Finite Group Databasebeta

← #10719457

Subgroups — #10719457

Order 768.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#387C211yesmaximal, characteristic, complemented
2C2×#4989C211yesmaximal, characteristic, complemented
3C2×#4988C211yesmaximal, characteristic
4C2×#4990C211yesmaximal, characteristic, complemented
5C2×#4940C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#4665C211yesmaximal, characteristic
8#71569C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14084—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×#387—24no—
39C2×C3×#95C2211yescharacteristic
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
52C2×C3⋊#95C2211yescharacteristic
53#4990—24no—
54#4989—24no—
55#4988C418yescomplemented
56#4940—24no—
57C4×(C2×D3)⋊C4—24no—
58#4665—24no—
59C2×#390—31no—
60C2×#388—31no—
61C2×#388—31no—
62C2×#387D311yescharacteristic, complemented
63C2×#386—31no—
64C2×#385—31no—
65C2×C4×C22⋊C4—31no—
66#1445—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1437—31no—
71#1437—31no—
72C4⋊#95—31no—
73C4×#95—31no—
74C24×D3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—41no—
94C22×D12—41no—
95C22×D12C2×C414yes—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—41no—
102C22×C4×D3—41no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4C2×C414yescomplemented
109C2×C3×C42—22no—
110C2×C3×C42—22no—
111C2×C3×C42—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
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—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
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—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4C2×C414yes—
142C2×(C2×D3)⋊C4C2×C414yes—
143C2×(C2×D3)⋊C4C2×C414yescomplemented
144C2×(C2×D3)⋊C4C2×C414yescomplemented
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×C4×Dic3—22no—
152C2×C4×Dic3—41no—
153C2×C4×Dic3—41no—
154C2×C4×Dic3—41no—
155C2×C4×Dic3—41no—
156C2×C4×Dic3—41no—
157C2×C4×Dic3—41no—
158C2×C4×Dic3C2×C414yescomplemented
159C2×C4×Dic3D414yescomplemented
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95D414yes—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95D414yescomplemented
174C23×D4—31no—
175C24×C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4C2×D311yescharacteristic
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C22⋊C4—31no—
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⋊C4—31no—
191C22×C42—31no—
192C22×C42—31no—
193C22×C42—31no—
194C22×C42C2×D311yescharacteristic
195#390—38no—
196#388—64no—
197#388—64no—
198#387—24no—
199#386—64no—
200#385—64no—
201C4×C22⋊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×#95—31no—
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C24×C3C2411yescharacteristic
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
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×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3C22×C412yes—
244C23×D3C22×C412yes—
245C23×D3#4112yes—
246C23×D3#4112yes—
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×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4C22×C412yes—
287C22×C3×C4C22×C412yes—
288C22×C3×C4C22×C412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4#4112yes—
295C22×C3×C4#4112yes—
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×Dic3C22×C412yes—
330C22×Dic3C22×C412yes—
331C22×Dic3C2×D412yes—
332C22×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3#4112yes—
336C22×Dic3#4112yes—
337C22×Dic3#4112yes—
338C2×D12—28no—
339C2×D12—28no—
340C2×D12—44no—
341C2×D12—44no—
342C2×D12—44no—
343C2×D12—44no—
344C2×D12—44no—
345C2×C4×D3—28no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C3×C4⋊C4—28no—
353C3×C4⋊C4—44no—
354C3×C42—44no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—28no—
357(C2×D3)⋊C4—28no—
358(C2×D3)⋊C4—28no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—44no—
361(C2×D3)⋊C4—44no—
362(C2×D3)⋊C4—44no—
363(C2×D3)⋊C4—44no—
364(C2×D3)⋊C4—44no—
365(C2×D3)⋊C4—44no—
366Dic3⋊C4—44no—
367Dic3⋊C4—44no—
368C4×Dic3—44no—
369C4×Dic3—44no—
370C4×Dic3—44no—
371C25—31no—
372C25—31no—
373C22×D4—34no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—121no—
379C22×D4—121no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—62no—
387C23×C4—62no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—121no—
392C23×C4—121no—
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—121no—
410C2×C4⋊C4—121no—
411C2×C4⋊C4C4×D314yescomplemented
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—121no—
440C2×C22⋊C4—121no—
441C2×C22⋊C4—121no—
442C2×C22⋊C4—121no—
443C2×C22⋊C4—121no—
444C2×C22⋊C4—121no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—34no—
449C2×C42—34no—
450C2×C42—62no—
451C2×C42—121no—
452C2×C42—121no—
453C2×C42—121no—
454C2×C42—121no—
455C2×C42—121no—
456C2×C42—121no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—34no—
461#95—62no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95#6714yes—
471C23×C3C23×C411yescharacteristic
472C23×C3C22×D411yescharacteristic
473C23×C3C22×D411yescharacteristic
474C23×C3C22×D411yescharacteristic
475C23×C3C2×#4111yescharacteristic
476C23×C3C2×#4111yescharacteristic
477C23×C3C2×#4111yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3H(5,𝔽2)11yescharacteristic
483C23×C3H(5,𝔽2)11yescharacteristic
484C23×C3H(5,𝔽2)11yescharacteristic
485C23×C32−1+411yescharacteristic
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
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—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3#11714yes—
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—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
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—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4C4×D414yes—
604C2×C3×C4#12714yes—
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—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
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—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3C4×D414yes—
646C2×Dic3C4×D414yes—
647D12—416no—
648C4×D3—416no—
649C24—32no—
650C24—32no—
651C24—32no—
652C24—32no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
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—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24C23×D311yescharacteristic
680C2×D4—68no—
681C2×D4—68no—
682C2×D4—124no—
683C2×D4—124no—
684C2×D4—124no—
685C2×D4—124no—
686C2×D4—124no—
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—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—32no—
732C22×C4—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—68no—
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—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—124no—
770C22×C4—124no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4C2×C4×D312yes—
776C22×C4C2×C4×D312yes—
777C22×C4C2×C4×D312yes—
778C22×C4#23512yes—
779C22×C4D3×D412yes—
780C22×C4D3×D412yes—
781C22×C4#23912yes—
782C22×C4C2×#6712yes—
783C22×C4C2×#6712yes—
784C22×C4C2×#6712yes—
785C4⋊C4—28no—
786C4⋊C4—44no—
787C4⋊C4—124no—
788C4⋊C4—124no—
789C22⋊C4—68no—
790C22⋊C4—68no—
791C22⋊C4—68no—
792C22⋊C4—68no—
793C22⋊C4—68no—
794C22⋊C4—124no—
795C22⋊C4—124no—
796C22⋊C4—124no—
797C22⋊C4—124no—
798C22⋊C4—124no—
799C22⋊C4—124no—
800C42—44no—
801C42—124no—
802C42—124no—
803C42—124no—
804C22×C3C2×#11711yescharacteristic
805C22×C3C2×C4×D411yescharacteristic
806C22×C3C2×C4×D411yescharacteristic
807C22×C3C2×C4×D411yescharacteristic
808C22×C3C4×#4111yescharacteristic
809C22×C3#51811yescharacteristic
810C22×C3#52011yescharacteristic
811C22×C3#52511yescharacteristic
812C22×C3#52511yescharacteristic
813C22×C3#52911yescharacteristic
814C22×C3#52911yescharacteristic
815C22×C3C2×#12711yescharacteristic
816C22×C3#53211yescharacteristic
817C22×C3#53211yescharacteristic
818C22×C3#53211yescharacteristic
819C22×C3#53411yescharacteristic
820C22×C3#53711yescharacteristic
821C22×C3#53811yescharacteristic
822C22×C3#53911yescharacteristic
823C22×C3#54611yescharacteristic
824C22×C3#54611yescharacteristic
825C22×C3#54611yescharacteristic
826C22×C3#54611yescharacteristic
827C22×C3#54611yescharacteristic
828C22×C3#54611yescharacteristic
829C22×C3#54811yescharacteristic
830C22×C3#54811yescharacteristic
831C22×C3#55111yescharacteristic
832C22×C3#55111yescharacteristic
833C22×C3#55211yescharacteristic
834C22×C3#55311yescharacteristic
835C22×C3#55311yescharacteristic
836C22×C3#55311yescharacteristic
837C22×C3#55611yescharacteristic
838C22×C3#55911yescharacteristic
839C2×D3—24no—
840C2×D3—24no—
841C2×D3—24no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—81no—
862C2×D3—81no—
863C2×D3—81no—
864C2×D3—81no—
865C2×D3—81no—
866C2×D3—81no—
867C2×D3—81no—
868C2×D3—81no—
869C3×C4—24no—
870C3×C4—24no—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4—42no—
875C3×C4—81no—
876Dic3—24no—
877Dic3—24no—
878Dic3—42no—
879Dic3—42no—
880Dic3—42no—
881Dic3—81no—
882C23—34no—
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—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—62no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
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—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23C22×C4×D311yescharacteristic
953C23C2×#23511yescharacteristic
954C23C2×D3×D411yescharacteristic
955C23C2×D3×D411yescharacteristic
956C23C2×#23911yescharacteristic
957C23#100711yescharacteristic
958C23D3×#4111yescharacteristic
959C23D3×#4111yescharacteristic
960C23D3×#4111yescharacteristic
961C23D3×#4111yescharacteristic
962C23D3×#4111yescharacteristic
963C23#100911yescharacteristic
964C23#100911yescharacteristic
965C23#100911yescharacteristic
966C23C22×#6711yescharacteristic
967D4—1216no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—34no—
993C2×C4—34no—
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—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—1216no—
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—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4C4×#6714yes—
1059C2×C4#94014yes—
1060C2×C3#229011yescharacteristic
1061C2×C3C4×#12711yescharacteristic
1062C2×C3#232511yescharacteristic
1063C2×C3#234211yescharacteristic
1064C2×C3#235211yescharacteristic
1065C2×C3#236411yescharacteristic
1066C2×C3#236711yescharacteristic
1067C2×C3#253911yescharacteristic
1068C2×C3#254011yescharacteristic
1069C2×C3#255711yescharacteristic
1070C2×C3#255811yescharacteristic
1071C2×C3#255911yescharacteristic
1072C2×C3#256011yescharacteristic
1073C2×C3#260111yescharacteristic
1074C2×C3#260211yescharacteristic
1075D3—44no—
1076D3—82no—
1077C22—64no—
1078C22—64no—
1079C22—64no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22—122no—
1088C22—122no—
1089C22—122no—
1090C22—122no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—241no—
1100C22—241no—
1101C22—241no—
1102C22—241no—
1103C22—241no—
1104C22—241no—
1105C22—241no—
1106C22—241no—
1107C22D3×#11711yescharacteristic
1108C22#552111yescharacteristic
1109C22#552711yescharacteristic
1110C22#552711yescharacteristic
1111C22C4×D3×D411yescharacteristic
1112C22C4×D3×D411yescharacteristic
1113C22#554811yescharacteristic
1114C22#554811yescharacteristic
1115C22#556811yescharacteristic
1116C22C4×#23911yescharacteristic
1117C22#557411yescharacteristic
1118C22#558511yescharacteristic
1119C22#562711yescharacteristic
1120C22#562911yescharacteristic
1121C22#563011yescharacteristic
1122C22#563311yescharacteristic
1123C22#565311yescharacteristic
1124C22#565411yescharacteristic
1125C22#565411yescharacteristic
1126C22#565611yescharacteristic
1127C22#569111yescharacteristic
1128C22#569211yescharacteristic
1129C22#569311yescharacteristic
1130C22#569511yescharacteristic
1131C22#570411yescharacteristic
1132C22#570611yescharacteristic
1133C22#570911yescharacteristic
1134C22#570911yescharacteristic
1135C22C2×C4×#6711yescharacteristic
1136C22C2×#94011yescharacteristic
1137C22#581711yescharacteristic
1138C22#582911yescharacteristic
1139C22#582911yescharacteristic
1140C22#582911yescharacteristic
1141C22#583211yescharacteristic
1142C4—24no—
1143C4—24no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—64no—
1149C4—64no—
1150C4—81no—
1151C4—122no—
1152C4—122no—
1153C4—122no—
1154C4—241no—
1155C3#1408411yescharacteristic, complemented, Sylow
1156C2—124no—
1157C2—242no—
1158C2#7493711yescharacteristic
1159C2#7529811yescharacteristic
1160C2#7530511yescharacteristic
1161C2#7530911yescharacteristic
1162C2#7535811yescharacteristic
1163C2#7535911yescharacteristic
1164C2#7537311yescharacteristic
1165C2#7537411yescharacteristic
1166C2#8227111yescharacteristic
1167C2C4×#94011yescharacteristic
1168C2#8246611yescharacteristic
1169C2#8277911yescharacteristic
1170C2#8290111yescharacteristic
1171C2#8306211yescharacteristic
1172C2#8310911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#387C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenterC2×#387D3
hypocenterC3#14084
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C2×C3×#387C2semidirect
2. C2×#4989C2semidirect
4. C2×#4990C2semidirect
5. C2×#4940C2semidirect
6. C2×C4×(C2×D3)⋊C4C2semidirect
8. #71569C2semidirect
9. #69428C2semidirect
10. #69428C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3×#95C2semidirect
55. #4988C4semidirect
62. C2×#387D3semidirect
108. C2×C3×C4⋊C4C2×C4semidirect
143. C2×(C2×D3)⋊C4C2×C4semidirect
144. C2×(C2×D3)⋊C4C2×C4semidirect
158. C2×C4×Dic3C2×C4semidirect
159. C2×C4×Dic3D4semidirect
173. C3⋊#95D4semidirect
411. C2×C4⋊C4C4×D3semidirect
1155. C3#14084semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3872
C2×#49892
C2×#49882
C2×#49902
C2×#49402
C2×C4×(C2×D3)⋊C42
C2×#46652
#715692
#694282
#694262
#694082
Dic3⋊#952
Dic3×#952
#140843