Finite Group Databasebeta

← #10733221

Subgroups — #10733221

Order 768.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4988C211yesmaximal, characteristic
2C2×#4675C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4664C211yesmaximal, characteristic, complemented
5C3×#1442C211yesmaximal, characteristic, complemented
6#71568C211yesmaximal, characteristic, complemented
7#69429C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69402C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#15285—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
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#4988—24no—
53#4675—24no—
54#4665—24no—
55#4664—24no—
56C2×#397—31no—
57C2×#390—31no—
58C2×#386—31no—
59C2×#381—31no—
60#1444—31no—
61#1442D311yescharacteristic, complemented
62#1440—31no—
63#1440—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1438—31no—
68#1434—31no—
69#1434—31no—
70C22⋊#95—31no—
71C24×D3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C22×D12—22no—
87C22×D12—22no—
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—41no—
91C22×D12—41no—
92C22×D12D414yes—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—41no—
99C22×C4×D3—41no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—41no—
102C2×C3×C4⋊C4—41no—
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—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—41no—
123C2×(C2×D3)⋊C4—41no—
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)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—41no—
150C3×#95—41no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95D414yescomplemented
163C23×D4—31no—
164C24×C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C42—31no—
180#397—64no—
181#390—64no—
182#386—64no—
183#381—64no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3C2411yescharacteristic
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
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×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3C2×D412yes—
230C23×D3C2×D412yes—
231C23×D3#4112yes—
232C23×D3#4112yes—
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×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×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
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×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×Dic3C2×D412yes—
320C22×Dic3C2×D412yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C22×Dic3#4112yes—
324C2×D12—28no—
325C2×D12—28no—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×C4×D3—28no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C3×C4⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350Dic3⋊C4—44no—
351Dic3⋊C4—44no—
352C4×Dic3—44no—
353C25—31no—
354C25—31no—
355C22×D4—34no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—121no—
361C22×D4—121no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—62no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—121no—
374C23×C4—121no—
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C2×C4⋊C4—22no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C4⋊C4—121no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
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—62no—
410C2×C22⋊C4—121no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C42—62no—
425C2×C42—62no—
426C2×C42—62no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—34no—
432#95—41no—
433#95—41no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—62no—
441#95—62no—
442#95—121no—
443#95—121no—
444#95—121no—
445C23×C3C22×D411yescharacteristic
446C23×C3C22×D411yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3C2×#4111yescharacteristic
450C23×C3C2×#4111yescharacteristic
451C23×C3C2×#4111yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3C2×#4111yescharacteristic
454C23×C3H(5,𝔽2)11yescharacteristic
455C23×C3H(5,𝔽2)11yescharacteristic
456C23×C3H(5,𝔽2)11yescharacteristic
457C23×C3H(5,𝔽2)11yescharacteristic
458C23×C3H(5,𝔽2)11yescharacteristic
459C23×C32−1+411yescharacteristic
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—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3#12314yes—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
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#12314yes—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621D12—416no—
622C4×D3—416no—
623C24—32no—
624C24—32no—
625C24—32no—
626C24—32no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24C23×D311yescharacteristic
654C2×D4—68no—
655C2×D4—68no—
656C2×D4—124no—
657C2×D4—124no—
658C2×D4—124no—
659C2×D4—124no—
660C2×D4—124no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
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—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—68no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
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—124no—
750C22×C4—124no—
751C22×C4—124no—
752C22×C4—124no—
753C22×C4—124no—
754C22×C4—124no—
755C22×C4#23512yes—
756C22×C4D3×D412yes—
757C22×C4D3×D412yes—
758C22×C4#23912yes—
759C4⋊C4—44no—
760C4⋊C4—124no—
761C4⋊C4—124no—
762C22⋊C4—124no—
763C22⋊C4—124no—
764C22⋊C4—124no—
765C22⋊C4—124no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C22⋊C4—124no—
773C42—124no—
774C22×C3C2×#12311yescharacteristic
775C22×C3C2×#12311yescharacteristic
776C22×C3#52511yescharacteristic
777C22×C3#52911yescharacteristic
778C22×C3#52911yescharacteristic
779C22×C3#53211yescharacteristic
780C22×C3#53411yescharacteristic
781C22×C3#53511yescharacteristic
782C22×C3#53811yescharacteristic
783C22×C3#53811yescharacteristic
784C22×C3#53911yescharacteristic
785C22×C3#54011yescharacteristic
786C22×C3#54011yescharacteristic
787C22×C3#54211yescharacteristic
788C22×C3#54211yescharacteristic
789C22×C3D4211yescharacteristic
790C22×C3#54611yescharacteristic
791C22×C3#54611yescharacteristic
792C22×C3#54611yescharacteristic
793C22×C3#54711yescharacteristic
794C22×C3#54711yescharacteristic
795C22×C3#55011yescharacteristic
796C22×C3#55111yescharacteristic
797C22×C3#55111yescharacteristic
798C22×C3#55111yescharacteristic
799C22×C3#55111yescharacteristic
800C22×C3#55111yescharacteristic
801C22×C3#55111yescharacteristic
802C22×C3#55211yescharacteristic
803C22×C3#55311yescharacteristic
804C22×C3#55311yescharacteristic
805C22×C3#55511yescharacteristic
806C22×C3#55511yescharacteristic
807C22×C3#56011yescharacteristic
808C22×C3#56211yescharacteristic
809C2×D3—24no—
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—42no—
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C3×C4—24no—
840C3×C4—42no—
841C3×C4—81no—
842C3×C4—81no—
843C3×C4—81no—
844C3×C4—81no—
845C3×C4—81no—
846Dic3—42no—
847Dic3—42no—
848Dic3—42no—
849Dic3—42no—
850Dic3—42no—
851Dic3—81no—
852C23—34no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—121no—
882C23—121no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23C2×#23511yescharacteristic
923C23C2×D3×D411yescharacteristic
924C23C2×D3×D411yescharacteristic
925C23#100411yescharacteristic
926C23#100411yescharacteristic
927C23C2×#23911yescharacteristic
928C23#100711yescharacteristic
929C23D3×#4111yescharacteristic
930C23D3×#4111yescharacteristic
931C23D3×#4111yescharacteristic
932C23D3×#4111yescharacteristic
933C23D3×#4111yescharacteristic
934C23#100911yescharacteristic
935C23#100911yescharacteristic
936C23#100911yescharacteristic
937D4—1216no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—1216no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4#89414yes—
1030C2×C3#241811yescharacteristic
1031C2×C3#241911yescharacteristic
1032C2×C3#242011yescharacteristic
1033C2×C3#242211yescharacteristic
1034C2×C3#247911yescharacteristic
1035C2×C3#248311yescharacteristic
1036C2×C3#252611yescharacteristic
1037C2×C3#255411yescharacteristic
1038C2×C3#261011yescharacteristic
1039C2×C3#267311yescharacteristic
1040C2×C3#268611yescharacteristic
1041C2×C3#270611yescharacteristic
1042C2×C3#273711yescharacteristic
1043C2×C3#274911yescharacteristic
1044C2×C3#276111yescharacteristic
1045D3—44no—
1046D3—82no—
1047C22—64no—
1048C22—64no—
1049C22—64no—
1050C22—122no—
1051C22—122no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22—122no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22—241no—
1076C22—241no—
1077C22C2×#89411yescharacteristic
1078C22#553011yescharacteristic
1079C22#553211yescharacteristic
1080C22#554811yescharacteristic
1081C22#555611yescharacteristic
1082C22#555611yescharacteristic
1083C22#558211yescharacteristic
1084C22#558911yescharacteristic
1085C22#559911yescharacteristic
1086C22#560711yescharacteristic
1087C22#560911yescharacteristic
1088C22#563111yescharacteristic
1089C22#563711yescharacteristic
1090C22#563711yescharacteristic
1091C22#564011yescharacteristic
1092C22#564711yescharacteristic
1093C22D3×#12311yescharacteristic
1094C22#565411yescharacteristic
1095C22#565611yescharacteristic
1096C22#566311yescharacteristic
1097C22#566611yescharacteristic
1098C22#567011yescharacteristic
1099C22#567611yescharacteristic
1100C22#567611yescharacteristic
1101C22#567811yescharacteristic
1102C22#569111yescharacteristic
1103C22#569211yescharacteristic
1104C22#569311yescharacteristic
1105C22#569511yescharacteristic
1106C22#569711yescharacteristic
1107C22#570411yescharacteristic
1108C22#570511yescharacteristic
1109C22#570511yescharacteristic
1110C22#570611yescharacteristic
1111C22#572611yescharacteristic
1112C4—24no—
1113C4—42no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—122no—
1120C4—122no—
1121C4—122no—
1122C4—122no—
1123C4—122no—
1124C4—241no—
1125C3#1528511yescharacteristic, complemented, Sylow
1126C2—124no—
1127C2—242no—
1128C2#7423111yescharacteristic
1129C2#7445511yescharacteristic
1130C2#7540011yescharacteristic
1131C2#7542911yescharacteristic
1132C2#7588311yescharacteristic
1133C2#7590011yescharacteristic
1134C2#7621511yescharacteristic
1135C2#7687711yescharacteristic
1136C2#7713411yescharacteristic
1137C2#7766911yescharacteristic
1138C2#7776311yescharacteristic
1139C2#7785311yescharacteristic
1140C2#7816611yescharacteristic
1141C2#7834111yescharacteristic
1142C2#7839011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1442C2
prime radicalC23×D12C22
hypercenter#1442D3
hypocenterC3#15285
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#4675C2semidirect
4. C2×#4664C2semidirect
5. C3×#1442C2semidirect
6. #71568C2semidirect
7. #69429C2semidirect
8. #69429C2semidirect
9. #69428C2semidirect
10. #69428C2semidirect
11. #69428C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69402C2semidirect
15. #69402C2semidirect
61. #1442D3semidirect
162. C3⋊#95D4semidirect
1125. C3#15285semidirect

Maximal subgroups

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

subgroupindex
C2×#49882
C2×#46752
C2×#46652
C2×#46642
C3×#14422
#715682
#694292
#694282
#694262
(C2×D3)⋊#952
#694022
#152853