Finite Group Databasebeta

← #10819992

Subgroups — #10819992

Order 768.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#435C211yesmaximal, characteristic
2C4×#936C211yesmaximal, characteristic
3C2×#4828C211yesmaximal, characteristic, complemented
4#71995C211yesmaximal, characteristic, complemented
5#71983C211yesmaximal, characteristic, complemented
6#71974C211yesmaximal, characteristic, complemented
7C8×#217C211yesmaximal, characteristic, complemented
8#71615C211yesmaximal, characteristic
9Dic3×C4⋊C8C211yesmaximal, characteristic, complemented
10#69914C211yesmaximal, characteristic, complemented
11#69913C211yesmaximal, characteristic, complemented
12#69913C211yesmaximal, characteristic, complemented
13#69912C211yesmaximal, characteristic, complemented
14#69838C211yesmaximal, characteristic, complemented
15#69809C211yesmaximal, characteristic, complemented
16#23206—31nomaximal, Sylow
17C22×C3×M16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#936C411yescharacteristic
21C2×C4×Dic6C2211yescharacteristic
22C3×#435—24no—
23C2×C3×C4⋊C8C2211yescharacteristic
24C2×C3×C22⋊C8C2211yescharacteristic
25C2×C3×C22⋊C8C2211yescharacteristic
26C2×C3×#97C2211yescharacteristic
27#5221C411yescharacteristic
28C4×#217C2211yescharacteristic
29C4×#217C2211yescharacteristic
30C4×#217C2211yescharacteristic
31C4×#217C2211yescharacteristic
32C2×#830C2211yescharacteristic
33C2×#830C2211yescharacteristic
34C2×#830C2211yescharacteristic
35C2×#830C2211yescharacteristic
36C2×#815C2211yescharacteristic
37C2×Dic3⋊C8C2211yescharacteristic
38C2×Dic3⋊C8C2211yescharacteristic
39C2×Dic3⋊C8C2211yescharacteristic
40C2×Dic3⋊C8C2211yescharacteristic
41C2×C8×Dic3C2211yescharacteristic
42C2×C8×Dic3C2211yescharacteristic
43C2×C8×Dic3C2211yescharacteristic
44#4977C411yescharacteristic
45#4973C411yescharacteristic
46#4945C411yescharacteristic
47#4945C411yescharacteristic
48#4945C411yescharacteristic
49#4945C411yescharacteristic
50C42×Dic3C2211yescharacteristic
51C2×C4⋊(C3⋊C8)C2211yescharacteristic
52C2×#803C2211yescharacteristic
53#4828—24no—
54#4550C2211yescharacteristic
55#4550C2211yescharacteristic
56#4550C2211yescharacteristic
57#4550C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62C2×#446—31no—
63C2×#435D311yescharacteristic
64C4×#124—31no—
65#1985—31no—
66#1955—31no—
67#1924—31no—
68#1923—31no—
69#1923—31no—
70#1923—31no—
71#1851—31no—
72#1850—31no—
73#1767—31no—
74C4×C4⋊C8—31no—
75#1753—31no—
76C8×C22⋊C4—31no—
77C22×C3×D4C2×C411yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C22×Dic6C2×C411yescharacteristic
81C2×C3×M16—22no—
82C2×C3×M16—22no—
83C2×C3×M16—41no—
84C22×C3×C8—22no—
85C22×C3×C8—22no—
86C22×C3×C8—41no—
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C2×C3×C4⋊C4C2×C411yescharacteristic
94C2×C3×C22⋊C4C2×C411yescharacteristic
95C2×C3×C22⋊C4C2×C411yescharacteristic
96C2×C3×C42C2311yescharacteristic
97C2×#217C2×C411yescharacteristic
98C2×#217C2×C411yescharacteristic
99C2×#217C2×C411yescharacteristic
100C2×#217C2×C411yescharacteristic
101C2×#217C2×C411yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×#217C2×C411yescharacteristic
104C2×#217C2×C411yescharacteristic
105#936—24no—
106C2×C4⋊Dic3C2×C411yescharacteristic
107C2×Dic3⋊C4C2×C411yescharacteristic
108C2×Dic3⋊C4C2×C411yescharacteristic
109C2×C4×Dic3C2×C411yescharacteristic
110C2×C4×Dic3C2×C411yescharacteristic
111C2×C4×Dic3C2×C411yescharacteristic
112C2×C4×Dic3C2×C411yescharacteristic
113C2×C4×Dic3C2311yescharacteristic
114C2×C4×Dic3C2311yescharacteristic
115C2×C4×Dic3C2311yescharacteristic
116C2×C4×Dic3C2311yescharacteristic
117C22×C3⋊C8C2311yescharacteristic
118C22×C3⋊C8C2311yescharacteristic
119C22×C3⋊C8C2311yescharacteristic
120C22×C3⋊C8C2311yescharacteristic
121C4×Dic6—22no—
122C4×Dic6—22no—
123C3×C4⋊C8D414yes—
124C3×C22⋊C8—22no—
125C3×C22⋊C8—22no—
126C3×#97—22no—
127C3⋊#95C2×C411yescharacteristic
128C3⋊#95C2×C411yescharacteristic
129C3⋊#95C2×C411yescharacteristic
130C3⋊#95C2×C411yescharacteristic
131C3⋊#95C2×C411yescharacteristic
132C3⋊#95C2×C411yescharacteristic
133C3⋊#95C2×C411yescharacteristic
134C3⋊#95C2×C411yescharacteristic
135#830—22no—
136#830—22no—
137#830—41no—
138#830—41no—
139#815—22no—
140Dic3⋊C8—22no—
141Dic3⋊C8—22no—
142Dic3⋊C8—22no—
143Dic3⋊C8—22no—
144C8×Dic3—22no—
145C8×Dic3—41no—
146C8×Dic3—41no—
147C4⋊(C3⋊C8)—22no—
148#803—22no—
149C22×M16C2×D311yescharacteristic
150C23×C8C2×D311yescharacteristic
151C2×#124—31no—
152C2×C4×Q8—31no—
153C2×C4×D4C2×D311yescharacteristic
154#446—64no—
155#435—24no—
156C2×C4⋊C8—31no—
157C2×C4⋊C8—31no—
158C2×C4⋊C8—31no—
159C2×C4⋊C8—31no—
160C2×C4⋊C8—31no—
161C2×C4⋊C8C2×D311yescharacteristic
162C2×C22⋊C8—31no—
163C2×C22⋊C8—31no—
164C2×C22⋊C8—31no—
165C2×C22⋊C8—31no—
166C2×C22⋊C8C2×D311yescharacteristic
167C2×C22⋊C8C2×D311yescharacteristic
168C2×#97—31no—
169C2×#97—31no—
170C2×#97C2×D311yescharacteristic
171C2×C4×C8—31no—
172C2×C4×C8—31no—
173C2×C4×C8—31no—
174#391—31no—
175#390—31no—
176#388—31no—
177#388—31no—
178#388—31no—
179#388—31no—
180#382—31no—
181C4×C22⋊C4—31no—
182C4×C22⋊C4—31no—
183C4×C22⋊C4—31no—
184C4×C22⋊C4—31no—
185C43—31no—
186#336—31no—
187#336—31no—
188#336—31no—
189#336—31no—
190#336—31no—
191#336—31no—
192#336—31no—
193#336—31no—
194C24×C3C22×C411yescharacteristic
195C24×C3C22×C411yescharacteristic
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—41no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4C22×C411yescharacteristic
212C22×C3×C4C22×C411yescharacteristic
213C22×C3×C4C22×C411yescharacteristic
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C2411yescharacteristic
216C22×Dic3C22×C411yescharacteristic
217C22×Dic3C22×C411yescharacteristic
218C22×Dic3C22×C411yescharacteristic
219C22×Dic3C22×C411yescharacteristic
220C22×Dic3C22×C411yescharacteristic
221C22×Dic3C22×C411yescharacteristic
222C22×Dic3C22×C411yescharacteristic
223C22×Dic3C22×C411yescharacteristic
224C2×Dic6—22no—
225C2×Dic6—22no—
226C2×Dic6—41no—
227C3×M16—44no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—44no—
238C2×C3×C8C2×D412yes—
239C2×C3×C8C2×D412yes—
240C2×C3×C8#4112yes—
241C3×C4⋊C4—22no—
242C3×C22⋊C4—22no—
243C3×C22⋊C4—22no—
244C3×C42C2×D412yes—
245C3×C42#4112yes—
246#217—22no—
247#217—22no—
248#217—22no—
249#217—22no—
250#217—22no—
251#217—22no—
252#217—22no—
253#217M1614yescomplemented
254C4⋊Dic3—22no—
255Dic3⋊C4—22no—
256Dic3⋊C4—22no—
257C4×Dic3—21no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—21no—
263C4×Dic3—21no—
264C4×Dic3—21no—
265C4×Dic3—22no—
266C4×Dic3—22no—
267C4×Dic3—22no—
268C4×Dic3—41no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—21no—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—21no—
280C2×C3⋊C8#4112yes—
281C22×Q8—31no—
282C22×D4C4×D311yescharacteristic
283C23×C4C22×D311yescharacteristic
284C23×C4C22×D311yescharacteristic
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—41no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—31no—
291C22×C8—31no—
292C22×C8—31no—
293C22×C8—31no—
294C22×C8—41no—
295C22×C8C22×D311yescharacteristic
296C22×C8C22×D311yescharacteristic
297C22×C8C22×D311yescharacteristic
298C22×C8C22×D311yescharacteristic
299#124—64no—
300C4×Q8—62no—
301C4×Q8—62no—
302C4×D4—22no—
303C4×D4—22no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4C4×D311yescharacteristic
308C2×C22⋊C4—31no—
309C2×C22⋊C4—31no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—31no—
314C2×C22⋊C4—31no—
315C2×C22⋊C4—31no—
316C2×C22⋊C4C4×D311yescharacteristic
317C2×C22⋊C4C4×D311yescharacteristic
318C2×C42—31no—
319C2×C42—31no—
320C2×C42—31no—
321C2×C42—31no—
322C2×C42—31no—
323C2×C42—31no—
324C2×C42—31no—
325C2×C42—31no—
326C2×C42C22×D311yescharacteristic
327C4⋊C8—62no—
328C4⋊C8—62no—
329C4⋊C8—62no—
330C4⋊C8—62no—
331C4⋊C8—62no—
332C4⋊C8#6714yes—
333C22⋊C8—22no—
334C22⋊C8—22no—
335C22⋊C8—62no—
336C22⋊C8—62no—
337C22⋊C8—121no—
338C22⋊C8—121no—
339#97—22no—
340#97—62no—
341#97—62no—
342C4×C8—62no—
343C4×C8—121no—
344C4×C8—121no—
345#95—31no—
346#95—31no—
347#95—31no—
348#95—31no—
349#95—31no—
350#95—31no—
351#95—31no—
352#95—31no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3C2×M1612yes—
367C23×C3C23×C411yescharacteristic
368C3×D4—44no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—41no—
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×C4C4×D412yes—
388C2×C3×C4C4×D412yes—
389C2×C3×C4C22×D411yescharacteristic
390C2×C3×C4C2×#4111yescharacteristic
391C2×C3×C4C2×#4111yescharacteristic
392C2×C3×C4C2×#4111yescharacteristic
393C2×C3×C4H(5,𝔽2)11yescharacteristic
394C2×C3×C42−1+411yescharacteristic
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3C2×M1612yes—
416C2×Dic3C2×M1612yes—
417C2×Dic3#13112yes—
418C2×Dic3#13112yes—
419Dic6—44no—
420C3×C8—22no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—41no—
424C3⋊C8—22no—
425C3⋊C8—41no—
426C3⋊C8—41no—
427C3⋊C8—41no—
428C24C2×C4×D311yescharacteristic
429C24C2×C4×D311yescharacteristic
430C2×Q8—62no—
431C2×Q8—62no—
432C2×Q8—121no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—41no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4C2×C4×D311yescharacteristic
457C22×C4C2×C4×D311yescharacteristic
458C22×C4C2×C4×D311yescharacteristic
459C22×C4C2×C4×D311yescharacteristic
460C22×C4C23×D311yescharacteristic
461M16—44no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—32no—
472C2×C8—44no—
473C2×C8—61no—
474C2×C8—61no—
475C2×C8—61no—
476C2×C8—61no—
477C2×C8—61no—
478C2×C8—61no—
479C2×C8—61no—
480C2×C8—61no—
481C2×C8—61no—
482C2×C8—61no—
483C2×C8—61no—
484C2×C8#23712yes—
485C2×C8C2×#6712yes—
486C2×C8C2×#6712yes—
487C4⋊C4—22no—
488C4⋊C4—62no—
489C4⋊C4—62no—
490C4⋊C4—62no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—34no—
494C22⋊C4—62no—
495C22⋊C4—62no—
496C22⋊C4—62no—
497C22⋊C4—62no—
498C22⋊C4—62no—
499C22⋊C4—62no—
500C22⋊C4—62no—
501C42—62no—
502C42—62no—
503C42—62no—
504C42—61no—
505C42—61no—
506C42—61no—
507C42—61no—
508C42—61no—
509C42—61no—
510C42—61no—
511C42—61no—
512C42—121no—
513C42#23512yes—
514C42C2×#6712yes—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3C2×C4×D411yescharacteristic
530C22×C3C4×#4111yescharacteristic
531C22×C3#52011yescharacteristic
532C22×C3C22×M1611yescharacteristic
533C22×C3C2×#13111yescharacteristic
534C22×C3C2×#13111yescharacteristic
535C22×C3#56811yescharacteristic
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—41no—
539C3×C4—41no—
540C3×C4#54611yescharacteristic
541C3×C4#54811yescharacteristic
542C3×C4#55611yescharacteristic
543C3×C4#55911yescharacteristic
544Dic3—22no—
545Dic3—22no—
546Dic3—22no—
547Dic3—22no—
548Dic3—41no—
549Dic3—41no—
550Dic3—41no—
551Dic3—41no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23D3×M1612yes—
566C23C22×C4×D311yescharacteristic
567Q8—124no—
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—32no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—32no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4C4×#6712yes—
612C2×C4C4×#6712yes—
613C2×C4C2×#23511yescharacteristic
614C2×C4C2×#23711yescharacteristic
615C2×C4#100411yescharacteristic
616C2×C4D3×#4111yescharacteristic
617C2×C4#101011yescharacteristic
618C2×C4C22×#6711yescharacteristic
619C8—22no—
620C8—22no—
621C8—22no—
622C8—41no—
623C8—62no—
624C8—121no—
625C8—121no—
626C8—121no—
627C2×C3—42no—
628C2×C3—81no—
629C2×C3#236711yescharacteristic
630C2×C3#293111yescharacteristic
631C2×C3D4×M1611yescharacteristic
632C2×C3#296511yescharacteristic
633C2×C3#296811yescharacteristic
634C2×C3#299011yescharacteristic
635C2×C3#299211yescharacteristic
636C22—22no—
637C22—22no—
638C22—22no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22C4×#23711yescharacteristic
651C22#554611yescharacteristic
652C22C2×D3×M1611yescharacteristic
653C22#574511yescharacteristic
654C22D3×#13111yescharacteristic
655C22D3×#13111yescharacteristic
656C22C2×C4×#6711yescharacteristic
657C4—22no—
658C4—22no—
659C4—41no—
660C4—41no—
661C4—62no—
662C4—62no—
663C4—62no—
664C4—62no—
665C4—121no—
666C4—121no—
667C4—121no—
668C4—121no—
669C4#554211yescharacteristic
670C4#555911yescharacteristic
671C4#580611yescharacteristic
672C4#583111yescharacteristic
673C3#2320611yescharacteristic, complemented, Sylow
674C2—42no—
675C2—81no—
676C2#7945311yescharacteristic
677C2#7945811yescharacteristic
678C2#7946211yescharacteristic
679C2#7946411yescharacteristic
680C2#8234411yescharacteristic
681C2M16×#6711yescharacteristic
682C2#8378611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC2×C3×#435C2
prime radicalC22×C3×D4C2×C4
cosocleC22×C3×C4C24
hypercenterC2×#435D3
hypocenterC3#23206
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. C2×#4828C2semidirect
4. #71995C2semidirect
5. #71983C2semidirect
6. #71974C2semidirect
7. C8×#217C2semidirect
9. Dic3×C4⋊C8C2semidirect
10. #69914C2semidirect
11. #69913C2semidirect
12. #69913C2semidirect
13. #69912C2semidirect
14. #69838C2semidirect
15. #69809C2semidirect
253. #217M16semidirect
673. C3#23206semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4352
C4×#9362
C2×#48282
#719952
#719832
#719742
C8×#2172
#716152
Dic3×C4⋊C82
#699142
#699132
#699122
#698382
#698092
#232063