Finite Group Databasebeta

← #10724482

Subgroups — #10724482

Order 768.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4665C211yesmaximal, characteristic
2C3×#1443C211yesmaximal, characteristic, complemented
3#69429C211yesmaximal, characteristic, complemented
4#69429C211yesmaximal, characteristic, complemented
5#69426C211yesmaximal, characteristic
6#69426C211yesmaximal, characteristic
7(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
9#69418C211yesmaximal, characteristic, complemented
10#69408C211yesmaximal, characteristic, complemented
11#69408C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69402C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14516—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×(C2×D3)⋊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×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
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#4665C418yescomplemented
53C2×#386—31no—
54#1443—31no—
55#1443D311yescharacteristic, complemented
56#1440—31no—
57#1440—31no—
58#1438—31no—
59#1438—31no—
60#1437—31no—
61#1437—31no—
62#1437—31no—
63#1437—31no—
64#1434—31no—
65#1434—31no—
66C22⋊#95—31no—
67C22⋊#95—31no—
68C24×D3C2311yescharacteristic
69C24×D3C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C22×D12—22no—
84C22×D12—22no—
85C22×D12—41no—
86C22×D12—41no—
87C22×D12—41no—
88C22×D12—41no—
89C22×D12C2×C414yes—
90C22×C4×D3—41no—
91C22×C4×D3—41no—
92C22×C4×D3—41no—
93C22×C4×D3—41no—
94C22×C4×D3—41no—
95C22×C4×D3—41no—
96C22×C4×D3C2×C414yes—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—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—41no—
110C2×(C2×D3)⋊C4—41no—
111C2×(C2×D3)⋊C4—41no—
112C2×(C2×D3)⋊C4—41no—
113C2×(C2×D3)⋊C4—41no—
114C2×(C2×D3)⋊C4—41no—
115C2×(C2×D3)⋊C4—41no—
116C2×(C2×D3)⋊C4—41no—
117C2×(C2×D3)⋊C4—41no—
118C2×(C2×D3)⋊C4—41no—
119C2×(C2×D3)⋊C4—41no—
120C2×(C2×D3)⋊C4—41no—
121C2×(C2×D3)⋊C4—41no—
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)⋊C4C2×C414yes—
128C2×(C2×D3)⋊C4C2×C414yes—
129C2×(C2×D3)⋊C4C2×C414yes—
130C2×C4×Dic3—22no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—41no—
133C2×C4×Dic3—41no—
134C2×C4×Dic3—41no—
135C2×C4×Dic3—41no—
136C3×#95—41no—
137C3×#95—41no—
138C3×#95—41no—
139C3×#95—41no—
140C3×#95—41no—
141C3×#95—41no—
142C3×#95C2×C414yes—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95C2×C414yes—
156C23×D4—31no—
157C24×C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4—31no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C42—31no—
170C22×C42—31no—
171#386—38no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95C2×D311yescharacteristic
186C2×#95C2×D311yescharacteristic
187C2×#95C2×D311yescharacteristic
188C2×#95C2×D311yescharacteristic
189C2×#95C2×D311yescharacteristic
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C24×C3C2411yescharacteristic
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
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×D3C22×C412yes—
220C23×D3C22×C412yes—
221C23×D3#4112yes—
222C23×D3#4112yes—
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×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×C4C22×C412yes—
269C22×C3×C4C22×C412yes—
270C22×C3×C4C22×C412yes—
271C22×C3×C4#4112yes—
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×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×Dic3C22×C412yes—
310C22×Dic3C22×C412yes—
311C22×Dic3#4112yes—
312C22×Dic3#4112yes—
313C22×Dic3#4112yes—
314C2×D12—28no—
315C2×D12—44no—
316C2×D12—44no—
317C2×D12—44no—
318C2×D12—44no—
319C2×D12—44no—
320C2×D12—44no—
321C2×C4×D3—44no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3—44no—
326C2×C4×D3—44no—
327C2×C4×D3—44no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339C4×Dic3—44no—
340C4×Dic3—44no—
341C25—31no—
342C25—31no—
343C22×D4—34no—
344C22×D4—62no—
345C22×D4—62no—
346C22×D4—121no—
347C22×D4—121no—
348C22×D4—121no—
349C22×D4—121no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—34no—
356C23×C4—31no—
357C23×C4—121no—
358C23×C4—121no—
359C23×C4—121no—
360C23×C4—121no—
361C23×C4—121no—
362C23×C4—121no—
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C2×C22⋊C4—34no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—62no—
377C2×C22⋊C4—62no—
378C2×C22⋊C4—62no—
379C2×C22⋊C4—62no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—121no—
386C2×C22⋊C4—121no—
387C2×C22⋊C4—121no—
388C2×C22⋊C4—121no—
389C2×C22⋊C4—121no—
390C2×C22⋊C4—121no—
391C2×C22⋊C4—121no—
392C2×C22⋊C4—121no—
393C2×C22⋊C4—121no—
394C2×C22⋊C4—121no—
395C2×C22⋊C4—121no—
396C2×C22⋊C4—121no—
397C2×C22⋊C4—121no—
398C2×C22⋊C4—121no—
399C2×C22⋊C4—121no—
400C2×C22⋊C4—121no—
401C2×C22⋊C4—121no—
402C2×C22⋊C4—121no—
403C2×C42—62no—
404C2×C42—62no—
405C2×C42—121no—
406C2×C42—121no—
407C2×C42—121no—
408C2×C42—121no—
409#95—34no—
410#95—41no—
411#95—41no—
412#95—41no—
413#95—41no—
414#95—41no—
415#95—41no—
416#95—62no—
417#95—62no—
418#95—121no—
419#95—121no—
420#95—121no—
421#95—121no—
422#95—121no—
423#95—121no—
424#95—121no—
425#95—121no—
426#95—121no—
427#95—121no—
428#95C4×D314yes—
429C23×C3C23×C411yescharacteristic
430C23×C3C2×#4111yescharacteristic
431C23×C3C2×#4111yescharacteristic
432C23×C3C2×#4111yescharacteristic
433C23×C3C2×#4111yescharacteristic
434C23×C3C2×#4111yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3H(5,𝔽2)11yescharacteristic
437C23×C3H(5,𝔽2)11yescharacteristic
438C23×C3H(5,𝔽2)11yescharacteristic
439C23×C3H(5,𝔽2)11yescharacteristic
440C23×C3H(5,𝔽2)11yescharacteristic
441C23×C3H(5,𝔽2)11yescharacteristic
442C23×C3H(5,𝔽2)11yescharacteristic
443C23×C3H(5,𝔽2)11yescharacteristic
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
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—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
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×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#11714yes—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
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×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×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
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—
605D12—416no—
606C4×D3—416no—
607C24—32no—
608C24—32no—
609C24—32no—
610C24—32no—
611C24—61no—
612C24—61no—
613C24—61no—
614C24—61no—
615C24—61no—
616C24—61no—
617C24—61no—
618C24—61no—
619C24—61no—
620C24—61no—
621C24—61no—
622C24—61no—
623C24—61no—
624C24—61no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24C23×D311yescharacteristic
638C2×D4—68no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
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—32no—
691C22×C4—32no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
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—124no—
733C22×C4—124no—
734C22×C4—124no—
735C22×C4—124no—
736C22×C4—124no—
737C22×C4—124no—
738C22×C4—124no—
739C22×C4C2×C4×D312yes—
740C22×C4C2×C4×D312yes—
741C22×C4C2×C4×D312yes—
742C22×C4#23912yes—
743C22⋊C4—124no—
744C22⋊C4—124no—
745C22⋊C4—124no—
746C22⋊C4—124no—
747C22⋊C4—124no—
748C22⋊C4—124no—
749C22⋊C4—124no—
750C22⋊C4—124no—
751C22⋊C4—124no—
752C22⋊C4—124no—
753C22⋊C4—124no—
754C42—124no—
755C42—124no—
756C22×C3C2×#11711yescharacteristic
757C22×C3C4×#4111yescharacteristic
758C22×C3C4×#4111yescharacteristic
759C22×C3#51811yescharacteristic
760C22×C3#51811yescharacteristic
761C22×C3#51811yescharacteristic
762C22×C3#51811yescharacteristic
763C22×C3#53811yescharacteristic
764C22×C3#53811yescharacteristic
765C22×C3#53811yescharacteristic
766C22×C3#53811yescharacteristic
767C22×C3#53811yescharacteristic
768C22×C3#53811yescharacteristic
769C22×C3#53811yescharacteristic
770C22×C3#53811yescharacteristic
771C22×C3#54011yescharacteristic
772C22×C3#54011yescharacteristic
773C22×C3#54011yescharacteristic
774C22×C3#54011yescharacteristic
775C22×C3#55111yescharacteristic
776C22×C3#55111yescharacteristic
777C22×C3#55111yescharacteristic
778C22×C3#55111yescharacteristic
779C22×C3#55111yescharacteristic
780C22×C3#55311yescharacteristic
781C22×C3#55311yescharacteristic
782C22×C3#55311yescharacteristic
783C22×C3#55311yescharacteristic
784C22×C3#55311yescharacteristic
785C22×C3#55311yescharacteristic
786C22×C3#55911yescharacteristic
787C22×C3#56011yescharacteristic
788C22×C3#56011yescharacteristic
789C22×C3#56011yescharacteristic
790C22×C3H(3,𝔽4)11yescharacteristic
791C2×D3—24no—
792C2×D3—24no—
793C2×D3—24no—
794C2×D3—42no—
795C2×D3—42no—
796C2×D3—42no—
797C2×D3—42no—
798C2×D3—42no—
799C2×D3—42no—
800C2×D3—42no—
801C2×D3—42no—
802C2×D3—42no—
803C2×D3—42no—
804C2×D3—42no—
805C2×D3—42no—
806C2×D3—42no—
807C2×D3—42no—
808C2×D3—42no—
809C2×D3—42no—
810C2×D3—42no—
811C2×D3—42no—
812C2×D3—42no—
813C2×D3—81no—
814C2×D3—81no—
815C2×D3—81no—
816C2×D3—81no—
817C2×D3—81no—
818C2×D3—81no—
819C2×D3—81no—
820C2×D3—81no—
821C3×C4—42no—
822C3×C4—42no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—81no—
826C3×C4—81no—
827C3×C4—81no—
828Dic3—42no—
829Dic3—42no—
830Dic3—42no—
831Dic3—42no—
832Dic3—42no—
833Dic3—81no—
834C23—34no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—121no—
861C23—121no—
862C23—121no—
863C23—121no—
864C23—121no—
865C23—121no—
866C23—121no—
867C23—121no—
868C23—121no—
869C23—121no—
870C23—121no—
871C23—121no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23—121no—
877C23—121no—
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—
904C23C22×C4×D311yescharacteristic
905C23#100411yescharacteristic
906C23#100411yescharacteristic
907C23#100411yescharacteristic
908C23C2×#23911yescharacteristic
909C23D3×#4111yescharacteristic
910C23D3×#4111yescharacteristic
911C23D3×#4111yescharacteristic
912C23D3×#4111yescharacteristic
913C23D3×#4111yescharacteristic
914C23#100911yescharacteristic
915C23#100911yescharacteristic
916C23#100911yescharacteristic
917C23#100911yescharacteristic
918C23#100911yescharacteristic
919D4—1216no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
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—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—1216no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
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×C3#231211yescharacteristic
1013C2×C3#233311yescharacteristic
1014C2×C3#233311yescharacteristic
1015C2×C3#235311yescharacteristic
1016C2×C3#235311yescharacteristic
1017C2×C3#237411yescharacteristic
1018C2×C3#237511yescharacteristic
1019C2×C3#274911yescharacteristic
1020C2×C3#274911yescharacteristic
1021C2×C3#275311yescharacteristic
1022C2×C3#275311yescharacteristic
1023C2×C3#277811yescharacteristic
1024C2×C3#277811yescharacteristic
1025C2×C3#279711yescharacteristic
1026C2×C3#279711yescharacteristic
1027D3—44no—
1028D3—82no—
1029C22—64no—
1030C22—64no—
1031C22—64no—
1032C22—122no—
1033C22—122no—
1034C22—122no—
1035C22—122no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—122no—
1040C22—122no—
1041C22—122no—
1042C22—122no—
1043C22—122no—
1044C22—122no—
1045C22—122no—
1046C22—122no—
1047C22—122no—
1048C22—122no—
1049C22—122no—
1050C22—122no—
1051C22—241no—
1052C22—241no—
1053C22—241no—
1054C22—241no—
1055C22—241no—
1056C22—241no—
1057C22—241no—
1058C22—241no—
1059C22D3×#11711yescharacteristic
1060C22#552111yescharacteristic
1061C22#552211yescharacteristic
1062C22#554511yescharacteristic
1063C22#554511yescharacteristic
1064C22#554511yescharacteristic
1065C22C4×#23911yescharacteristic
1066C22#561311yescharacteristic
1067C22#561511yescharacteristic
1068C22#562011yescharacteristic
1069C22#563711yescharacteristic
1070C22#563711yescharacteristic
1071C22#564411yescharacteristic
1072C22#565711yescharacteristic
1073C22#566111yescharacteristic
1074C22#566311yescharacteristic
1075C22#566311yescharacteristic
1076C22#566411yescharacteristic
1077C22#566611yescharacteristic
1078C22#567811yescharacteristic
1079C22#567811yescharacteristic
1080C22#568311yescharacteristic
1081C22#569511yescharacteristic
1082C22#569511yescharacteristic
1083C22#569711yescharacteristic
1084C22#570411yescharacteristic
1085C22#570411yescharacteristic
1086C22#570411yescharacteristic
1087C22#570511yescharacteristic
1088C22#570511yescharacteristic
1089C22#570511yescharacteristic
1090C22#570911yescharacteristic
1091C22#570911yescharacteristic
1092C22#570911yescharacteristic
1093C22#571111yescharacteristic
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—122no—
1102C4—122no—
1103C4—122no—
1104C4—122no—
1105C4—122no—
1106C4—241no—
1107C3#1451611yescharacteristic, complemented, Sylow
1108C2—124no—
1109C2—242no—
1110C2#7429711yescharacteristic
1111C2#7495211yescharacteristic
1112C2#7497511yescharacteristic
1113C2#7530611yescharacteristic
1114C2#7582511yescharacteristic
1115C2#7583011yescharacteristic
1116C2#7584011yescharacteristic
1117C2#7737811yescharacteristic
1118C2#7760411yescharacteristic
1119C2#7772411yescharacteristic
1120C2#7772511yescharacteristic
1121C2#7825211yescharacteristic
1122C2#7839011yescharacteristic
1123C2#7839811yescharacteristic
1124C2#7842311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1443C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1443D3
hypocenterC3#14516
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. C3×#1443C2semidirect
3. #69429C2semidirect
4. #69429C2semidirect
7. (C2×D3)⋊#95C2semidirect
8. (C2×D3)⋊#95C2semidirect
9. #69418C2semidirect
10. #69408C2semidirect
11. #69408C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. #69402C2semidirect
15. #69401C2semidirect
52. #4665C4semidirect
55. #1443D3semidirect
1107. C3#14516semidirect

Maximal subgroups

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

subgroupindex
C2×#46652
C3×#14432
#694292
#694262
(C2×D3)⋊#952
#694182
#694082
#694022
#694012
#145163