Finite Group Databasebeta

← #10724534

Subgroups — #10724534

Order 768.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4960C211yesmaximal, characteristic
2C2×#4957C211yesmaximal, characteristic, complemented
3C2×#4958C211yesmaximal, characteristic, complemented
4C2×#4958C211yesmaximal, characteristic, complemented
5C2×#4940C211yesmaximal, characteristic, complemented
6C3×#1437C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic, complemented
8#71544C211yesmaximal, characteristic, complemented
9#71537C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69413C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14520—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
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#4960C418yescomplemented
53#4958—24no—
54#4958—24no—
55#4957—24no—
56#4940—24no—
57C2×#392—31no—
58C2×#390—31no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386—31no—
62#1442—31no—
63#1440—31no—
64#1438—31no—
65#1438—31no—
66#1438—31no—
67#1437—31no—
68#1437—31no—
69#1437D311yescharacteristic, complemented
70#1434—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—41no—
88C22×#67—41no—
89C22×#67—41no—
90C22×#67—41no—
91C22×#67—41no—
92C22×#67—41no—
93C22×#67C2×C414yes—
94C22×#67C2×C414yes—
95C23×Dic3—22no—
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—41no—
99C23×Dic3—41no—
100C23×Dic3—41no—
101C23×Dic3—41no—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C22×D12—41no—
109C22×D12—41no—
110C22×D12—41no—
111C22×D12—41no—
112C22×D12—41no—
113C22×D12—41no—
114C22×D12C2×C414yescomplemented
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—41no—
118C2×C3×C22⋊C4—41no—
119C2×C3×C22⋊C4—41no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4C2×C414yes—
123C2×C3×C22⋊C4D414yescomplemented
124C2×C3×C42—22no—
125C2×C3×C42—41no—
126C2×C3×C42—41no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—41no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4—41no—
149C2×(C2×D3)⋊C4—41no—
150C2×(C2×D3)⋊C4—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4C2×C414yescomplemented
159C2×(C2×D3)⋊C4C2×C414yescomplemented
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—41no—
163C2×C4×Dic3—22no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—41no—
166C3×#95—41no—
167C3×#95—41no—
168C3×#95—41no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—41no—
174C3⋊#95—41no—
175C3⋊#95—41no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95C2×C414yescomplemented
179C3⋊#95D414yescomplemented
180C23×D4—31no—
181C23×D4—31no—
182C23×D4—31no—
183C24×C4—31no—
184C22×C4⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C42—31no—
200C22×C42C2×D311yescharacteristic
201#392—38no—
202#390—64no—
203#388—64no—
204#386—64no—
205#386—64no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
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×C3—21no—
231C24×C3—21no—
232C24×C3C22×C412yes—
233C24×C3C2×D412yes—
234C24×C3#4112yes—
235C24×C3C2411yescharacteristic
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×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3C22×C412yes—
265C23×D3C22×C412yes—
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×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4C22×C412yes—
304C22×C3×C4C22×C412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—28no—
311C2×#67—44no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—44no—
317C2×#67—44no—
318C2×#67—44no—
319C2×#67—44no—
320C2×#67—44no—
321C2×#67—44no—
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×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—44no—
358C22×Dic3—44no—
359C22×Dic3—44no—
360C22×Dic3—44no—
361C22×Dic3—44no—
362C22×Dic3—44no—
363C22×Dic3—44no—
364C22×Dic3C22×C412yes—
365C22×Dic3C22×C412yes—
366C22×Dic3C2×D412yes—
367C22×Dic3C2×D412yes—
368C22×Dic3#4112yes—
369C22×Dic3#4112yes—
370C22×Dic3#4112yes—
371C2×D12—44no—
372C2×D12—44no—
373C2×D12—44no—
374C2×D12—44no—
375C2×D12—44no—
376C2×D12—44no—
377C2×D12—44no—
378C3×C22⋊C4—44no—
379C3×C22⋊C4—44no—
380C3×C22⋊C4—44no—
381C3×C42—44no—
382#217—44no—
383(C2×D3)⋊C4—28no—
384(C2×D3)⋊C4—44no—
385(C2×D3)⋊C4—44no—
386(C2×D3)⋊C4—44no—
387(C2×D3)⋊C4—44no—
388(C2×D3)⋊C4—44no—
389(C2×D3)⋊C4—44no—
390(C2×D3)⋊C4—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393Dic3⋊C4—44no—
394C4×Dic3—44no—
395C25—31no—
396C25—31no—
397C25C22×D311yescharacteristic
398C22×D4—34no—
399C22×D4—34no—
400C22×D4—34no—
401C22×D4—62no—
402C22×D4—62no—
403C22×D4—62no—
404C22×D4—62no—
405C22×D4—62no—
406C22×D4—62no—
407C22×D4—121no—
408C22×D4—121no—
409C22×D4—121no—
410C22×D4—121no—
411C22×D4—121no—
412C22×D4—121no—
413C22×D4—121no—
414C22×D4—121no—
415C22×D4—121no—
416C22×D4—121no—
417C22×D4—121no—
418C22×D4—121no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—62no—
426C23×C4—62no—
427C23×C4—62no—
428C23×C4—121no—
429C23×C4—121no—
430C23×C4—121no—
431C23×C4—121no—
432C23×C4C22×D311yescharacteristic
433C23×C4C22×D311yescharacteristic
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—121no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—34no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—41no—
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—121no—
467C2×C22⋊C4—121no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C22⋊C4—121no—
473C2×C22⋊C4—121no—
474C2×C22⋊C4—121no—
475C2×C22⋊C4—121no—
476C2×C22⋊C4—121no—
477C2×C22⋊C4—121no—
478C2×C22⋊C4—121no—
479C2×C22⋊C4—121no—
480C2×C22⋊C4—121no—
481C2×C22⋊C4C4×D314yes—
482C2×C22⋊C4D1214yescomplemented
483C2×C42—22no—
484C2×C42—41no—
485C2×C42—41no—
486C2×C42—62no—
487C2×C42—62no—
488C2×C42—121no—
489#95—34no—
490#95—34no—
491#95—41no—
492#95—41no—
493#95—41no—
494#95—62no—
495#95—62no—
496#95—62no—
497#95—62no—
498#95—121no—
499#95—121no—
500#95—121no—
501#95—121no—
502#95—121no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3C4×D414yes—
538C23×C3C23×C411yescharacteristic
539C23×C3C22×D411yescharacteristic
540C23×C3C22×D411yescharacteristic
541C23×C3C2×#4111yescharacteristic
542C23×C3C2×#4111yescharacteristic
543C23×C3C2×#4111yescharacteristic
544C23×C3C2×#4111yescharacteristic
545C23×C3H(5,𝔽2)11yescharacteristic
546C23×C3H(5,𝔽2)11yescharacteristic
547C23×C3H(5,𝔽2)11yescharacteristic
548C23×C3H(5,𝔽2)11yescharacteristic
549C23×C3H(5,𝔽2)11yescharacteristic
550C23×C3H(5,𝔽2)11yescharacteristic
551C23×C3H(5,𝔽2)11yescharacteristic
552C23×C3H(5,𝔽2)11yescharacteristic
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665#67—416no—
666#67—416no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—416no—
686C2×Dic3—41no—
687C2×Dic3—41no—
688C2×Dic3—41no—
689C2×Dic3—41no—
690C2×Dic3—41no—
691C2×Dic3—41no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3C4×D414yes—
710D12—416no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—32no—
724C24—32no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24—61no—
733C24—61no—
734C24—61no—
735C24—61no—
736C24—61no—
737C24—61no—
738C24—61no—
739C24—61no—
740C24—61no—
741C24—61no—
742C24—61no—
743C24—61no—
744C24—61no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24C2×C4×D312yes—
754C24C2×D1212yes—
755C24#23512yes—
756C24C23×D311yescharacteristic
757C2×D4—68no—
758C2×D4—68no—
759C2×D4—68no—
760C2×D4—124no—
761C2×D4—124no—
762C2×D4—124no—
763C2×D4—124no—
764C2×D4—124no—
765C2×D4—124no—
766C2×D4—124no—
767C2×D4—124no—
768C2×D4—124no—
769C2×D4—124no—
770C2×D4—124no—
771C2×D4—124no—
772C2×D4—124no—
773C2×D4—124no—
774C2×D4—124no—
775C2×D4—124no—
776C2×D4—124no—
777C2×D4—124no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—32no—
816C22×C4—32no—
817C22×C4—32no—
818C22×C4—32no—
819C22×C4—32no—
820C22×C4—32no—
821C22×C4—32no—
822C22×C4—61no—
823C22×C4—61no—
824C22×C4—61no—
825C22×C4—61no—
826C22×C4—61no—
827C22×C4—61no—
828C22×C4—61no—
829C22×C4—61no—
830C22×C4—61no—
831C22×C4—61no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—124no—
858C22×C4—124no—
859C22×C4—124no—
860C22×C4—124no—
861C22×C4—124no—
862C22×C4—124no—
863C22×C4—124no—
864C22×C4C2×C4×D312yes—
865C22×C4C2×C4×D312yes—
866C22×C4C2×D1212yes—
867C22×C4C2×D1212yes—
868C22×C4D3×D412yes—
869C4⋊C4—124no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—68no—
874C22⋊C4—124no—
875C22⋊C4—124no—
876C22⋊C4—124no—
877C22⋊C4—124no—
878C22⋊C4—124no—
879C22⋊C4—124no—
880C22⋊C4—124no—
881C22⋊C4—124no—
882C22⋊C4—124no—
883C22⋊C4—124no—
884C42—44no—
885C42—124no—
886C22×C3—24no—
887C22×C3—24no—
888C22×C3—24no—
889C22×C3—42no—
890C22×C3—42no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—42no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3C2×C4×D411yescharacteristic
902C22×C3C2×C4×D411yescharacteristic
903C22×C3C4×#4111yescharacteristic
904C22×C3#51811yescharacteristic
905C22×C3#51811yescharacteristic
906C22×C3#51811yescharacteristic
907C22×C3#51811yescharacteristic
908C22×C3#53411yescharacteristic
909C22×C3#53511yescharacteristic
910C22×C3#53511yescharacteristic
911C22×C3#53511yescharacteristic
912C22×C3#53811yescharacteristic
913C22×C3#53811yescharacteristic
914C22×C3#53811yescharacteristic
915C22×C3#53811yescharacteristic
916C22×C3#54011yescharacteristic
917C22×C3#54011yescharacteristic
918C22×C3#54011yescharacteristic
919C22×C3#54011yescharacteristic
920C22×C3D4211yescharacteristic
921C22×C3#54611yescharacteristic
922C22×C3#54611yescharacteristic
923C22×C3#54611yescharacteristic
924C22×C3#54611yescharacteristic
925C22×C3#54611yescharacteristic
926C22×C3#55011yescharacteristic
927C22×C3#55111yescharacteristic
928C22×C3#55311yescharacteristic
929C22×C3#55311yescharacteristic
930C22×C3#55311yescharacteristic
931C22×C3#55511yescharacteristic
932C22×C3#56011yescharacteristic
933C22×C3#56011yescharacteristic
934C22×C3#56011yescharacteristic
935C22×C3H(3,𝔽4)11yescharacteristic
936C2×D3—42no—
937C2×D3—42no—
938C2×D3—42no—
939C2×D3—42no—
940C2×D3—42no—
941C2×D3—42no—
942C2×D3—42no—
943C2×D3—42no—
944C2×D3—42no—
945C2×D3—42no—
946C2×D3—42no—
947C2×D3—42no—
948C2×D3—42no—
949C2×D3—42no—
950C2×D3—81no—
951C2×D3—81no—
952C2×D3—81no—
953C2×D3—81no—
954C2×D3—81no—
955C2×D3—81no—
956C2×D3—81no—
957C2×D3—81no—
958C2×D3—81no—
959C2×D3—81no—
960C2×D3—81no—
961C2×D3—81no—
962C2×D3—81no—
963C2×D3—81no—
964C2×D3—81no—
965C2×D3—81no—
966C3×C4—42no—
967C3×C4—42no—
968C3×C4—42no—
969C3×C4—42no—
970C3×C4—42no—
971C3×C4—81no—
972Dic3—24no—
973Dic3—42no—
974Dic3—42no—
975Dic3—42no—
976Dic3—42no—
977Dic3—81no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—62no—
1013C23—62no—
1014C23—62no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—62no—
1019C23—62no—
1020C23—62no—
1021C23—62no—
1022C23—62no—
1023C23—62no—
1024C23—62no—
1025C23—62no—
1026C23—121no—
1027C23—121no—
1028C23—121no—
1029C23—121no—
1030C23—121no—
1031C23—121no—
1032C23—121no—
1033C23—121no—
1034C23—121no—
1035C23—121no—
1036C23—121no—
1037C23—121no—
1038C23—121no—
1039C23—121no—
1040C23—121no—
1041C23—121no—
1042C23—121no—
1043C23—121no—
1044C23—121no—
1045C23—121no—
1046C23—121no—
1047C23—121no—
1048C23—121no—
1049C23—121no—
1050C23—121no—
1051C23—121no—
1052C23—121no—
1053C23—121no—
1054C23—121no—
1055C23—121no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—121no—
1060C23—121no—
1061C23—121no—
1062C23—121no—
1063C23—121no—
1064C23—121no—
1065C23—121no—
1066C23—121no—
1067C23—121no—
1068C23—121no—
1069C23—121no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23C4×D1214yes—
1083C23C22×C4×D311yescharacteristic
1084C23C22×D1211yescharacteristic
1085C23C2×#23511yescharacteristic
1086C23C2×D3×D411yescharacteristic
1087C23#100411yescharacteristic
1088C23#100411yescharacteristic
1089C23#100411yescharacteristic
1090C23#100411yescharacteristic
1091C23#100411yescharacteristic
1092C23D3×#4111yescharacteristic
1093C23D3×#4111yescharacteristic
1094C23D3×#4111yescharacteristic
1095C23#100911yescharacteristic
1096C23#100911yescharacteristic
1097C23#100911yescharacteristic
1098D4—1216no—
1099D4—1216no—
1100D4—1216no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—34no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—62no—
1145C2×C4—62no—
1146C2×C4—62no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
1151C2×C4—62no—
1152C2×C4—62no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—62no—
1157C2×C4—62no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—1216no—
1163C2×C4—121no—
1164C2×C4—121no—
1165C2×C4—121no—
1166C2×C4—121no—
1167C2×C4—121no—
1168C2×C4—121no—
1169C2×C4—121no—
1170C2×C4—121no—
1171C2×C4—121no—
1172C2×C4—121no—
1173C2×C4—121no—
1174C2×C4—121no—
1175C2×C4—121no—
1176C2×C4—121no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4—121no—
1180C2×C4—121no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C3—44no—
1187C2×C3#232111yescharacteristic
1188C2×C3#232811yescharacteristic
1189C2×C3#233311yescharacteristic
1190C2×C3#235811yescharacteristic
1191C2×C3#236311yescharacteristic
1192C2×C3#236411yescharacteristic
1193C2×C3#237511yescharacteristic
1194C2×C3#267011yescharacteristic
1195C2×C3#267311yescharacteristic
1196C2×C3#269911yescharacteristic
1197C2×C3#270311yescharacteristic
1198C2×C3#270311yescharacteristic
1199C2×C3#271411yescharacteristic
1200C2×C3#275311yescharacteristic
1201C2×C3#275611yescharacteristic
1202D3—82no—
1203D3—82no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—122no—
1220C22—122no—
1221C22—122no—
1222C22—122no—
1223C22—122no—
1224C22—122no—
1225C22—122no—
1226C22—122no—
1227C22—122no—
1228C22—122no—
1229C22—122no—
1230C22—122no—
1231C22—122no—
1232C22—122no—
1233C22—241no—
1234C22—241no—
1235C22—241no—
1236C22—241no—
1237C22—241no—
1238C22—241no—
1239C22—241no—
1240C22—241no—
1241C22—241no—
1242C22—241no—
1243C22—241no—
1244C22—241no—
1245C22—241no—
1246C22—241no—
1247C22—241no—
1248C22—241no—
1249C22C2×C4×D1211yescharacteristic
1250C22#548611yescharacteristic
1251C22#549011yescharacteristic
1252C22#549311yescharacteristic
1253C22#552211yescharacteristic
1254C22#552511yescharacteristic
1255C22#552711yescharacteristic
1256C22#554011yescharacteristic
1257C22#554011yescharacteristic
1258C22C4×D3×D411yescharacteristic
1259C22#554511yescharacteristic
1260C22#554511yescharacteristic
1261C22#554511yescharacteristic
1262C22D4×D1211yescharacteristic
1263C22#555411yescharacteristic
1264C22#555411yescharacteristic
1265C22#555411yescharacteristic
1266C22#556011yescharacteristic
1267C22#556011yescharacteristic
1268C22#559211yescharacteristic
1269C22#559911yescharacteristic
1270C22#560711yescharacteristic
1271C22#561511yescharacteristic
1272C22#561511yescharacteristic
1273C22#562011yescharacteristic
1274C22#562011yescharacteristic
1275C22#565411yescharacteristic
1276C22#566311yescharacteristic
1277C22#566311yescharacteristic
1278C22#567011yescharacteristic
1279C22#567811yescharacteristic
1280C22#568311yescharacteristic
1281C22#570411yescharacteristic
1282C22#570911yescharacteristic
1283C22#572011yescharacteristic
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—64no—
1290C4—81no—
1291C4—122no—
1292C4—122no—
1293C4—122no—
1294C4—122no—
1295C4—241no—
1296C3#1452011yescharacteristic, complemented, Sylow
1297C2—44no—
1298C2—242no—
1299C2—242no—
1300C2#7347111yescharacteristic
1301C2#7356911yescharacteristic
1302C2#7357711yescharacteristic
1303C2#7466711yescharacteristic
1304C2#7479211yescharacteristic
1305C2#7481411yescharacteristic
1306C2#7548011yescharacteristic
1307C2#7573511yescharacteristic
1308C2#7574111yescharacteristic
1309C2#7583011yescharacteristic
1310C2#7591311yescharacteristic
1311C2#7592711yescharacteristic
1312C2#7638511yescharacteristic
1313C2#7639411yescharacteristic
1314C2#7643411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC2×#4960C2
hypercenter#1437D3
hypocenterC3#14520
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#4957C2semidirect
3. C2×#4958C2semidirect
4. C2×#4958C2semidirect
5. C2×#4940C2semidirect
6. C3×#1437C2semidirect
7. #71550C2semidirect
8. #71544C2semidirect
9. #71537C2semidirect
10. #69429C2semidirect
11. #69426C2semidirect
12. #69426C2semidirect
13. #69413C2semidirect
14. #69408C2semidirect
15. #69402C2semidirect
52. #4960C4semidirect
69. #1437D3semidirect
114. C22×D12C2×C4semidirect
123. C2×C3×C22⋊C4D4semidirect
158. C2×(C2×D3)⋊C4C2×C4semidirect
159. C2×(C2×D3)⋊C4C2×C4semidirect
178. C3⋊#95C2×C4semidirect
179. C3⋊#95D4semidirect
482. C2×C22⋊C4D12semidirect
1296. C3#14520semidirect

Maximal subgroups

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

subgroupindex
C2×#49602
C2×#49572
C2×#49582
C2×#49402
C3×#14372
#715502
#715442
#715372
#694292
#694262
#694132
#694082
#694022
#145203