Finite Group Databasebeta

← #10720220

Subgroups — #10720220

Order 768.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4957C211yesmaximal, characteristic
2C2×#4957C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C2×#4945C211yesmaximal, characteristic, complemented
5C2×#4647C211yesmaximal, characteristic, complemented
6C2×#4670C211yesmaximal, characteristic, complemented
7C2×#4649C211yesmaximal, characteristic, complemented
8C3×#1440C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14141—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4957—24no—
53#4957—24no—
54#4957C418yescomplemented
55#4945—24no—
56#4670—24no—
57#4649—24no—
58#4647—24no—
59C2×#390—31no—
60C2×#390—31no—
61C2×#390—31no—
62C2×#389—31no—
63C2×#388—31no—
64C2×#388—31no—
65C2×C4×C4⋊C4—31no—
66#1440—31no—
67#1440D311yescharacteristic, complemented
68#1439—31no—
69#1439—31no—
70#1437—31no—
71#1437—31no—
72C4⋊#95—31no—
73C4×#95—31no—
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67C2×C414yes—
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—41no—
101C2×C3×C22⋊C4—41no—
102C2×C3×C22⋊C4—41no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4C2×C414yes—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—41no—
112C2×#217—41no—
113C2×#217C2×C414yes—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—41no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4C2×C414yes—
131C2×(C2×D3)⋊C4C2×C414yes—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—41no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—41no—
144C2×Dic3⋊C4C2×C414yes—
145C2×Dic3⋊C4D414yes—
146C2×Dic3⋊C4D414yes—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—41no—
160C2×C4×Dic3—41no—
161C2×C4×Dic3C2×C414yes—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C3⋊#95D414yescomplemented
174C23×D4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C42—31no—
193C22×C42—31no—
194C22×C42—31no—
195C22×C42—31no—
196C22×C42—31no—
197#390—38no—
198#390—64no—
199#390—64no—
200#389—64no—
201#388—64no—
202#388—64no—
203C4×C4⋊C4—64no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3C22×C412yes—
231C24×C3C2411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3C22×C412yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4C22×C412yes—
284C22×C3×C4C22×C412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D412yes—
287C22×C3×C4C2×D412yes—
288C22×C3×C4#4112yes—
289C2×#67—28no—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67—44no—
295C2×#67—44no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3C22×C412yes—
331C22×Dic3C22×C412yes—
332C22×Dic3C22×C412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×D412yes—
339C22×Dic3#4112yes—
340C22×Dic3#4112yes—
341C22×Dic3#4112yes—
342C22×Dic3#4112yes—
343C22×Dic3#4112yes—
344C22×Dic3#4112yes—
345C3×C22⋊C4—44no—
346C3×C22⋊C4—44no—
347C3×C22⋊C4—44no—
348#217—28no—
349#217—44no—
350#217—44no—
351(C2×D3)⋊C4—28no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—44no—
358Dic3⋊C4—28no—
359Dic3⋊C4—28no—
360Dic3⋊C4—28no—
361Dic3⋊C4—44no—
362C4×Dic3—28no—
363C4×Dic3—44no—
364C4×Dic3—44no—
365C4×Dic3—44no—
366C4×Dic3—44no—
367C25—31no—
368C25C22×D311yescharacteristic
369C22×D4—34no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—62no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C2×C4⋊C4—34no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—121no—
403C2×C4⋊C4—121no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4—121no—
439C2×C22⋊C4C4×D314yes—
440C2×C42—34no—
441C2×C42—62no—
442C2×C42—62no—
443C2×C42—62no—
444C2×C42—62no—
445C2×C42—62no—
446C2×C42—62no—
447C2×C42—62no—
448C2×C42—62no—
449C2×C42—62no—
450C2×C42—62no—
451C2×C42—62no—
452C2×C42—62no—
453C2×C42—121no—
454C2×C42—121no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—34no—
460#95—62no—
461#95—62no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—121no—
466#95—121no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3C23×C411yescharacteristic
503C23×C3C22×D411yescharacteristic
504C23×C3C22×D411yescharacteristic
505C23×C3C22×D411yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4111yescharacteristic
512C23×C3C2×#4111yescharacteristic
513C23×C3H(5,𝔽2)11yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C23×C3H(5,𝔽2)11yescharacteristic
516C23×C32−1+411yescharacteristic
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594#67—416no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3#11714yes—
637C2×Dic3C4×D414yes—
638C2×Dic3C4×D414yes—
639C2×Dic3C4×D414yes—
640C2×Dic3#12114yes—
641C2×Dic3#12314yes—
642C2×Dic3#12414yes—
643C2×Dic3#12614yes—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—32no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24C2×C4×D312yes—
674C24C23×D311yescharacteristic
675C2×D4—68no—
676C2×D4—68no—
677C2×D4—68no—
678C2×D4—124no—
679C2×D4—124no—
680C2×D4—124no—
681C2×D4—124no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—32no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—32no—
732C22×C4—32no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4C2×C4×D312yes—
768C22×C4C2×C4×D312yes—
769C22×C4D3×D412yes—
770C22×C4D3×D412yes—
771C22×C4D3×D412yes—
772C22×C4#23712yes—
773C4⋊C4—68no—
774C4⋊C4—68no—
775C4⋊C4—68no—
776C4⋊C4—124no—
777C4⋊C4—124no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—68no—
782C22⋊C4—68no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—124no—
788C22⋊C4—124no—
789C22⋊C4—124no—
790C42—68no—
791C42—124no—
792C42—124no—
793C42—124no—
794C42—124no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3C2×#11711yescharacteristic
811C22×C3C2×C4×D411yescharacteristic
812C22×C3C2×C4×D411yescharacteristic
813C22×C3C2×C4×D411yescharacteristic
814C22×C3C4×#4111yescharacteristic
815C22×C3#51811yescharacteristic
816C22×C3#52011yescharacteristic
817C22×C3C2×#12111yescharacteristic
818C22×C3C2×#12311yescharacteristic
819C22×C3C2×#12411yescharacteristic
820C22×C3C2×#12611yescharacteristic
821C22×C3#52911yescharacteristic
822C22×C3#52911yescharacteristic
823C22×C3#53211yescharacteristic
824C22×C3#53211yescharacteristic
825C22×C3#54011yescharacteristic
826C22×C3#54011yescharacteristic
827C22×C3#54211yescharacteristic
828C22×C3#54211yescharacteristic
829C22×C3D4211yescharacteristic
830C22×C3D4211yescharacteristic
831C22×C3#54611yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#54711yescharacteristic
834C22×C3#54811yescharacteristic
835C22×C3#54811yescharacteristic
836C22×C3#55011yescharacteristic
837C22×C3#55011yescharacteristic
838C22×C3#55011yescharacteristic
839C22×C3#55311yescharacteristic
840C22×C3#55311yescharacteristic
841C22×C3#55511yescharacteristic
842C22×C3#55611yescharacteristic
843C22×C3#55911yescharacteristic
844C22×C3#55911yescharacteristic
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—81no—
853C2×D3—81no—
854C2×D3—81no—
855C2×D3—81no—
856C2×D3—81no—
857C2×D3—81no—
858C2×D3—81no—
859C2×D3—81no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—42no—
866Dic3—24no—
867Dic3—42no—
868Dic3—42no—
869Dic3—42no—
870Dic3—42no—
871Dic3—42no—
872Dic3#38818yescomplemented
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23C22×C4×D311yescharacteristic
944C23C2×D3×D411yescharacteristic
945C23C2×D3×D411yescharacteristic
946C23C2×D3×D411yescharacteristic
947C23C2×#23711yescharacteristic
948C23#100411yescharacteristic
949C23#100411yescharacteristic
950C23D3×#4111yescharacteristic
951C23D3×#4111yescharacteristic
952C23D3×#4111yescharacteristic
953C23D3×#4111yescharacteristic
954C23D3×#4111yescharacteristic
955C23D3×#4111yescharacteristic
956C23#100911yescharacteristic
957C23#101011yescharacteristic
958D4—1216no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—34no—
978C2×C4—34no—
979C2×C4—34no—
980C2×C4—34no—
981C2×C4—34no—
982C2×C4—34no—
983C2×C4—34no—
984C2×C4—34no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C3—82no—
1051C2×C3C2×#38811yescharacteristic
1052C2×C3#229311yescharacteristic
1053C2×C3#231911yescharacteristic
1054C2×C3#236111yescharacteristic
1055C2×C3#236311yescharacteristic
1056C2×C3#236611yescharacteristic
1057C2×C3#236711yescharacteristic
1058C2×C3#242611yescharacteristic
1059C2×C3#242811yescharacteristic
1060C2×C3#244511yescharacteristic
1061C2×C3#244811yescharacteristic
1062C2×C3#249011yescharacteristic
1063C2×C3#249111yescharacteristic
1064C2×C3#251211yescharacteristic
1065C2×C3#251311yescharacteristic
1066D3—82no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22—122no—
1088C22—122no—
1089C22—241no—
1090C22—241no—
1091C22—241no—
1092C22—241no—
1093C22—241no—
1094C22—241no—
1095C22—241no—
1096C22—241no—
1097C22#548611yescharacteristic
1098C22D3×#11711yescharacteristic
1099C22#552311yescharacteristic
1100C22C4×#23711yescharacteristic
1101C22C4×D3×D411yescharacteristic
1102C22C4×D3×D411yescharacteristic
1103C22C4×D3×D411yescharacteristic
1104C22#559011yescharacteristic
1105C22#559111yescharacteristic
1106C22#559611yescharacteristic
1107C22#559811yescharacteristic
1108C22#559911yescharacteristic
1109C22#559911yescharacteristic
1110C22#559911yescharacteristic
1111C22D3×#12111yescharacteristic
1112C22#560911yescharacteristic
1113C22#561611yescharacteristic
1114C22#564911yescharacteristic
1115C22D3×#12311yescharacteristic
1116C22#565411yescharacteristic
1117C22#565511yescharacteristic
1118C22#566111yescharacteristic
1119C22#566211yescharacteristic
1120C22#566211yescharacteristic
1121C22#566311yescharacteristic
1122C22#566311yescharacteristic
1123C22#566411yescharacteristic
1124C22#566811yescharacteristic
1125C22D3×#12411yescharacteristic
1126C22#567711yescharacteristic
1127C22#568111yescharacteristic
1128C22#570211yescharacteristic
1129C22D3×#12611yescharacteristic
1130C22#570611yescharacteristic
1131C22#570911yescharacteristic
1132C4—38no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—64no—
1140C4—122no—
1141C4—122no—
1142C4—122no—
1143C4—122no—
1144C4—122no—
1145C3#1414111yescharacteristic, complemented, Sylow
1146C2—82no—
1147C2—242no—
1148C2#7405511yescharacteristic
1149C2#7467711yescharacteristic
1150C2#7467911yescharacteristic
1151C2#7545011yescharacteristic
1152C2#7547711yescharacteristic
1153C2#7548211yescharacteristic
1154C2D3×#38811yescharacteristic
1155C2#7690111yescharacteristic
1156C2#7690311yescharacteristic
1157C2#7690611yescharacteristic
1158C2#7693511yescharacteristic
1159C2#7746911yescharacteristic
1160C2#7748711yescharacteristic
1161C2#7749311yescharacteristic
1162C2#7749511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1440C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1440D3
hypocenterC3#14141
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. C2×#4945C2semidirect
5. C2×#4647C2semidirect
6. C2×#4670C2semidirect
7. C2×#4649C2semidirect
8. C3×#1440C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. #69429C2semidirect
12. #69428C2semidirect
13. #69408C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3×#95C2semidirect
54. #4957C4semidirect
67. #1440D3semidirect
173. C3⋊#95D4semidirect
872. Dic3#388semidirect
1145. C3#14141semidirect

Maximal subgroups

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

subgroupindex
C2×#49572
C2×#49452
C2×#46472
C2×#46702
C2×#46492
C3×#14402
#715462
#715452
#694292
#694282
#694082
Dic3⋊#952
Dic3×#952
#141413