Finite Group Databasebeta

← #10729120

Subgroups — #10729120

Order 768.

2162 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4989C211yesmaximal, characteristic, complemented
2C2×#4956C211yesmaximal, characteristic
3C2×#4956C211yesmaximal, characteristic
4C2×#4956C211yesmaximal, characteristic
5C2×#4667C211yesmaximal, characteristic, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71566C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69418C211yesmaximal, characteristic, complemented
14#69418C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#14921—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4989—24no—
53#4956—24no—
54#4956—24no—
55#4956—24no—
56#4667—24no—
57D3×#95—24no—
58C2×#386—31no—
59C2×#386—31no—
60C2×#386—31no—
61C2×#385—31no—
62C2×#380—31no—
63C22×#95—31no—
64#1443—31no—
65#1443—31no—
66#1441—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439D311yescharacteristic, complemented
72C22⋊#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
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C22×C4×D3—41no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3D414yes—
115C22×C4×D3D414yes—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—41no—
135C2×#217—41no—
136C2×#217—41no—
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)⋊C4D414yes—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—41no—
152C2×Dic3⋊C4—41no—
153C2×Dic3⋊C4—41no—
154C2×Dic3⋊C4—41no—
155C3×#95—22no—
156C3×#95—22no—
157C3×#95—41no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—41no—
173C23×D4—31no—
174C24×C4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4C2×D311yescharacteristic
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4C2×D311yescharacteristic
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C22⋊C4C2×D311yescharacteristic
190#386—64no—
191#386—64no—
192#386—64no—
193#385—64no—
194#380—64no—
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×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—64no—
211C2×#95C2×D311yescharacteristic
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C24×C3—21no—
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×C3C2×Q812yes—
229C24×C3C2411yescharacteristic
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3C2×D412yes—
239C23×D3C2×D412yes—
240C23×D3C2×D412yes—
241C23×D3C2×Q812yes—
242C23×D3#4112yes—
243C23×D3#4112yes—
244C23×D3#4112yes—
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—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—
287C2×#67—28no—
288C2×#67—28no—
289C2×#67—28no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
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×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×D412yes—
339C22×Dic3C2×Q812yes—
340C22×Dic3#4112yes—
341C22×Dic3#4112yes—
342C22×Dic3#4112yes—
343C2×C4×D3—28no—
344C2×C4×D3—28no—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C3×C4⋊C4—44no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—44no—
367C3×C22⋊C4—44no—
368#217—44no—
369#217—44no—
370#217—44no—
371(C2×D3)⋊C4—28no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374Dic3⋊C4—44no—
375Dic3⋊C4—44no—
376Dic3⋊C4—44no—
377C25—31no—
378C25C22×D311yescharacteristic
379C22×D4—34no—
380C22×D4—62no—
381C22×D4—62no—
382C22×D4—62no—
383C22×D4—62no—
384C22×D4—62no—
385C22×D4—62no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—34no—
392C23×C4—34no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—62no—
396C23×C4—62no—
397C23×C4—62no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—121no—
407C23×C4—121no—
408C23×C4—121no—
409C23×C4—121no—
410C23×C4—121no—
411C23×C4—121no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C2×C4⋊C4—22no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—62no—
428C2×C4⋊C4—121no—
429C2×C4⋊C4—121no—
430C2×C4⋊C4—121no—
431C2×C4⋊C4—121no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4—41no—
438C2×C22⋊C4—41no—
439C2×C22⋊C4—41no—
440C2×C22⋊C4—41no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—121no—
457C2×C22⋊C4—121no—
458C2×C22⋊C4—121no—
459#95—22no—
460#95—22no—
461#95—41no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—121no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
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×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3C22×D411yescharacteristic
513C23×C3C22×D411yescharacteristic
514C23×C3C22×D411yescharacteristic
515C23×C3C22×Q811yescharacteristic
516C23×C3C2×#4111yescharacteristic
517C23×C3C2×#4111yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3C2×#4111yescharacteristic
521C23×C3C2×#4111yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3H(5,𝔽2)11yescharacteristic
524C23×C3H(5,𝔽2)11yescharacteristic
525C23×C3H(5,𝔽2)11yescharacteristic
526C23×C3H(5,𝔽2)11yescharacteristic
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3#12114yes—
556C22×D3#12114yes—
557C22×D3#12114yes—
558C22×D3C22⋊Q814yes—
559C22×D3C22⋊Q814yes—
560C22×D3C22⋊Q814yes—
561C22×D3#12614yes—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
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—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604#67—416no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
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—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3#12314yes—
654C4×D3—416no—
655C4×D3—416no—
656C4×D3—416no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—32no—
672C24—32no—
673C24—32no—
674C24—32no—
675C24—32no—
676C24—32no—
677C24—32no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24D3×Q812yes—
687C24C23×D311yescharacteristic
688C2×D4—68no—
689C2×D4—68no—
690C2×D4—68no—
691C2×D4—124no—
692C2×D4—124no—
693C2×D4—124no—
694C2×D4—124no—
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—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—68no—
741C22×C4—68no—
742C22×C4—68no—
743C22×C4—68no—
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—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4—124no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4—124no—
801C22×C4—124no—
802C22×C4—124no—
803C22×C4#23512yes—
804C22×C4D3×D412yes—
805C22×C4D3×D412yes—
806C22×C4D3×D412yes—
807C4⋊C4—44no—
808C4⋊C4—124no—
809C4⋊C4—124no—
810C4⋊C4—124no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—68no—
815C22⋊C4—124no—
816C22⋊C4—124no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C22⋊C4—124no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3C2×#12111yescharacteristic
836C22×C3C2×#12111yescharacteristic
837C22×C3C2×#12111yescharacteristic
838C22×C3C2×C22⋊Q811yescharacteristic
839C22×C3C2×C22⋊Q811yescharacteristic
840C22×C3C2×C22⋊Q811yescharacteristic
841C22×C3C2×#12311yescharacteristic
842C22×C3#52511yescharacteristic
843C22×C3C2×#12611yescharacteristic
844C22×C3#52911yescharacteristic
845C22×C3#52911yescharacteristic
846C22×C3#53211yescharacteristic
847C22×C3#53211yescharacteristic
848C22×C3#53411yescharacteristic
849C22×C3#53411yescharacteristic
850C22×C3#53411yescharacteristic
851C22×C3#53511yescharacteristic
852C22×C3#53811yescharacteristic
853C22×C3#53811yescharacteristic
854C22×C3#54611yescharacteristic
855C22×C3#54611yescharacteristic
856C22×C3#54611yescharacteristic
857C22×C3#54611yescharacteristic
858C22×C3#55111yescharacteristic
859C22×C3#55111yescharacteristic
860C22×C3#55111yescharacteristic
861C22×C3#55111yescharacteristic
862C22×C3#55311yescharacteristic
863C22×C3#55311yescharacteristic
864C22×C3#55311yescharacteristic
865C22×C3#55311yescharacteristic
866C22×C3#55411yescharacteristic
867C22×C3#55411yescharacteristic
868C22×C3#55411yescharacteristic
869C22×C3#55411yescharacteristic
870C2×D3—24no—
871C2×D3—24no—
872C2×D3—24no—
873C2×D3—24no—
874C2×D3—24no—
875C2×D3—24no—
876C2×D3—24no—
877C2×D3—24no—
878C2×D3—24no—
879C2×D3—24no—
880C2×D3—24no—
881C2×D3—24no—
882C2×D3—24no—
883C2×D3—24no—
884C2×D3#39618yes—
885C3×C4—42no—
886C3×C4—42no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—81no—
890C3×C4—81no—
891Dic3—24no—
892Dic3—42no—
893Dic3—42no—
894Dic3—42no—
895Dic3—42no—
896Dic3—81no—
897Dic3—81no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—34no—
906C23—34no—
907C23—34no—
908C23—34no—
909C23—34no—
910C23—34no—
911C23—34no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23C2×#23511yescharacteristic
969C23C2×D3×D411yescharacteristic
970C23C2×D3×D411yescharacteristic
971C23C2×D3×D411yescharacteristic
972C23#100411yescharacteristic
973C23#100411yescharacteristic
974C23#100411yescharacteristic
975C23#100411yescharacteristic
976C23C2×D3×Q811yescharacteristic
977C23D3×#4111yescharacteristic
978C23D3×#4111yescharacteristic
979C23D3×#4111yescharacteristic
980C23D3×#4111yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983D4—1216no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—34no—
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—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—1216no—
1046C2×C4—1216no—
1047C2×C4—1216no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C3—82no—
1079C2×C3C2×#39611yescharacteristic
1080C2×C3#241111yescharacteristic
1081C2×C3#241211yescharacteristic
1082C2×C3#245011yescharacteristic
1083C2×C3#245011yescharacteristic
1084C2×C3#248711yescharacteristic
1085C2×C3#251011yescharacteristic
1086C2×C3#251011yescharacteristic
1087C2×C3#254311yescharacteristic
1088C2×C3#254311yescharacteristic
1089C2×C3#256411yescharacteristic
1090C2×C3#256411yescharacteristic
1091C2×C3#257911yescharacteristic
1092C2×C3#261711yescharacteristic
1093C2×C3#285411yescharacteristic
1094D3—28no—
1095C22—38no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—64no—
1104C22—64no—
1105C22—64no—
1106C22—64no—
1107C22—64no—
1108C22—64no—
1109C22—64no—
1110C22—64no—
1111C22—64no—
1112C22—64no—
1113C22—64no—
1114C22—64no—
1115C22—64no—
1116C22—64no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22#549011yescharacteristic
1126C22#551111yescharacteristic
1127C22#552811yescharacteristic
1128C22#554711yescharacteristic
1129C22#554811yescharacteristic
1130C22#555611yescharacteristic
1131C22#555811yescharacteristic
1132C22#558911yescharacteristic
1133C22#558911yescharacteristic
1134C22#558911yescharacteristic
1135C22D3×#12111yescharacteristic
1136C22D3×#12111yescharacteristic
1137C22D3×#12111yescharacteristic
1138C22#561011yescharacteristic
1139C22#561211yescharacteristic
1140C22#561211yescharacteristic
1141C22#561311yescharacteristic
1142C22#561311yescharacteristic
1143C22D3×C22⋊Q811yescharacteristic
1144C22D3×C22⋊Q811yescharacteristic
1145C22D3×C22⋊Q811yescharacteristic
1146C22#563611yescharacteristic
1147C22#563611yescharacteristic
1148C22#563611yescharacteristic
1149C22D3×#12311yescharacteristic
1150C22#565911yescharacteristic
1151C22#566111yescharacteristic
1152C22#566111yescharacteristic
1153C22#566111yescharacteristic
1154C22#566811yescharacteristic
1155C22#567911yescharacteristic
1156C22#567911yescharacteristic
1157C22D3×#12611yescharacteristic
1158C22#570611yescharacteristic
1159C22#571511yescharacteristic
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—64no—
1165C4—81no—
1166C4—81no—
1167C4—122no—
1168C4—122no—
1169C4—122no—
1170C4—122no—
1171C4—241no—
1172C4—241no—
1173C3#1492111yescharacteristic, complemented, Sylow
1174C2—68no—
1175C2—82no—
1176C2#7402311yescharacteristic
1177C2#7461511yescharacteristic
1178C2#7461611yescharacteristic
1179C2#7490211yescharacteristic
1180C2#7587111yescharacteristic
1181C2#7596011yescharacteristic
1182C2#7643711yescharacteristic
1183C2#7676111yescharacteristic
1184C2#7686911yescharacteristic
1185C2#7711011yescharacteristic
1186C2#7712011yescharacteristic
1187C2D3×#39611yescharacteristic
1188C2#7742011yescharacteristic
1189C2#7768111yescharacteristic
1190C2#7802911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14921
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#4989C2semidirect
5. C2×#4667C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1439C2semidirect
8. #71566C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69418C2semidirect
14. #69418C2semidirect
15. #69409C2semidirect
71. #1439D3semidirect
1173. C3#14921semidirect

Maximal subgroups

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

subgroupindex
C2×#49892
C2×#49562
C2×#46672
C2×D3×#952
C3×#14392
#715662
#715472
(C2×D3)⋊#952
#694182
#694092
#149213