Finite Group Databasebeta

← #10723729

Subgroups — #10723729

Order 768.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4667C211yesmaximal, characteristic
2C3×#1436C211yesmaximal, characteristic, complemented
3#71570C211yesmaximal, characteristic
4#71566C211yesmaximal, characteristic, complemented
5#71537C211yesmaximal, characteristic
6#71536C211yesmaximal, characteristic, complemented
7#69428C211yesmaximal, characteristic
8(C2×D3)⋊#95C211yesmaximal, characteristic
9(C2×D3)⋊#95C211yesmaximal, characteristic
10#69417C211yesmaximal, characteristic, complemented
11#69416C211yesmaximal, characteristic, complemented
12#69409C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic
14#69406C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#14453—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
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#4667C418yescomplemented
53C2×#380—31no—
54#1443—31no—
55#1443—31no—
56#1441—31no—
57#1441—31no—
58#1439—31no—
59#1439—31no—
60#1437—31no—
61#1437—31no—
62#1436—31no—
63#1436—31no—
64#1436—31no—
65#1436D311yescharacteristic, complemented
66C22⋊#95—31no—
67C22⋊#95—31no—
68C24×D3C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C22×C4×D3—22no—
84C22×C4×D3—22no—
85C22×C4×D3—41no—
86C22×C4×D3—41no—
87C22×C4×D3—41no—
88C22×C4×D3—41no—
89C22×C4×D3C2×C414yes—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—41no—
92C2×C3×C4⋊C4—41no—
93C2×C3×C42—41no—
94C2×C3×C42—41no—
95C2×C3×C42—41no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—41no—
102C2×(C2×D3)⋊C4—41no—
103C2×(C2×D3)⋊C4—41no—
104C2×(C2×D3)⋊C4—41no—
105C2×(C2×D3)⋊C4—41no—
106C2×(C2×D3)⋊C4—41no—
107C2×(C2×D3)⋊C4—41no—
108C2×(C2×D3)⋊C4—41no—
109C2×(C2×D3)⋊C4—41no—
110C2×(C2×D3)⋊C4—41no—
111C2×(C2×D3)⋊C4C2×C414yes—
112C2×(C2×D3)⋊C4C2×C414yes—
113C2×(C2×D3)⋊C4Q814yes—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—41no—
116C2×Dic3⋊C4—41no—
117C2×Dic3⋊C4—41no—
118C2×Dic3⋊C4—41no—
119C2×Dic3⋊C4—41no—
120C2×Dic3⋊C4—41no—
121C2×Dic3⋊C4C2×C414yes—
122C2×Dic3⋊C4C2×C414yes—
123C2×C4×Dic3—41no—
124C2×C4×Dic3—41no—
125C2×C4×Dic3—41no—
126C3×#95—22no—
127C3×#95—41no—
128C3×#95—41no—
129C3×#95—41no—
130C3×#95C2×C414yes—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—22no—
136C3⋊#95—41no—
137C3⋊#95—41no—
138C3⋊#95—41no—
139C3⋊#95—41no—
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95C2×C414yes—
148C24×C4—31no—
149C22×C4⋊C4—31no—
150C22×C4⋊C4—31no—
151C22×C4⋊C4—31no—
152C22×C4⋊C4C2×D311yescharacteristic
153C22×C22⋊C4—31no—
154C22×C22⋊C4—31no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4—31no—
159C22×C42—31no—
160C22×C42C2×D311yescharacteristic
161#380—38no—
162C2×#95—31no—
163C2×#95—31no—
164C2×#95—31no—
165C2×#95—31no—
166C2×#95—31no—
167C2×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95C2×D311yescharacteristic
180C2×#95C2×D311yescharacteristic
181C2×#95C2×D311yescharacteristic
182C2×#95C2×D311yescharacteristic
183C2×#95C2×D311yescharacteristic
184C24×C3C2411yescharacteristic
185C23×D3—21no—
186C23×D3—21no—
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—21no—
190C23×D3—21no—
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3C22×C412yes—
198C23×D3C2×Q812yes—
199C23×D3#4112yes—
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×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C22×C412yes—
244C22×C3×C4C22×C412yes—
245C22×C3×C4C22×C412yes—
246C22×C3×C4C2×Q812yes—
247C22×C3×C4#4112yes—
248C22×C3×C4#4112yes—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3C22×C412yes—
293C22×Dic3C22×C412yes—
294C22×Dic3C22×C412yes—
295C22×Dic3C2×Q812yes—
296C22×Dic3#4112yes—
297C22×Dic3#4112yes—
298C2×C4×D3—28no—
299C2×C4×D3—44no—
300C2×C4×D3—44no—
301C2×C4×D3—44no—
302C2×C4×D3—44no—
303C2×C4×D3—44no—
304C2×C4×D3—44no—
305C3×C4⋊C4—44no—
306C3×C42—44no—
307(C2×D3)⋊C4—44no—
308(C2×D3)⋊C4—44no—
309(C2×D3)⋊C4—44no—
310(C2×D3)⋊C4—44no—
311(C2×D3)⋊C4—44no—
312(C2×D3)⋊C4—44no—
313Dic3⋊C4—44no—
314Dic3⋊C4—44no—
315Dic3⋊C4—44no—
316C4×Dic3—44no—
317C25—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—34no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—62no—
327C23×C4—62no—
328C23×C4—121no—
329C23×C4—121no—
330C23×C4—121no—
331C23×C4—121no—
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D311yescharacteristic
339C2×C4⋊C4—22no—
340C2×C4⋊C4—34no—
341C2×C4⋊C4—34no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—121no—
346C2×C4⋊C4—121no—
347C2×C4⋊C4—121no—
348C2×C4⋊C4—121no—
349C2×C4⋊C4—121no—
350C2×C4⋊C4—121no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—34no—
353C2×C22⋊C4—34no—
354C2×C22⋊C4—62no—
355C2×C22⋊C4—62no—
356C2×C22⋊C4—62no—
357C2×C22⋊C4—62no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—121no—
360C2×C22⋊C4—121no—
361C2×C22⋊C4—121no—
362C2×C22⋊C4—121no—
363C2×C22⋊C4—121no—
364C2×C22⋊C4—121no—
365C2×C22⋊C4—121no—
366C2×C22⋊C4—121no—
367C2×C22⋊C4—121no—
368C2×C22⋊C4—121no—
369C2×C42—41no—
370C2×C42—41no—
371C2×C42—41no—
372C2×C42—121no—
373C2×C42—121no—
374C2×C42—121no—
375#95—22no—
376#95—34no—
377#95—41no—
378#95—41no—
379#95—41no—
380#95—62no—
381#95—62no—
382#95—62no—
383#95—62no—
384#95—62no—
385#95—121no—
386#95—121no—
387#95—121no—
388#95—121no—
389#95—121no—
390#95—121no—
391#95—121no—
392#95—121no—
393#95—121no—
394#95—121no—
395#95—121no—
396#95C4×D314yes—
397C23×C3C23×C411yescharacteristic
398C23×C3C22×Q811yescharacteristic
399C23×C3C2×#4111yescharacteristic
400C23×C3C2×#4111yescharacteristic
401C23×C3C2×#4111yescharacteristic
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3H(5,𝔽2)11yescharacteristic
405C23×C3H(5,𝔽2)11yescharacteristic
406C23×C3H(5,𝔽2)11yescharacteristic
407C23×C3H(5,𝔽2)11yescharacteristic
408C23×C3H(5,𝔽2)11yescharacteristic
409C23×C3H(5,𝔽2)11yescharacteristic
410C23×C3H(5,𝔽2)11yescharacteristic
411C23×C32−1+411yescharacteristic
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3C4×Q814yes—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3#11714yes—
545C4×D3—416no—
546C24—32no—
547C24—32no—
548C24—32no—
549C24—61no—
550C24—61no—
551C24—61no—
552C24—61no—
553C24—61no—
554C24—61no—
555C24—61no—
556C24—61no—
557C24—61no—
558C24—61no—
559C24—61no—
560C24—61no—
561C24C23×D311yescharacteristic
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—32no—
610C22×C4—32no—
611C22×C4—68no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—124no—
656C22×C4—124no—
657C22×C4—124no—
658C22×C4—124no—
659C22×C4—124no—
660C22×C4—124no—
661C22×C4C2×C4×D312yes—
662C22×C4C2×C4×D312yes—
663C22×C4C2×C4×D312yes—
664C22×C4#23512yes—
665C22×C4#23512yes—
666C22×C4D3×Q812yes—
667C4⋊C4—44no—
668C4⋊C4—124no—
669C4⋊C4—124no—
670C4⋊C4—124no—
671C22⋊C4—124no—
672C22⋊C4—124no—
673C22⋊C4—124no—
674C22⋊C4—124no—
675C22⋊C4—124no—
676C22⋊C4—124no—
677C42—44no—
678C42—124no—
679C22×C3C2×#11711yescharacteristic
680C22×C3C2×C4×Q811yescharacteristic
681C22×C3C4×#4111yescharacteristic
682C22×C3#51811yescharacteristic
683C22×C3#51811yescharacteristic
684C22×C3#51811yescharacteristic
685C22×C3#52011yescharacteristic
686C22×C3#53811yescharacteristic
687C22×C3#53811yescharacteristic
688C22×C3#53811yescharacteristic
689C22×C3#53811yescharacteristic
690C22×C3#53811yescharacteristic
691C22×C3#53811yescharacteristic
692C22×C3#53811yescharacteristic
693C22×C3#53911yescharacteristic
694C22×C3#54011yescharacteristic
695C22×C3#54011yescharacteristic
696C22×C3#54311yescharacteristic
697C22×C3#54411yescharacteristic
698C22×C3#55111yescharacteristic
699C22×C3#55111yescharacteristic
700C22×C3#55311yescharacteristic
701C22×C3#55311yescharacteristic
702C22×C3#55311yescharacteristic
703C22×C3#55311yescharacteristic
704C22×C3#55411yescharacteristic
705C22×C3#55411yescharacteristic
706C22×C3#55411yescharacteristic
707C22×C3#55411yescharacteristic
708C22×C3#55611yescharacteristic
709C22×C3#55611yescharacteristic
710C22×C3#56011yescharacteristic
711C22×C3#56011yescharacteristic
712C22×C3#56211yescharacteristic
713C22×C3#56211yescharacteristic
714C2×D3—24no—
715C2×D3—24no—
716C2×D3—24no—
717C2×D3—42no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—42no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—81no—
736Dic3—24no—
737Dic3—42no—
738Dic3—42no—
739Dic3—42no—
740Dic3—81no—
741Dic3—81no—
742Dic3—81no—
743C23—34no—
744C23—62no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—121no—
776C23—121no—
777C23—121no—
778C23C22×C4×D311yescharacteristic
779C23C2×#23511yescharacteristic
780C23C2×#23511yescharacteristic
781C23#100411yescharacteristic
782C23#100411yescharacteristic
783C23#100411yescharacteristic
784C23#100411yescharacteristic
785C23C2×D3×Q811yescharacteristic
786C23#100711yescharacteristic
787C23D3×#4111yescharacteristic
788C23D3×#4111yescharacteristic
789C23D3×#4111yescharacteristic
790C23#100911yescharacteristic
791C23#100911yescharacteristic
792C23#100911yescharacteristic
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—34no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—1216no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—121no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C3#231211yescharacteristic
893C2×C3#232911yescharacteristic
894C2×C3#233311yescharacteristic
895C2×C3#234511yescharacteristic
896C2×C3#234711yescharacteristic
897C2×C3#236811yescharacteristic
898C2×C3#237711yescharacteristic
899C2×C3#277811yescharacteristic
900C2×C3#277811yescharacteristic
901C2×C3#278011yescharacteristic
902C2×C3#278011yescharacteristic
903C2×C3#278611yescharacteristic
904C2×C3#278611yescharacteristic
905C2×C3#278811yescharacteristic
906C2×C3#278811yescharacteristic
907D3—44no—
908C22—64no—
909C22—64no—
910C22—64no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—122no—
917C22—122no—
918C22—122no—
919C22—122no—
920C22—122no—
921C22—122no—
922C22—122no—
923C22C4×#23511yescharacteristic
924C22#549411yescharacteristic
925C22#550411yescharacteristic
926C22#551111yescharacteristic
927C22D3×#11711yescharacteristic
928C22#552711yescharacteristic
929C22#553511yescharacteristic
930C22#554011yescharacteristic
931C22#554011yescharacteristic
932C22#554511yescharacteristic
933C22#554511yescharacteristic
934C22#554511yescharacteristic
935C22#555611yescharacteristic
936C22#556011yescharacteristic
937C22#556211yescharacteristic
938C22#556811yescharacteristic
939C22#556811yescharacteristic
940C22C4×D3×Q811yescharacteristic
941C22#557911yescharacteristic
942C22#559511yescharacteristic
943C22#561311yescharacteristic
944C22#561311yescharacteristic
945C22#563411yescharacteristic
946C22#563611yescharacteristic
947C22#564711yescharacteristic
948C22#564711yescharacteristic
949C22#565711yescharacteristic
950C22#566111yescharacteristic
951C22#566611yescharacteristic
952C22#567811yescharacteristic
953C22#569011yescharacteristic
954C22#569211yescharacteristic
955C22#570411yescharacteristic
956C22#570911yescharacteristic
957C22#572911yescharacteristic
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—64no—
965C4—81no—
966C4—122no—
967C4—122no—
968C4—122no—
969C4—241no—
970C4—241no—
971C4—241no—
972C3#1445311yescharacteristic, complemented, Sylow
973C2—124no—
974C2#7357011yescharacteristic
975C2#7363511yescharacteristic
976C2#7377511yescharacteristic
977C2#7440111yescharacteristic
978C2#7456511yescharacteristic
979C2#7485511yescharacteristic
980C2#7496211yescharacteristic
981C2#7523711yescharacteristic
982C2#7524211yescharacteristic
983C2#7524311yescharacteristic
984C2#7577011yescharacteristic
985C2#7582511yescharacteristic
986C2#7616411yescharacteristic
987C2#7619911yescharacteristic
988C2#7659011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14453
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C3×#1436C2semidirect
4. #71566C2semidirect
6. #71536C2semidirect
10. #69417C2semidirect
11. #69416C2semidirect
12. #69409C2semidirect
14. #69406C2semidirect
15. #69405C2semidirect
52. #4667C4semidirect
65. #1436D3semidirect
972. C3#14453semidirect

Maximal subgroups

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

subgroupindex
C2×#46672
C3×#14362
#715702
#715662
#715372
#715362
#694282
(C2×D3)⋊#952
#694172
#694162
#694092
#694082
#694062
#694052
#144533