Finite Group Databasebeta

← #10733817

Subgroups — #10733817

Order 768.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#380C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C2×#4982C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic
5#72127C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#71564C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic
10#71547C211yesmaximal, characteristic, complemented
11#71546C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#15326—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C3×#380—24no—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39#5213—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54#4982—24no—
55#4957—24no—
56C2×#398—31no—
57C2×#390—31no—
58C2×#386—31no—
59C2×#380D311yescharacteristic, complemented
60#1442—31no—
61#1439—31no—
62#1439—31no—
63#1439—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1438—31no—
68#1436—31no—
69#1434—31no—
70C22⋊#95—31no—
71C25×C3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—41no—
79C23×C3×C4—41no—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—41no—
91C22×#67—41no—
92C22×#67Q814yes—
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—41no—
105C2×C3×C4⋊C4—41no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—41no—
108C2×C3×C22⋊C4—41no—
109C2×C3×C22⋊C4—41no—
110C2×C3×C22⋊C4—41no—
111C2×C3×C22⋊C4D414yes—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—41no—
118C2×#217—41no—
119C2×#217—41no—
120C2×#217—41no—
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—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
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×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×C4⋊Dic3—22no—
140C2×C4⋊Dic3—41no—
141C2×C4⋊Dic3—41no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—41no—
146C2×Dic3⋊C4—41no—
147C2×Dic3⋊C4—41no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—41no—
151C3×#95—22no—
152C3×#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95D414yes—
167C23×D4—31no—
168C24×C4C2×D311yescharacteristic
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4C2×D311yescharacteristic
173C22×C4⋊C4C2×D311yescharacteristic
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4C2×D311yescharacteristic
184C22×C22⋊C4C2×D311yescharacteristic
185C22×C42—31no—
186#398—64no—
187#390—64no—
188#386—64no—
189#380—24no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3C2×D412yes—
219C24×C3C2×Q812yes—
220C24×C3#4112yes—
221C24×C3C2411yescharacteristic
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3C2×Q812yes—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—28no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×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—44no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4—44no—
279C22×C3×C4—44no—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4#4112yes—
284C22×C3×C4#4112yes—
285C22×C3×C4#4112yes—
286C2×#67—28no—
287C2×#67—28no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×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×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×D412yes—
339C22×Dic3C2×Q812yes—
340C22×Dic3#4112yes—
341C22×Dic3#4112yes—
342C3×C4⋊C4—44no—
343C3×C4⋊C4—44no—
344C3×C22⋊C4—44no—
345C3×C22⋊C4—44no—
346#217—44no—
347#217—44no—
348#217—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355C4⋊Dic3—44no—
356Dic3⋊C4—44no—
357Dic3⋊C4—44no—
358C4×Dic3—44no—
359C25—31no—
360C25C22×D311yescharacteristic
361C22×D4—34no—
362C22×D4—62no—
363C22×D4—62no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—121no—
367C22×D4—121no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—41no—
381C23×C4—41no—
382C23×C4C22×D311yescharacteristic
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—121no—
399C2×C4⋊C4—121no—
400C2×C4⋊C4—121no—
401C2×C4⋊C4—121no—
402C2×C4⋊C4—121no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4—121no—
429C2×C22⋊C4—121no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4#6714yes—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—121no—
439#95—22no—
440#95—22no—
441#95—34no—
442#95—62no—
443#95—62no—
444#95—62no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—121no—
450#95—121no—
451#95—121no—
452#95—121no—
453#95—121no—
454#95—121no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—41no—
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×C3C22⋊Q814yes—
490C23×C3C22×D411yescharacteristic
491C23×C3C22×D411yescharacteristic
492C23×C3C22×Q811yescharacteristic
493C23×C3C2×#4111yescharacteristic
494C23×C3C2×#4111yescharacteristic
495C23×C3C2×#4111yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3C2×#4111yescharacteristic
498C23×C3C2×#4111yescharacteristic
499C23×C3H(5,𝔽2)11yescharacteristic
500C23×C3H(5,𝔽2)11yescharacteristic
501C23×C3H(5,𝔽2)11yescharacteristic
502C23×C3H(5,𝔽2)11yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
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—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—416no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
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#12414yes—
583#67—416no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
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×Dic3C22⋊Q814yes—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—32no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24D3×Q812yes—
661C24#23912yes—
662C24C2×#6712yes—
663C24C23×D311yescharacteristic
664C2×D4—68no—
665C2×D4—68no—
666C2×D4—124no—
667C2×D4—124no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—28no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—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—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—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#23512yes—
764C22×C4#23512yes—
765C22×C4D3×D412yes—
766C22×C4#23712yes—
767C22×C4C2×#6712yes—
768C22×C4C2×#6712yes—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—124no—
772C4⋊C4—124no—
773C4⋊C4—124no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C22⋊C4—124no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C42—124no—
786C22×C3—24no—
787C22×C3—24no—
788C22×C3—24no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3C2×C22⋊Q811yescharacteristic
802C22×C3C2×C22⋊Q811yescharacteristic
803C22×C3#52511yescharacteristic
804C22×C3C2×#12411yescharacteristic
805C22×C3#52911yescharacteristic
806C22×C3#52911yescharacteristic
807C22×C3#53411yescharacteristic
808C22×C3#53511yescharacteristic
809C22×C3#53811yescharacteristic
810C22×C3#53811yescharacteristic
811C22×C3#54011yescharacteristic
812C22×C3#54011yescharacteristic
813C22×C3#54011yescharacteristic
814C22×C3#54011yescharacteristic
815C22×C3#54311yescharacteristic
816C22×C3D4211yescharacteristic
817C22×C3#54611yescharacteristic
818C22×C3#54611yescharacteristic
819C22×C3#54611yescharacteristic
820C22×C3#54611yescharacteristic
821C22×C3#54611yescharacteristic
822C22×C3#55011yescharacteristic
823C22×C3#55111yescharacteristic
824C22×C3#55111yescharacteristic
825C22×C3#55311yescharacteristic
826C22×C3#55311yescharacteristic
827C22×C3#55311yescharacteristic
828C22×C3#55411yescharacteristic
829C22×C3#55411yescharacteristic
830C22×C3#55411yescharacteristic
831C22×C3#55411yescharacteristic
832C22×C3#55511yescharacteristic
833C22×C3#55511yescharacteristic
834C22×C3#56011yescharacteristic
835C22×C3#56011yescharacteristic
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—81no—
844C2×D3—81no—
845C2×D3—81no—
846C2×D3—81no—
847C2×D3—81no—
848C2×D3—81no—
849C2×D3—81no—
850C2×D3—81no—
851C3×C4—24no—
852C3×C4—42no—
853C3×C4—42no—
854C3×C4—42no—
855C3×C4—81no—
856C3×C4—81no—
857Dic3—24no—
858Dic3—42no—
859Dic3—42no—
860Dic3—81no—
861Dic3—81no—
862Dic3—81no—
863Dic3—81no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
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—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
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#94614yes—
934C23C2×#23511yescharacteristic
935C23C2×#23511yescharacteristic
936C23C2×D3×D411yescharacteristic
937C23C2×#23711yescharacteristic
938C23#100411yescharacteristic
939C23#100411yescharacteristic
940C23#100411yescharacteristic
941C23#100411yescharacteristic
942C23C2×D3×Q811yescharacteristic
943C23C2×#23911yescharacteristic
944C23D3×#4111yescharacteristic
945C23D3×#4111yescharacteristic
946C23#100911yescharacteristic
947C23#100911yescharacteristic
948C23C22×#6711yescharacteristic
949D4—1216no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—34no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
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—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
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#88514yes—
1042C2×C3—44no—
1043C2×C3#243711yescharacteristic
1044C2×C3#245011yescharacteristic
1045C2×C3#245411yescharacteristic
1046C2×C3#247211yescharacteristic
1047C2×C3#247611yescharacteristic
1048C2×C3#249011yescharacteristic
1049C2×C3#253111yescharacteristic
1050C2×C3#256311yescharacteristic
1051C2×C3#257911yescharacteristic
1052C2×C3#267311yescharacteristic
1053C2×C3#269911yescharacteristic
1054C2×C3#270311yescharacteristic
1055C2×C3#274811yescharacteristic
1056C2×C3#275611yescharacteristic
1057C2×C3#278011yescharacteristic
1058D3—82no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—241no—
1082C22—241no—
1083C22—241no—
1084C22—241no—
1085C22—241no—
1086C22—241no—
1087C22—241no—
1088C22—241no—
1089C22#549011yescharacteristic
1090C22C2×#88511yescharacteristic
1091C22#549411yescharacteristic
1092C22#549511yescharacteristic
1093C22#551111yescharacteristic
1094C22#551111yescharacteristic
1095C22#551411yescharacteristic
1096C22#551411yescharacteristic
1097C22#552811yescharacteristic
1098C22#553011yescharacteristic
1099C22#553211yescharacteristic
1100C22#553511yescharacteristic
1101C22#559911yescharacteristic
1102C22#560711yescharacteristic
1103C22#561511yescharacteristic
1104C22#561511yescharacteristic
1105C22#561611yescharacteristic
1106C22#561911yescharacteristic
1107C22#562011yescharacteristic
1108C22#562011yescharacteristic
1109C22#562411yescharacteristic
1110C22D3×C22⋊Q811yescharacteristic
1111C22#563011yescharacteristic
1112C22#563411yescharacteristic
1113C22#563511yescharacteristic
1114C22#563611yescharacteristic
1115C22#563711yescharacteristic
1116C22#564411yescharacteristic
1117C22#579111yescharacteristic
1118C22D4×#6711yescharacteristic
1119C22#580411yescharacteristic
1120C22#580611yescharacteristic
1121C22C2×#94611yescharacteristic
1122C22#582911yescharacteristic
1123C22#582911yescharacteristic
1124C4—24no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—64no—
1129C4—81no—
1130C4—81no—
1131C4—122no—
1132C4—122no—
1133C4—241no—
1134C4—241no—
1135C4—241no—
1136C4—241no—
1137C3#1532611yescharacteristic, complemented, Sylow
1138C2—44no—
1139C2—242no—
1140C2#7390311yescharacteristic
1141C2#7391411yescharacteristic
1142C2#7393211yescharacteristic
1143C2#7394211yescharacteristic
1144C2#7396611yescharacteristic
1145C2#7398611yescharacteristic
1146C2#7398711yescharacteristic
1147C2#7399111yescharacteristic
1148C2#8211111yescharacteristic
1149C2#8219811yescharacteristic
1150C2#8228011yescharacteristic
1151C2#8268311yescharacteristic
1152C2#8269111yescharacteristic
1153C2#8276511yescharacteristic
1154C2#8281611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC23×#67C22
hypercenterC2×#380D3
hypocenterC3#15326
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×C3×#380C2semidirect
3. C2×#4982C2semidirect
5. #72127C2semidirect
6. #71570C2semidirect
7. #71570C2semidirect
8. #71564C2semidirect
10. #71547C2semidirect
11. #71546C2semidirect
12. #69428C2semidirect
13. #69427C2semidirect
14. #69414C2semidirect
15. #69402C2semidirect
59. C2×#380D3semidirect
1137. C3#15326semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3802
C2×#52132
C2×#49822
C2×#49572
#721272
#715702
#715642
#715502
#715472
#715462
#694282
#694272
#694142
#694022
#153263