Finite Group Databasebeta

← #10733609

Subgroups — #10733609

Order 768.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#885C211yesmaximal, characteristic
2C2×#4992C211yesmaximal, characteristic, complemented
3C2×#4979C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic
5C2×#4956C211yesmaximal, characteristic
6C2×#4667C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71549C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69424C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#15311—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×#885—24no—
37C2×#885—24no—
38C2×#885—24no—
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#4992—24no—
56#4979—24no—
57#4959—24no—
58#4956—24no—
59#4667—24no—
60C22×#124—31no—
61C2×#397—31no—
62C2×#395—31no—
63C2×#394—31no—
64C2×#386—31no—
65C2×#380—31no—
66#1446—31no—
67#1440—31no—
68#1440—31no—
69#1439—31no—
70#1439—31no—
71#1439D311yescharacteristic, complemented
72#1436—31no—
73#1436—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—41no—
88C22×#67—41no—
89C22×#67D414yes—
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—41no—
103C22×C4×D3—41no—
104C22×Dic6—22no—
105C22×Dic6—22no—
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—22no—
109C22×Dic6—41no—
110C22×Dic6—41no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—41no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4D414yes—
146C2×(C2×D3)⋊C4D414yes—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4—41no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159#885—232no—
160C3×#95—22no—
161C3×#95—41no—
162C3×#95—41no—
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—22no—
173C3⋊#95—22no—
174C3⋊#95—41no—
175C3⋊#95D414yes—
176C23×Q8—31no—
177C23×D4—31no—
178C24×C4—31no—
179C2×#124—64no—
180C2×#124—64no—
181C2×#124—64no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4C2×D311yescharacteristic
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—
198#397—64no—
199#395—64no—
200#394—64no—
201#386—64no—
202#380—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×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
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×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3C2×D412yes—
234C24×C3C2411yescharacteristic
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×D3—21no—
246C23×D3—21no—
247C23×D3C2×D412yes—
248C23×D3C2×D412yes—
249C23×D3C2×D412yes—
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×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4#4112yes—
292C2×#67—28no—
293C2×#67—28no—
294C2×#67—44no—
295C2×#67—44no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
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×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3C2×D412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3#4112yes—
345C22×Dic3#4112yes—
346C22×Dic3#4112yes—
347C22×Dic3#4112yes—
348C2×C4×D3—28no—
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×Dic6—28no—
356C2×Dic6—44no—
357C2×Dic6—44no—
358C2×Dic6—44no—
359C2×Dic6—44no—
360C2×Dic6—44no—
361C2×Dic6—44no—
362C3×C4⋊C4—44no—
363C3×C22⋊C4—28no—
364C3×C22⋊C4—44no—
365C3×C22⋊C4—44no—
366#217—28no—
367#217—44no—
368#217—44no—
369(C2×D3)⋊C4—28no—
370(C2×D3)⋊C4—28no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374Dic3⋊C4—44no—
375Dic3⋊C4—44no—
376Dic3⋊C4—44no—
377C4×Dic3—28no—
378C25—31no—
379C25C22×D311yescharacteristic
380C22×Q8—62no—
381C22×Q8—62no—
382C22×Q8—62no—
383C22×Q8—62no—
384C22×Q8—62no—
385C22×Q8—121no—
386C22×Q8—121no—
387C22×D4—34no—
388C22×D4—62no—
389C22×D4—62no—
390C22×D4—62no—
391C22×D4—62no—
392C22×D4—121no—
393C22×D4—121no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—121no—
407C23×C4—121no—
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413C23×C4C22×D311yescharacteristic
414#124—632no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—121no—
426C2×C4⋊C4—121no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—34no—
434C2×C22⋊C4—34no—
435C2×C22⋊C4—41no—
436C2×C22⋊C4—41no—
437C2×C22⋊C4—41no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
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—62no—
457C2×C22⋊C4—121no—
458C2×C22⋊C4—121no—
459C2×C22⋊C4—121no—
460C2×C42—62no—
461C2×C42—62no—
462C2×C42—62no—
463#95—22no—
464#95—34no—
465#95—41no—
466#95—41no—
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—62no—
477#95—62no—
478#95—121no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
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×C3—41no—
513C23×C3—41no—
514C23×C3C22×D411yescharacteristic
515C23×C3C22×D411yescharacteristic
516C23×C3C22×D411yescharacteristic
517C23×C3C22×D411yescharacteristic
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×C32−1+411yescharacteristic
527C23×C32−1+411yescharacteristic
528C23×C32−1+411yescharacteristic
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—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3#12014yes—
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—22no—
575C2×C3×C4—22no—
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—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606#67—416no—
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—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
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—41no—
654C2×Dic3#12114yes—
655C2×Dic3#12414yescomplemented
656C4×D3—416no—
657Dic6—416no—
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—21no—
672C24—32no—
673C24—32no—
674C24—32no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24D3×D412yes—
688C24C23×D311yescharacteristic
689C2×Q8—68no—
690C2×Q8—124no—
691C2×Q8—124no—
692C2×Q8—124no—
693C2×Q8—124no—
694C2×Q8—124no—
695C2×Q8—124no—
696C2×D4—68no—
697C2×D4—68no—
698C2×D4—124no—
699C2×D4—124no—
700C2×D4—124no—
701C2×D4—124no—
702C2×D4—124no—
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—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—68no—
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—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4#23512yes—
798C22×C4D3×D412yes—
799C22×C4D3×D412yes—
800C22×C4D3×D412yes—
801C4⋊C4—44no—
802C4⋊C4—124no—
803C4⋊C4—124no—
804C4⋊C4—124no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—68no—
809C22⋊C4—68no—
810C22⋊C4—68no—
811C22⋊C4—124no—
812C22⋊C4—124no—
813C22⋊C4—124no—
814C22⋊C4—124no—
815C22⋊C4—124no—
816C42—68no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3C2×#12011yescharacteristic
833C22×C3C2×#12111yescharacteristic
834C22×C3#52511yescharacteristic
835C22×C3C2×#12411yescharacteristic
836C22×C3#52911yescharacteristic
837C22×C3#53211yescharacteristic
838C22×C3#53411yescharacteristic
839C22×C3#53611yescharacteristic
840C22×C3#53611yescharacteristic
841C22×C3#53711yescharacteristic
842C22×C3#53811yescharacteristic
843C22×C3#54211yescharacteristic
844C22×C3#54211yescharacteristic
845C22×C3#54211yescharacteristic
846C22×C3#54211yescharacteristic
847C22×C3D4211yescharacteristic
848C22×C3D4211yescharacteristic
849C22×C3#54611yescharacteristic
850C22×C3#54611yescharacteristic
851C22×C3#54611yescharacteristic
852C22×C3#54611yescharacteristic
853C22×C3#54611yescharacteristic
854C22×C3#54711yescharacteristic
855C22×C3#54711yescharacteristic
856C22×C3#54711yescharacteristic
857C22×C3#54711yescharacteristic
858C22×C3#54711yescharacteristic
859C22×C3#54711yescharacteristic
860C22×C3#54811yescharacteristic
861C22×C3#55111yescharacteristic
862C22×C3#55511yescharacteristic
863C22×C3#55611yescharacteristic
864C22×C3#55611yescharacteristic
865C22×C3#56211yescharacteristic
866C22×C3#56311yescharacteristic
867C2×D3—24no—
868C2×D3—24no—
869C2×D3—24no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C3×C4—42no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—81no—
887C3×C4—81no—
888Dic3—24no—
889Dic3—24no—
890Dic3—42no—
891Dic3—42no—
892Dic3—42no—
893Dic3—81no—
894Dic3—81no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—34no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
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—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23C2×#23511yescharacteristic
966C23C2×D3×D411yescharacteristic
967C23C2×D3×D411yescharacteristic
968C23C2×D3×D411yescharacteristic
969C23C2×D3×D411yescharacteristic
970C23#100411yescharacteristic
971C23#100411yescharacteristic
972C23#100411yescharacteristic
973C23#100711yescharacteristic
974C23D3×#4111yescharacteristic
975C23D3×#4111yescharacteristic
976C23D3×#4111yescharacteristic
977C23D3×#4111yescharacteristic
978C23#101011yescharacteristic
979C23#101011yescharacteristic
980Q8—1216no—
981D4—1216no—
982C2×C4—22no—
983C2×C4—22no—
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—34no—
995C2×C4—34no—
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—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—62no—
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—62no—
1046C2×C4—62no—
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×C3—82no—
1075C2×C3#240611yescharacteristic
1076C2×C3#241011yescharacteristic
1077C2×C3#242711yescharacteristic
1078C2×C3#243011yescharacteristic
1079C2×C3#247211yescharacteristic
1080C2×C3#247411yescharacteristic
1081C2×C3#249111yescharacteristic
1082C2×C3#252111yescharacteristic
1083C2×C3#254711yescharacteristic
1084C2×C3#267211yescharacteristic
1085C2×C3#267411yescharacteristic
1086C2×C3#268611yescharacteristic
1087C2×C3#270011yescharacteristic
1088C2×C3#271511yescharacteristic
1089C2×C3#271711yescharacteristic
1090D3—44no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—64no—
1099C22—64no—
1100C22—64no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22#549011yescharacteristic
1122C22#550711yescharacteristic
1123C22#552811yescharacteristic
1124C22#554711yescharacteristic
1125C22#555111yescharacteristic
1126C22#555611yescharacteristic
1127C22#556111yescharacteristic
1128C22D3×#12011yescharacteristic
1129C22#558911yescharacteristic
1130C22#559011yescharacteristic
1131C22D3×#12111yescharacteristic
1132C22#560811yescharacteristic
1133C22#561011yescharacteristic
1134C22#561011yescharacteristic
1135C22#561011yescharacteristic
1136C22#561211yescharacteristic
1137C22#561311yescharacteristic
1138C22#562111yescharacteristic
1139C22#562811yescharacteristic
1140C22#563111yescharacteristic
1141C22#563311yescharacteristic
1142C22#564011yescharacteristic
1143C22#564011yescharacteristic
1144C22#564611yescharacteristic
1145C22#564811yescharacteristic
1146C22#565511yescharacteristic
1147C22#565511yescharacteristic
1148C22#565511yescharacteristic
1149C22#566211yescharacteristic
1150C22#566811yescharacteristic
1151C22#567011yescharacteristic
1152C22D3×#12411yescharacteristic
1153C22#570211yescharacteristic
1154C22#570211yescharacteristic
1155C22#571711yescharacteristic
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—64no—
1161C4—64no—
1162C4—81no—
1163C4—81no—
1164C4—122no—
1165C4—122no—
1166C4—122no—
1167C4—241no—
1168C4—241no—
1169C3#1531111yescharacteristic, complemented, Sylow
1170C2—82no—
1171C2—124no—
1172C2#7389511yescharacteristic
1173C2#7460011yescharacteristic
1174C2#7464011yescharacteristic
1175C2#7491411yescharacteristic
1176C2#7552811yescharacteristic
1177C2#7587611yescharacteristic
1178C2#7633011yescharacteristic
1179C2#7675511yescharacteristic
1180C2#7679211yescharacteristic
1181C2#7700911yescharacteristic
1182C2#7711611yescharacteristic
1183C2#7736011yescharacteristic
1184C2#7743811yescharacteristic
1185C2#7751411yescharacteristic
1186C2#7811511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15311
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#4992C2semidirect
3. C2×#4979C2semidirect
6. C2×#4667C2semidirect
7. C3×#1439C2semidirect
8. #71549C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #69429C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69424C2semidirect
14. #69406C2semidirect
15. #69405C2semidirect
71. #1439D3semidirect
655. C2×Dic3#124semidirect
1169. C3#15311semidirect

Maximal subgroups

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

subgroupindex
C22×#8852
C2×#49922
C2×#49792
C2×#49592
C2×#49562
C2×#46672
C3×#14392
#715492
#715472
#694292
(C2×D3)⋊#952
#694242
#694062
#694052
#153113