Finite Group Databasebeta

← #10733220

Subgroups — #10733220

Order 768.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5213C211yesmaximal, characteristic
2C2×#5211C211yesmaximal, characteristic, complemented
3C2×#4957C211yesmaximal, characteristic
4C2×#4675C211yesmaximal, characteristic, complemented
5C3×C22⋊#95C211yesmaximal, characteristic, complemented
6#71550C211yesmaximal, characteristic
7#71547C211yesmaximal, characteristic, complemented
8#71546C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12#69420C211yesmaximal, characteristic, complemented
13#69413C211yesmaximal, characteristic, complemented
14#69403C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#15285—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38#5213—24no—
39#5211—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#4957—24no—
55#4675—24no—
56C2×#397—31no—
57C2×#390—31no—
58C2×#386—31no—
59C2×#381—31no—
60#1444—31no—
61#1442—31no—
62#1440—31no—
63#1440—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1438—31no—
68#1434—31no—
69#1434—31no—
70C22⋊#95D311yescharacteristic, complemented
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×#67D414yes—
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—41no—
105C2×C3×C22⋊C4—41no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—41no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×C4⋊Dic3—41no—
134C2×C4⋊Dic3—41no—
135C2×C4⋊Dic3—41no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—41no—
148C3×#95—41no—
149C3⋊#95—22no—
150C3⋊#95—22no—
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—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95D414yescomplemented
163C23×D4—31no—
164C24×C4C2×D311yescharacteristic
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C42—31no—
180#397—64no—
181#390—64no—
182#386—64no—
183#381—64no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
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×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
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×C3C2×D412yes—
215C24×C3#4112yes—
216C24×C3#4112yes—
217C24×C3C2411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
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×D3C2×D412yes—
233C22×C3×C4—28no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
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—44no—
273C22×C3×C4—44no—
274C22×C3×C4—44no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4C2×D412yes—
279C22×C3×C4#4112yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
282C2×#67—28no—
283C2×#67—28no—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C2×#67—44no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
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×Dic3C2×D412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3#4112yes—
337C22×Dic3#4112yes—
338C3×C22⋊C4—44no—
339C3×C22⋊C4—44no—
340#217—44no—
341#217—44no—
342#217—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349C4⋊Dic3—44no—
350Dic3⋊C4—44no—
351Dic3⋊C4—44no—
352C4×Dic3—44no—
353C25—31no—
354C25C22×D311yescharacteristic
355C22×D4—34no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—121no—
361C22×D4—121no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—41no—
375C23×C4—41no—
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—121no—
385C2×C4⋊C4—121no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C4⋊C4—121no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C42—62no—
425C2×C42—62no—
426C2×C42—62no—
427#95—22no—
428#95—22no—
429#95—34no—
430#95—41no—
431#95—41no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—62no—
441#95—62no—
442#95—121no—
443#95—121no—
444#95—121no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
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—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3#12314yes—
480C23×C3C22×D411yescharacteristic
481C23×C3C22×D411yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4111yescharacteristic
487C23×C3C2×#4111yescharacteristic
488C23×C3C2×#4111yescharacteristic
489C23×C3H(5,𝔽2)11yescharacteristic
490C23×C3H(5,𝔽2)11yescharacteristic
491C23×C3H(5,𝔽2)11yescharacteristic
492C23×C3H(5,𝔽2)11yescharacteristic
493C23×C3H(5,𝔽2)11yescharacteristic
494C23×C32−1+411yescharacteristic
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
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—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—416no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
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—
573#67—416no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
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#12314yes—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—32no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24#23512yes—
651C24D3×D412yes—
652C24#23712yes—
653C24C23×D311yescharacteristic
654C2×D4—68no—
655C2×D4—68no—
656C2×D4—124no—
657C2×D4—124no—
658C2×D4—124no—
659C2×D4—124no—
660C2×D4—124no—
661C22×C4—28no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
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—32no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
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#23512yes—
756C22×C4#23512yes—
757C22×C4D3×D412yes—
758C22×C4#23712yes—
759C4⋊C4—124no—
760C4⋊C4—124no—
761C4⋊C4—124no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—124no—
765C22⋊C4—124no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C22⋊C4—124no—
773C42—124no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—24no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3C2×#12311yescharacteristic
790C22×C3C2×#12311yescharacteristic
791C22×C3#52511yescharacteristic
792C22×C3#52911yescharacteristic
793C22×C3#52911yescharacteristic
794C22×C3#53211yescharacteristic
795C22×C3#53411yescharacteristic
796C22×C3#53511yescharacteristic
797C22×C3#53811yescharacteristic
798C22×C3#53811yescharacteristic
799C22×C3#53911yescharacteristic
800C22×C3#54011yescharacteristic
801C22×C3#54011yescharacteristic
802C22×C3#54211yescharacteristic
803C22×C3#54211yescharacteristic
804C22×C3D4211yescharacteristic
805C22×C3#54611yescharacteristic
806C22×C3#54611yescharacteristic
807C22×C3#54611yescharacteristic
808C22×C3#54711yescharacteristic
809C22×C3#54711yescharacteristic
810C22×C3#55011yescharacteristic
811C22×C3#55111yescharacteristic
812C22×C3#55111yescharacteristic
813C22×C3#55111yescharacteristic
814C22×C3#55111yescharacteristic
815C22×C3#55111yescharacteristic
816C22×C3#55111yescharacteristic
817C22×C3#55211yescharacteristic
818C22×C3#55311yescharacteristic
819C22×C3#55311yescharacteristic
820C22×C3#55511yescharacteristic
821C22×C3#55511yescharacteristic
822C22×C3#56011yescharacteristic
823C22×C3#56211yescharacteristic
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C3×C4—42no—
840C3×C4—42no—
841C3×C4—42no—
842C3×C4—42no—
843C3×C4—81no—
844C3×C4—81no—
845Dic3—24no—
846Dic3—42no—
847Dic3—42no—
848Dic3—81no—
849Dic3—81no—
850Dic3—81no—
851Dic3—81no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
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#88314yes—
922C23C2×#23511yescharacteristic
923C23C2×#23511yescharacteristic
924C23C2×#23511yescharacteristic
925C23C2×D3×D411yescharacteristic
926C23C2×D3×D411yescharacteristic
927C23C2×#23711yescharacteristic
928C23C2×#23711yescharacteristic
929C23#100411yescharacteristic
930C23#100411yescharacteristic
931C23#100411yescharacteristic
932C23#100711yescharacteristic
933C23D3×#4111yescharacteristic
934C23D3×#4111yescharacteristic
935C23#100911yescharacteristic
936C23#100911yescharacteristic
937D4—1216no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—34no—
951C2×C4—416no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
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—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
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×C3—44no—
1031C2×C3#241811yescharacteristic
1032C2×C3#241911yescharacteristic
1033C2×C3#242011yescharacteristic
1034C2×C3#242211yescharacteristic
1035C2×C3#247911yescharacteristic
1036C2×C3#248311yescharacteristic
1037C2×C3#252611yescharacteristic
1038C2×C3#255411yescharacteristic
1039C2×C3#261011yescharacteristic
1040C2×C3#267311yescharacteristic
1041C2×C3#268611yescharacteristic
1042C2×C3#270611yescharacteristic
1043C2×C3#273711yescharacteristic
1044C2×C3#274911yescharacteristic
1045C2×C3#276111yescharacteristic
1046D3—82no—
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22—241no—
1076C22—241no—
1077C22#547911yescharacteristic
1078C22C2×#88311yescharacteristic
1079C22#549011yescharacteristic
1080C22#549011yescharacteristic
1081C22#549511yescharacteristic
1082C22#549511yescharacteristic
1083C22#550711yescharacteristic
1084C22#551311yescharacteristic
1085C22#551511yescharacteristic
1086C22#552711yescharacteristic
1087C22#552711yescharacteristic
1088C22#553811yescharacteristic
1089C22#554011yescharacteristic
1090C22#554011yescharacteristic
1091C22#554811yescharacteristic
1092C22#555311yescharacteristic
1093C22#556011yescharacteristic
1094C22#556211yescharacteristic
1095C22#556311yescharacteristic
1096C22#558611yescharacteristic
1097C22#559011yescharacteristic
1098C22#559111yescharacteristic
1099C22#559311yescharacteristic
1100C22#560711yescharacteristic
1101C22#561511yescharacteristic
1102C22#561611yescharacteristic
1103C22#562011yescharacteristic
1104C22#563111yescharacteristic
1105C22#564011yescharacteristic
1106C22#564311yescharacteristic
1107C22#564711yescharacteristic
1108C22D3×#12311yescharacteristic
1109C22#565311yescharacteristic
1110C22#565811yescharacteristic
1111C22#565811yescharacteristic
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—64no—
1117C4—81no—
1118C4—81no—
1119C4—122no—
1120C4—122no—
1121C4—241no—
1122C4—241no—
1123C4—241no—
1124C4—241no—
1125C3#1528511yescharacteristic, complemented, Sylow
1126C2—44no—
1127C2—242no—
1128C2#7337511yescharacteristic
1129C2#7353011yescharacteristic
1130C2#7353511yescharacteristic
1131C2#7382611yescharacteristic
1132C2#7396911yescharacteristic
1133C2#7397311yescharacteristic
1134C2#7413011yescharacteristic
1135C2#7440911yescharacteristic
1136C2#7445111yescharacteristic
1137C2#7451211yescharacteristic
1138C2#7455211yescharacteristic
1139C2#7469511yescharacteristic
1140C2#7478011yescharacteristic
1141C2#7479111yescharacteristic
1142C2#7484011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#15285
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#5211C2semidirect
4. C2×#4675C2semidirect
5. C3×C22⋊#95C2semidirect
7. #71547C2semidirect
8. #71546C2semidirect
9. #69429C2semidirect
10. #69429C2semidirect
11. #69427C2semidirect
12. #69420C2semidirect
13. #69413C2semidirect
14. #69403C2semidirect
15. #69401C2semidirect
70. C22⋊#95D3semidirect
162. C3⋊#95D4semidirect
1125. C3#15285semidirect

Maximal subgroups

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

subgroupindex
C2×#52132
C2×#52112
C2×#49572
C2×#46752
C3×C22⋊#952
#715502
#715472
#715462
#694292
#694272
#694202
#694132
#694032
#694012
#152853