Finite Group Databasebeta

← #10720112

Subgroups — #10720112

Order 768.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#872C211yesmaximal, characteristic
2C2×#4976C211yesmaximal, characteristic, complemented
3C2×#4667C211yesmaximal, characteristic
4C2×#4647C211yesmaximal, characteristic, complemented
5C2×#4666C211yesmaximal, characteristic
6C3×#1436C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic
8#71536C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic
10#69428C211yesmaximal, characteristic
11#69427C211yesmaximal, characteristic
12#69407C211yesmaximal, characteristic, complemented
13#69406C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#14129—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×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×#872—24no—
37C2×#872—24no—
38C2×#872—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4976—24no—
56#4667C418yescomplemented
57#4666—24no—
58#4647—24no—
59C22×#117—31no—
60C2×#389—31no—
61C2×#389—31no—
62C2×#380—31no—
63C2×C4×C22⋊C4—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1436—31no—
69#1436—31no—
70#1436—31no—
71#1436D311yescharacteristic, complemented
72C4⋊#95—31no—
73C4⋊#95—31no—
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3C2×C414yes—
94C22×C4×D3D414yes—
95C22×C4×D3Q814yes—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—41no—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—41no—
115C2×(C2×D3)⋊C4—41no—
116C2×(C2×D3)⋊C4—41no—
117C2×(C2×D3)⋊C4—41no—
118C2×(C2×D3)⋊C4C2×C414yes—
119C2×(C2×D3)⋊C4C2×C414yes—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—41no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—41no—
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4C2×C414yes—
138C2×Dic3⋊C4C2×C414yes—
139C2×Dic3⋊C4D414yes—
140C2×Dic3⋊C4D414yes—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—22no—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150#872—232no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—41no—
155C3×#95C2×C414yes—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95C2×C414yes—
167C24×C4—31no—
168C2×#117—64no—
169C2×#117—64no—
170C2×#117—64no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4C2×D311yescharacteristic
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C42—31no—
186C22×C42—31no—
187C22×C42—31no—
188C22×C42C2×D311yescharacteristic
189#389—64no—
190#389—64no—
191#380—38no—
192C4×C22⋊C4—64no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C24×C3C2411yescharacteristic
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3C22×C412yes—
223C23×D3C2×D412yes—
224C23×D3C2×Q812yes—
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×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
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×C4C22×C412yes—
266C22×C3×C4C22×C412yes—
267C22×C3×C4C22×C412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4C2×Q812yes—
272C22×C3×C4#4112yes—
273C22×C3×C4#4112yes—
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×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
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×Dic3C22×C412yes—
311C22×Dic3C22×C412yes—
312C22×Dic3C22×C412yes—
313C22×Dic3C2×D412yes—
314C22×Dic3C2×D412yes—
315C22×Dic3C2×D412yes—
316C22×Dic3C2×D412yes—
317C22×Dic3C2×D412yes—
318C22×Dic3C2×Q812yes—
319C22×Dic3#4112yes—
320C22×Dic3#4112yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C2×C4×D3—28no—
324C2×C4×D3—28no—
325C2×C4×D3—28no—
326C2×C4×D3—28no—
327C2×C4×D3—28no—
328C2×C4×D3—28no—
329C2×C4×D3C4⋊C4116yescomplemented
330C3×C4⋊C4—44no—
331C3×C42—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338C4⋊Dic3—44no—
339Dic3⋊C4—28no—
340Dic3⋊C4—28no—
341Dic3⋊C4—28no—
342Dic3⋊C4—28no—
343Dic3⋊C4—44no—
344Dic3⋊C4—44no—
345C4×Dic3—28no—
346C4×Dic3—44no—
347C4×Dic3—44no—
348C25—31no—
349C23×C4—31no—
350C23×C4—34no—
351C23×C4—34no—
352C23×C4—34no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—62no—
360C23×C4—62no—
361C23×C4—62no—
362C23×C4—62no—
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370#117—632no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—34no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—62no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—121no—
393C2×C4⋊C4—121no—
394C2×C4⋊C4—121no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—121no—
410C2×C22⋊C4—121no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—62no—
417C2×C42—62no—
418C2×C42—62no—
419C2×C42—62no—
420C2×C42—62no—
421C2×C42—62no—
422C2×C42—62no—
423C2×C42—62no—
424C2×C42—62no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—34no—
429#95—41no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95C4×D314yes—
441C23×C3C23×C411yescharacteristic
442C23×C3C22×D411yescharacteristic
443C23×C3C22×D411yescharacteristic
444C23×C3C22×D411yescharacteristic
445C23×C3C22×Q811yescharacteristic
446C23×C3C2×#4111yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3C2×#4111yescharacteristic
450C23×C3C2×#4111yescharacteristic
451C23×C3C2×#4111yescharacteristic
452C23×C3H(5,𝔽2)11yescharacteristic
453C23×C3H(5,𝔽2)11yescharacteristic
454C23×C32−1+411yescharacteristic
455C23×C32−1+411yescharacteristic
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3C2×C4⋊C414yes—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4C2×C4⋊C414yes—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3C2×C4⋊C414yes—
583C2×Dic3C4×D414yes—
584C2×Dic3C4×D414yes—
585C2×Dic3#12014yes—
586C2×Dic3C22⋊Q814yes—
587C2×Dic3C22⋊Q814yes—
588C2×Dic3#12314yes—
589C4×D3—232no—
590C24—32no—
591C24—32no—
592C24—32no—
593C24—61no—
594C24—61no—
595C24—61no—
596C24—61no—
597C24—61no—
598C24—61no—
599C24—61no—
600C24—61no—
601C24—61no—
602C24—61no—
603C24—61no—
604C24—61no—
605C24C23×D311yescharacteristic
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—316no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—32no—
659C22×C4—32no—
660C22×C4—68no—
661C22×C4—68no—
662C22×C4—68no—
663C22×C4—68no—
664C22×C4—68no—
665C22×C4—68no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4C2×C4×D312yes—
703C22×C4C2×C4×D312yes—
704C22×C4C2×C4×D312yes—
705C22×C4#23512yes—
706C22×C4#23512yes—
707C22×C4D3×D412yes—
708C22×C4D3×D412yes—
709C22×C4D3×D412yes—
710C22×C4D3×Q812yes—
711C4⋊C4—44no—
712C4⋊C4—68no—
713C4⋊C4—68no—
714C4⋊C4—68no—
715C4⋊C4—68no—
716C4⋊C4—124no—
717C4⋊C4—124no—
718C4⋊C4—124no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—68no—
723C22⋊C4—124no—
724C22⋊C4—124no—
725C42—28no—
726C42—68no—
727C42—124no—
728C42—124no—
729C22×C3C22×C4⋊C411yescharacteristic
730C22×C3C2×C4×D411yescharacteristic
731C22×C3C2×C4×D411yescharacteristic
732C22×C3C4×#4111yescharacteristic
733C22×C3C4×#4111yescharacteristic
734C22×C3#51811yescharacteristic
735C22×C3#51911yescharacteristic
736C22×C3C2×#12011yescharacteristic
737C22×C3C2×C22⋊Q811yescharacteristic
738C22×C3C2×C22⋊Q811yescharacteristic
739C22×C3C2×#12311yescharacteristic
740C22×C3#52511yescharacteristic
741C22×C3#52511yescharacteristic
742C22×C3#53311yescharacteristic
743C22×C3#53311yescharacteristic
744C22×C3#53711yescharacteristic
745C22×C3#53711yescharacteristic
746C22×C3#54411yescharacteristic
747C22×C3#54411yescharacteristic
748C22×C3#54611yescharacteristic
749C22×C3#54611yescharacteristic
750C22×C3#54711yescharacteristic
751C22×C3#54711yescharacteristic
752C22×C3#54811yescharacteristic
753C22×C3#54811yescharacteristic
754C22×C3#55011yescharacteristic
755C22×C3#55011yescharacteristic
756C22×C3#55211yescharacteristic
757C22×C3#55211yescharacteristic
758C22×C3#55311yescharacteristic
759C22×C3#55311yescharacteristic
760C22×C3#55511yescharacteristic
761C22×C3#55511yescharacteristic
762C22×C3#55611yescharacteristic
763C22×C3#55611yescharacteristic
764C2×D3—24no—
765C2×D3—24no—
766C2×D3—24no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—42no—
774C2×D3—42no—
775C2×D3—42no—
776C2×D3—42no—
777C2×D3—42no—
778C2×D3—42no—
779C3×C4—24no—
780C3×C4—42no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—42no—
784C3×C4—42no—
785C3×C4—42no—
786Dic3—42no—
787Dic3—42no—
788Dic3—42no—
789Dic3—42no—
790Dic3—42no—
791Dic3—42no—
792Dic3#38518yes—
793C23—34no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—121no—
813C23—121no—
814C23—121no—
815C23—121no—
816C23—121no—
817C23—121no—
818C23—121no—
819C23—121no—
820C23—121no—
821C23—121no—
822C23—121no—
823C23—121no—
824C23—121no—
825C23—121no—
826C23—121no—
827C23—121no—
828C23C22×C4×D311yescharacteristic
829C23C2×#23511yescharacteristic
830C23C2×#23511yescharacteristic
831C23C2×D3×D411yescharacteristic
832C23C2×D3×D411yescharacteristic
833C23C2×D3×D411yescharacteristic
834C23#100411yescharacteristic
835C23C2×D3×Q811yescharacteristic
836C23#100711yescharacteristic
837C23D3×#4111yescharacteristic
838C23D3×#4111yescharacteristic
839C23D3×#4111yescharacteristic
840C23D3×#4111yescharacteristic
841C23#100911yescharacteristic
842C23#101011yescharacteristic
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—34no—
868C2×C4—34no—
869C2×C4—34no—
870C2×C4—34no—
871C2×C4—34no—
872C2×C4—34no—
873C2×C4—34no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—632no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4D3×C4⋊C414yes—
942C2×C3C2×#38511yescharacteristic
943C2×C3#229611yescharacteristic
944C2×C3#231611yescharacteristic
945C2×C3#236211yescharacteristic
946C2×C3#236211yescharacteristic
947C2×C3#236311yescharacteristic
948C2×C3#236311yescharacteristic
949C2×C3#240711yescharacteristic
950C2×C3#240711yescharacteristic
951C2×C3#243911yescharacteristic
952C2×C3#243911yescharacteristic
953C2×C3#244111yescharacteristic
954C2×C3#244111yescharacteristic
955C2×C3#248511yescharacteristic
956C2×C3#248511yescharacteristic
957D3—44no—
958C22—64no—
959C22—64no—
960C22—64no—
961C22—122no—
962C22—122no—
963C22—122no—
964C22—122no—
965C22—122no—
966C22—122no—
967C22—122no—
968C22—122no—
969C22—122no—
970C22—122no—
971C22—122no—
972C22—122no—
973C22C4×#23511yescharacteristic
974C22#549011yescharacteristic
975C22C2×D3×C4⋊C411yescharacteristic
976C22#550711yescharacteristic
977C22#552211yescharacteristic
978C22#553111yescharacteristic
979C22#553211yescharacteristic
980C22#554011yescharacteristic
981C22C4×D3×D411yescharacteristic
982C22C4×D3×D411yescharacteristic
983C22#554511yescharacteristic
984C22#554711yescharacteristic
985C22#554711yescharacteristic
986C22#555211yescharacteristic
987C22#555311yescharacteristic
988C22#556811yescharacteristic
989C22#557211yescharacteristic
990C22#557811yescharacteristic
991C22#557811yescharacteristic
992C22D3×#12011yescharacteristic
993C22#559911yescharacteristic
994C22#560811yescharacteristic
995C22D3×C22⋊Q811yescharacteristic
996C22D3×C22⋊Q811yescharacteristic
997C22#562911yescharacteristic
998C22#563311yescharacteristic
999C22D3×#12311yescharacteristic
1000C22#565411yescharacteristic
1001C22#565511yescharacteristic
1002C22#567011yescharacteristic
1003C22#568911yescharacteristic
1004C22#569311yescharacteristic
1005C22#570211yescharacteristic
1006C22#570911yescharacteristic
1007C22#572911yescharacteristic
1008C4—24no—
1009C4—38no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—122no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4—122no—
1021C4—122no—
1022C3#1412911yescharacteristic, complemented, Sylow
1023C2—124no—
1024C2#7347011yescharacteristic
1025C2#7364811yescharacteristic
1026C2#7375511yescharacteristic
1027C2#7440411yescharacteristic
1028C2D3×#38511yescharacteristic
1029C2#7468811yescharacteristic
1030C2#7496611yescharacteristic
1031C2#7498311yescharacteristic
1032C2#7498411yescharacteristic
1033C2#7502111yescharacteristic
1034C2#7548011yescharacteristic
1035C2#7554311yescharacteristic
1036C2#7600111yescharacteristic
1037C2#7619511yescharacteristic
1038C2#7650111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14129
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#4976C2semidirect
4. C2×#4647C2semidirect
6. C3×#1436C2semidirect
8. #71536C2semidirect
12. #69407C2semidirect
13. #69406C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3⋊#95C2semidirect
56. #4667C4semidirect
71. #1436D3semidirect
329. C2×C4×D3C4⋊C4semidirect
1022. C3#14129semidirect

Maximal subgroups

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

subgroupindex
C22×#8722
C2×#49762
C2×#46672
C2×#46472
C2×#46662
C3×#14362
#715702
#715362
#694282
#694272
#694072
#694062
Dic3⋊#952
#141293