Finite Group Databasebeta

← #10726605

Subgroups — #10726605

Order 768.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic
2C22×D3×C4⋊C4C211yesmaximal, characteristic
3C2×#4989C211yesmaximal, characteristic
4C2×#4979C211yesmaximal, characteristic, complemented
5C2×#4668C211yesmaximal, characteristic
6C2×#4656C211yesmaximal, characteristic, complemented
7C3×#1444C211yesmaximal, characteristic, complemented
8#71568C211yesmaximal, characteristic, complemented
9#71568C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic
11(C2×D3)⋊#95C211yesmaximal, characteristic
12(C2×D3)⋊#95C211yesmaximal, characteristic
13#69420C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#14720—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C2×#896—24no—
37C2×#896—24no—
38C2×#896—24no—
39C2×D3×C4⋊C4—24no—
40C2×D3×C4⋊C4—24no—
41C2×D3×C4⋊C4—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
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4989—24no—
59#4979—24no—
60#4668—24no—
61#4656—24no—
62C22×C22⋊Q8—31no—
63C23×C4⋊C4—31no—
64C2×#395—31no—
65C2×#395—31no—
66C2×#385—31no—
67C2×#385—31no—
68#1444—31no—
69#1444—31no—
70#1444—31no—
71#1444D311yescharacteristic, complemented
72#1441—31no—
73#1441—31no—
74C22⋊#95—31no—
75C22⋊#95—31no—
76C22⋊#95—31no—
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C22×C4×D3—41no—
110C22×C4×D3—41no—
111C22×C4×D3D414yes—
112C22×C4×D3Q814yescomplemented
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—22no—
116C22×Dic6—22no—
117C22×Dic6—22no—
118C22×Dic6—41no—
119C22×Dic6—41no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—41no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4D414yes—
138C2×(C2×D3)⋊C4D414yes—
139C2×(C2×D3)⋊C4Q814yescomplemented
140C2×(C2×D3)⋊C4Q814yescomplemented
141C2×C4⋊Dic3—22no—
142C2×C4⋊Dic3—22no—
143C2×C4⋊Dic3—22no—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—41no—
146C2×C4⋊Dic3D414yes—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—41no—
163C2×Dic3⋊C4—41no—
164C2×Dic3⋊C4D414yes—
165#896—232no—
166D3×C4⋊C4—232no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—22no—
170C3×#95—41no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—41no—
183C23×Q8—31no—
184C24×C4—31no—
185C24×C4—31no—
186C24×C4—31no—
187C2×C22⋊Q8—64no—
188C2×C22⋊Q8—64no—
189C2×C22⋊Q8—64no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—64no—
199C22×C4⋊C4—64no—
200C22×C4⋊C4—64no—
201C22×C4⋊C4C2×D311yescharacteristic
202C22×C4⋊C4C2×D311yescharacteristic
203C22×C4⋊C4C2×D311yescharacteristic
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208#395—64no—
209#395—64no—
210#385—64no—
211#385—64no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C24×C3C2411yescharacteristic
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3C2×D412yes—
238C23×D3C2×D412yes—
239C23×D3C2×D412yes—
240C23×D3C2×Q812yes—
241C23×D3C2×Q812yes—
242C23×D3C2×Q812yes—
243C23×D3#4112yes—
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—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D412yes—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×Q812yes—
290C22×C3×C4C2×Q812yes—
291C22×C3×C4C2×Q812yes—
292C22×C3×C4#4112yes—
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×Dic3C2×D412yes—
338C22×Dic3C2×Q812yes—
339C22×Dic3C2×Q812yes—
340C22×Dic3C2×Q812yes—
341C22×Dic3#4112yes—
342C2×C4×D3—28no—
343C2×C4×D3—28no—
344C2×C4×D3—28no—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—28no—
348C2×C4×D3—28no—
349C2×C4×D3—28no—
350C2×C4×D3—28no—
351C2×C4×D3—28no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×Dic6—28no—
364C2×Dic6—44no—
365C2×Dic6—44no—
366C2×Dic6—44no—
367C2×Dic6—44no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C3×C4⋊C4—28no—
371C3×C4⋊C4—28no—
372C3×C4⋊C4—44no—
373(C2×D3)⋊C4—28no—
374(C2×D3)⋊C4—28no—
375(C2×D3)⋊C4—28no—
376(C2×D3)⋊C4—28no—
377C4⋊Dic3—28no—
378C4⋊Dic3—44no—
379Dic3⋊C4—28no—
380Dic3⋊C4—28no—
381Dic3⋊C4—28no—
382Dic3⋊C4—28no—
383Dic3⋊C4—44no—
384Dic3⋊C4—44no—
385C25—31no—
386C22×Q8—62no—
387C22×Q8—62no—
388C22×Q8—62no—
389C22×Q8—62no—
390C22×Q8—62no—
391C22×Q8—121no—
392C22×Q8—121no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—34no—
401C23×C4—34no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—62no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—62no—
416C23×C4—62no—
417C23×C4—121no—
418C23×C4—121no—
419C23×C4—121no—
420C23×C4—121no—
421C23×C4C22×D311yescharacteristic
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428C22⋊Q8—632no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—34no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—632no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—62no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—62no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—62no—
460C2×C4⋊C4—121no—
461C2×C4⋊C4—121no—
462C2×C4⋊C4—121no—
463C2×C22⋊C4—34no—
464C2×C22⋊C4—34no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—41no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—121no—
491C23×C3C22×D411yescharacteristic
492C23×C3C22×D411yescharacteristic
493C23×C3C22×D411yescharacteristic
494C23×C3C22×D411yescharacteristic
495C23×C3C22×D411yescharacteristic
496C23×C3C22×Q811yescharacteristic
497C23×C3C22×Q811yescharacteristic
498C23×C3C22×Q811yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3H(5,𝔽2)11yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C32−1+411yescharacteristic
505C23×C32−1+411yescharacteristic
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3#12014yes—
535C22×D3C22⋊Q814yes—
536C22×D3C22⋊Q814yes—
537C22×D3C22⋊Q814yes—
538C22×D3C4⋊Q814yes—
539C22×D3C4⋊Q814yes—
540C22×D3C4⋊Q814yes—
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—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×C4C22⋊Q814yescomplemented
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
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—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—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—41no—
636C2×Dic3—41no—
637C2×Dic3#12014yes—
638C2×Dic3C22⋊Q814yescomplemented
639C4×D3—232no—
640C4×D3—416no—
641C4×D3—416no—
642Dic6—416no—
643C24—32no—
644C24—32no—
645C24—32no—
646C24—32no—
647C24—32no—
648C24—32no—
649C24—32no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24C23×D311yescharacteristic
659C2×Q8—68no—
660C2×Q8—124no—
661C2×Q8—124no—
662C2×Q8—124no—
663C2×Q8—124no—
664C2×Q8—124no—
665C2×Q8—124no—
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—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—32no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—68no—
718C22×C4—68no—
719C22×C4—68no—
720C22×C4—68no—
721C22×C4—68no—
722C22×C4—68no—
723C22×C4—68no—
724C22×C4—68no—
725C22×C4—68no—
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—68no—
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—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4—124no—
769C22×C4—124no—
770C22×C4—124no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4#23512yes—
777C22×C4D3×D412yes—
778C22×C4D3×D412yes—
779C22×C4D3×D412yes—
780C22×C4D3×D412yes—
781C22×C4D3×D412yes—
782C22×C4D3×Q812yes—
783C22×C4D3×Q812yes—
784C22×C4D3×Q812yes—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—44no—
788C4⋊C4—68no—
789C4⋊C4—68no—
790C4⋊C4—68no—
791C4⋊C4—68no—
792C4⋊C4—68no—
793C4⋊C4—124no—
794C4⋊C4—124no—
795C4⋊C4—124no—
796C22⋊C4—68no—
797C22⋊C4—68no—
798C22⋊C4—68no—
799C22⋊C4—68no—
800C22×C3C2×#12011yescharacteristic
801C22×C3C2×#12011yescharacteristic
802C22×C3C2×C22⋊Q811yescharacteristic
803C22×C3C2×C22⋊Q811yescharacteristic
804C22×C3C2×C22⋊Q811yescharacteristic
805C22×C3C2×C22⋊Q811yescharacteristic
806C22×C3C2×C22⋊Q811yescharacteristic
807C22×C3#52511yescharacteristic
808C22×C3#52511yescharacteristic
809C22×C3#52511yescharacteristic
810C22×C3C2×C4⋊Q811yescharacteristic
811C22×C3C2×C4⋊Q811yescharacteristic
812C22×C3C2×C4⋊Q811yescharacteristic
813C22×C3#53411yescharacteristic
814C22×C3#53611yescharacteristic
815C22×C3#53911yescharacteristic
816C22×C3#53911yescharacteristic
817C22×C3#54411yescharacteristic
818C22×C3#54411yescharacteristic
819C22×C3D4211yescharacteristic
820C22×C3D4211yescharacteristic
821C22×C3D4211yescharacteristic
822C22×C3D4211yescharacteristic
823C22×C3#54711yescharacteristic
824C22×C3#54711yescharacteristic
825C22×C3#54711yescharacteristic
826C22×C3#54711yescharacteristic
827C22×C3D4×Q811yescharacteristic
828C22×C3D4×Q811yescharacteristic
829C22×C3D4×Q811yescharacteristic
830C22×C3D4×Q811yescharacteristic
831C22×C3#55411yescharacteristic
832C22×C3#55411yescharacteristic
833C22×C3#55411yescharacteristic
834C22×C3#55411yescharacteristic
835C2×D3—24no—
836C2×D3—24no—
837C2×D3—24no—
838C2×D3—24no—
839C2×D3—24no—
840C2×D3—24no—
841C2×D3—24no—
842C2×D3—24no—
843C2×D3—24no—
844C2×D3—24no—
845C2×D3—24no—
846C2×D3—24no—
847C2×D3—24no—
848C2×D3—24no—
849C2×D3#39518yescomplemented
850C3×C4—24no—
851C3×C4—42no—
852C3×C4—42no—
853C3×C4—42no—
854C3×C4—42no—
855C3×C4—42no—
856C3×C4—42no—
857Dic3—24no—
858Dic3—24no—
859Dic3—42no—
860Dic3—42no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864C23—34no—
865C23—34no—
866C23—34no—
867C23—34no—
868C23—34no—
869C23—34no—
870C23—34no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23C2×#23511yescharacteristic
900C23C2×D3×D411yescharacteristic
901C23C2×D3×D411yescharacteristic
902C23C2×D3×D411yescharacteristic
903C23C2×D3×D411yescharacteristic
904C23C2×D3×D411yescharacteristic
905C23#100411yescharacteristic
906C23C2×D3×Q811yescharacteristic
907C23C2×D3×Q811yescharacteristic
908C23C2×D3×Q811yescharacteristic
909C23#100711yescharacteristic
910C23D3×#4111yescharacteristic
911C23D3×#4111yescharacteristic
912C23#100911yescharacteristic
913C23#101011yescharacteristic
914Q8—1216no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—34no—
940C2×C4—34no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
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—632no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
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—1216no—
994C2×C4—1216no—
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#89614yescomplemented
1016C2×C3C2×#39511yescharacteristic
1017C2×C3#240311yescharacteristic
1018C2×C3#240611yescharacteristic
1019C2×C3#243411yescharacteristic
1020C2×C3#244011yescharacteristic
1021C2×C3#244011yescharacteristic
1022C2×C3#244011yescharacteristic
1023C2×C3#244011yescharacteristic
1024C2×C3#244911yescharacteristic
1025C2×C3#244911yescharacteristic
1026C2×C3#244911yescharacteristic
1027C2×C3#244911yescharacteristic
1028C2×C3#258311yescharacteristic
1029C2×C3#262711yescharacteristic
1030C2×C3#284811yescharacteristic
1031D3—28no—
1032C22—38no—
1033C22—64no—
1034C22—64no—
1035C22—64no—
1036C22—64no—
1037C22—64no—
1038C22—64no—
1039C22—64no—
1040C22—64no—
1041C22—64no—
1042C22—64no—
1043C22—64no—
1044C22—64no—
1045C22—64no—
1046C22—64no—
1047C22#550711yescharacteristic
1048C22C2×#89611yescharacteristic
1049C22#551111yescharacteristic
1050C22#554711yescharacteristic
1051C22#554711yescharacteristic
1052C22#555111yescharacteristic
1053C22#557911yescharacteristic
1054C22D3×#12011yescharacteristic
1055C22D3×#12011yescharacteristic
1056C22#559011yescharacteristic
1057C22#560511yescharacteristic
1058C22#560911yescharacteristic
1059C22#560911yescharacteristic
1060C22D3×C22⋊Q811yescharacteristic
1061C22D3×C22⋊Q811yescharacteristic
1062C22D3×C22⋊Q811yescharacteristic
1063C22D3×C22⋊Q811yescharacteristic
1064C22#562811yescharacteristic
1065C22#563111yescharacteristic
1066C22#563211yescharacteristic
1067C22#563211yescharacteristic
1068C22#563611yescharacteristic
1069C22#565511yescharacteristic
1070C22#565611yescharacteristic
1071C22#566011yescharacteristic
1072C22#568911yescharacteristic
1073C22#569011yescharacteristic
1074C22#569211yescharacteristic
1075C22#571711yescharacteristic
1076C22D3×C4⋊Q811yescharacteristic
1077C22D3×C4⋊Q811yescharacteristic
1078C22D3×C4⋊Q811yescharacteristic
1079C22#572711yescharacteristic
1080C22#572711yescharacteristic
1081C22#572911yescharacteristic
1082C4—24no—
1083C4—42no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—64no—
1090C4—64no—
1091C4—122no—
1092C4—122no—
1093C4—122no—
1094C4—122no—
1095C4—122no—
1096C3#1472011yescharacteristic, complemented, Sylow
1097C2—68no—
1098C2#7432611yescharacteristic
1099C2#7460011yescharacteristic
1100C2#7460911yescharacteristic
1101C2#7465511yescharacteristic
1102C2#7599811yescharacteristic
1103C2#7622511yescharacteristic
1104C2#7624711yescharacteristic
1105C2#7675311yescharacteristic
1106C2#7717311yescharacteristic
1107C2#7717411yescharacteristic
1108C2D3×#39511yescharacteristic
1109C2#7774511yescharacteristic
1110C2#7795211yescharacteristic
1111C2#7796411yescharacteristic
1112C2#7810411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1444C2
prime radicalC24×D3C23
hypercenter#1444D3
hypocenterC3#14720
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. C2×#4979C2semidirect
6. C2×#4656C2semidirect
7. C3×#1444C2semidirect
8. #71568C2semidirect
9. #71568C2semidirect
13. #69420C2semidirect
14. #69411C2semidirect
15. #69409C2semidirect
71. #1444D3semidirect
112. C22×C4×D3Q8semidirect
139. C2×(C2×D3)⋊C4Q8semidirect
140. C2×(C2×D3)⋊C4Q8semidirect
589. C2×C3×C4C22⋊Q8semidirect
638. C2×Dic3C22⋊Q8semidirect
849. C2×D3#395semidirect
1015. C2×C4#896semidirect
1096. C3#14720semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C22×D3×C4⋊C42
C2×#49892
C2×#49792
C2×#46682
C2×#46562
C3×#14442
#715682
(C2×D3)⋊#952
#694202
#694112
#694092
#147203