Finite Group Databasebeta

← #10732627

Subgroups — #10732627

Order 768.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#889C211yesmaximal, characteristic, complemented
2C2×#4957C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C2×#4957C211yesmaximal, characteristic
5C3×#1439C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71547C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13Dic3⋊#95C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#15229—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#889—24no—
41C2×#889—24no—
42C2×#889—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4957—24no—
56#4957—24no—
57#4957—24no—
58C22×#125—31no—
59C2×#390—31no—
60C2×#390—31no—
61C2×#390—31no—
62#1439—31no—
63#1439—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439D311yescharacteristic, complemented
70C4⋊#95—31no—
71C4⋊#95—31no—
72C4×#95—31no—
73C25×C3C2311yescharacteristic
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×#67Q814yes—
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4—41no—
105C2×C3×C22⋊C4—41no—
106C2×C3×C22⋊C4—41no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×#217—41no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4D414yes—
151C2×Dic3⋊C4D414yes—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3D414yes—
161#889—232no—
162C3×#95—22no—
163C3×#95—41no—
164C3×#95—41no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—41no—
169C3⋊#95—41no—
170C3⋊#95—41no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C3⋊#95—41no—
174C23×D4—31no—
175C2×#125—64no—
176C2×#125—64no—
177C2×#125—64no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
195C22×C22⋊C4C2×D311yescharacteristic
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C42—31no—
198C22×C42—31no—
199C22×C42—31no—
200#390—64no—
201#390—64no—
202#390—64no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
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×C3C2×Q812yes—
230C24×C3C2411yescharacteristic
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
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×D3C2×Q812yes—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
288C2×#67—28no—
289C2×#67—28no—
290C2×#67—28no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67—44no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
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×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×Q812yes—
339C22×Dic3#4112yes—
340C22×Dic3#4112yes—
341C22×Dic3#4112yes—
342C22×Dic3#4112yes—
343C22×Dic3#4112yes—
344C3×C4⋊C4—28no—
345C3×C22⋊C4—44no—
346C3×C22⋊C4—44no—
347C3×C22⋊C4—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—28no—
358Dic3⋊C4—28no—
359Dic3⋊C4—28no—
360Dic3⋊C4—28no—
361Dic3⋊C4—28no—
362Dic3⋊C4—44no—
363C4×Dic3—28no—
364C4×Dic3—44no—
365C4×Dic3—44no—
366C25—31no—
367C25C22×D311yescharacteristic
368C22×D4—34no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4C22×D311yescharacteristic
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388#125—632no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4—121no—
439C2×C22⋊C4—121no—
440C2×C22⋊C4—121no—
441C2×C22⋊C4—121no—
442C2×C22⋊C4—121no—
443C2×C22⋊C4—121no—
444C2×C22⋊C4—121no—
445C2×C22⋊C4—121no—
446C2×C42—34no—
447C2×C42—62no—
448C2×C42—62no—
449C2×C42—62no—
450C2×C42—62no—
451C2×C42—62no—
452C2×C42—62no—
453C2×C42—62no—
454C2×C42—62no—
455#95—22no—
456#95—41no—
457#95—41no—
458#95—62no—
459#95—62no—
460#95—62no—
461#95—121no—
462#95—121no—
463#95—121no—
464#95—121no—
465#95—121no—
466#95—121no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3C22×D411yescharacteristic
503C23×C3C22×D411yescharacteristic
504C23×C3C22×D411yescharacteristic
505C23×C3C22×Q811yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4111yescharacteristic
512C23×C3C2×#4111yescharacteristic
513C23×C3H(5,𝔽2)11yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C23×C3H(5,𝔽2)11yescharacteristic
516C23×C3H(5,𝔽2)11yescharacteristic
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594#67—416no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3#12014yes—
638C2×Dic3C22⋊Q814yes—
639C2×Dic3C22⋊Q814yes—
640C2×Dic3C22⋊Q814yes—
641C2×Dic3#12414yes—
642C2×Dic3#12414yes—
643C2×Dic3#12414yes—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—32no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24D3×Q812yes—
674C24C23×D311yescharacteristic
675C2×D4—68no—
676C2×D4—68no—
677C2×D4—68no—
678C2×D4—124no—
679C2×D4—124no—
680C2×D4—124no—
681C2×D4—124no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4#23512yes—
769C22×C4D3×D412yes—
770C22×C4D3×D412yes—
771C22×C4D3×D412yes—
772C22×C4#23712yes—
773C4⋊C4—28no—
774C4⋊C4—68no—
775C4⋊C4—68no—
776C4⋊C4—68no—
777C4⋊C4—68no—
778C4⋊C4—68no—
779C4⋊C4—124no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—124no—
788C22⋊C4—124no—
789C22⋊C4—124no—
790C22⋊C4—124no—
791C22⋊C4—124no—
792C42—68no—
793C42—124no—
794C42—124no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3C2×#12011yescharacteristic
811C22×C3C2×C22⋊Q811yescharacteristic
812C22×C3C2×C22⋊Q811yescharacteristic
813C22×C3C2×C22⋊Q811yescharacteristic
814C22×C3C2×#12411yescharacteristic
815C22×C3C2×#12411yescharacteristic
816C22×C3C2×#12411yescharacteristic
817C22×C3#52911yescharacteristic
818C22×C3#52911yescharacteristic
819C22×C3#52911yescharacteristic
820C22×C3#52911yescharacteristic
821C22×C3#53211yescharacteristic
822C22×C3#53211yescharacteristic
823C22×C3#53511yescharacteristic
824C22×C3#53511yescharacteristic
825C22×C3#54011yescharacteristic
826C22×C3#54011yescharacteristic
827C22×C3#54011yescharacteristic
828C22×C3#54011yescharacteristic
829C22×C3#54611yescharacteristic
830C22×C3#54611yescharacteristic
831C22×C3#54611yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#55011yescharacteristic
834C22×C3#55011yescharacteristic
835C22×C3#55011yescharacteristic
836C22×C3#55011yescharacteristic
837C22×C3#55311yescharacteristic
838C22×C3#55311yescharacteristic
839C22×C3#55311yescharacteristic
840C22×C3#55311yescharacteristic
841C22×C3#55411yescharacteristic
842C22×C3#55411yescharacteristic
843C22×C3#55411yescharacteristic
844C22×C3#55411yescharacteristic
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—81no—
853C2×D3—81no—
854C2×D3—81no—
855C2×D3—81no—
856C2×D3—81no—
857C2×D3—81no—
858C2×D3—81no—
859C2×D3—81no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—81no—
866Dic3—42no—
867Dic3—42no—
868Dic3—42no—
869Dic3—42no—
870Dic3—42no—
871Dic3—81no—
872Dic3#39318yes—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23C2×#23511yescharacteristic
944C23C2×D3×D411yescharacteristic
945C23C2×D3×D411yescharacteristic
946C23C2×D3×D411yescharacteristic
947C23C2×#23711yescharacteristic
948C23#100411yescharacteristic
949C23#100411yescharacteristic
950C23#100411yescharacteristic
951C23C2×D3×Q811yescharacteristic
952C23D3×#4111yescharacteristic
953C23D3×#4111yescharacteristic
954C23D3×#4111yescharacteristic
955C23D3×#4111yescharacteristic
956C23D3×#4111yescharacteristic
957C23#100911yescharacteristic
958D4—1216no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—34no—
975C2×C4—34no—
976C2×C4—34no—
977C2×C4—34no—
978C2×C4—34no—
979C2×C4—34no—
980C2×C4—34no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C3—82no—
1051C2×C3C2×#39311yescharacteristic
1052C2×C3#243111yescharacteristic
1053C2×C3#243111yescharacteristic
1054C2×C3#245411yescharacteristic
1055C2×C3#245411yescharacteristic
1056C2×C3#245411yescharacteristic
1057C2×C3#245411yescharacteristic
1058C2×C3#249011yescharacteristic
1059C2×C3#249011yescharacteristic
1060C2×C3#249011yescharacteristic
1061C2×C3#249011yescharacteristic
1062C2×C3#256611yescharacteristic
1063C2×C3#256611yescharacteristic
1064C2×C3#264111yescharacteristic
1065C2×C3#286111yescharacteristic
1066D3—82no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22—122no—
1088C22—122no—
1089C22—241no—
1090C22—241no—
1091C22—241no—
1092C22—241no—
1093C22—241no—
1094C22—241no—
1095C22—241no—
1096C22—241no—
1097C22#549011yescharacteristic
1098C22#551111yescharacteristic
1099C22#552811yescharacteristic
1100C22#553811yescharacteristic
1101C22#554011yescharacteristic
1102C22#554811yescharacteristic
1103C22#555311yescharacteristic
1104C22D3×#12011yescharacteristic
1105C22#559111yescharacteristic
1106C22#559211yescharacteristic
1107C22#559611yescharacteristic
1108C22#559911yescharacteristic
1109C22#559911yescharacteristic
1110C22#560111yescharacteristic
1111C22#560711yescharacteristic
1112C22#561011yescharacteristic
1113C22#561511yescharacteristic
1114C22#561511yescharacteristic
1115C22D3×C22⋊Q811yescharacteristic
1116C22D3×C22⋊Q811yescharacteristic
1117C22D3×C22⋊Q811yescharacteristic
1118C22#563511yescharacteristic
1119C22#563611yescharacteristic
1120C22#563611yescharacteristic
1121C22#564911yescharacteristic
1122C22#565411yescharacteristic
1123C22#566111yescharacteristic
1124C22#566311yescharacteristic
1125C22#566311yescharacteristic
1126C22D3×#12411yescharacteristic
1127C22D3×#12411yescharacteristic
1128C22D3×#12411yescharacteristic
1129C22#570611yescharacteristic
1130C22#570911yescharacteristic
1131C22#571811yescharacteristic
1132C4—38no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—122no—
1140C4—122no—
1141C4—122no—
1142C4—122no—
1143C4—122no—
1144C4—241no—
1145C3#1522911yescharacteristic, complemented, Sylow
1146C2—82no—
1147C2—242no—
1148C2#7390311yescharacteristic
1149C2#7442611yescharacteristic
1150C2#7447711yescharacteristic
1151C2#7470011yescharacteristic
1152C2#7554511yescharacteristic
1153C2#7582111yescharacteristic
1154C2#7633311yescharacteristic
1155C2#7667211yescharacteristic
1156C2D3×#39311yescharacteristic
1157C2#7693411yescharacteristic
1158C2#7698411yescharacteristic
1159C2#7729111yescharacteristic
1160C2#7732011yescharacteristic
1161C2#7748711yescharacteristic
1162C2#7802311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15229
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#889C2semidirect
5. C3×#1439C2semidirect
6. #71570C2semidirect
7. #71547C2semidirect
8. #71547C2semidirect
9. #71546C2semidirect
10. #69428C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
13. Dic3⋊#95C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3×#95C2semidirect
69. #1439D3semidirect
1145. C3#15229semidirect

Maximal subgroups

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

subgroupindex
C22×#8892
C2×#49572
C3×#14392
#715702
#715472
#715462
#694282
#694272
Dic3⋊#952
Dic3×#952
#152293