Finite Group Databasebeta

← #10732572

Subgroups — #10732572

Order 768.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#4957C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C2×#4957C211yesmaximal, characteristic
5C2×#4647C211yesmaximal, characteristic, complemented
6C2×#4650C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71546C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69427C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#15222—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
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
52Dic3×C4⋊C4—24no—
53#4957—24no—
54#4957—24no—
55#4957—24no—
56#4650—24no—
57#4647—24no—
58C2×#390—31no—
59C2×#390—31no—
60C2×#390—31no—
61C2×#389—31no—
62C2×#382—31no—
63C2×C4×C4⋊C4—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439D311yescharacteristic, complemented
72C4⋊#95—31no—
73C25×C3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67Q814yes—
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
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×C3×C22⋊C4—41no—
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×#217—41no—
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—22no—
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×(C2×D3)⋊C4—41no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3—41no—
139C2×C4⋊Dic3—41no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—41no—
150C2×Dic3⋊C4—41no—
151C2×Dic3⋊C4D414yes—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3D414yes—
160C2×C4×Dic3D414yes—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—41no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—41no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C23×D4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4C2×D311yescharacteristic
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C22⋊C4C2×D311yescharacteristic
193C22×C42—31no—
194C22×C42—31no—
195C22×C42—31no—
196#390—64no—
197#390—64no—
198#390—64no—
199#389—64no—
200#382—64no—
201C4×C4⋊C4—64no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95C2×D311yescharacteristic
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3C2×Q812yes—
229C24×C3C2411yescharacteristic
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3C2×Q812yes—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4#4112yes—
285C22×C3×C4#4112yes—
286C22×C3×C4#4112yes—
287C2×#67—28no—
288C2×#67—28no—
289C2×#67—28no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×Q812yes—
339C22×Dic3#4112yes—
340C22×Dic3#4112yes—
341C22×Dic3#4112yes—
342C22×Dic3#4112yes—
343C3×C4⋊C4—28no—
344C3×C22⋊C4—44no—
345C3×C22⋊C4—44no—
346C3×C22⋊C4—44no—
347#217—44no—
348#217—44no—
349#217—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356C4⋊Dic3—28no—
357C4⋊Dic3—44no—
358Dic3⋊C4—28no—
359Dic3⋊C4—44no—
360Dic3⋊C4—44no—
361Dic3⋊C4—44no—
362C4×Dic3—28no—
363C4×Dic3—28no—
364C4×Dic3—44no—
365C25—31no—
366C25C22×D311yescharacteristic
367C22×D4—34no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—62no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D311yescharacteristic
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—121no—
405C2×C4⋊C4—121no—
406C2×C4⋊C4—121no—
407C2×C4⋊C4—121no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—41no—
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—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4—121no—
439C2×C22⋊C4—121no—
440C2×C22⋊C4—121no—
441C2×C22⋊C4—121no—
442C2×C22⋊C4—121no—
443C2×C22⋊C4—121no—
444C2×C42—34no—
445C2×C42—34no—
446C2×C42—62no—
447C2×C42—62no—
448C2×C42—62no—
449C2×C42—62no—
450C2×C42—62no—
451C2×C42—62no—
452C2×C42—62no—
453#95—22no—
454#95—22no—
455#95—41no—
456#95—62no—
457#95—62no—
458#95—62no—
459#95—62no—
460#95—62no—
461#95—62no—
462#95—121no—
463#95—121no—
464#95—121no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
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×C3C22×D411yescharacteristic
501C23×C3C22×D411yescharacteristic
502C23×C3C22×D411yescharacteristic
503C23×C3C22×Q811yescharacteristic
504C23×C3C2×#4111yescharacteristic
505C23×C3C2×#4111yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3H(5,𝔽2)11yescharacteristic
512C23×C3H(5,𝔽2)11yescharacteristic
513C23×C3H(5,𝔽2)11yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
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—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4#12414yes—
592#67—416no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
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—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3#12114yes—
636C2×Dic3#12114yes—
637C2×Dic3#12114yes—
638C2×Dic3C22⋊Q814yes—
639C2×Dic3C22⋊Q814yes—
640C2×Dic3C22⋊Q814yes—
641C2×Dic3#12614yes—
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—32no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24D3×Q812yes—
672C24C23×D311yescharacteristic
673C2×D4—68no—
674C2×D4—68no—
675C2×D4—68no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—124no—
679C2×D4—124no—
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—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—32no—
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—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#23512yes—
766C22×C4D3×D412yes—
767C22×C4D3×D412yes—
768C22×C4D3×D412yes—
769C22×C4#23712yes—
770C22×C4#23712yes—
771C4⋊C4—28no—
772C4⋊C4—68no—
773C4⋊C4—68no—
774C4⋊C4—124no—
775C4⋊C4—124no—
776C4⋊C4—124no—
777C4⋊C4—124no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—124no—
788C22⋊C4—124no—
789C22⋊C4—124no—
790C42—68no—
791C42—68no—
792C42—124no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
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×C3C2×#12111yescharacteristic
809C22×C3C2×#12111yescharacteristic
810C22×C3C2×#12111yescharacteristic
811C22×C3C2×C22⋊Q811yescharacteristic
812C22×C3C2×C22⋊Q811yescharacteristic
813C22×C3C2×C22⋊Q811yescharacteristic
814C22×C3#52511yescharacteristic
815C22×C3#52511yescharacteristic
816C22×C3C2×#12411yescharacteristic
817C22×C3C2×#12611yescharacteristic
818C22×C3#52911yescharacteristic
819C22×C3#52911yescharacteristic
820C22×C3#53211yescharacteristic
821C22×C3#53511yescharacteristic
822C22×C3#53511yescharacteristic
823C22×C3#53511yescharacteristic
824C22×C3#53511yescharacteristic
825C22×C3#54011yescharacteristic
826C22×C3#54011yescharacteristic
827C22×C3#54611yescharacteristic
828C22×C3#54611yescharacteristic
829C22×C3#55011yescharacteristic
830C22×C3#55011yescharacteristic
831C22×C3#55311yescharacteristic
832C22×C3#55311yescharacteristic
833C22×C3#55411yescharacteristic
834C22×C3#55411yescharacteristic
835C22×C3#55411yescharacteristic
836C22×C3#55411yescharacteristic
837C22×C3#55511yescharacteristic
838C22×C3#55511yescharacteristic
839C22×C3#55911yescharacteristic
840C22×C3#55911yescharacteristic
841C22×C3#55911yescharacteristic
842C22×C3#55911yescharacteristic
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—81no—
851C2×D3—81no—
852C2×D3—81no—
853C2×D3—81no—
854C2×D3—81no—
855C2×D3—81no—
856C2×D3—81no—
857C2×D3—81no—
858C3×C4—24no—
859C3×C4—42no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—81no—
863C3×C4—81no—
864Dic3—42no—
865Dic3—42no—
866Dic3—42no—
867Dic3—42no—
868Dic3—81no—
869Dic3—81no—
870Dic3#39618yes—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
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—62no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23C2×#23511yescharacteristic
942C23C2×D3×D411yescharacteristic
943C23C2×D3×D411yescharacteristic
944C23C2×D3×D411yescharacteristic
945C23C2×#23711yescharacteristic
946C23C2×#23711yescharacteristic
947C23#100411yescharacteristic
948C23#100411yescharacteristic
949C23C2×D3×Q811yescharacteristic
950C23D3×#4111yescharacteristic
951C23D3×#4111yescharacteristic
952C23D3×#4111yescharacteristic
953C23D3×#4111yescharacteristic
954C23#100911yescharacteristic
955C23#100911yescharacteristic
956D4—1216no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—34no—
973C2×C4—34no—
974C2×C4—34no—
975C2×C4—34no—
976C2×C4—34no—
977C2×C4—34no—
978C2×C4—34no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
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—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
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—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4#88514yes—
1048C2×C3—82no—
1049C2×C3C2×#39611yescharacteristic
1050C2×C3#241411yescharacteristic
1051C2×C3#241411yescharacteristic
1052C2×C3#245411yescharacteristic
1053C2×C3#245411yescharacteristic
1054C2×C3#251311yescharacteristic
1055C2×C3#251311yescharacteristic
1056C2×C3#254411yescharacteristic
1057C2×C3#254811yescharacteristic
1058C2×C3#256311yescharacteristic
1059C2×C3#256611yescharacteristic
1060C2×C3#258011yescharacteristic
1061C2×C3#258011yescharacteristic
1062C2×C3#261911yescharacteristic
1063C2×C3#285011yescharacteristic
1064D3—82no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22—241no—
1088C22—241no—
1089C22—241no—
1090C22—241no—
1091C22—241no—
1092C22—241no—
1093C22—241no—
1094C22—241no—
1095C22C2×#88511yescharacteristic
1096C22#551111yescharacteristic
1097C22#553211yescharacteristic
1098C22#553811yescharacteristic
1099C22#554711yescharacteristic
1100C22#555311yescharacteristic
1101C22#555911yescharacteristic
1102C22#558611yescharacteristic
1103C22#559111yescharacteristic
1104C22#559211yescharacteristic
1105C22#559611yescharacteristic
1106C22#560111yescharacteristic
1107C22D3×#12111yescharacteristic
1108C22D3×#12111yescharacteristic
1109C22D3×#12111yescharacteristic
1110C22#560711yescharacteristic
1111C22#560711yescharacteristic
1112C22#561611yescharacteristic
1113C22D3×C22⋊Q811yescharacteristic
1114C22D3×C22⋊Q811yescharacteristic
1115C22D3×C22⋊Q811yescharacteristic
1116C22#563511yescharacteristic
1117C22#563511yescharacteristic
1118C22#563611yescharacteristic
1119C22#564911yescharacteristic
1120C22#565411yescharacteristic
1121C22#566311yescharacteristic
1122C22#566311yescharacteristic
1123C22#566411yescharacteristic
1124C22#567411yescharacteristic
1125C22#568111yescharacteristic
1126C22#568111yescharacteristic
1127C22D3×#12611yescharacteristic
1128C22#570911yescharacteristic
1129C22#571811yescharacteristic
1130C4—24no—
1131C4—38no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—81no—
1136C4—81no—
1137C4—122no—
1138C4—122no—
1139C4—122no—
1140C4—122no—
1141C4—241no—
1142C4—241no—
1143C3#1522211yescharacteristic, complemented, Sylow
1144C2—82no—
1145C2—242no—
1146C2#7394211yescharacteristic
1147C2#7442611yescharacteristic
1148C2#7448711yescharacteristic
1149C2#7486911yescharacteristic
1150C2#7549511yescharacteristic
1151C2#7555311yescharacteristic
1152C2#7635311yescharacteristic
1153C2#7667011yescharacteristic
1154C2#7680211yescharacteristic
1155C2#7694511yescharacteristic
1156C2#7697111yescharacteristic
1157C2#7732011yescharacteristic
1158C2D3×#39611yescharacteristic
1159C2#7749511yescharacteristic
1160C2#7802311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15222
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×C4⋊C4C2semidirect
5. C2×#4647C2semidirect
6. C2×#4650C2semidirect
7. C3×#1439C2semidirect
8. #71570C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71546C2semidirect
12. #69428C2semidirect
13. #69427C2semidirect
14. #69427C2semidirect
15. Dic3⋊#95C2semidirect
71. #1439D3semidirect
1143. C3#15222semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×C4⋊C42
C2×#49572
C2×#46472
C2×#46502
C3×#14392
#715702
#715472
#715462
#694282
#694272
Dic3⋊#952
#152223