Finite Group Databasebeta

← #10724524

Subgroups — #10724524

Order 768.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5213C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic, complemented
3C2×#4960C211yesmaximal, characteristic
4C2×#4956C211yesmaximal, characteristic, complemented
5C2×#4957C211yesmaximal, characteristic, complemented
6C2×#4665C211yesmaximal, characteristic, complemented
7C2×#4668C211yesmaximal, characteristic, complemented
8C3×C22⋊#95C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69413C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14519—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42#5213—24no—
43#5213—24no—
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
54#4960C418yescomplemented
55#4957—24no—
56#4956—24no—
57#4668—24no—
58#4665—24no—
59C2×#392—31no—
60C2×#390—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#386—31no—
65C2×#385—31no—
66#1442—31no—
67#1440—31no—
68#1439—31no—
69#1439—31no—
70#1438—31no—
71#1437—31no—
72#1434—31no—
73C22⋊#95D311yescharacteristic, complemented
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—41no—
81C23×C3×C4—41no—
82C23×C3×C4—41no—
83C23×C3×C4—41no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—41no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67—41no—
102C22×#67C2×C414yes—
103C22×#67C2×C414yescomplemented
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C22×D12—22no—
111C22×D12—22no—
112C22×D12—41no—
113C22×D12—41no—
114C22×D12—41no—
115C22×D12—41no—
116C22×D12C2×C414yescomplemented
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—41no—
121C22×C4×D3—41no—
122C22×C4×D3—41no—
123C22×C4×D3—41no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
128C2×C3×C22⋊C4C2×C414yescomplemented
129C2×C3×C22⋊C4D414yescomplemented
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—41no—
135C2×#217—41no—
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—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
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)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4C2×C414yescomplemented
161C2×(C2×D3)⋊C4C2×C414yescomplemented
162C2×(C2×D3)⋊C4D414yescomplemented
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3—41no—
165C2×C4⋊Dic3—41no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—41no—
169C2×C4×Dic3—22no—
170C2×C4×Dic3—22no—
171C2×C4×Dic3—41no—
172C3×#95—22no—
173C3×#95—22no—
174C3×#95—41no—
175C3×#95—41no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—41no—
183C3⋊#95—41no—
184C3⋊#95C2×C414yescomplemented
185C3⋊#95D414yescomplemented
186C23×D4—31no—
187C23×D4—31no—
188C23×D4—31no—
189C24×C4—31no—
190C24×C4C2×D311yescharacteristic
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4C2×D311yescharacteristic
205C22×C22⋊C4C2×D311yescharacteristic
206C22×C42—31no—
207#392—38no—
208#390—64no—
209#386—64no—
210#386—64no—
211#386—64no—
212#386—64no—
213#385—64no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3C22×C412yes—
241C24×C3C2×D412yes—
242C24×C3#4112yes—
243C24×C3C2411yescharacteristic
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×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3C22×C412yes—
271C23×D3C22×C412yes—
272C23×D3C2×D412yes—
273C23×D3#4112yes—
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×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—44no—
311C22×C3×C4—44no—
312C22×C3×C4—44no—
313C22×C3×C4—44no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4C22×C412yes—
318C22×C3×C4C22×C412yes—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C2×#67—28no—
324C2×#67—28no—
325C2×#67—28no—
326C2×#67—28no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
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—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3C22×C412yes—
374C22×Dic3C22×C412yes—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378C22×Dic3#4112yes—
379C2×D12—28no—
380C2×D12—44no—
381C2×D12—44no—
382C2×D12—44no—
383C2×D12—44no—
384C2×D12—44no—
385C2×D12—44no—
386C2×C4×D3—44no—
387C2×C4×D3—44no—
388C2×C4×D3—44no—
389C2×C4×D3—44no—
390C2×C4×D3—44no—
391C2×C4×D3—44no—
392C2×C4×D3—44no—
393C3×C22⋊C4—44no—
394C3×C22⋊C4—44no—
395#217—44no—
396#217—44no—
397(C2×D3)⋊C4—28no—
398(C2×D3)⋊C4—44no—
399(C2×D3)⋊C4—44no—
400(C2×D3)⋊C4—44no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405(C2×D3)⋊C4—44no—
406C4⋊Dic3—44no—
407Dic3⋊C4—44no—
408C4×Dic3—44no—
409C25—31no—
410C25—31no—
411C25C22×D311yescharacteristic
412C22×D4—34no—
413C22×D4—34no—
414C22×D4—34no—
415C22×D4—62no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—121no—
426C22×D4—121no—
427C22×D4—121no—
428C22×D4—121no—
429C22×D4—121no—
430C22×D4—121no—
431C22×D4—121no—
432C22×D4—121no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—41no—
443C23×C4—41no—
444C23×C4—41no—
445C23×C4—41no—
446C23×C4—62no—
447C23×C4—62no—
448C23×C4—62no—
449C23×C4—121no—
450C23×C4—121no—
451C23×C4—121no—
452C23×C4—121no—
453C23×C4C22×D311yescharacteristic
454C23×C4C22×D311yescharacteristic
455C23×C4C22×D311yescharacteristic
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—121no—
463C2×C4⋊C4—121no—
464C2×C4⋊C4—121no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—34no—
468C2×C22⋊C4—41no—
469C2×C22⋊C4—41no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4—41no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—121no—
489C2×C22⋊C4—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4C4×D314yescomplemented
503C2×C22⋊C4D1214yescomplemented
504C2×C42—62no—
505C2×C42—62no—
506C2×C42—121no—
507#95—22no—
508#95—22no—
509#95—34no—
510#95—34no—
511#95—41no—
512#95—41no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—121no—
520#95—121no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3C4×D414yes—
556C23×C3C23×C411yescharacteristic
557C23×C3C22×D411yescharacteristic
558C23×C3C22×D411yescharacteristic
559C23×C3C22×D411yescharacteristic
560C23×C3C2×#4111yescharacteristic
561C23×C3C2×#4111yescharacteristic
562C23×C3C2×#4111yescharacteristic
563C23×C3H(5,𝔽2)11yescharacteristic
564C23×C3H(5,𝔽2)11yescharacteristic
565C23×C3H(5,𝔽2)11yescharacteristic
566C23×C3H(5,𝔽2)11yescharacteristic
567C23×C3H(5,𝔽2)11yescharacteristic
568C23×C3H(5,𝔽2)11yescharacteristic
569C23×C3H(5,𝔽2)11yescharacteristic
570C23×C32−1+411yescharacteristic
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
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—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3C4×D414yes—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—416no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684#67—416no—
685#67—416no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
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×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3C4×D414yes—
728D12—416no—
729C4×D3—416no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—32no—
743C24—32no—
744C24—32no—
745C24—32no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24—61no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24C2×C4×D312yes—
773C24C2×D1212yes—
774C24#23512yes—
775C24C23×D311yescharacteristic
776C2×D4—68no—
777C2×D4—68no—
778C2×D4—68no—
779C2×D4—68no—
780C2×D4—68no—
781C2×D4—124no—
782C2×D4—124no—
783C2×D4—124no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—124no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
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—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—32no—
834C22×C4—32no—
835C22×C4—32no—
836C22×C4—32no—
837C22×C4—32no—
838C22×C4—32no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
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—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—124no—
883C22×C4—124no—
884C22×C4—124no—
885C22×C4—124no—
886C22×C4—124no—
887C22×C4—124no—
888C22×C4—124no—
889C22×C4C2×C4×D312yes—
890C22×C4C2×C4×D312yes—
891C22×C4C2×D1212yes—
892C22×C4C2×D1212yes—
893C22×C4D3×D412yes—
894C22×C4D3×D412yes—
895C4⋊C4—124no—
896C4⋊C4—124no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—68no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C22⋊C4—124no—
905C22⋊C4—124no—
906C22⋊C4—124no—
907C22⋊C4—124no—
908C22⋊C4—124no—
909C22⋊C4—124no—
910C42—124no—
911C22×C3—24no—
912C22×C3—24no—
913C22×C3—24no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3C2×C4×D411yescharacteristic
927C22×C3C2×C4×D411yescharacteristic
928C22×C3C2×C4×D411yescharacteristic
929C22×C3#51811yescharacteristic
930C22×C3#51811yescharacteristic
931C22×C3#51811yescharacteristic
932C22×C3#52011yescharacteristic
933C22×C3#53411yescharacteristic
934C22×C3#53411yescharacteristic
935C22×C3#53511yescharacteristic
936C22×C3#53511yescharacteristic
937C22×C3#53511yescharacteristic
938C22×C3#53711yescharacteristic
939C22×C3#53811yescharacteristic
940C22×C3#53811yescharacteristic
941C22×C3#53811yescharacteristic
942C22×C3#53911yescharacteristic
943C22×C3#54011yescharacteristic
944C22×C3#54011yescharacteristic
945C22×C3D4211yescharacteristic
946C22×C3D4211yescharacteristic
947C22×C3D4211yescharacteristic
948C22×C3#54611yescharacteristic
949C22×C3#54611yescharacteristic
950C22×C3#54611yescharacteristic
951C22×C3#54611yescharacteristic
952C22×C3#54711yescharacteristic
953C22×C3#54811yescharacteristic
954C22×C3#55111yescharacteristic
955C22×C3#55111yescharacteristic
956C22×C3#55311yescharacteristic
957C22×C3#56011yescharacteristic
958C22×C3#56011yescharacteristic
959C22×C3#56211yescharacteristic
960C22×C3#56211yescharacteristic
961C2×D3—24no—
962C2×D3—24no—
963C2×D3—24no—
964C2×D3—42no—
965C2×D3—42no—
966C2×D3—42no—
967C2×D3—42no—
968C2×D3—42no—
969C2×D3—42no—
970C2×D3—42no—
971C2×D3—42no—
972C2×D3—42no—
973C2×D3—42no—
974C2×D3—42no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—81no—
984C2×D3—81no—
985C2×D3—81no—
986C2×D3—81no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C3×C4—42no—
992C3×C4—42no—
993C3×C4—42no—
994C3×C4—42no—
995C3×C4—42no—
996C3×C4—42no—
997Dic3—24no—
998Dic3—42no—
999Dic3—42no—
1000Dic3—42no—
1001Dic3—81no—
1002Dic3—81no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—34no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—62no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—62no—
1048C23—62no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
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—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23C4×D1214yes—
1108C23C22×C4×D311yescharacteristic
1109C23C22×D1211yescharacteristic
1110C23C2×#23511yescharacteristic
1111C23C2×D3×D411yescharacteristic
1112C23C2×D3×D411yescharacteristic
1113C23#100411yescharacteristic
1114C23#100411yescharacteristic
1115C23#100411yescharacteristic
1116C23#100411yescharacteristic
1117C23#100411yescharacteristic
1118C23#100711yescharacteristic
1119C23D3×#4111yescharacteristic
1120C23D3×#4111yescharacteristic
1121C23#100911yescharacteristic
1122C23#100911yescharacteristic
1123D4—1216no—
1124D4—1216no—
1125D4—1216no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—34no—
1145C2×C4—416no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—1216no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C3—44no—
1213C2×C3#232111yescharacteristic
1214C2×C3#232511yescharacteristic
1215C2×C3#232811yescharacteristic
1216C2×C3#235811yescharacteristic
1217C2×C3#235811yescharacteristic
1218C2×C3#236111yescharacteristic
1219C2×C3#237711yescharacteristic
1220C2×C3#266911yescharacteristic
1221C2×C3#267111yescharacteristic
1222C2×C3#267611yescharacteristic
1223C2×C3#267811yescharacteristic
1224C2×C3#268811yescharacteristic
1225C2×C3#269611yescharacteristic
1226C2×C3#270611yescharacteristic
1227C2×C3#274911yescharacteristic
1228D3—44no—
1229D3—82no—
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—64no—
1246C22—64no—
1247C22—64no—
1248C22—122no—
1249C22—122no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—122no—
1254C22—122no—
1255C22—122no—
1256C22—122no—
1257C22—122no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—241no—
1268C22—241no—
1269C22—241no—
1270C22—241no—
1271C22—241no—
1272C22—241no—
1273C22—241no—
1274C22—241no—
1275C22C2×C4×D1211yescharacteristic
1276C22#548611yescharacteristic
1277C22#549011yescharacteristic
1278C22#549011yescharacteristic
1279C22#549311yescharacteristic
1280C22#549411yescharacteristic
1281C22#550411yescharacteristic
1282C22#551011yescharacteristic
1283C22#551511yescharacteristic
1284C22#552711yescharacteristic
1285C22#552711yescharacteristic
1286C22C4×D3×D411yescharacteristic
1287C22C4×D3×D411yescharacteristic
1288C22#554511yescharacteristic
1289C22#554511yescharacteristic
1290C22D4×D1211yescharacteristic
1291C22D4×D1211yescharacteristic
1292C22#555411yescharacteristic
1293C22#555411yescharacteristic
1294C22#558911yescharacteristic
1295C22#559011yescharacteristic
1296C22#559211yescharacteristic
1297C22#559511yescharacteristic
1298C22#560711yescharacteristic
1299C22#560711yescharacteristic
1300C22#561311yescharacteristic
1301C22#561511yescharacteristic
1302C22#563111yescharacteristic
1303C22#563311yescharacteristic
1304C22#564711yescharacteristic
1305C22#564711yescharacteristic
1306C22#565711yescharacteristic
1307C22#566111yescharacteristic
1308C22#566311yescharacteristic
1309C22#566611yescharacteristic
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—64no—
1317C4—122no—
1318C4—122no—
1319C4—122no—
1320C4—241no—
1321C4—241no—
1322C3#1451911yescharacteristic, complemented, Sylow
1323C2—44no—
1324C2—124no—
1325C2—242no—
1326C2#7333311yescharacteristic
1327C2#7357711yescharacteristic
1328C2#7357711yescharacteristic
1329C2#7385811yescharacteristic
1330C2#7396411yescharacteristic
1331C2#7396911yescharacteristic
1332C2#7414111yescharacteristic
1333C2#7439711yescharacteristic
1334C2#7440111yescharacteristic
1335C2#7450911yescharacteristic
1336C2#7462811yescharacteristic
1337C2#7466711yescharacteristic
1338C2#7479911yescharacteristic
1339C2#7487611yescharacteristic
1340C2#7491211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC2×#4960C2
hypercenterC22⋊#95D3
hypocenterC3#14519
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#5213C2semidirect
2. C2×#5213C2semidirect
4. C2×#4956C2semidirect
5. C2×#4957C2semidirect
6. C2×#4665C2semidirect
7. C2×#4668C2semidirect
8. C3×C22⋊#95C2semidirect
9. #71546C2semidirect
10. #69429C2semidirect
11. #69427C2semidirect
12. #69426C2semidirect
13. #69413C2semidirect
14. #69408C2semidirect
15. #69402C2semidirect
54. #4960C4semidirect
73. C22⋊#95D3semidirect
103. C22×#67C2×C4semidirect
116. C22×D12C2×C4semidirect
128. C2×C3×C22⋊C4C2×C4semidirect
129. C2×C3×C22⋊C4D4semidirect
160. C2×(C2×D3)⋊C4C2×C4semidirect
161. C2×(C2×D3)⋊C4C2×C4semidirect
162. C2×(C2×D3)⋊C4D4semidirect
184. C3⋊#95C2×C4semidirect
185. C3⋊#95D4semidirect
502. C2×C22⋊C4C4×D3semidirect
503. C2×C22⋊C4D12semidirect
1322. C3#14519semidirect

Maximal subgroups

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

subgroupindex
C2×#52132
C2×#49602
C2×#49562
C2×#49572
C2×#46652
C2×#46682
C3×C22⋊#952
#715462
#694292
#694272
#694262
#694132
#694082
#694022
#145193