Finite Group Databasebeta

← #10845340

Subgroups — #10845340

Order 768.

914 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4847C211yesmaximal, characteristic, complemented
2C2×#4834C211yesmaximal, characteristic, complemented
3#74239C211yesmaximal, characteristic
4#73806C211yesmaximal, characteristic, complemented
5C3×#1949C211yesmaximal, characteristic, complemented
6#70634C211yesmaximal, characteristic, complemented
7#70630C211yesmaximal, characteristic, complemented
8#70581C211yesmaximal, characteristic, complemented
9#70577C211yesmaximal, characteristic, complemented
10#69554C211yesmaximal, characteristic, complemented
11C4×#809C211yesmaximal, characteristic, complemented
12#68883C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68832C211yesmaximal, characteristic, complemented
15#68831C211yesmaximal, characteristic, complemented
16#25342—31nomaximal, Sylow
17C22×D3×C8C2211yescharacteristic
18C22×D3×C8C2211yescharacteristic
19C2×#895C2211yescharacteristic
20C2×#895C2211yescharacteristic
21C2×C4×D12C2211yescharacteristic
22C2×C4×D12C2211yescharacteristic
23C2×#870C2211yescharacteristic
24C2×C3×#107C2211yescharacteristic
25C2×C3×#106C2211yescharacteristic
26C2×C3×C4⋊C8C2211yescharacteristic
27C3×#382C2211yescharacteristic
28C3×C4×C4⋊C4C2211yescharacteristic
29C2×#821C2211yescharacteristic
30C2×#821C2211yescharacteristic
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×(C2×D3)⋊C8C2211yescharacteristic
33C2×#818C2211yescharacteristic
34C2×#817C2211yescharacteristic
35#4987C2211yescharacteristic
36#4987C2211yescharacteristic
37#4987C2211yescharacteristic
38#4987C2211yescharacteristic
39#4987C2211yescharacteristic
40#4987C2211yescharacteristic
41C2×#809C2211yescharacteristic
42C2×#809C2211yescharacteristic
43#4940—21no—
44#4940—21no—
45C2×C4×C3⋊C8C2211yescharacteristic
46#4847—24no—
47#4834—24no—
48#4674—21no—
49#4672—21no—
50#4671—21no—
51#4665—21no—
52#4665—21no—
53#4659—21no—
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56#4529C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62C2×#478—31no—
63C2×C8×D4—31no—
64#2562—31no—
65#2535—31no—
66#2077—31no—
67#2076—31no—
68#2034—31no—
69#2033—31no—
70#1991—31no—
71#1949D311yescharacteristic, complemented
72#1893—31no—
73#1893—31no—
74#1808—31no—
75#1807—31no—
76C4×#102—31no—
77C22×D12—21no—
78C22×D12—21no—
79C22×D12D411yescharacteristic
80C22×D12C2311yescharacteristic
81C22×C4×D3—21no—
82C22×C4×D3C2311yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C2×C3×C4⋊C4C2311yescharacteristic
87C2×C3×C4⋊C4C2311yescharacteristic
88C2×C3×C4⋊C4C2311yescharacteristic
89C2×C3×C4⋊C4C2311yescharacteristic
90C2×C3×C42—21no—
91C2×C3×C42C2311yescharacteristic
92C2×(C2×D3)⋊C4—21no—
93C2×(C2×D3)⋊C4—21no—
94C2×(C2×D3)⋊C4—21no—
95C2×(C2×D3)⋊C4—21no—
96C2×(C2×D3)⋊C4—21no—
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4D411yescharacteristic
102C2×(C2×D3)⋊C4D411yescharacteristic
103C2×C4⋊Dic3D411yescharacteristic
104C2×C4⋊Dic3C2311yescharacteristic
105C2×C4⋊Dic3C2311yescharacteristic
106C2×C4⋊Dic3C2311yescharacteristic
107C2×Dic3⋊C4—21no—
108C2×Dic3⋊C4—21no—
109C22×C3⋊C8C2311yescharacteristic
110C22×C3⋊C8C2311yescharacteristic
111C2×D3×C8—22no—
112C2×D3×C8—22no—
113C2×D3×C8—22no—
114C2×D3×C8—22no—
115C2×D3×C8—41no—
116C2×D3×C8—41no—
117#895—22no—
118#895—22no—
119#895—41no—
120#895—41no—
121C4×D12—22no—
122C4×D12—22no—
123C4×D12—22no—
124C4×D12—22no—
125#870—22no—
126#870—22no—
127C3×#107—41no—
128C3×#106—41no—
129C3×C4⋊C8D414yescomplemented
130C3×#95—21no—
131C3×#95—21no—
132C3×#95—21no—
133C3⋊#95—21no—
134C3⋊#95—21no—
135C3⋊#95—21no—
136C3⋊#95—21no—
137C3⋊#95—21no—
138C3⋊#95—21no—
139#821—22no—
140#821—22no—
141(C2×D3)⋊C8—22no—
142(C2×D3)⋊C8—22no—
143#818—22no—
144#817—22no—
145#809—22no—
146#809—22no—
147C4×C3⋊C8—22no—
148C23×C8—31no—
149C23×C8—31no—
150C2×#125—31no—
151C2×#121—31no—
152C2×#121—31no—
153C2×C4×D4—31no—
154C2×C4×D4—31no—
155#478—64no—
156C8×D4—64no—
157C2×#107—31no—
158C2×#107C2×D311yescharacteristic
159C2×#106—31no—
160C2×#106C2×D311yescharacteristic
161C2×C4⋊C8C2×D311yescharacteristic
162C2×#102—31no—
163C2×#102—31no—
164C2×#102—31no—
165C2×#102—31no—
166C2×C22⋊C8—31no—
167C2×C22⋊C8—31no—
168C2×C4×C8—31no—
169#400—61no—
170#397—61no—
171#394—61no—
172#392—61no—
173#388—61no—
174#388—61no—
175#386—61no—
176#386—61no—
177#382C2×D311yescharacteristic
178#380—31no—
179#380—31no—
180#380—31no—
181#380—31no—
182#380—31no—
183#380—31no—
184C4×C4⋊C4C2×D311yescharacteristic
185#340—31no—
186#340—31no—
187#340—31no—
188#340—31no—
189#340—31no—
190#340—31no—
191#340C2×D311yescharacteristic
192#340C2×D311yescharacteristic
193C23×D3—21no—
194C23×D3C2×D411yescharacteristic
195C23×D3C2×D411yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4C2×D411yescharacteristic
201C22×C3×C4C2×D411yescharacteristic
202C22×C3×C4C2411yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3C2×D411yescharacteristic
207C22×Dic3C2×D411yescharacteristic
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—22no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—42no—
217C2×D12—42no—
218C2×D12—42no—
219C2×D12—42no—
220C2×D12—81no—
221C2×D12—81no—
222C2×D12#4112yes—
223C2×C4×D3—21no—
224C2×C4×D3—21no—
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—42no—
236C2×C4×D3—81no—
237C2×C4×D3—81no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8C2×D412yes—
243C2×C3×C8C2×D412yes—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C42—81no—
253C3×C42C2×D412yes—
254C3×C42#4112yes—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—42no—
258(C2×D3)⋊C4—42no—
259(C2×D3)⋊C4—42no—
260(C2×D3)⋊C4—42no—
261(C2×D3)⋊C4—42no—
262(C2×D3)⋊C4—81no—
263(C2×D3)⋊C4—81no—
264(C2×D3)⋊C4—81no—
265(C2×D3)⋊C4—81no—
266C4⋊Dic3—22no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273Dic3⋊C4—42no—
274Dic3⋊C4—42no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—21no—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—21no—
280C2×C3⋊C8#4112yes—
281D3×C8—44no—
282D3×C8—44no—
283C22×D4—31no—
284C22×D4—31no—
285C22×D4—61no—
286C22×D4—61no—
287C23×C4—31no—
288C23×C4—31no—
289C23×C4—61no—
290C22×C8—31no—
291C22×C8—31no—
292C22×C8—62no—
293C22×C8—62no—
294C22×C8—62no—
295C22×C8—62no—
296C22×C8—121no—
297C22×C8—121no—
298C22×C8C22×D311yescharacteristic
299C22×C8C22×D311yescharacteristic
300#125—62no—
301#125—62no—
302#121—62no—
303#121—62no—
304#121—121no—
305#121—121no—
306C4×D4—62no—
307C4×D4—62no—
308C4×D4—62no—
309C4×D4—62no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—61no—
315C2×C4⋊C4—61no—
316C2×C4⋊C4C22×D311yescharacteristic
317C2×C4⋊C4C22×D311yescharacteristic
318C2×C4⋊C4C22×D311yescharacteristic
319C2×C4⋊C4C22×D311yescharacteristic
320C2×C22⋊C4—31no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—61no—
323C2×C22⋊C4—61no—
324C2×C22⋊C4—61no—
325C2×C22⋊C4—61no—
326C2×C22⋊C4—61no—
327C2×C22⋊C4—61no—
328C2×C22⋊C4—61no—
329C2×C22⋊C4—61no—
330C2×C22⋊C4—61no—
331C2×C42—21no—
332C2×C42C22×D311yescharacteristic
333#107—41no—
334#107—62no—
335#106—41no—
336#106—62no—
337C4⋊C8D1214yescomplemented
338#102—62no—
339#102—62no—
340#102—62no—
341#102—62no—
342C22⋊C8—62no—
343C22⋊C8—62no—
344C4×C8—62no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—61no—
349#95—61no—
350#95—61no—
351#95—61no—
352#95—61no—
353#95—61no—
354C23×C3C22×D411yescharacteristic
355C22×D3—21no—
356C22×D3—21no—
357C22×D3—21no—
358C22×D3—21no—
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—21no—
362C22×D3—21no—
363C22×D3—21no—
364C22×D3—21no—
365C22×D3—21no—
366C22×D3—21no—
367C22×D3—22no—
368C22×D3—41no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3#13512yes—
375C22×D3#13512yes—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4#12112yes—
393C2×C3×C4#12112yes—
394C2×C3×C4C22×D411yescharacteristic
395C2×C3×C4C2×#4111yescharacteristic
396C2×C3×C4C2×#4111yescharacteristic
397C2×C3×C4C2×#4111yescharacteristic
398C2×C3×C4H(5,𝔽2)11yescharacteristic
399C2×C3×C42−1+411yescharacteristic
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415D12—28no—
416D12—22no—
417D12—22no—
418D12—41no—
419D12—41no—
420D12—84no—
421D12—84no—
422C4×D3—41no—
423C4×D3—41no—
424C4×D3—41no—
425C4×D3—41no—
426C4×D3—41no—
427C4×D3—41no—
428C4×D3—41no—
429C4×D3—41no—
430C4×D3—84no—
431C3×C8—22no—
432C3×C8—22no—
433C3⋊C8—22no—
434C3⋊C8—41no—
435C24—31no—
436C24—31no—
437C24—61no—
438C2×D4—32no—
439C2×D4—62no—
440C2×D4—62no—
441C2×D4—62no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—122no—
448C2×D4—122no—
449C2×D4—122no—
450C2×D4—122no—
451C2×D4—241no—
452C2×D4—241no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—31no—
458C22×C4—31no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—61no—
473C22×C4—61no—
474C22×C4—122no—
475C22×C4—241no—
476C22×C4—241no—
477C22×C4D3×D411yescharacteristic
478C22×C4D3×D411yescharacteristic
479C22×C4C23×D311yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—32no—
485C2×C8—61no—
486C2×C8—61no—
487C2×C8—61no—
488C2×C8—61no—
489C2×C8—61no—
490C2×C8—124no—
491C2×C8—124no—
492C2×C8C2×D1212yes—
493C2×C8C2×D1212yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—62no—
503C4⋊C4—61no—
504C4⋊C4—61no—
505C4⋊C4—61no—
506C4⋊C4—61no—
507C4⋊C4—61no—
508C4⋊C4—61no—
509C4⋊C4—122no—
510C4⋊C4—122no—
511C22⋊C4—62no—
512C22⋊C4—62no—
513C22⋊C4—122no—
514C22⋊C4—122no—
515C22⋊C4—122no—
516C22⋊C4—122no—
517C22⋊C4—122no—
518C22⋊C4—241no—
519C22⋊C4—241no—
520C22⋊C4—241no—
521C22⋊C4—241no—
522C42—81no—
523C42C2×D1212yes—
524C42#23912yes—
525C22×C3C2×#12111yescharacteristic
526C22×C3#54611yescharacteristic
527C22×C3#54711yescharacteristic
528C22×C3C2×#13511yescharacteristic
529C22×C3C2×#13511yescharacteristic
530C22×C3#57611yescharacteristic
531C22×C3#57711yescharacteristic
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—22no—
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—41no—
539C2×D3—41no—
540C2×D3—41no—
541C2×D3—41no—
542C2×D3—41no—
543C2×D3—41no—
544C2×D3—41no—
545C2×D3—41no—
546C2×D3—42no—
547C2×D3—42no—
548C2×D3—42no—
549C2×D3—81no—
550C2×D3—81no—
551C2×D3—81no—
552C2×D3—81no—
553C3×C4—22no—
554C3×C4—22no—
555C3×C4—81no—
556C3×C4—81no—
557C3×C4—81no—
558C3×C4—81no—
559C3×C4#52911yescharacteristic
560C3×C4#54211yescharacteristic
561C3×C4#54611yescharacteristic
562C3×C4#54811yescharacteristic
563Dic3—41no—
564Dic3—41no—
565Dic3—81no—
566Dic3—81no—
567Dic3—81no—
568C23—32no—
569C23—32no—
570C23—61no—
571C23—61no—
572C23—61no—
573C23—61no—
574C23—61no—
575C23—61no—
576C23—61no—
577C23—61no—
578C23—61no—
579C23—61no—
580C23—61no—
581C23—61no—
582C23—62no—
583C23—121no—
584C23—121no—
585C23—121no—
586C23—121no—
587C23—121no—
588C23—121no—
589C23C2×D3×D411yescharacteristic
590D4—68no—
591D4—62no—
592D4—62no—
593D4—121no—
594D4—121no—
595D4—244no—
596D4—244no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—121no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—121no—
624C2×C4—121no—
625C2×C4—121no—
626C2×C4—121no—
627C2×C4—121no—
628C2×C4—121no—
629C2×C4—121no—
630C2×C4—121no—
631C2×C4—121no—
632C2×C4—121no—
633C2×C4—121no—
634C2×C4—121no—
635C2×C4—121no—
636C2×C4—244no—
637C2×C4#89512yes—
638C2×C4#89512yes—
639C2×C4C22×D1211yescharacteristic
640C2×C4#100411yescharacteristic
641C2×C4C2×#23911yescharacteristic
642C2×C4#100711yescharacteristic
643C2×C4D3×#4111yescharacteristic
644C2×C4D3×#4111yescharacteristic
645C8—22no—
646C8—22no—
647C8—62no—
648C8—121no—
649C2×C3#242711yescharacteristic
650C2×C3#305011yescharacteristic
651C2×C3#306211yescharacteristic
652C2×C3#329611yescharacteristic
653C2×C3#329711yescharacteristic
654C2×C3#333711yescharacteristic
655C2×C3#333911yescharacteristic
656D3—42no—
657D3—42no—
658D3—82no—
659C22—62no—
660C22—62no—
661C22—62no—
662C22—62no—
663C22—62no—
664C22—62no—
665C22—121no—
666C22—121no—
667C22—121no—
668C22—121no—
669C22—121no—
670C22—121no—
671C22—121no—
672C22—121no—
673C22—122no—
674C22—122no—
675C22—122no—
676C22—241no—
677C22—241no—
678C22—241no—
679C22—241no—
680C22C2×#89511yescharacteristic
681C22#561211yescharacteristic
682C22#563111yescharacteristic
683C22D3×#13511yescharacteristic
684C22D3×#13511yescharacteristic
685C22#577411yescharacteristic
686C22#577811yescharacteristic
687C4—22no—
688C4—22no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—121no—
694C4—121no—
695C4—241no—
696C4—241no—
697C4—241no—
698C4#555411yescharacteristic
699C4#557611yescharacteristic
700C4#569111yescharacteristic
701C4#573311yescharacteristic
702C3#2534211yescharacteristic, complemented, Sylow
703C2—122no—
704C2—122no—
705C2—242no—
706C2#7621911yescharacteristic
707C2#7918011yescharacteristic
708C2#7921311yescharacteristic
709C2#8055911yescharacteristic
710C2#8061511yescharacteristic
711C2#8119511yescharacteristic
712C2#8125411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1949C2
socleC23×C3C22×D4
prime radical#74239C2
hypercenter#1949D3
hypocenterC3#25342
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. C2×#4847C2semidirect
2. C2×#4834C2semidirect
4. #73806C2semidirect
5. C3×#1949C2semidirect
6. #70634C2semidirect
7. #70630C2semidirect
8. #70581C2semidirect
9. #70577C2semidirect
10. #69554C2semidirect
11. C4×#809C2semidirect
12. #68883C2semidirect
13. #68883C2semidirect
14. #68832C2semidirect
15. #68831C2semidirect
71. #1949D3semidirect
129. C3×C4⋊C8D4semidirect
337. C4⋊C8D12semidirect
702. C3#25342semidirect

Maximal subgroups

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

subgroupindex
C2×#48472
C2×#48342
#742392
#738062
C3×#19492
#706342
#706302
#705812
#705772
#695542
C4×#8092
#688832
#688322
#688312
#253423