Finite Group Databasebeta

← #10726578

Subgroups — #10726578

Order 768.

3654 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C22×D3×C22⋊C4C211yesmaximal, characteristic
3C2×#4955C211yesmaximal, characteristic
4C2×#4955C211yesmaximal, characteristic
5C2×#4947C211yesmaximal, characteristic, complemented
6C2×#4673C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
16#14717—31nomaximal, Sylow
17C25×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic, complemented
21C22×C3×C4⋊C4C2211yescharacteristic, complemented
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic, complemented
39C22×Dic3⋊C4C2211yescharacteristic, complemented
40C2×#896—24no—
41C2×#896—24no—
42C2×#896—24no—
43C2×D3×C22⋊C4—24no—
44C2×D3×C22⋊C4—24no—
45C2×D3×C22⋊C4—24no—
46C2×C3×#95C2211yescharacteristic, complemented
47C2×C3×#95C2211yescharacteristic, complemented
48C2×C3×#95C2211yescharacteristic, complemented
49C2×C3⋊#95C2211yescharacteristic, complemented
50C2×C3⋊#95C2211yescharacteristic, complemented
51C2×C3⋊#95C2211yescharacteristic, complemented
52C2×C3⋊#95C2211yescharacteristic, complemented
53C2×C3⋊#95C2211yescharacteristic, complemented
54C2×C3⋊#95C2211yescharacteristic, complemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57C2×C3⋊#95C2211yescharacteristic, complemented
58#4955—24no—
59#4955—24no—
60#4947—24no—
61#4673—24no—
62C22×C22⋊Q8—31no—
63C23×C22⋊C4—31no—
64C2×#393—31no—
65C2×#393—31no—
66C2×#379—31no—
67C2×#379—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1439—31no—
73#1439D311yescharacteristic, complemented
74C22⋊#95—31no—
75C22⋊#95—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3—22no—
79C24×D3—22no—
80C24×D3—22no—
81C24×D3—22no—
82C24×D3—22no—
83C24×D3—22no—
84C24×D3—22no—
85C24×D3—22no—
86C24×D3—22no—
87C24×D3—22no—
88C24×D3—41no—
89C24×D3—41no—
90C24×D3—41no—
91C24×D3—41no—
92C24×D3Q814yescomplemented
93C24×D3C2311yescharacteristic
94C24×D3C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—41no—
117C22×C4×D3—41no—
118C22×C4×D3—41no—
119C22×C4×D3—41no—
120C22×C4×D3D414yes—
121C22×Dic6—22no—
122C22×Dic6—22no—
123C22×Dic6—22no—
124C22×Dic6—22no—
125C22×Dic6—22no—
126C22×Dic6—41no—
127C22×Dic6—41no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—41no—
139C2×C3×C22⋊C4—41no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—41no—
147C2×#217—41no—
148C2×#217D414yes—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—22no—
168C2×(C2×D3)⋊C4—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—22no—
171C2×(C2×D3)⋊C4—22no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4—41no—
174C2×(C2×D3)⋊C4—41no—
175C2×(C2×D3)⋊C4—41no—
176C2×(C2×D3)⋊C4D414yes—
177C2×(C2×D3)⋊C4D414yes—
178C2×(C2×D3)⋊C4D414yes—
179C2×Dic3⋊C4—22no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4—22no—
183C2×Dic3⋊C4—22no—
184C2×Dic3⋊C4—22no—
185#896—232no—
186D3×C22⋊C4—232no—
187C3×#95—22no—
188C3×#95—41no—
189C3×#95—41no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194C3⋊#95—22no—
195C3⋊#95—41no—
196C3⋊#95—41no—
197C3⋊#95—41no—
198C3⋊#95—41no—
199C26—31no—
200C23×Q8—31no—
201C24×C4—31no—
202C24×C4—31no—
203C2×C22⋊Q8—64no—
204C2×C22⋊Q8—64no—
205C2×C22⋊Q8—64no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4C2×D311yescharacteristic, complemented
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—64no—
223C22×C22⋊C4—64no—
224C22×C22⋊C4—64no—
225C22×C22⋊C4C2×D311yescharacteristic
226C22×C22⋊C4C2×D311yescharacteristic
227C22×C22⋊C4C2×D311yescharacteristic
228#393—64no—
229#393—64no—
230#379—64no—
231#379—64no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95C2×D311yescharacteristic, complemented
242C2×#95C2×D311yescharacteristic, complemented
243C2×#95C2×D311yescharacteristic, complemented
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3C2×D412yes—
257C24×C3C2×Q812yes—
258C24×C3#4112yes—
259C24×C3C2411yescharacteristic
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—28no—
269C23×D3—28no—
270C23×D3—28no—
271C23×D3—28no—
272C23×D3—28no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—28no—
286C23×D3—28no—
287C23×D3—28no—
288C23×D3—28no—
289C23×D3—44no—
290C23×D3—44no—
291C23×D3—44no—
292C23×D3—44no—
293C23×D3—44no—
294C23×D3—44no—
295C23×D3—44no—
296C23×D3—44no—
297C23×D3—44no—
298C23×D3—44no—
299C23×D3—44no—
300C23×D3—44no—
301C23×D3—44no—
302C23×D3—44no—
303C23×D3—44no—
304C23×D3—44no—
305C23×D3—44no—
306C23×D3—44no—
307C23×D3—44no—
308C23×D3—44no—
309C23×D3—44no—
310C23×D3—44no—
311C23×D3—44no—
312C23×D3—44no—
313C23×D3—44no—
314C23×D3—44no—
315C23×D3C2×D412yes—
316C23×D3C2×D412yes—
317C23×D3C2×D412yes—
318C23×D3C2×D412yes—
319C23×D3C2×Q812yes—
320C23×D3C2×Q812yes—
321C23×D3#4112yes—
322C23×D3#4112yes—
323C23×D3#4112yes—
324C23×D3#4112yes—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4C2×D412yes—
364C22×C3×C4C2×D412yes—
365C22×C3×C4C2×D412yes—
366C22×C3×C4C2×D412yes—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3—21no—
386C22×Dic3—21no—
387C22×Dic3—21no—
388C22×Dic3—21no—
389C22×Dic3—21no—
390C22×Dic3—21no—
391C22×Dic3—21no—
392C22×Dic3—21no—
393C22×Dic3—21no—
394C22×Dic3—21no—
395C22×Dic3—21no—
396C22×Dic3—21no—
397C22×Dic3—21no—
398C22×Dic3—21no—
399C22×Dic3—21no—
400C22×Dic3—21no—
401C22×Dic3—21no—
402C22×Dic3—21no—
403C22×Dic3C2×D412yes—
404C22×Dic3C2×D412yes—
405C22×Dic3C2×D412yes—
406C22×Dic3C2×D412yes—
407C22×Dic3C2×D412yes—
408C22×Dic3C2×D412yes—
409C2×C4×D3—28no—
410C2×C4×D3—28no—
411C2×C4×D3—28no—
412C2×C4×D3—44no—
413C2×C4×D3—44no—
414C2×C4×D3—44no—
415C2×C4×D3—44no—
416C2×C4×D3—44no—
417C2×C4×D3—44no—
418C2×C4×D3—44no—
419C2×C4×D3—44no—
420C2×C4×D3—44no—
421C2×C4×D3—44no—
422C2×C4×D3—44no—
423C2×Dic6—28no—
424C2×Dic6—44no—
425C2×Dic6—44no—
426C2×Dic6—44no—
427C2×Dic6—44no—
428C2×Dic6—44no—
429C2×Dic6—44no—
430C3×C4⋊C4—28no—
431C3×C22⋊C4—28no—
432C3×C22⋊C4—44no—
433C3×C22⋊C4—44no—
434#217—28no—
435#217—44no—
436#217—44no—
437(C2×D3)⋊C4—28no—
438(C2×D3)⋊C4—28no—
439(C2×D3)⋊C4—28no—
440(C2×D3)⋊C4—28no—
441(C2×D3)⋊C4—44no—
442(C2×D3)⋊C4—44no—
443(C2×D3)⋊C4—44no—
444(C2×D3)⋊C4—44no—
445(C2×D3)⋊C4—44no—
446(C2×D3)⋊C4—44no—
447Dic3⋊C4—28no—
448Dic3⋊C4—28no—
449C25—31no—
450C25—31no—
451C25—34no—
452C25—62no—
453C25—62no—
454C25—62no—
455C25—62no—
456C25—62no—
457C25—62no—
458C25—62no—
459C25—62no—
460C25—62no—
461C25—62no—
462C25—121no—
463C25—121no—
464C25—121no—
465C25—121no—
466C25C22×D311yescharacteristic
467C22×Q8—62no—
468C22×Q8—62no—
469C22×Q8—62no—
470C22×Q8—62no—
471C22×Q8—62no—
472C22×Q8—121no—
473C22×Q8—121no—
474C23×C4—31no—
475C23×C4—31no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—34no—
479C23×C4—31no—
480C23×C4—31no—
481C23×C4—62no—
482C23×C4—62no—
483C23×C4—62no—
484C23×C4—62no—
485C23×C4—62no—
486C23×C4—62no—
487C23×C4—62no—
488C23×C4—62no—
489C23×C4—62no—
490C23×C4—121no—
491C23×C4—121no—
492C23×C4—121no—
493C23×C4—121no—
494C23×C4C22×D311yescharacteristic
495C23×C4C22×D311yescharacteristic
496C23×C4C22×D311yescharacteristic
497C23×C4C22×D311yescharacteristic
498C23×C4C22×D311yescharacteristic
499C23×C4C22×D311yescharacteristic
500C22⋊Q8—632no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—62no—
505C2×C4⋊C4—62no—
506C2×C4⋊C4—62no—
507C2×C4⋊C4—62no—
508C2×C4⋊C4—62no—
509C2×C4⋊C4—62no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—34no—
518C2×C22⋊C4—34no—
519C2×C22⋊C4—34no—
520C2×C22⋊C4—34no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—632no—
524C2×C22⋊C4—62no—
525C2×C22⋊C4—62no—
526C2×C22⋊C4—62no—
527C2×C22⋊C4—62no—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C22⋊C4—62no—
531C2×C22⋊C4—62no—
532C2×C22⋊C4—62no—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—62no—
535C2×C22⋊C4—62no—
536C2×C22⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—62no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C22⋊C4—62no—
543C2×C22⋊C4—62no—
544C2×C22⋊C4—62no—
545C2×C22⋊C4—62no—
546C2×C22⋊C4—62no—
547C2×C22⋊C4—62no—
548C2×C22⋊C4—62no—
549C2×C22⋊C4—62no—
550C2×C22⋊C4—62no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4—62no—
553C2×C22⋊C4—121no—
554C2×C22⋊C4—121no—
555C2×C22⋊C4—121no—
556C2×C22⋊C4—121no—
557C2×C22⋊C4—121no—
558C2×C22⋊C4—121no—
559#95—22no—
560#95—41no—
561#95—41no—
562#95—62no—
563#95—62no—
564#95—62no—
565#95—62no—
566#95—62no—
567#95—121no—
568#95—121no—
569#95—121no—
570#95—121no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3C22⋊Q814yescomplemented
606C23×C3C22×D411yescharacteristic
607C23×C3C22×D411yescharacteristic
608C23×C3C22×D411yescharacteristic
609C23×C3C22×D411yescharacteristic
610C23×C3C22×D411yescharacteristic
611C23×C3C22×Q811yescharacteristic
612C23×C3C2×#4111yescharacteristic
613C23×C3C2×#4111yescharacteristic
614C23×C3C2×#4111yescharacteristic
615C23×C3C2×#4111yescharacteristic
616C23×C3C2×#4111yescharacteristic
617C23×C3H(5,𝔽2)11yescharacteristic
618C23×C3H(5,𝔽2)11yescharacteristic
619C23×C3H(5,𝔽2)11yescharacteristic
620C23×C3H(5,𝔽2)11yescharacteristic
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—22no—
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—232no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—416no—
669C22×D3—416no—
670C22×D3—416no—
671C22×D3—416no—
672C22×D3—416no—
673C22×D3—416no—
674C22×D3—416no—
675C22×D3—416no—
676C22×D3—416no—
677C22×D3—416no—
678C22×D3—416no—
679C22×D3—416no—
680C22×D3—416no—
681C22×D3—41no—
682C22×D3—41no—
683C22×D3—41no—
684C22×D3—41no—
685C22×D3—41no—
686C22×D3—41no—
687C22×D3—41no—
688C22×D3—41no—
689C22×D3—41no—
690C22×D3—41no—
691C22×D3—41no—
692C22×D3—41no—
693C22×D3—41no—
694C22×D3—41no—
695C22×D3—41no—
696C22×D3—41no—
697C22×D3—416no—
698C22×D3#12014yes—
699C22×D3C22⋊Q814yes—
700C22×D3C22⋊Q814yes—
701C22×D3C22⋊Q814yes—
702C22×D3C22⋊Q814yescomplemented
703C22×D3#12414yes—
704C22×D3#12414yes—
705C22×D3#12414yes—
706C2×C3×C4—22no—
707C2×C3×C4—22no—
708C2×C3×C4—22no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723C2×C3×C4—41no—
724C2×C3×C4—41no—
725C2×C3×C4—41no—
726C2×C3×C4—41no—
727C2×C3×C4—41no—
728C2×C3×C4—41no—
729C2×C3×C4—41no—
730C2×C3×C4—41no—
731C2×C3×C4—41no—
732C2×C3×C4—41no—
733C2×C3×C4—41no—
734C2×C3×C4—41no—
735C2×C3×C4—41no—
736C2×C3×C4—41no—
737C2×C3×C4—41no—
738C2×C3×C4—41no—
739C2×C3×C4—41no—
740C2×C3×C4—41no—
741C2×C3×C4—41no—
742C2×C3×C4—41no—
743C2×C3×C4—41no—
744C2×C3×C4—41no—
745C2×C3×C4—41no—
746C2×C3×C4—41no—
747C2×C3×C4—41no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—22no—
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—22no—
757C2×Dic3—22no—
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—22no—
761C2×Dic3—22no—
762C2×Dic3—22no—
763C2×Dic3—41no—
764C2×Dic3—41no—
765C2×Dic3—41no—
766C2×Dic3—41no—
767C2×Dic3—41no—
768C2×Dic3—41no—
769C2×Dic3—41no—
770C2×Dic3—41no—
771C2×Dic3—41no—
772C2×Dic3—41no—
773C2×Dic3—41no—
774C2×Dic3—41no—
775C2×Dic3—41no—
776C2×Dic3—41no—
777C2×Dic3—41no—
778C2×Dic3—41no—
779C2×Dic3—41no—
780C2×Dic3—41no—
781C2×Dic3—41no—
782C2×Dic3—41no—
783C2×Dic3—41no—
784C2×Dic3—41no—
785C2×Dic3—41no—
786C2×Dic3—41no—
787C2×Dic3—41no—
788C2×Dic3—41no—
789C2×Dic3#12014yes—
790C4×D3—416no—
791C4×D3—416no—
792Dic6—416no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—32no—
806C24—32no—
807C24—32no—
808C24—32no—
809C24—32no—
810C24—32no—
811C24—32no—
812C24—32no—
813C24—32no—
814C24—32no—
815C24—68no—
816C24—68no—
817C24—68no—
818C24—68no—
819C24—68no—
820C24—68no—
821C24—68no—
822C24—68no—
823C24—61no—
824C24—61no—
825C24—61no—
826C24—61no—
827C24—61no—
828C24—61no—
829C24—61no—
830C24—61no—
831C24—68no—
832C24—61no—
833C24—61no—
834C24—61no—
835C24—61no—
836C24—61no—
837C24—61no—
838C24—61no—
839C24—61no—
840C24—61no—
841C24—61no—
842C24—61no—
843C24—61no—
844C24—124no—
845C24—124no—
846C24—124no—
847C24—124no—
848C24—124no—
849C24—124no—
850C24—124no—
851C24—124no—
852C24—124no—
853C24—124no—
854C24—124no—
855C24—124no—
856C24—124no—
857C24—124no—
858C24—124no—
859C24—124no—
860C24—124no—
861C24—124no—
862C24—124no—
863C24—124no—
864C24—124no—
865C24—124no—
866C24—124no—
867C24—124no—
868C24—124no—
869C24—124no—
870C24#23512yes—
871C24D3×D412yes—
872C24D3×Q812yes—
873C24C23×D311yescharacteristic
874C2×Q8—68no—
875C2×Q8—124no—
876C2×Q8—124no—
877C2×Q8—124no—
878C2×Q8—124no—
879C2×Q8—124no—
880C2×Q8—124no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—32no—
920C22×C4—32no—
921C22×C4—32no—
922C22×C4—32no—
923C22×C4—32no—
924C22×C4—32no—
925C22×C4—68no—
926C22×C4—68no—
927C22×C4—68no—
928C22×C4—61no—
929C22×C4—61no—
930C22×C4—61no—
931C22×C4—61no—
932C22×C4—61no—
933C22×C4—61no—
934C22×C4—61no—
935C22×C4—61no—
936C22×C4—61no—
937C22×C4—61no—
938C22×C4—61no—
939C22×C4—61no—
940C22×C4—61no—
941C22×C4—61no—
942C22×C4—61no—
943C22×C4—61no—
944C22×C4—61no—
945C22×C4—61no—
946C22×C4—61no—
947C22×C4—61no—
948C22×C4—61no—
949C22×C4—61no—
950C22×C4—61no—
951C22×C4—61no—
952C22×C4—61no—
953C22×C4—61no—
954C22×C4—61no—
955C22×C4—61no—
956C22×C4—61no—
957C22×C4—61no—
958C22×C4—61no—
959C22×C4—61no—
960C22×C4—61no—
961C22×C4—61no—
962C22×C4—61no—
963C22×C4—61no—
964C22×C4—124no—
965C22×C4—124no—
966C22×C4—124no—
967C22×C4—124no—
968C22×C4—124no—
969C22×C4—124no—
970C22×C4—124no—
971C22×C4—124no—
972C22×C4—124no—
973C22×C4—124no—
974C22×C4—124no—
975C22×C4D3×D412yes—
976C22×C4D3×D412yes—
977C22×C4D3×D412yes—
978C22×C4D3×D412yes—
979C4⋊C4—28no—
980C4⋊C4—68no—
981C4⋊C4—68no—
982C22⋊C4—28no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—68no—
986C22⋊C4—68no—
987C22⋊C4—68no—
988C22⋊C4—68no—
989C22⋊C4—68no—
990C22⋊C4—124no—
991C22⋊C4—124no—
992C22⋊C4—124no—
993C22⋊C4—124no—
994C22⋊C4—124no—
995C22⋊C4—124no—
996C22⋊C4—124no—
997C22⋊C4—124no—
998C22×C3—24no—
999C22×C3—24no—
1000C22×C3—24no—
1001C22×C3—42no—
1002C22×C3—42no—
1003C22×C3—42no—
1004C22×C3—42no—
1005C22×C3—42no—
1006C22×C3—42no—
1007C22×C3—42no—
1008C22×C3—42no—
1009C22×C3—42no—
1010C22×C3—42no—
1011C22×C3—42no—
1012C22×C3—42no—
1013C22×C3C2×#12011yescharacteristic
1014C22×C3C2×#12011yescharacteristic
1015C22×C3C2×C22⋊Q811yescharacteristic
1016C22×C3C2×C22⋊Q811yescharacteristic
1017C22×C3C2×C22⋊Q811yescharacteristic
1018C22×C3C2×C22⋊Q811yescharacteristic
1019C22×C3C2×C22⋊Q811yescharacteristic
1020C22×C3#52511yescharacteristic
1021C22×C3#52511yescharacteristic
1022C22×C3#52511yescharacteristic
1023C22×C3C2×#12411yescharacteristic
1024C22×C3C2×#12411yescharacteristic
1025C22×C3C2×#12411yescharacteristic
1026C22×C3#53411yescharacteristic
1027C22×C3#53511yescharacteristic
1028C22×C3#53811yescharacteristic
1029C22×C3#53811yescharacteristic
1030C22×C3#54311yescharacteristic
1031C22×C3#54311yescharacteristic
1032C22×C3D4211yescharacteristic
1033C22×C3D4211yescharacteristic
1034C22×C3D4211yescharacteristic
1035C22×C3D4211yescharacteristic
1036C22×C3#54611yescharacteristic
1037C22×C3#54611yescharacteristic
1038C22×C3#54611yescharacteristic
1039C22×C3#54611yescharacteristic
1040C22×C3#54611yescharacteristic
1041C22×C3#54611yescharacteristic
1042C22×C3#54611yescharacteristic
1043C22×C3#54611yescharacteristic
1044C22×C3#55111yescharacteristic
1045C22×C3#55111yescharacteristic
1046C22×C3#55111yescharacteristic
1047C22×C3#55111yescharacteristic
1048C2×D3—24no—
1049C2×D3—24no—
1050C2×D3—24no—
1051C2×D3—24no—
1052C2×D3—24no—
1053C2×D3—24no—
1054C2×D3—24no—
1055C2×D3—24no—
1056C2×D3—24no—
1057C2×D3—24no—
1058C2×D3—24no—
1059C2×D3—24no—
1060C2×D3—24no—
1061C2×D3—24no—
1062C2×D3—24no—
1063C2×D3—24no—
1064C2×D3—24no—
1065C2×D3—464no—
1066C2×D3—42no—
1067C2×D3—42no—
1068C2×D3—42no—
1069C2×D3—42no—
1070C2×D3—42no—
1071C2×D3—42no—
1072C2×D3—42no—
1073C2×D3—42no—
1074C2×D3—42no—
1075C2×D3—42no—
1076C2×D3—42no—
1077C2×D3—42no—
1078C2×D3#39318yescomplemented
1079C3×C4—42no—
1080C3×C4—42no—
1081C3×C4—42no—
1082C3×C4—42no—
1083C3×C4—81no—
1084C3×C4—81no—
1085Dic3—24no—
1086Dic3—42no—
1087Dic3—42no—
1088Dic3—42no—
1089Dic3—81no—
1090Dic3—81no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—34no—
1110C23—34no—
1111C23—34no—
1112C23—34no—
1113C23—34no—
1114C23—34no—
1115C23—34no—
1116C23—34no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—632no—
1134C23—62no—
1135C23—62no—
1136C23—62no—
1137C23—62no—
1138C23—62no—
1139C23—62no—
1140C23—62no—
1141C23—62no—
1142C23—62no—
1143C23—62no—
1144C23—62no—
1145C23—62no—
1146C23—62no—
1147C23—62no—
1148C23—62no—
1149C23—62no—
1150C23—62no—
1151C23—62no—
1152C23—62no—
1153C23—62no—
1154C23—62no—
1155C23—62no—
1156C23—62no—
1157C23—62no—
1158C23—62no—
1159C23—62no—
1160C23—62no—
1161C23—62no—
1162C23—62no—
1163C23—62no—
1164C23—62no—
1165C23—62no—
1166C23—62no—
1167C23—62no—
1168C23—62no—
1169C23—62no—
1170C23—62no—
1171C23—62no—
1172C23—62no—
1173C23—62no—
1174C23—62no—
1175C23—62no—
1176C23—62no—
1177C23—62no—
1178C23—62no—
1179C23—62no—
1180C23—1216no—
1181C23—1216no—
1182C23—1216no—
1183C23—1216no—
1184C23—1216no—
1185C23—1216no—
1186C23—1216no—
1187C23—1216no—
1188C23—1216no—
1189C23—1216no—
1190C23—1216no—
1191C23—1216no—
1192C23—1216no—
1193C23—1216no—
1194C23—121no—
1195C23—121no—
1196C23—121no—
1197C23—121no—
1198C23—121no—
1199C23—121no—
1200C23—121no—
1201C23—121no—
1202C23—121no—
1203C23—121no—
1204C23—121no—
1205C23—121no—
1206C23—121no—
1207C23—121no—
1208C23—121no—
1209C23—121no—
1210C23#89614yescomplemented
1211C23C2×#23511yescharacteristic
1212C23C2×D3×D411yescharacteristic
1213C23C2×D3×D411yescharacteristic
1214C23C2×D3×D411yescharacteristic
1215C23C2×D3×D411yescharacteristic
1216C23C2×D3×D411yescharacteristic
1217C23#100411yescharacteristic
1218C23#100411yescharacteristic
1219C23C2×D3×Q811yescharacteristic
1220C23D3×#4111yescharacteristic
1221C23D3×#4111yescharacteristic
1222C23D3×#4111yescharacteristic
1223C23D3×#4111yescharacteristic
1224C23#100911yescharacteristic
1225C23#100911yescharacteristic
1226Q8—1216no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—34no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—62no—
1271C2×C4—62no—
1272C2×C4—62no—
1273C2×C4—62no—
1274C2×C4—62no—
1275C2×C4—62no—
1276C2×C4—62no—
1277C2×C4—62no—
1278C2×C4—62no—
1279C2×C4—62no—
1280C2×C4—62no—
1281C2×C4—62no—
1282C2×C4—62no—
1283C2×C4—62no—
1284C2×C4—62no—
1285C2×C4—1216no—
1286C2×C4—1216no—
1287C2×C4—121no—
1288C2×C4—121no—
1289C2×C4—121no—
1290C2×C4—121no—
1291C2×C4—121no—
1292C2×C4—121no—
1293C2×C4—121no—
1294C2×C4—121no—
1295C2×C4—121no—
1296C2×C4—121no—
1297C2×C4—121no—
1298C2×C4—121no—
1299C2×C4—121no—
1300C2×C4—121no—
1301C2×C4—121no—
1302C2×C4—121no—
1303C2×C4—121no—
1304C2×C4—121no—
1305C2×C4—121no—
1306C2×C4—121no—
1307C2×C4—121no—
1308C2×C4—121no—
1309C2×C4—121no—
1310C2×C4—121no—
1311C2×C4—121no—
1312C2×C4—121no—
1313C2×C3—44no—
1314C2×C3C2×#39311yescharacteristic
1315C2×C3#240311yescharacteristic
1316C2×C3#240411yescharacteristic
1317C2×C3#243511yescharacteristic
1318C2×C3#243711yescharacteristic
1319C2×C3#243711yescharacteristic
1320C2×C3#243711yescharacteristic
1321C2×C3#243711yescharacteristic
1322C2×C3#247211yescharacteristic
1323C2×C3#247211yescharacteristic
1324C2×C3#247211yescharacteristic
1325C2×C3#247211yescharacteristic
1326C2×C3#256111yescharacteristic
1327C2×C3#262611yescharacteristic
1328C2×C3#284811yescharacteristic
1329D3—28no—
1330D3—44no—
1331C22—24no—
1332C22—24no—
1333C22—24no—
1334C22—38no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—64no—
1348C22—64no—
1349C22—64no—
1350C22—64no—
1351C22—64no—
1352C22—64no—
1353C22—64no—
1354C22—64no—
1355C22—64no—
1356C22—64no—
1357C22—64no—
1358C22—64no—
1359C22—64no—
1360C22—64no—
1361C22—64no—
1362C22—64no—
1363C22—64no—
1364C22—1264no—
1365C22—122no—
1366C22—122no—
1367C22—122no—
1368C22—122no—
1369C22—122no—
1370C22—122no—
1371C22—122no—
1372C22—122no—
1373C22—122no—
1374C22—122no—
1375C22—122no—
1376C22—122no—
1377C22#549011yescharacteristic
1378C22C2×#89611yescharacteristic
1379C22#552711yescharacteristic
1380C22#554711yescharacteristic
1381C22#554711yescharacteristic
1382C22#555011yescharacteristic
1383C22#555611yescharacteristic
1384C22D3×#12011yescharacteristic
1385C22D3×#12011yescharacteristic
1386C22#559011yescharacteristic
1387C22#560511yescharacteristic
1388C22#560711yescharacteristic
1389C22#560911yescharacteristic
1390C22#560911yescharacteristic
1391C22#561011yescharacteristic
1392C22#561011yescharacteristic
1393C22#561211yescharacteristic
1394C22#561311yescharacteristic
1395C22D3×C22⋊Q811yescharacteristic
1396C22D3×C22⋊Q811yescharacteristic
1397C22D3×C22⋊Q811yescharacteristic
1398C22D3×C22⋊Q811yescharacteristic
1399C22#563411yescharacteristic
1400C22#563411yescharacteristic
1401C22#565411yescharacteristic
1402C22#565411yescharacteristic
1403C22#565411yescharacteristic
1404C22#565611yescharacteristic
1405C22#565911yescharacteristic
1406C22D3×#12411yescharacteristic
1407C22D3×#12411yescharacteristic
1408C22D3×#12411yescharacteristic
1409C22#570411yescharacteristic
1410C22#570511yescharacteristic
1411C22#571711yescharacteristic
1412C4—42no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—64no—
1417C4—81no—
1418C4—81no—
1419C4—122no—
1420C4—122no—
1421C4—122no—
1422C4—241no—
1423C4—241no—
1424C3#1471711yescharacteristic, complemented, Sylow
1425C2—44no—
1426C2—68no—
1427C2—124no—
1428C2#7389611yescharacteristic
1429C2#7460711yescharacteristic
1430C2#7465511yescharacteristic
1431C2#7488611yescharacteristic
1432C2#7552611yescharacteristic
1433C2#7589011yescharacteristic
1434C2#7633011yescharacteristic
1435C2#7675311yescharacteristic
1436C2D3×#39311yescharacteristic
1437C2#7690511yescharacteristic
1438C2#7692611yescharacteristic
1439C2#7741811yescharacteristic
1440C2#7742411yescharacteristic
1441C2#7747411yescharacteristic
1442C2#7810211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC25×D3C22
hypercenter#1439D3
hypocenterC3#14717
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
5. C2×#4947C2semidirect
6. C2×#4673C2semidirect
7. C3×#1439C2semidirect
8. #71570C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #69428C2semidirect
12. #69428C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. (C2×D3)⋊#95C2semidirect
20. C23×Dic6C22semidirect
21. C22×C3×C4⋊C4C22semidirect
38. C22×Dic3⋊C4C22semidirect
39. C22×Dic3⋊C4C22semidirect
46. C2×C3×#95C22semidirect
47. C2×C3×#95C22semidirect
48. C2×C3×#95C22semidirect
49. C2×C3⋊#95C22semidirect
50. C2×C3⋊#95C22semidirect
51. C2×C3⋊#95C22semidirect
52. C2×C3⋊#95C22semidirect
53. C2×C3⋊#95C22semidirect
54. C2×C3⋊#95C22semidirect
55. C2×C3⋊#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. C2×C3⋊#95C22semidirect
73. #1439D3semidirect
92. C24×D3Q8semidirect
208. C22×C4⋊C4C2×D3semidirect
241. C2×#95C2×D3semidirect
242. C2×#95C2×D3semidirect
243. C2×#95C2×D3semidirect
605. C23×C3C22⋊Q8semidirect
702. C22×D3C22⋊Q8semidirect
1078. C2×D3#393semidirect
1210. C23#896semidirect
1424. C3#14717semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C22×D3×C22⋊C42
C2×#49552
C2×#49472
C2×#46732
C3×#14392
#715702
#715472
#694282
(C2×D3)⋊#952
#147173