Finite Group Databasebeta

← #10727113

Subgroups — #10727113

Order 768.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C2×#4956C211yesmaximal, characteristic
3C2×#4956C211yesmaximal, characteristic
4C2×#4956C211yesmaximal, characteristic
5C2×#4947C211yesmaximal, characteristic, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71567C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69424C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69413C211yesmaximal, characteristic, complemented
16#14759—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×#896—24no—
35C2×#896—24no—
36C2×#896—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4956—24no—
56#4956—24no—
57#4956—24no—
58#4947—24no—
59D3×#95—24no—
60C22×C22⋊Q8—31no—
61C2×#393—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#386—31no—
65C22×#95—31no—
66#1446—31no—
67#1442—31no—
68#1442—31no—
69#1442—31no—
70#1439—31no—
71#1439—31no—
72#1439D311yescharacteristic, complemented
73C22⋊#95—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67Q814yescomplemented
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
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—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3—41no—
117C22×C4×D3D414yes—
118C22×Dic6—22no—
119C22×Dic6—22no—
120C22×Dic6—22no—
121C22×Dic6—22no—
122C22×Dic6—22no—
123C22×Dic6—41no—
124C22×Dic6—41no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—41no—
134C2×C3×C22⋊C4—41no—
135C2×C3×C22⋊C4—41no—
136C2×C3×C22⋊C4—41no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—41no—
145C2×#217—41no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4D414yes—
154C2×(C2×D3)⋊C4D414yes—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161#896—232no—
162C3×#95—22no—
163C3×#95—41no—
164C3×#95—41no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95D414yescomplemented
180C23×Q8—31no—
181C23×D4—31no—
182C24×C4—31no—
183C24×C4—31no—
184C24×C4—31no—
185C2×C22⋊Q8—64no—
186C2×C22⋊Q8—64no—
187C2×C22⋊Q8—64no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C22⋊C4C2×D311yescharacteristic
200#393—64no—
201#386—64no—
202#386—64no—
203#386—64no—
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×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—64no—
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
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—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3C2×Q812yes—
238C24×C3C2411yescharacteristic
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×D3C2×D412yes—
248C23×D3C2×D412yes—
249C23×D3C2×D412yes—
250C23×D3C2×Q812yes—
251C23×D3#4112yes—
252C23×D3#4112yes—
253C23×D3#4112yes—
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×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4#4112yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—28no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
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×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×Q812yes—
350C22×Dic3#4112yes—
351C22×Dic3#4112yes—
352C2×C4×D3—28no—
353C2×C4×D3—28no—
354C2×C4×D3—28no—
355C2×C4×D3—28no—
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—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3—44no—
372C2×C4×D3—44no—
373C2×Dic6—28no—
374C2×Dic6—44no—
375C2×Dic6—44no—
376C2×Dic6—44no—
377C2×Dic6—44no—
378C2×Dic6—44no—
379C2×Dic6—44no—
380C3×C4⋊C4—28no—
381C3×C22⋊C4—44no—
382C3×C22⋊C4—44no—
383C3×C22⋊C4—44no—
384#217—44no—
385#217—44no—
386#217—44no—
387(C2×D3)⋊C4—28no—
388(C2×D3)⋊C4—28no—
389(C2×D3)⋊C4—44no—
390Dic3⋊C4—28no—
391Dic3⋊C4—28no—
392C25—31no—
393C25C22×D311yescharacteristic
394C22×Q8—62no—
395C22×Q8—62no—
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—62no—
399C22×Q8—121no—
400C22×Q8—121no—
401C22×D4—34no—
402C22×D4—62no—
403C22×D4—62no—
404C22×D4—62no—
405C22×D4—62no—
406C22×D4—62no—
407C22×D4—62no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—34no—
415C23×C4—31no—
416C23×C4—62no—
417C23×C4—62no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4—62no—
427C23×C4—62no—
428C23×C4—62no—
429C23×C4—62no—
430C23×C4—121no—
431C23×C4—121no—
432C23×C4—121no—
433C23×C4—121no—
434C23×C4—121no—
435C23×C4—121no—
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442C22⋊Q8—632no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—62no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4—41no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—41no—
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—121no—
478C2×C22⋊C4—121no—
479#95—22no—
480#95—34no—
481#95—41no—
482#95—41no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—62no—
493#95—62no—
494#95—62no—
495#95—121no—
496#95—121no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
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×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3C22×D411yescharacteristic
533C23×C3C22×D411yescharacteristic
534C23×C3C22×D411yescharacteristic
535C23×C3C22×D411yescharacteristic
536C23×C3C22×Q811yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3C2×#4111yescharacteristic
539C23×C3C2×#4111yescharacteristic
540C23×C3C2×#4111yescharacteristic
541C23×C3C2×#4111yescharacteristic
542C23×C3C2×#4111yescharacteristic
543C23×C3H(5,𝔽2)11yescharacteristic
544C23×C3H(5,𝔽2)11yescharacteristic
545C23×C3H(5,𝔽2)11yescharacteristic
546C23×C32−1+411yescharacteristic
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—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
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#12014yes—
576C22×D3C22⋊Q814yes—
577C22×D3C22⋊Q814yes—
578C22×D3C22⋊Q814yes—
579C22×D3#12414yes—
580C22×D3#12414yes—
581C22×D3#12414yes—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
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—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624#67—416no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3#12114yes—
674C4×D3—416no—
675C4×D3—416no—
676C4×D3—416no—
677Dic6—416no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—32no—
693C24—32no—
694C24—32no—
695C24—32no—
696C24—32no—
697C24—32no—
698C24—32no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24D3×Q812yes—
708C24C23×D311yescharacteristic
709C2×Q8—68no—
710C2×Q8—124no—
711C2×Q8—124no—
712C2×Q8—124no—
713C2×Q8—124no—
714C2×Q8—124no—
715C2×Q8—124no—
716C2×D4—68no—
717C2×D4—68no—
718C2×D4—68no—
719C2×D4—124no—
720C2×D4—124no—
721C2×D4—124no—
722C2×D4—124no—
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—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—32no—
767C22×C4—32no—
768C22×C4—68no—
769C22×C4—68no—
770C22×C4—68no—
771C22×C4—68no—
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—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4—124no—
818C22×C4—124no—
819C22×C4—124no—
820C22×C4—124no—
821C22×C4—124no—
822C22×C4—124no—
823C22×C4—124no—
824C22×C4—124no—
825C22×C4—124no—
826C22×C4—124no—
827C22×C4—124no—
828C22×C4—124no—
829C22×C4—124no—
830C22×C4#23512yes—
831C22×C4D3×D412yes—
832C22×C4D3×D412yes—
833C22×C4D3×D412yes—
834C22×C4D3×D412yes—
835C4⋊C4—28no—
836C4⋊C4—68no—
837C4⋊C4—68no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—68no—
842C22⋊C4—68no—
843C22⋊C4—124no—
844C22⋊C4—124no—
845C22⋊C4—124no—
846C22⋊C4—124no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—81no—
855C22×C3—81no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—81no—
861C22×C3—81no—
862C22×C3C2×#12011yescharacteristic
863C22×C3C2×#12111yescharacteristic
864C22×C3C2×C22⋊Q811yescharacteristic
865C22×C3C2×C22⋊Q811yescharacteristic
866C22×C3C2×C22⋊Q811yescharacteristic
867C22×C3#52511yescharacteristic
868C22×C3#52511yescharacteristic
869C22×C3C2×#12411yescharacteristic
870C22×C3C2×#12411yescharacteristic
871C22×C3C2×#12411yescharacteristic
872C22×C3#52911yescharacteristic
873C22×C3#52911yescharacteristic
874C22×C3#53211yescharacteristic
875C22×C3#53411yescharacteristic
876C22×C3#53711yescharacteristic
877C22×C3#53811yescharacteristic
878C22×C3#53811yescharacteristic
879C22×C3#53911yescharacteristic
880C22×C3#53911yescharacteristic
881C22×C3D4211yescharacteristic
882C22×C3D4211yescharacteristic
883C22×C3#54611yescharacteristic
884C22×C3#54611yescharacteristic
885C22×C3#54611yescharacteristic
886C22×C3#54611yescharacteristic
887C22×C3#54611yescharacteristic
888C22×C3#54711yescharacteristic
889C22×C3#54711yescharacteristic
890C22×C3D4×Q811yescharacteristic
891C22×C3#55111yescharacteristic
892C22×C3#55111yescharacteristic
893C22×C3#55211yescharacteristic
894C22×C3#55411yescharacteristic
895C22×C3#55411yescharacteristic
896C22×C3#55411yescharacteristic
897C2×D3—24no—
898C2×D3—24no—
899C2×D3—24no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—24no—
903C2×D3—24no—
904C2×D3—24no—
905C2×D3—24no—
906C2×D3—24no—
907C2×D3—24no—
908C2×D3—24no—
909C2×D3—24no—
910C2×D3—24no—
911C2×D3#39318yescomplemented
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—42no—
916C3×C4—42no—
917C3×C4—81no—
918Dic3—24no—
919Dic3—42no—
920Dic3—42no—
921Dic3—42no—
922Dic3—42no—
923Dic3—42no—
924Dic3—81no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—34no—
933C23—34no—
934C23—34no—
935C23—34no—
936C23—34no—
937C23—34no—
938C23—34no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23C2×#23511yescharacteristic
996C23C2×D3×D411yescharacteristic
997C23C2×D3×D411yescharacteristic
998C23C2×D3×D411yescharacteristic
999C23C2×D3×D411yescharacteristic
1000C23#100411yescharacteristic
1001C23#100411yescharacteristic
1002C23#100411yescharacteristic
1003C23C2×D3×Q811yescharacteristic
1004C23D3×#4111yescharacteristic
1005C23D3×#4111yescharacteristic
1006C23D3×#4111yescharacteristic
1007C23D3×#4111yescharacteristic
1008C23D3×#4111yescharacteristic
1009C23#101011yescharacteristic
1010Q8—1216no—
1011D4—1216no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—34no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—1216no—
1077C2×C4—1216no—
1078C2×C4—1216no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4—121no—
1102C2×C4—121no—
1103C2×C4—121no—
1104C2×C4—121no—
1105C2×C4—121no—
1106C2×C3—82no—
1107C2×C3C2×#39311yescharacteristic
1108C2×C3#241011yescharacteristic
1109C2×C3#241711yescharacteristic
1110C2×C3#243011yescharacteristic
1111C2×C3#244911yescharacteristic
1112C2×C3#244911yescharacteristic
1113C2×C3#245011yescharacteristic
1114C2×C3#245011yescharacteristic
1115C2×C3#247211yescharacteristic
1116C2×C3#247211yescharacteristic
1117C2×C3#248811yescharacteristic
1118C2×C3#248811yescharacteristic
1119C2×C3#256411yescharacteristic
1120C2×C3#263911yescharacteristic
1121C2×C3#285011yescharacteristic
1122D3—28no—
1123C22—38no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—64no—
1132C22—64no—
1133C22—64no—
1134C22—64no—
1135C22—64no—
1136C22—64no—
1137C22—64no—
1138C22—64no—
1139C22—64no—
1140C22—64no—
1141C22—64no—
1142C22—64no—
1143C22—64no—
1144C22—64no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22#549011yescharacteristic
1154C22#551111yescharacteristic
1155C22#552811yescharacteristic
1156C22#554711yescharacteristic
1157C22#554811yescharacteristic
1158C22#555111yescharacteristic
1159C22#555611yescharacteristic
1160C22D3×#12011yescharacteristic
1161C22#558911yescharacteristic
1162C22#559011yescharacteristic
1163C22D3×#12111yescharacteristic
1164C22#560811yescharacteristic
1165C22#561011yescharacteristic
1166C22#561011yescharacteristic
1167C22#561211yescharacteristic
1168C22#561211yescharacteristic
1169C22#561311yescharacteristic
1170C22#561311yescharacteristic
1171C22D3×C22⋊Q811yescharacteristic
1172C22D3×C22⋊Q811yescharacteristic
1173C22D3×C22⋊Q811yescharacteristic
1174C22#563211yescharacteristic
1175C22#563611yescharacteristic
1176C22#563611yescharacteristic
1177C22#565511yescharacteristic
1178C22#565611yescharacteristic
1179C22#565911yescharacteristic
1180C22#566011yescharacteristic
1181C22#566011yescharacteristic
1182C22D3×#12411yescharacteristic
1183C22D3×#12411yescharacteristic
1184C22D3×#12411yescharacteristic
1185C22#570611yescharacteristic
1186C22#570811yescharacteristic
1187C22#571711yescharacteristic
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—64no—
1194C4—81no—
1195C4—122no—
1196C4—122no—
1197C4—122no—
1198C4—122no—
1199C4—122no—
1200C4—241no—
1201C3#1475911yescharacteristic, complemented, Sylow
1202C2—68no—
1203C2—82no—
1204C2#7402311yescharacteristic
1205C2#7460911yescharacteristic
1206C2#7461511yescharacteristic
1207C2#7489611yescharacteristic
1208C2#7586711yescharacteristic
1209C2#7595711yescharacteristic
1210C2#7633011yescharacteristic
1211C2#7675511yescharacteristic
1212C2D3×#39311yescharacteristic
1213C2#7692611yescharacteristic
1214C2#7712611yescharacteristic
1215C2#7728511yescharacteristic
1216C2#7742011yescharacteristic
1217C2#7767811yescharacteristic
1218C2#7810411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14759
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
5. C2×#4947C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1439C2semidirect
8. #71567C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69424C2semidirect
14. #69413C2semidirect
15. #69413C2semidirect
72. #1439D3semidirect
89. C22×#67Q8semidirect
179. C3⋊#95D4semidirect
911. C2×D3#393semidirect
1201. C3#14759semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C2×#49562
C2×#49472
C2×D3×#952
C3×#14392
#715672
#715472
(C2×D3)⋊#952
#694242
#694132
#147593