Finite Group Databasebeta

← #10735752

Subgroups — #10735752

Order 768.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5222C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C2×#4948C211yesmaximal, characteristic, complemented
4C2×#4951C211yesmaximal, characteristic, complemented
5C2×#4647C211yesmaximal, characteristic, complemented
6C2×#4653C211yesmaximal, characteristic, complemented
7C3×#1438C211yesmaximal, characteristic
8#71548C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#71545C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#15458—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40#5222—24no—
41#5221—24no—
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#4951—24no—
55#4948—24no—
56#4653—24no—
57#4647—24no—
58C2×#396—31no—
59C2×#394—31no—
60C2×#390—31no—
61C2×#389—31no—
62C2×#388—31no—
63C2×#387—31no—
64#1441—31no—
65#1440—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1438D311yescharacteristic
71#1437—31no—
72#1434—31no—
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—41no—
102C2×C3×C22⋊C4—41no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4—41no—
105C2×C3×C22⋊C4—41no—
106C2×C3×C22⋊C4—41no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—41no—
126C2×#217—41no—
127C2×#217—41no—
128C2×#217—41no—
129C2×#217—41no—
130C2×#217—41no—
131C2×C4⋊Dic3—22no—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—41no—
134C2×C4⋊Dic3—41no—
135C2×C4⋊Dic3D414yes—
136C2×C4⋊Dic3D414yescomplemented
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—41no—
144C2×Dic3⋊C4—41no—
145C2×Dic3⋊C4—41no—
146C2×Dic3⋊C4—41no—
147C2×Dic3⋊C4—41no—
148C2×Dic3⋊C4D414yes—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—41no—
155C3×#95—22no—
156C3×#95—22no—
157C3⋊#95—22no—
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—41no—
168C3⋊#95—41no—
169C23×D4C2×D311yescharacteristic
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4C2×D311yescharacteristic
185C22×C22⋊C4C2×D311yescharacteristic
186C22×C22⋊C4C2×D311yescharacteristic
187C22×C22⋊C4C2×D311yescharacteristic
188C22×C42—31no—
189C22×C42—31no—
190#396—64no—
191#394—64no—
192#390—64no—
193#389—64no—
194#388—64no—
195#387—64no—
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×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×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×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×C3—21no—
238C24×C3#4112yes—
239C24×C3#4112yes—
240C24×C3C2411yescharacteristic
241C2×C3×D4—28no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
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×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4#4112yes—
282C22×C3×C4#4112yes—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
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×Dic3C2×D412yes—
332C22×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3#4112yes—
338C22×Dic3#4112yes—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—44no—
342C3×C22⋊C4—44no—
343#217—44no—
344#217—44no—
345#217—44no—
346#217—44no—
347#217—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351C4⋊Dic3—28no—
352C4⋊Dic3—44no—
353Dic3⋊C4—28no—
354Dic3⋊C4—44no—
355Dic3⋊C4—44no—
356Dic3⋊C4—44no—
357C4×Dic3—44no—
358C4×Dic3—44no—
359C25C22×D311yescharacteristic
360C25C22×D311yescharacteristic
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—41no—
367C22×D4—41no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—121no—
393C2×C4⋊C4—121no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4—121no—
396C2×C4⋊C4—121no—
397C2×C4⋊C4—121no—
398C2×C4⋊C4—121no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—121no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C42—62no—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42—121no—
441#95—22no—
442#95—22no—
443#95—62no—
444#95—62no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—121no—
454#95—121no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—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—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×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×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×C3C22×D411yescharacteristic
526C23×C3C22×D411yescharacteristic
527C23×C3C22×D411yescharacteristic
528C23×C3C2×#4111yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3C2×#4111yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C3H(5,𝔽2)11yescharacteristic
536C23×C3H(5,𝔽2)11yescharacteristic
537C23×C3H(5,𝔽2)11yescharacteristic
538C23×C32−1+411yescharacteristic
539C23×C32−1+411yescharacteristic
540C3×D4—416no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—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—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4#12114yes—
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—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3#12114yes—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24#23712yes—
661C24#23712yes—
662C24C23×D311yescharacteristic
663C2×D4—28no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
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—32no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
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—61no—
756C22×C4#23512yes—
757C22×C4D3×D412yes—
758C22×C4D3×D412yes—
759C22×C4D3×D412yes—
760C22×C4#23712yes—
761C4⋊C4—68no—
762C4⋊C4—68no—
763C4⋊C4—124no—
764C4⋊C4—124no—
765C4⋊C4—124no—
766C4⋊C4—124no—
767C22⋊C4—28no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—124no—
772C22⋊C4—124no—
773C22⋊C4—124no—
774C22⋊C4—124no—
775C22⋊C4—124no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C42—124no—
780C42—124no—
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×C3—42no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—81no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3—81no—
811C22×C3C2×#12111yescharacteristic
812C22×C3C2×#12111yescharacteristic
813C22×C3#52511yescharacteristic
814C22×C3#52511yescharacteristic
815C22×C3#52911yescharacteristic
816C22×C3#52911yescharacteristic
817C22×C3#53411yescharacteristic
818C22×C3#53511yescharacteristic
819C22×C3#53711yescharacteristic
820C22×C3#53911yescharacteristic
821C22×C3#53911yescharacteristic
822C22×C3#54011yescharacteristic
823C22×C3#54211yescharacteristic
824C22×C3#54211yescharacteristic
825C22×C3#54211yescharacteristic
826C22×C3D4211yescharacteristic
827C22×C3#54611yescharacteristic
828C22×C3#54611yescharacteristic
829C22×C3#54611yescharacteristic
830C22×C3#54711yescharacteristic
831C22×C3#54811yescharacteristic
832C22×C3#54811yescharacteristic
833C22×C3#54811yescharacteristic
834C22×C3#54811yescharacteristic
835C22×C3#55011yescharacteristic
836C22×C3#55011yescharacteristic
837C22×C3#55111yescharacteristic
838C22×C3#55111yescharacteristic
839C22×C3#55111yescharacteristic
840C22×C3#55211yescharacteristic
841C22×C3#55311yescharacteristic
842C22×C3#55311yescharacteristic
843C22×C3#55511yescharacteristic
844C22×C3#56011yescharacteristic
845C22×C3#56311yescharacteristic
846C3×C4—24no—
847C3×C4—42no—
848C3×C4—42no—
849C3×C4—81no—
850C3×C4—81no—
851Dic3—24no—
852Dic3—42no—
853Dic3—42no—
854Dic3—42no—
855Dic3—42no—
856Dic3—42no—
857Dic3—81no—
858Dic3—81no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
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—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
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—
929C23C2×#23511yescharacteristic
930C23C2×D3×D411yescharacteristic
931C23C2×D3×D411yescharacteristic
932C23C2×D3×D411yescharacteristic
933C23C2×#23711yescharacteristic
934C23C2×#23711yescharacteristic
935C23C2×#23711yescharacteristic
936C23#100411yescharacteristic
937C23#100411yescharacteristic
938C23#100411yescharacteristic
939C23#100411yescharacteristic
940C23D3×#4111yescharacteristic
941C23D3×#4111yescharacteristic
942C23#101011yescharacteristic
943C23#101011yescharacteristic
944D4—416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—34no—
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—62no—
981C2×C4—62no—
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—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
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×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4#88414yes—
1036C2×C3—82no—
1037C2×C3—82no—
1038C2×C3#241411yescharacteristic
1039C2×C3#241611yescharacteristic
1040C2×C3#242611yescharacteristic
1041C2×C3#242611yescharacteristic
1042C2×C3#246011yescharacteristic
1043C2×C3#246311yescharacteristic
1044C2×C3#247911yescharacteristic
1045C2×C3#252611yescharacteristic
1046C2×C3#253411yescharacteristic
1047C2×C3#267311yescharacteristic
1048C2×C3#270511yescharacteristic
1049C2×C3#270711yescharacteristic
1050C2×C3#272311yescharacteristic
1051C2×C3#273111yescharacteristic
1052C2×C3#275711yescharacteristic
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22C2×#88411yescharacteristic
1084C22#549511yescharacteristic
1085C22#549511yescharacteristic
1086C22#555111yescharacteristic
1087C22#555711yescharacteristic
1088C22#555811yescharacteristic
1089C22#556111yescharacteristic
1090C22#558611yescharacteristic
1091C22#558611yescharacteristic
1092C22#558711yescharacteristic
1093C22#558911yescharacteristic
1094C22#559111yescharacteristic
1095C22#559111yescharacteristic
1096C22#559211yescharacteristic
1097C22#559511yescharacteristic
1098C22#559811yescharacteristic
1099C22#559811yescharacteristic
1100C22#559911yescharacteristic
1101C22#560111yescharacteristic
1102C22#560211yescharacteristic
1103C22#560211yescharacteristic
1104C22#560311yescharacteristic
1105C22D3×#12111yescharacteristic
1106C22#560811yescharacteristic
1107C22#561211yescharacteristic
1108C22#561511yescharacteristic
1109C22#561611yescharacteristic
1110C22#564911yescharacteristic
1111C22#565011yescharacteristic
1112C22#565111yescharacteristic
1113C22#566211yescharacteristic
1114C22#567711yescharacteristic
1115C22#567711yescharacteristic
1116C22#571711yescharacteristic
1117C22#571811yescharacteristic
1118C4—24no—
1119C4—42no—
1120C4—42no—
1121C4—64no—
1122C4—81no—
1123C4—81no—
1124C4—122no—
1125C4—122no—
1126C4—122no—
1127C4—122no—
1128C4—122no—
1129C4—241no—
1130C4—241no—
1131C3#1545811yescharacteristic, complemented, Sylow
1132C2—82no—
1133C2—82no—
1134C2#7383411yescharacteristic
1135C2#7473411yescharacteristic
1136C2#7474911yescharacteristic
1137C2#7482611yescharacteristic
1138C2#7485011yescharacteristic
1139C2#7643911yescharacteristic
1140C2#7644311yescharacteristic
1141C2#7667011yescharacteristic
1142C2#7668111yescharacteristic
1143C2#7672411yescharacteristic
1144C2#7676811yescharacteristic
1145C2#7690111yescharacteristic
1146C2#7691311yescharacteristic
1147C2#7702711yescharacteristic
1148C2#7704611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC23×C3×D4C22
hypercenter#1438D3
hypocenterC3#15458
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
3. C2×#4948C2semidirect
4. C2×#4951C2semidirect
5. C2×#4647C2semidirect
6. C2×#4653C2semidirect
8. #71548C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. #71547C2semidirect
13. #71545C2semidirect
14. #69411C2semidirect
15. #69402C2semidirect
136. C2×C4⋊Dic3D4semidirect
1131. C3#15458semidirect

Maximal subgroups

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

subgroupindex
C2×#52222
C2×#52212
C2×#49482
C2×#49512
C2×#46472
C2×#46532
C3×#14382
#715482
#715472
#715452
#694112
#694022
#154583