteristic
159C2×#10596831C2×D411yescharacteristic
160C2×#10596831C2×D411yescharacteristic
161#41×C73—22no—
162#41×C73—22no—
163#41×C73—81no—
164#41×C73—81no—
165C2×Q8×C73—21no—
166C2×Q8×C73C22×C411yescharacteristic
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73C22×C411yescharacteristic
173C2×D4×C73C22×C411yescharacteristic
174C2×D4×C73C22×C411yescharacteristic
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73C22×C411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73#4111yescharacteristic
183SD16×C73—22no—
184SD16×C73—22no—
185D8×C73—22no—
186D8×C73—22no—
187C2×C8×C73C22×C411yescharacteristic
188C2×C8×C73C22×C411yescharacteristic
189C2×C8×C73C22×C411yescharacteristic
190C2×C8×C73C22×C411yescharacteristic
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73C22×C411yescharacteristic
195C4⋊C4×C73C22×C411yescharacteristic
196C4⋊C4×C73C22×C411yescharacteristic
197C4⋊C4×C73C22×C411yescharacteristic
198C22⋊C4×C73—21no—
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73C22×C411yescharacteristic
209C42×C73C2×D411yescharacteristic
210C42×C73#4111yescharacteristic
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73C4×D411yescharacteristic
216Q8×C73—21no—
217Q8×C73—81no—
218Q8×C73#13112yes—
219D4×C73—24no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—21no—
224D4×C73—21no—
225D4×C73—81no—
226D4×C73—81no—
227D4×C73—81no—
228D4×C73—81no—
229D4×C73#13112yes—
230C2×C4×C73—24no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—81no—
248C2×C4×C73C4×D411yescharacteristic
249C2×C4×C73C4×D411yescharacteristic
250C2×C4×C73C4×D411yescharacteristic
251C2×C4×C73C23×C411yescharacteristic
252C2×C4×C73C22×D411yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258#10596831—21no—
259#10596831—21no—
260#10596831—21no—
261#10596831—21no—
262#10596831—41no—
263#10596831—41no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—21no—
269C22×C73—22no—
270C22×C73—21no—
271C22×C73—21no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73C2×C4×D411yescharacteristic
281C4×C73—21no—
282C4×C73—22no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73C2×#13111yescharacteristic
291C4×C73C2×#13111yescharacteristic
292C4×C73#57611yescharacteristic
293C4×C73#57711yescharacteristic
294#17920—731nomaximal, Sylow
295C2×C73—41no—
296C2×C73—42no—
297C2×C73—81no—
298C2×C73—81no—
299C2×C73#292911yescharacteristic
300C2×C73#294611yescharacteristic
301C2×C73#295711yescharacteristic
302#3106D7311yescharacteristic
303#2988—731no—
304#2981—731no—
305#1588—731no—
306#1586—731no—
307#1583—731no—
308#1581—731no—
309#1580—731no—
310SD16⋊C8—731no—
311C8×SD16—731no—
312C8×D8—731no—
313#1573—731no—
314#1488—731no—
315#1480—731no—
316#1454—731no—
317C73#1792011yescharacteristic, complemented, Sylow
318#532C2×D7311yescharacteristic
319C4×#41C2×D7311yescharacteristic
320#482Dic7311yescharacteristic
321#482Dic7311yescharacteristic
322#477Dic7311yescharacteristic
323#476Dic7311yescharacteristic
324#460Dic7311yescharacteristic
325#459Dic7311yescharacteristic
326#449Dic7311yescharacteristic
327#449Dic7311yescharacteristic
328C8×Q8—731no—
329C8×Q8—731no—
330C4×SD16C2×D7311yescharacteristic
331C4×SD16C2×D7311yescharacteristic
332C4×D8C2×D7311yescharacteristic
333C4×D8C2×D7311yescharacteristic
334#436—731no—
335#436—731no—
336#435—1461no—
337#435—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—1461no—
343C8×D4—1461no—
344#432—731no—
345#431—731no—
346#431—731no—
347#431—1461no—
348#431C2×D7311yescharacteristic
349C2×C4⋊C8—731no—
350C2×C4⋊C8—1461no—
351#408—1461no—
352#408—1461no—
353#335—731no—
354#335—731no—
355#334—731no—
356#334—731no—
357Q8⋊C8—731no—
358Q8⋊C8—731no—
359D4⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365#322—731no—
366#322—731no—
367#322—731no—
368C82—731no—
369C2×#41—21no—
370C2×#41C2×Dic7311yescharacteristic
371C2×SD16C2×Dic7311yescharacteristic
372C2×SD16C2×Dic7311yescharacteristic
373C2×D8C2×Dic7311yescharacteristic
374C2×D8C2×Dic7311yescharacteristic
375C2×M16—1461no—
376C2×M16—1461no—
377C22×C8—1461no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C4⋊Q8C2×Dic7311yescharacteristic
383#127C2×Dic7311yescharacteristic
384#124—21no—
385#121—21no—
386#121C2×Dic7311yescharacteristic
387#121C2×Dic7311yescharacteristic
388C4×Q8C2×Dic7311yescharacteristic
389C4×Q8C22×D7311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C2×Dic7311yescharacteristic
394C4×D4C22×D7311yescharacteristic
395C4×D4C22×D7311yescharacteristic
396C4×D4C22×D7311yescharacteristic
397#117—21no—
398#117C2×Dic7311yescharacteristic
399C2×C42—21no—
400C2×C42C22×D7311yescharacteristic
401#107C2×Dic7311yescharacteristic
402#107C2×Dic7311yescharacteristic
403#106C2×Dic7311yescharacteristic
404#106C2×Dic7311yescharacteristic
405C4⋊C8—731no—
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—1461no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8—1461no—
415C4⋊C8C2×Dic7311yescharacteristic
416C4⋊C8C2×Dic7311yescharacteristic
417#103C2×Dic7311yescharacteristic
418#103C2×Dic7311yescharacteristic
419#102C2×Dic7311yescharacteristic
420#102C2×Dic7311yescharacteristic
421#102C2×Dic7311yescharacteristic
422#102C2×Dic7311yescharacteristic
423#102C2×Dic7311yescharacteristic
424#102C2×Dic7311yescharacteristic
425C22⋊C8—731no—
426C22⋊C8—731no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8C2×Dic7311yescharacteristic
436C22⋊C8C2×Dic7311yescharacteristic
437#97—1461no—
438C4×C8—731no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—1461no—
443C4×C8—1461no—
444C4×C8C22×D7311yescharacteristic
445C4×C8C22×D7311yescharacteristic
446#41—22no—
447#41—22no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8C22×Dic7311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C22×Dic7311yescharacteristic
458C2×D4C22×Dic7311yescharacteristic
459C2×D4C22×Dic7311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C22×Dic7311yescharacteristic
466C22×C4D4×D7311yescharacteristic
467C22×C4#1192402711yescharacteristic
468SD16—22no—
469SD16—22no—
470D8—22no—
471D8—22no—
472M16—5841no—
473M16—5841no—
474C2×C8—5841no—
475C2×C8—5841no—
476C2×C8—5841no—
477C2×C8—5841no—
478C2×C8—5841no—
479C2×C8—731no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8C22×Dic7311yescharacteristic
490C2×C8C22×Dic7311yescharacteristic
491C2×C8C22×Dic7311yescharacteristic
492C2×C8C22×Dic7311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C22×Dic7311yescharacteristic
497C4⋊C4C22×Dic7311yescharacteristic
498C4⋊C4C22×Dic7311yescharacteristic
499C4⋊C4C22×Dic7311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C22×Dic7311yescharacteristic
511C42D4×D7311yescharacteristic
512C42#1192402711yescharacteristic
513C42C23×D7311yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic7311yescharacteristic
518Q8—21no—
519Q8—81no—
520Q8#1455659812yes—
521D4—24no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4#1455659812yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4D4×Dic7311yescharacteristic
551C2×C4D4×Dic7311yescharacteristic
552C2×C4D4×Dic7311yescharacteristic
553C2×C4C23×Dic7311yescharacteristic
554C2×C4C2×D4×D7311yescharacteristic
555C2×C4C2×#1192402711yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—2921no—
561C8—2921no—
562C8—2921no—
563C8—2921no—
564C8—2921no—
565C8—2921no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C22—21no—
571C22—22no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C2×D4×Dic7311yescharacteristic
583C4—21no—
584C4—22no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4C2×#1455659811yescharacteristic
593C4C2×#1455659811yescharacteristic
594C4#1798939111yescharacteristic
595C4#1798939711yescharacteristic
596C2—41no—
597C2—42no—
598C2—81no—
599C2—81no—
600C2#2261862611yescharacteristic
601C2#2261876411yescharacteristic
602C2#2261884811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
Fitting, prime radicalC73×#3106C2
socleC22×C73C2×C4×D4
cosocleC42×C73C24
hypercenter#3106D73
hypocenterC73#17920
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #22619042C2semidirect
2. #22619007C2semidirect
3. #22608810C2semidirect
4. #22608796C2semidirect
5. #22608775C2semidirect
6. #22608761C2semidirect
7. #22608755C2semidirect
8. SD16⋊#10596831C2semidirect
9. SD16×#10596831C2semidirect
10. D8×#10596831C2semidirect
11. #22608716C2semidirect
12. #22608365C2semidirect
13. #22608330C2semidirect
14. #22608231C2semidirect
317. C73#17920semidirect

Maximal subgroups

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

subgroupindex
#226190422
#226190072
#226088102
#226087962
#226087752
#226087612
#226087552
SD16⋊#105968312
SD16×#105968312
D8×#105968312
#226087162
#226083652
#226083302
#226082312
C73×#31062
#1792073