Finite Group Databasebeta

← #10733176

Subgroups — #10733176

Order 768.

2834 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4992C211yesmaximal, characteristic, complemented
2C2×#4990C211yesmaximal, characteristic, complemented
3C2×#4955C211yesmaximal, characteristic
4C2×#4955C211yesmaximal, characteristic
5C2×#4955C211yesmaximal, characteristic
6C2×#4669C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69427C211yesmaximal, characteristic, complemented
15#69427C211yesmaximal, characteristic, complemented
16#15282—31nomaximal, Sylow
17C25×D3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic, complemented
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic, complemented
38C22×Dic3⋊C4C2211yescharacteristic, complemented
39C22×C4×Dic3C2211yescharacteristic, complemented
40C2×C3×#95C2211yescharacteristic, complemented
41C2×C3×#95C2211yescharacteristic, complemented
42C2×C3×#95C2211yescharacteristic, complemented
43C2×C3⋊#95C2211yescharacteristic, complemented
44C2×C3⋊#95C2211yescharacteristic, complemented
45C2×C3⋊#95C2211yescharacteristic, complemented
46C2×C3⋊#95C2211yescharacteristic, complemented
47C2×C3⋊#95C2211yescharacteristic, complemented
48C2×C3⋊#95C2211yescharacteristic, complemented
49C2×C3⋊#95C2211yescharacteristic, complemented
50C2×C3⋊#95C2211yescharacteristic, complemented
51C2×C3⋊#95C2211yescharacteristic, complemented
52#4992—24no—
53#4990—24no—
54#4955—24no—
55#4955—24no—
56#4955—24no—
57#4669—24no—
58C2×#397—31no—
59C2×#388—31no—
60C2×#388—31no—
61C2×#379—31no—
62C2×#379—31no—
63C2×#379—31no—
64#1440—31no—
65#1440—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439D311yescharacteristic, complemented
72#1437—31no—
73C25×C3C2311yescharacteristic
74C24×D3—22no—
75C24×D3—22no—
76C24×D3—22no—
77C24×D3—22no—
78C24×D3—22no—
79C24×D3—22no—
80C24×D3—22no—
81C24×D3—22no—
82C24×D3—22no—
83C24×D3—41no—
84C24×D3—41no—
85C24×D3—41no—
86C24×D3—41no—
87C24×D3—41no—
88C24×D3—41no—
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—41no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—41no—
122C2×#217—41no—
123C2×#217—41no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
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—22no—
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)⋊C4D414yes—
158C2×(C2×D3)⋊C4D414yes—
159C2×(C2×D3)⋊C4D414yes—
160C2×C4⋊Dic3—41no—
161C2×C4⋊Dic3—41no—
162C2×C4⋊Dic3—41no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—41no—
165C2×Dic3⋊C4—41no—
166C2×C4×Dic3—22no—
167C2×C4×Dic3—22no—
168C2×C4×Dic3—41no—
169C3×#95—22no—
170C3×#95—41no—
171C3×#95—41no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—41no—
179C3⋊#95—41no—
180C3⋊#95—41no—
181C26—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4C2×D311yescharacteristic, complemented
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⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C42—31no—
204#397—64no—
205#388—64no—
206#388—64no—
207#379—64no—
208#379—64no—
209#379—64no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95C2×D311yescharacteristic, complemented
220C2×#95C2×D311yescharacteristic, complemented
221C2×#95C2×D311yescharacteristic, complemented
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×C3—21no—
233C24×C3—21no—
234C24×C3#4112yes—
235C24×C3#4112yes—
236C24×C3#4112yes—
237C24×C3C2411yescharacteristic
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—28no—
263C23×D3—28no—
264C23×D3—28no—
265C23×D3—44no—
266C23×D3—44no—
267C23×D3—44no—
268C23×D3—44no—
269C23×D3—44no—
270C23×D3—44no—
271C23×D3—44no—
272C23×D3—44no—
273C23×D3—44no—
274C23×D3—44no—
275C23×D3—44no—
276C23×D3—44no—
277C23×D3—44no—
278C23×D3—44no—
279C23×D3—44no—
280C23×D3—44no—
281C23×D3—44no—
282C23×D3—44no—
283C23×D3—44no—
284C23×D3—44no—
285C23×D3—44no—
286C23×D3—44no—
287C23×D3—44no—
288C23×D3—44no—
289C23×D3—44no—
290C23×D3—44no—
291C23×D3—44no—
292C23×D3—44no—
293C23×D3—44no—
294C23×D3—44no—
295C23×D3—44no—
296C23×D3—44no—
297C23×D3C2×D412yes—
298C23×D3C2×D412yes—
299C23×D3C2×D412yes—
300C23×D3#4112yes—
301C23×D3#4112yes—
302C23×D3#4112yes—
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—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4C2×D412yes—
343C22×C3×C4C2×D412yes—
344C22×C3×C4C2×D412yes—
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×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C3×C4⋊C4—44no—
388C3×C22⋊C4—44no—
389C3×C22⋊C4—44no—
390C3×C22⋊C4—44no—
391#217—44no—
392#217—44no—
393#217—44no—
394(C2×D3)⋊C4—28no—
395(C2×D3)⋊C4—28no—
396(C2×D3)⋊C4—44no—
397(C2×D3)⋊C4—44no—
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—
411C25—62no—
412C25—62no—
413C25—62no—
414C25—62no—
415C25—62no—
416C25—62no—
417C25—62no—
418C25—62no—
419C25—62no—
420C25—121no—
421C25—121no—
422C25—121no—
423C25—121no—
424C25—121no—
425C25—121no—
426C25C22×D311yescharacteristic
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—31no—
433C23×C4C22×D311yescharacteristic
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—121no—
444C2×C4⋊C4—121no—
445C2×C4⋊C4—121no—
446C2×C4⋊C4—121no—
447C2×C4⋊C4—121no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—41no—
458C2×C22⋊C4—41no—
459C2×C22⋊C4—41no—
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—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
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—121no—
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×C42—62no—
503C2×C42—62no—
504C2×C42—121no—
505#95—22no—
506#95—41no—
507#95—41no—
508#95—62no—
509#95—62no—
510#95—62no—
511#95—62no—
512#95—62no—
513#95—62no—
514#95—121no—
515#95—121no—
516#95—121no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
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—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
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#12614yes—
552C23×C3C22×D411yescharacteristic
553C23×C3C22×D411yescharacteristic
554C23×C3C22×D411yescharacteristic
555C23×C3C2×#4111yescharacteristic
556C23×C3C2×#4111yescharacteristic
557C23×C3C2×#4111yescharacteristic
558C23×C3C2×#4111yescharacteristic
559C23×C3C2×#4111yescharacteristic
560C23×C3C2×#4111yescharacteristic
561C23×C3H(5,𝔽2)11yescharacteristic
562C23×C3H(5,𝔽2)11yescharacteristic
563C23×C3H(5,𝔽2)11yescharacteristic
564C23×C3H(5,𝔽2)11yescharacteristic
565C23×C3H(5,𝔽2)11yescharacteristic
566C23×C3H(5,𝔽2)11yescharacteristic
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
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—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—416no—
604C22×D3—416no—
605C22×D3—416no—
606C22×D3—416no—
607C22×D3—416no—
608C22×D3—416no—
609C22×D3—416no—
610C22×D3—416no—
611C22×D3—416no—
612C22×D3—416no—
613C22×D3—416no—
614C22×D3—416no—
615C22×D3—416no—
616C22×D3—416no—
617C22×D3—416no—
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×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3#12114yes—
651C22×D3#12314yes—
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—22no—
660C2×C3×C4—22no—
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—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
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×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—32no—
749C24—32no—
750C24—32no—
751C24—32no—
752C24—32no—
753C24—32no—
754C24—68no—
755C24—68no—
756C24—68no—
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—
772C24—61no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—124no—
782C24—124no—
783C24—124no—
784C24—124no—
785C24—124no—
786C24—124no—
787C24—124no—
788C24—124no—
789C24—124no—
790C24—124no—
791C24—124no—
792C24—124no—
793C24—124no—
794C24—124no—
795C24—124no—
796C24—124no—
797C24—124no—
798C24—124no—
799C24—124no—
800C24—124no—
801C24—124no—
802C24—124no—
803C24—124no—
804C24—124no—
805C24—124no—
806C24—124no—
807C24—124no—
808C24—124no—
809C24—124no—
810C24—124no—
811C24—124no—
812C24—124no—
813C24#23512yes—
814C24#23712yes—
815C24#23912yes—
816C24C23×D311yescharacteristic
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—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—32no—
857C22×C4—32no—
858C22×C4—32no—
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—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4D3×D412yes—
899C22×C4D3×D412yes—
900C22×C4D3×D412yes—
901C4⋊C4—44no—
902C4⋊C4—124no—
903C4⋊C4—124no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—68no—
908C22⋊C4—68no—
909C22⋊C4—124no—
910C22⋊C4—124no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22⋊C4—124no—
916C22⋊C4—124no—
917C22⋊C4—124no—
918C22⋊C4—124no—
919C22⋊C4—124no—
920C22⋊C4—124no—
921C22⋊C4—124no—
922C42—124no—
923C22×C3—24no—
924C22×C3—24no—
925C22×C3—24no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3C2×#12111yescharacteristic
939C22×C3C2×#12311yescharacteristic
940C22×C3#52511yescharacteristic
941C22×C3#52511yescharacteristic
942C22×C3#52511yescharacteristic
943C22×C3C2×#12611yescharacteristic
944C22×C3#53411yescharacteristic
945C22×C3#53511yescharacteristic
946C22×C3#53511yescharacteristic
947C22×C3#53811yescharacteristic
948C22×C3#53811yescharacteristic
949C22×C3#53811yescharacteristic
950C22×C3#53811yescharacteristic
951C22×C3#53811yescharacteristic
952C22×C3#53811yescharacteristic
953C22×C3D4211yescharacteristic
954C22×C3D4211yescharacteristic
955C22×C3#54611yescharacteristic
956C22×C3#54611yescharacteristic
957C22×C3#54611yescharacteristic
958C22×C3#54611yescharacteristic
959C22×C3#54611yescharacteristic
960C22×C3#54611yescharacteristic
961C22×C3#54611yescharacteristic
962C22×C3#54611yescharacteristic
963C22×C3#55111yescharacteristic
964C22×C3#55111yescharacteristic
965C22×C3#55111yescharacteristic
966C22×C3#55111yescharacteristic
967C22×C3#55111yescharacteristic
968C22×C3#55111yescharacteristic
969C22×C3#55111yescharacteristic
970C22×C3#55111yescharacteristic
971C22×C3#56011yescharacteristic
972C22×C3H(3,𝔽4)11yescharacteristic
973C2×D3—24no—
974C2×D3—24no—
975C2×D3—24no—
976C2×D3—24no—
977C2×D3—24no—
978C2×D3—24no—
979C2×D3—464no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—42no—
1004C3×C4—42no—
1005C3×C4—42no—
1006C3×C4—42no—
1007C3×C4—81no—
1008C3×C4—81no—
1009C3×C4—81no—
1010Dic3—42no—
1011Dic3—42no—
1012Dic3—42no—
1013Dic3—81no—
1014Dic3—81no—
1015Dic3—81no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—34no—
1035C23—34no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—62no—
1084C23—62no—
1085C23—62no—
1086C23—62no—
1087C23—62no—
1088C23—1216no—
1089C23—1216no—
1090C23—1216no—
1091C23—1216no—
1092C23—1216no—
1093C23—1216no—
1094C23—1216no—
1095C23—1216no—
1096C23—1216no—
1097C23—1216no—
1098C23—1216no—
1099C23—1216no—
1100C23—1216no—
1101C23—1216no—
1102C23—1216no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23—121no—
1128C23—121no—
1129C23—121no—
1130C23—121no—
1131C23—121no—
1132C23—121no—
1133C23—121no—
1134C23—121no—
1135C23#89814yes—
1136C23C2×#23511yescharacteristic
1137C23C2×D3×D411yescharacteristic
1138C23C2×D3×D411yescharacteristic
1139C23C2×D3×D411yescharacteristic
1140C23C2×#23711yescharacteristic
1141C23#100411yescharacteristic
1142C23#100411yescharacteristic
1143C23#100411yescharacteristic
1144C23C2×#23911yescharacteristic
1145C23D3×#4111yescharacteristic
1146C23D3×#4111yescharacteristic
1147C23D3×#4111yescharacteristic
1148C23#100911yescharacteristic
1149C23#100911yescharacteristic
1150C23#100911yescharacteristic
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
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—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
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×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4—121no—
1232C2×C4—121no—
1233C2×C4—121no—
1234C2×C4—121no—
1235C2×C3—44no—
1236C2×C3#241111yescharacteristic
1237C2×C3#241811yescharacteristic
1238C2×C3#241811yescharacteristic
1239C2×C3#242411yescharacteristic
1240C2×C3#248011yescharacteristic
1241C2×C3#248011yescharacteristic
1242C2×C3#248011yescharacteristic
1243C2×C3#248211yescharacteristic
1244C2×C3#253411yescharacteristic
1245C2×C3#267011yescharacteristic
1246C2×C3#267811yescharacteristic
1247C2×C3#268411yescharacteristic
1248C2×C3#268511yescharacteristic
1249C2×C3#273511yescharacteristic
1250C2×C3#273611yescharacteristic
1251D3—44no—
1252D3—44no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—64no—
1269C22—64no—
1270C22—64no—
1271C22—64no—
1272C22—64no—
1273C22—64no—
1274C22—1264no—
1275C22—122no—
1276C22—122no—
1277C22—122no—
1278C22—122no—
1279C22—122no—
1280C22—122no—
1281C22—122no—
1282C22—122no—
1283C22—122no—
1284C22—122no—
1285C22—122no—
1286C22—122no—
1287C22—122no—
1288C22—122no—
1289C22—122no—
1290C22—122no—
1291C22—122no—
1292C22—122no—
1293C22—122no—
1294C22—122no—
1295C22—122no—
1296C22—122no—
1297C22—122no—
1298C22—122no—
1299C22#549011yescharacteristic
1300C22C2×#89811yescharacteristic
1301C22#552711yescharacteristic
1302C22#554711yescharacteristic
1303C22#555011yescharacteristic
1304C22#555611yescharacteristic
1305C22#556011yescharacteristic
1306C22#559011yescharacteristic
1307C22#559111yescharacteristic
1308C22#559111yescharacteristic
1309C22D3×#12111yescharacteristic
1310C22#560511yescharacteristic
1311C22#560611yescharacteristic
1312C22#561211yescharacteristic
1313C22#561311yescharacteristic
1314C22#561311yescharacteristic
1315C22#561711yescharacteristic
1316C22#562011yescharacteristic
1317C22#562711yescharacteristic
1318C22#563011yescharacteristic
1319C22#563011yescharacteristic
1320C22#563711yescharacteristic
1321C22#563711yescharacteristic
1322C22#564411yescharacteristic
1323C22D3×#12311yescharacteristic
1324C22#565411yescharacteristic
1325C22#565711yescharacteristic
1326C22#565811yescharacteristic
1327C22#565811yescharacteristic
1328C22#567411yescharacteristic
1329C22#567411yescharacteristic
1330C22#568311yescharacteristic
1331C22#570511yescharacteristic
1332C22#570511yescharacteristic
1333C22#571711yescharacteristic
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—122no—
1341C4—122no—
1342C4—122no—
1343C4—241no—
1344C4—241no—
1345C4—241no—
1346C3#1528211yescharacteristic, complemented, Sylow
1347C2—44no—
1348C2—124no—
1349C2—124no—
1350C2#7390911yescharacteristic
1351C2#7445211yescharacteristic
1352C2#7445311yescharacteristic
1353C2#7489211yescharacteristic
1354C2#7584211yescharacteristic
1355C2#7593611yescharacteristic
1356C2#7646211yescharacteristic
1357C2#7675611yescharacteristic
1358C2#7687311yescharacteristic
1359C2#7714011yescharacteristic
1360C2#7714411yescharacteristic
1361C2#7742111yescharacteristic
1362C2#7744211yescharacteristic
1363C2#7767611yescharacteristic
1364C2#7810111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC25×D3C22
hypercenter#1439D3
hypocenterC3#15282
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#4992C2semidirect
2. C2×#4990C2semidirect
6. C2×#4669C2semidirect
7. C3×#1439C2semidirect
8. #71547C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. #69429C2semidirect
12. #69429C2semidirect
13. #69428C2semidirect
14. #69427C2semidirect
15. #69427C2semidirect
18. C22×C3×C4⋊C4C22semidirect
37. C22×C4⋊Dic3C22semidirect
38. C22×Dic3⋊C4C22semidirect
39. C22×C4×Dic3C22semidirect
40. C2×C3×#95C22semidirect
41. C2×C3×#95C22semidirect
42. C2×C3×#95C22semidirect
43. C2×C3⋊#95C22semidirect
44. C2×C3⋊#95C22semidirect
45. C2×C3⋊#95C22semidirect
46. C2×C3⋊#95C22semidirect
47. C2×C3⋊#95C22semidirect
48. C2×C3⋊#95C22semidirect
49. C2×C3⋊#95C22semidirect
50. C2×C3⋊#95C22semidirect
51. C2×C3⋊#95C22semidirect
71. #1439D3semidirect
184. C22×C4⋊C4C2×D3semidirect
219. C2×#95C2×D3semidirect
220. C2×#95C2×D3semidirect
221. C2×#95C2×D3semidirect
1346. C3#15282semidirect

Maximal subgroups

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

subgroupindex
C2×#49922
C2×#49902
C2×#49552
C2×#46692
C3×#14392
#715472
#715462
#715452
#694292
#694282
#694272
#152823