Finite Group Databasebeta

← #10796342

Subgroups — #10796342

Order 768.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#907C211yesmaximal, characteristic, complemented
2C2×#5547C211yesmaximal, characteristic
3C2×#4727C211yesmaximal, characteristic, complemented
4C2×#4726C211yesmaximal, characteristic, complemented
5C2×D3×C22⋊C8C211yesmaximal, characteristic, complemented
6C3×#1870C211yesmaximal, characteristic, complemented
7#71996C211yesmaximal, characteristic, complemented
8#71610C211yesmaximal, characteristic, complemented
9#69958C211yesmaximal, characteristic, complemented
10#69957C211yesmaximal, characteristic, complemented
11#69952C211yesmaximal, characteristic, complemented
12#68669C211yesmaximal, characteristic, complemented
13#68668C211yesmaximal, characteristic, complemented
14#68661C211yesmaximal, characteristic, complemented
15#68661C211yesmaximal, characteristic, complemented
16#20899—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic, complemented
20C2×C3×C4×D4C2211yescharacteristic
21C2×#939C411yescharacteristic
22C2×#937C411yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic, complemented
26C2×#907—24no—
27C2×#907—24no—
28C2×#907—24no—
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C22×ΓL(1,𝔽25)C2211yescharacteristic
31C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
32C22×D3×C8C2211yescharacteristic
33C22×D3×C8C2211yescharacteristic
34C22×D3×C8C2211yescharacteristic, complemented
35#5547—24no—
36#5547—24no—
37C2×#896C411yescharacteristic
38C2×#894C411yescharacteristic
39C2×#884C411yescharacteristic
40C2×#883C411yescharacteristic
41C2×#882C411yescharacteristic
42C2×#878C411yescharacteristic
43C2×C4×D12C2211yescharacteristic
44C2×#872C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic, complemented
48C2×#830C2211yescharacteristic
49C2×#830C2211yescharacteristic
50C2×#830C2211yescharacteristic, complemented
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
57#4727—24no—
58#4726—24no—
59D3×C22⋊C8—24no—
60C3×#336C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4550C2211yescharacteristic, complemented
64#4550C2211yescharacteristic, complemented
65#4550C2211yescharacteristic, complemented
66#4524C2211yescharacteristic, complemented
67#4524C2211yescharacteristic, complemented
68C22×#131—31no—
69C2×#525—31no—
70C2×#408—31no—
71C2×#407—31no—
72C22×C22⋊C8—31no—
73#1870—31no—
74#1870—31no—
75#1870—31no—
76#1870D311yescharacteristic, complemented
77#1869—31no—
78#1869—31no—
79#1869—31no—
80#1869—31no—
81#1729—31no—
82#1729—31no—
83C24×D3C2×C411yescharacteristic
84C22×C3×D4C2×C411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67C2×C411yescharacteristic
88C22×#67C2×C411yescharacteristic
89C22×#67C2×C411yescharacteristic
90C22×#67C2×C411yescharacteristic
91C23×Dic3C2×C411yescharacteristic
92C2×#235—22no—
93C2×#235—22no—
94C2×#235—22no—
95C2×#235—22no—
96C2×#235D414yes—
97C2×#235D414yes—
98C22×D12C2×C411yescharacteristic
99C22×D12C2×C411yescharacteristic
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×D3C2×C411yescharacteristic
107C22×C4×D3C2×C411yescharacteristic
108C22×C4×D3C2311yescharacteristic
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×Dic6C2×C411yescharacteristic
112C2×C3×M16—22no—
113C2×C3×M16—22no—
114C2×C3×M16—22no—
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C2×C3×C4⋊C4C2×C411yescharacteristic
122C2×C3×C22⋊C4C2×C411yescharacteristic
123C2×C3×C22⋊C4C2×C411yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×#217C2×C411yescharacteristic
126C2×#217C2×C411yescharacteristic
127#939—24no—
128#937—24no—
129C4×#67—22no—
130C4×#67—22no—
131C4×#67—22no—
132C4×#67—22no—
133C2×(C2×D3)⋊C4C2×C411yescharacteristic
134C2×(C2×D3)⋊C4C2×C411yescharacteristic
135C2×(C2×D3)⋊C4C2×C411yescharacteristic
136C2×(C2×D3)⋊C4C2×C411yescharacteristic
137C2×(C2×D3)⋊C4C2×C411yescharacteristic
138C2×(C2×D3)⋊C4C2×C411yescharacteristic
139C2×C4⋊Dic3C2×C411yescharacteristic
140C2×Dic3⋊C4C2×C411yescharacteristic
141C2×Dic3⋊C4C2×C411yescharacteristic
142C2×Dic3⋊C4C2×C411yescharacteristic
143C2×Dic3⋊C4C2×C411yescharacteristic
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8—22no—
146C22×C3⋊C8—22no—
147C22×C3⋊C8—22no—
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152#907—232no—
153C2×ΓL(1,𝔽25)—22no—
154C2×ΓL(1,𝔽25)—22no—
155C2×ΓL(1,𝔽25)—22no—
156C2×ΓL(1,𝔽25)—22no—
157C2×ΓL(1,𝔽25)—22no—
158C2×ΓL(1,𝔽25)—22no—
159C2×ΓL(1,𝔽25)—22no—
160C2×ΓL(1,𝔽25)—22no—
161C2×ΓL(1,𝔽25)D414yescomplemented
162C2×D3×C8—22no—
163C2×D3×C8—22no—
164C2×D3×C8—22no—
165C2×D3×C8—22no—
166C2×D3×C8—22no—
167C2×D3×C8—22no—
168C2×D3×C8—22no—
169C2×D3×C8—22no—
170C2×D3×C8D414yescomplemented
171#896—24no—
172#894—24no—
173#884—24no—
174#883—24no—
175#882—24no—
176#878—24no—
177C4×D12—22no—
178C4×D12—22no—
179#872—22no—
180#872—22no—
181C3×C22⋊C8—22no—
182C3×C22⋊C8—22no—
183C3×C22⋊C8—22no—
184#830—22no—
185#830—22no—
186#830—22no—
187(C2×D3)⋊C8—22no—
188(C2×D3)⋊C8—22no—
189(C2×D3)⋊C8—22no—
190(C2×D3)⋊C8—22no—
191(C2×D3)⋊C8—22no—
192(C2×D3)⋊C8—22no—
193C22×#41—31no—
194C24×C4—31no—
195C2×#131—64no—
196C2×#131—64no—
197C2×#131—64no—
198C22×M16—31no—
199C22×M16—31no—
200C22×M16—31no—
201C22×M16C2×D311yescharacteristic, complemented
202C23×C8—31no—
203C23×C8—31no—
204C23×C8—31no—
205C23×C8—31no—
206#525—64no—
207#525—64no—
208C2×#123—31no—
209C2×#123—31no—
210C2×C22⋊Q8—31no—
211C2×C22⋊Q8—31no—
212C2×#121—31no—
213C2×#121—31no—
214C2×#120—31no—
215C2×#120—31no—
216C2×C4×D4—31no—
217C2×C4×D4—31no—
218C2×C4×D4—31no—
219C2×C4×D4C2×D311yescharacteristic
220C2×#117—31no—
221#408—64no—
222#407—64no—
223C2×C22⋊C8—31no—
224C2×C22⋊C8—31no—
225C2×C22⋊C8—31no—
226C2×C22⋊C8—31no—
227C2×C22⋊C8—31no—
228C2×C22⋊C8—31no—
229C2×C22⋊C8—31no—
230C2×C22⋊C8—31no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—64no—
233C2×C22⋊C8C2×D311yescharacteristic
234C2×C22⋊C8C2×D311yescharacteristic
235C2×C22⋊C8C2×D311yescharacteristic, complemented
236#336—31no—
237#336—31no—
238#336—31no—
239#336—31no—
240#336—31no—
241#336—31no—
242#336C2×D311yescharacteristic, complemented
243#336C2×D311yescharacteristic, complemented
244C24×C3C22×C411yescharacteristic
245C24×C3C22×C411yescharacteristic
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—41no—
252C23×D3—41no—
253C23×D3C22×C411yescharacteristic
254C23×D3C22×C411yescharacteristic
255C23×D3C22×C411yescharacteristic
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4—41no—
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×C4C22×C411yescharacteristic
270C22×C3×C4C22×C411yescharacteristic
271C22×C3×C4C22×C411yescharacteristic
272C22×C3×C4C22×C411yescharacteristic
273C22×C3×C4C2×D412yes—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2411yescharacteristic
276C2×#67—22no—
277C2×#67—22no—
278C2×#67—22no—
279C2×#67—22no—
280C2×#67—22no—
281C2×#67—22no—
282C2×#67—22no—
283C2×#67—22no—
284C2×#67—41no—
285C2×#67—41no—
286C2×#67C22⋊C414yes—
287C2×#67C22⋊C414yes—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3C22×C411yescharacteristic
292C22×Dic3C22×C411yescharacteristic
293C22×Dic3C22×C411yescharacteristic
294C22×Dic3C22×C411yescharacteristic
295C22×Dic3C22×C411yescharacteristic
296#235—28no—
297#235—28no—
298#235—28no—
299#235—28no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—41no—
305C2×D12C22⋊C414yes—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—22no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—22no—
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3—44no—
326C2×C4×D3C2×D412yes—
327C2×C4×D3C2×D412yes—
328C2×C4×D3C2×D412yes—
329C2×C4×D3C2×D412yes—
330C2×C4×D3C2×D412yes—
331C2×C4×D3C2×D412yes—
332C2×C4×D3#4112yes—
333C2×C4×D3#4112yes—
334C2×Dic6—22no—
335C2×Dic6—22no—
336C2×Dic6C22⋊C414yes—
337C3×M16—28no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8C2×D412yes—
349C2×C3×C8C2×D412yes—
350C3×C4⋊C4—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C42—21no—
354C3×C42—21no—
355#217—22no—
356#217—22no—
357(C2×D3)⋊C4—22no—
358(C2×D3)⋊C4—22no—
359(C2×D3)⋊C4—22no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—22no—
363C4⋊Dic3—22no—
364Dic3⋊C4—22no—
365Dic3⋊C4—22no—
366Dic3⋊C4—22no—
367Dic3⋊C4—22no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C2×C3⋊C8—28no—
371C2×C3⋊C8—21no—
372C2×C3⋊C8—21no—
373C2×C3⋊C8—21no—
374C2×C3⋊C8—21no—
375C2×C3⋊C8—21no—
376C2×C3⋊C8—21no—
377C2×C3⋊C8—21no—
378C2×C3⋊C8—21no—
379C2×C3⋊C8—21no—
380C2×C3⋊C8—21no—
381C2×C3⋊C8C2×D412yes—
382C2×C3⋊C8C2×D412yes—
383ΓL(1,𝔽25)—28no—
384ΓL(1,𝔽25)—28no—
385ΓL(1,𝔽25)—44no—
386D3×C8—28no—
387D3×C8—28no—
388D3×C8—44no—
389C25—31no—
390C2×#41—34no—
391C2×#41—34no—
392C2×#41—62no—
393C2×#41—62no—
394C2×#41—62no—
395C2×#41—62no—
396C22×Q8—31no—
397C22×D4—31no—
398C22×D4—31no—
399C22×D4—31no—
400C22×D4—31no—
401C22×D4—31no—
402C22×D4—31no—
403C22×D4C4×D311yescharacteristic
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—62no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—62no—
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418#131—632no—
419C2×M16—22no—
420C2×M16—22no—
421C2×M16—22no—
422C2×M16—34no—
423C2×M16—62no—
424C2×M16—62no—
425C2×M16—62no—
426C2×M16—62no—
427C2×M16—62no—
428C2×M16—62no—
429C2×M16—62no—
430C2×M16—62no—
431C22×C8—31no—
432C22×C8—31no—
433C22×C8—34no—
434C22×C8—31no—
435C22×C8—31no—
436C22×C8—62no—
437C22×C8—62no—
438C22×C8—62no—
439C22×C8—62no—
440C22×C8—62no—
441C22×C8—62no—
442C22×C8—62no—
443C22×C8—62no—
444C22×C8—62no—
445C22×C8—62no—
446C22×C8—62no—
447C22×C8C22×D311yescharacteristic
448C22×C8C22×D311yescharacteristic
449C22×C8C22×D311yescharacteristic
450C22×C8C22×D311yescharacteristic
451#123—64no—
452#123—64no—
453C22⋊Q8—64no—
454C22⋊Q8—64no—
455#121—64no—
456#121—64no—
457#120—64no—
458#120—64no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—62no—
462C4×D4—62no—
463C4×D4—62no—
464C4×D4—62no—
465C4×D4—62no—
466C4×D4—62no—
467#117—62no—
468#117—62no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4C4×D311yescharacteristic
475C2×C22⋊C4—31no—
476C2×C22⋊C4—31no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4C4×D311yescharacteristic
484C2×C22⋊C4C4×D311yescharacteristic
485C2×C42—31no—
486C2×C42C22×D311yescharacteristic
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—62no—
491C22⋊C8—62no—
492C22⋊C8—62no—
493C22⋊C8—62no—
494C22⋊C8—62no—
495C22⋊C8—62no—
496C22⋊C8—62no—
497C22⋊C8—62no—
498C22⋊C8—62no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3C2×C22⋊C412yes—
512C23×C3#13112yescomplemented
513C23×C3C23×C411yescharacteristic
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—28no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—44no—
532C22×D3—44no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3C2×C22⋊C412yes—
538C22×D3C2×C22⋊C412yes—
539C22×D3C4×D412yes—
540C22×D3C4×D412yes—
541C22×D3#13112yescomplemented
542C3×D4—44no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4C2×C22⋊C412yes—
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C22×D411yescharacteristic
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C22×D411yescharacteristic
567C2×C3×C4C2×#4111yescharacteristic
568C2×C3×C4C2×#4111yescharacteristic
569#67—28no—
570#67—28no—
571#67—44no—
572#67—44no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—44no—
585C2×Dic3C2×C22⋊C412yes—
586C2×Dic3C2×C22⋊C412yes—
587C2×Dic3C4×D412yes—
588C2×Dic3C4×D412yes—
589D12—28no—
590D12—44no—
591C4×D3—22no—
592C4×D3—22no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—44no—
596C4×D3—41no—
597C4×D3—41no—
598C4×D3—41no—
599C4×D3—41no—
600C4×D3—44no—
601C4×D3#12014yes—
602C4×D3#12114yes—
603C4×D3#12114yes—
604C4×D3#12314yes—
605Dic6—28no—
606C3×C8—22no—
607C3×C8—22no—
608C3×C8—41no—
609C3×C8—41no—
610C3⋊C8—22no—
611C3⋊C8—22no—
612C3⋊C8—41no—
613C3⋊C8—41no—
614C24—31no—
615C24—31no—
616C24—31no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24—62no—
622C24—121no—
623C24—121no—
624C24C2×C4×D311yescharacteristic
625C24C2×C4×D311yescharacteristic
626#41—68no—
627#41—68no—
628#41—68no—
629#41—68no—
630C2×Q8—34no—
631C2×Q8—62no—
632C2×Q8—62no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—34no—
636C2×D4—34no—
637C2×D4—34no—
638C2×D4—41no—
639C2×D4—62no—
640C2×D4—62no—
641C2×D4—62no—
642C2×D4—62no—
643C2×D4—62no—
644C2×D4—62no—
645C2×D4—62no—
646C2×D4—62no—
647C2×D4—62no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4—62no—
651C2×D4—121no—
652C2×D4—121no—
653C2×D4—121no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—31no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—31no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—124no—
697C22×C4—124no—
698C22×C4—124no—
699C22×C4—124no—
700C22×C4C2×C4×D311yescharacteristic
701C22×C4C2×C4×D311yescharacteristic
702C22×C4C2×C4×D311yescharacteristic
703C22×C4C2×C4×D311yescharacteristic
704C22×C4D3×D412yes—
705C22×C4D3×D412yes—
706C22×C4C23×D311yescharacteristic
707M16—28no—
708M16—68no—
709M16—68no—
710M16—124no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—32no—
722C2×C8—32no—
723C2×C8—68no—
724C2×C8—68no—
725C2×C8—68no—
726C2×C8—61no—
727C2×C8—61no—
728C2×C8—61no—
729C2×C8—61no—
730C2×C8—61no—
731C2×C8—61no—
732C2×C8—61no—
733C2×C8—61no—
734C2×C8—61no—
735C2×C8—61no—
736C2×C8—124no—
737C2×C8D3×D412yes—
738C2×C8D3×D412yes—
739C4⋊C4—22no—
740C4⋊C4—62no—
741C4⋊C4—62no—
742C4⋊C4—62no—
743C4⋊C4—62no—
744C4⋊C4—62no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—62no—
748C22⋊C4—62no—
749C22⋊C4—62no—
750C22⋊C4—62no—
751C22⋊C4—62no—
752C22⋊C4—62no—
753C22⋊C4—62no—
754C22⋊C4—62no—
755C42—21no—
756C42—21no—
757C42—61no—
758C42—61no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3C22×C22⋊C411yescharacteristic
774C22×C3C2×C4×D411yescharacteristic
775C22×C3C2×C4×D411yescharacteristic
776C22×C3C2×#13111yescharacteristic
777C22×C3C2×#13111yescharacteristic
778C22×C3#56811yescharacteristic
779C22×C3#56811yescharacteristic
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—416no—
793C2×D3—41no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3#38614yes—
802C3×C4—22no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4C2×#12011yescharacteristic
807C3×C4C2×#12111yescharacteristic
808C3×C4C2×#12111yescharacteristic
809C3×C4C2×#12311yescharacteristic
810Dic3—22no—
811Dic3—41no—
812Dic3—41no—
813Dic3—41no—
814Dic3#38614yes—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—32no—
828C23—32no—
829C23—32no—
830C23—32no—
831C23—32no—
832C23—68no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—124no—
850C23—124no—
851C23—124no—
852C23—124no—
853C23—124no—
854C23—124no—
855C23D3×C22⋊C412yes—
856C23#90712yescomplemented
857C23C22×C4×D311yescharacteristic
858Q8—68no—
859D4—44no—
860D4—68no—
861D4—68no—
862D4—68no—
863D4—124no—
864D4—124no—
865D4—124no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—34no—
885C2×C4—34no—
886C2×C4—34no—
887C2×C4—34no—
888C2×C4—32no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—124no—
909C2×C4—124no—
910C2×C4—124no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4D3×C22⋊C412yes—
916C2×C4C2×D3×D411yescharacteristic
917C2×C4C2×D3×D411yescharacteristic
918C2×C4C2×D3×D411yescharacteristic
919C2×C4C2×D3×D411yescharacteristic
920C2×C4D3×#4111yescharacteristic
921C2×C4D3×#4111yescharacteristic
922C8—22no—
923C8—22no—
924C8—41no—
925C8—41no—
926C8—62no—
927C8—62no—
928C8—121no—
929C8—121no—
930C2×C3—42no—
931C2×C3—42no—
932C2×C3C2×#38611yescharacteristic
933C2×C3#288011yescharacteristic
934C2×C3#288011yescharacteristic
935C2×C3#292911yescharacteristic
936C2×C3#293011yescharacteristic
937C2×C3#293311yescharacteristic
938C2×C3#293311yescharacteristic
939D3—24no—
940D3—42no—
941D3—42no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—34no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—1216no—
970C22—121no—
971C22—121no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22C2×D3×C22⋊C411yescharacteristic
979C22C4×D3×D411yescharacteristic
980C22C4×D3×D411yescharacteristic
981C22C2×#90711yescharacteristic
982C22#574511yescharacteristic
983C22D3×#13111yescharacteristic
984C22#575011yescharacteristic
985C4—22no—
986C4—34no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—62no—
991C4—121no—
992C4—121no—
993C4—121no—
994C4D3×#12011yescharacteristic
995C4D3×#12111yescharacteristic
996C4D3×#12111yescharacteristic
997C4D3×#12311yescharacteristic
998C3#2089911yescharacteristic, complemented, Sylow
999C2—42no—
1000C2—42no—
1001C2—64no—
1002C2—122no—
1003C2—122no—
1004C2D3×#38611yescharacteristic
1005C2#7863111yescharacteristic
1006C2#7866311yescharacteristic
1007C2#7947811yescharacteristic
1008C2#7948111yescharacteristic
1009C2#7953711yescharacteristic
1010C2#7953911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1870C2
prime radicalC2×#5547C2
cosocleC22×C3×C4C24
hypercenter#1870D3
hypocenterC3#20899
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C22×#907C2semidirect
3. C2×#4727C2semidirect
4. C2×#4726C2semidirect
5. C2×D3×C22⋊C8C2semidirect
6. C3×#1870C2semidirect
7. #71996C2semidirect
8. #71610C2semidirect
9. #69958C2semidirect
10. #69957C2semidirect
11. #69952C2semidirect
12. #68669C2semidirect
13. #68668C2semidirect
14. #68661C2semidirect
15. #68661C2semidirect
19. C22×C3×M16C22semidirect
25. C23×C3⋊C8C22semidirect
31. C22×ΓL(1,𝔽25)C22semidirect
34. C22×D3×C8C22semidirect
47. C2×C3×C22⋊C8C22semidirect
50. C2×#830C22semidirect
55. C2×(C2×D3)⋊C8C22semidirect
56. C2×(C2×D3)⋊C8C22semidirect
60. C3×#336C22semidirect
61. C3×#336C22semidirect
62. #4550C22semidirect
63. #4550C22semidirect
64. #4550C22semidirect
65. #4550C22semidirect
66. #4524C22semidirect
67. #4524C22semidirect
76. #1870D3semidirect
161. C2×ΓL(1,𝔽25)D4semidirect
170. C2×D3×C8D4semidirect
201. C22×M16C2×D3semidirect
235. C2×C22⋊C8C2×D3semidirect
242. #336C2×D3semidirect
243. #336C2×D3semidirect
512. C23×C3#131semidirect
541. C22×D3#131semidirect
856. C23#907semidirect
998. C3#20899semidirect

Maximal subgroups

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

subgroupindex
C22×#9072
C2×#55472
C2×#47272
C2×#47262
C2×D3×C22⋊C82
C3×#18702
#719962
#716102
#699582
#699572
#699522
#686692
#686682
#686612
#208993