Finite Group Databasebeta

← #10728166

Subgroups — #10728166

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C2×#4665C211yesmaximal, characteristic
3C2×#4664C211yesmaximal, characteristic, complemented
4C2×#4672C211yesmaximal, characteristic
5C3×#1434C211yesmaximal, characteristic, complemented
6#71537C211yesmaximal, characteristic, complemented
7#69429C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic
12#69417C211yesmaximal, characteristic, complemented
13#69414C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#14838—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
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
52C4×(C2×D3)⋊C4—24no—
53#4672—24no—
54#4665—24no—
55#4664—24no—
56C2×#394—31no—
57C2×#386—31no—
58C2×#381—31no—
59C2×C4×C22⋊C4—31no—
60#1443—31no—
61#1442—31no—
62#1440—31no—
63#1440—31no—
64#1439—31no—
65#1439—31no—
66#1438—31no—
67#1437—31no—
68#1437—31no—
69C4⋊#95—31no—
70#1434D311yescharacteristic, complemented
71C24×D3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C22×D12—22no—
87C22×D12—22no—
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—41no—
92C22×D12—41no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—41no—
98C22×C4×D3—41no—
99C22×C4×D3D414yes—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×C3×C42—41no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—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—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4D414yes—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—41no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—41no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C23×D4—31no—
164C24×C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C42—31no—
179C22×C42C2×D311yescharacteristic
180#394—64no—
181#386—64no—
182#381—64no—
183C4×C22⋊C4—64no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3C2411yescharacteristic
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
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×D3C2×D412yes—
230C23×D3C2×D412yes—
231C23×D3#4112yes—
232C23×D3#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
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×C4C2×D412yes—
277C22×C3×C4C2×D412yes—
278C22×C3×C4#4112yes—
279C22×C3×C4#4112yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
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×Dic3C2×D412yes—
320C22×Dic3C2×D412yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C22×Dic3#4112yes—
324C2×D12—28no—
325C2×D12—44no—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×C4×D3—28no—
332C2×C4×D3—28no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C3×C42—44no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—28no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350Dic3⋊C4—44no—
351Dic3⋊C4—44no—
352C4×Dic3—44no—
353C25—31no—
354C25—31no—
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—121no—
361C22×D4—121no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—34no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—121no—
374C23×C4—121no—
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—121no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C22⋊C4—34no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—41no—
424C2×C42—62no—
425C2×C42—62no—
426C2×C42—121no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—41no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—62no—
441#95—121no—
442#95—121no—
443#95—121no—
444#95—121no—
445C23×C3C22×D411yescharacteristic
446C23×C3C22×D411yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3C2×#4111yescharacteristic
450C23×C3C2×#4111yescharacteristic
451C23×C3C2×#4111yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3C2×#4111yescharacteristic
454C23×C3C2×#4111yescharacteristic
455C23×C3C2×#4111yescharacteristic
456C23×C3H(5,𝔽2)11yescharacteristic
457C23×C3H(5,𝔽2)11yescharacteristic
458C23×C3H(5,𝔽2)11yescharacteristic
459C23×C3H(5,𝔽2)11yescharacteristic
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
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#12114yes—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
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#12314yes—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3#12314yes—
621D12—416no—
622C4×D3—416no—
623C24—32no—
624C24—32no—
625C24—32no—
626C24—32no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24C23×D311yescharacteristic
654C2×D4—68no—
655C2×D4—124no—
656C2×D4—124no—
657C2×D4—124no—
658C2×D4—124no—
659C2×D4—124no—
660C2×D4—124no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
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—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—68no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—68no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—124no—
749C22×C4—124no—
750C22×C4—124no—
751C22×C4—124no—
752C22×C4—124no—
753C22×C4#23512yes—
754C22×C4#23512yes—
755C22×C4#23512yes—
756C22×C4D3×D412yes—
757C22×C4D3×D412yes—
758C22×C4#23912yes—
759C4⋊C4—124no—
760C4⋊C4—124no—
761C22⋊C4—68no—
762C22⋊C4—68no—
763C22⋊C4—124no—
764C22⋊C4—124no—
765C22⋊C4—124no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C42—44no—
773C42—124no—
774C22×C3C2×#12111yescharacteristic
775C22×C3C2×#12311yescharacteristic
776C22×C3C2×#12311yescharacteristic
777C22×C3#52511yescharacteristic
778C22×C3#52511yescharacteristic
779C22×C3#52911yescharacteristic
780C22×C3#52911yescharacteristic
781C22×C3#52911yescharacteristic
782C22×C3#52911yescharacteristic
783C22×C3#52911yescharacteristic
784C22×C3#52911yescharacteristic
785C22×C3#53211yescharacteristic
786C22×C3#53211yescharacteristic
787C22×C3#53411yescharacteristic
788C22×C3#53511yescharacteristic
789C22×C3#53811yescharacteristic
790C22×C3#53811yescharacteristic
791C22×C3#54011yescharacteristic
792C22×C3#54011yescharacteristic
793C22×C3#54611yescharacteristic
794C22×C3#54611yescharacteristic
795C22×C3#54611yescharacteristic
796C22×C3#54611yescharacteristic
797C22×C3#55111yescharacteristic
798C22×C3#55111yescharacteristic
799C22×C3#55111yescharacteristic
800C22×C3#55111yescharacteristic
801C22×C3#55111yescharacteristic
802C22×C3#55311yescharacteristic
803C22×C3#55311yescharacteristic
804C22×C3#55311yescharacteristic
805C22×C3#55311yescharacteristic
806C22×C3#55511yescharacteristic
807C22×C3#55511yescharacteristic
808C22×C3#55911yescharacteristic
809C2×D3—24no—
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—42no—
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C3×C4—24no—
840C3×C4—42no—
841C3×C4—42no—
842C3×C4—42no—
843C3×C4—81no—
844C3×C4—81no—
845C3×C4—81no—
846Dic3—24no—
847Dic3—42no—
848Dic3—42no—
849Dic3—81no—
850Dic3—81no—
851Dic3—81no—
852C23—34no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—121no—
882C23—121no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
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—
922C23C2×#23511yescharacteristic
923C23C2×#23511yescharacteristic
924C23C2×#23511yescharacteristic
925C23C2×D3×D411yescharacteristic
926C23C2×D3×D411yescharacteristic
927C23#100411yescharacteristic
928C23C2×#23911yescharacteristic
929C23D3×#4111yescharacteristic
930C23D3×#4111yescharacteristic
931C23D3×#4111yescharacteristic
932C23D3×#4111yescharacteristic
933C23D3×#4111yescharacteristic
934C23#100911yescharacteristic
935C23#100911yescharacteristic
936C23#100911yescharacteristic
937D4—1216no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—34no—
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—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—1216no—
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—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4#89414yes—
1030C2×C3#239511yescharacteristic
1031C2×C3#241111yescharacteristic
1032C2×C3#241211yescharacteristic
1033C2×C3#242011yescharacteristic
1034C2×C3#244411yescharacteristic
1035C2×C3#245711yescharacteristic
1036C2×C3#245911yescharacteristic
1037C2×C3#250011yescharacteristic
1038C2×C3#251611yescharacteristic
1039C2×C3#252611yescharacteristic
1040C2×C3#257211yescharacteristic
1041C2×C3#257611yescharacteristic
1042C2×C3#260211yescharacteristic
1043C2×C3#266111yescharacteristic
1044C2×C3#285411yescharacteristic
1045D3—44no—
1046D3—82no—
1047C22—64no—
1048C22—64no—
1049C22—64no—
1050C22—122no—
1051C22—122no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22—122no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22—241no—
1076C22—241no—
1077C22#547911yescharacteristic
1078C22#549011yescharacteristic
1079C22C2×#89411yescharacteristic
1080C22#552711yescharacteristic
1081C22#552711yescharacteristic
1082C22#552811yescharacteristic
1083C22#552811yescharacteristic
1084C22#553011yescharacteristic
1085C22#553211yescharacteristic
1086C22#553211yescharacteristic
1087C22#553511yescharacteristic
1088C22#554711yescharacteristic
1089C22#554711yescharacteristic
1090C22#554811yescharacteristic
1091C22#555011yescharacteristic
1092C22#555911yescharacteristic
1093C22#556011yescharacteristic
1094C22#558011yescharacteristic
1095C22#558011yescharacteristic
1096C22D3×#12111yescharacteristic
1097C22#560511yescharacteristic
1098C22#563011yescharacteristic
1099C22#563711yescharacteristic
1100C22D3×#12311yescharacteristic
1101C22#565411yescharacteristic
1102C22#566111yescharacteristic
1103C22#566311yescharacteristic
1104C22#566811yescharacteristic
1105C22#567411yescharacteristic
1106C22#569511yescharacteristic
1107C22#569511yescharacteristic
1108C22#570411yescharacteristic
1109C22#570511yescharacteristic
1110C22#570511yescharacteristic
1111C22#570611yescharacteristic
1112C4—24no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—64no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—122no—
1121C4—122no—
1122C4—241no—
1123C4—241no—
1124C4—241no—
1125C3#1483811yescharacteristic, complemented, Sylow
1126C2—124no—
1127C2—242no—
1128C2#7342111yescharacteristic
1129C2#7359011yescharacteristic
1130C2#7377711yescharacteristic
1131C2#7401811yescharacteristic
1132C2#7406611yescharacteristic
1133C2#7416611yescharacteristic
1134C2#7430311yescharacteristic
1135C2#7532011yescharacteristic
1136C2#7532411yescharacteristic
1137C2#7534611yescharacteristic
1138C2#7536611yescharacteristic
1139C2#7564611yescharacteristic
1140C2#7584211yescharacteristic
1141C2#7591011yescharacteristic
1142C2#7596011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1434C2
prime radicalC23×D12C22
hypercenter#1434D3
hypocenterC3#14838
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×C4×(C2×D3)⋊C4C2semidirect
3. C2×#4664C2semidirect
5. C3×#1434C2semidirect
6. #71537C2semidirect
7. #69429C2semidirect
8. #69429C2semidirect
9. #69428C2semidirect
10. #69428C2semidirect
12. #69417C2semidirect
13. #69414C2semidirect
14. #69408C2semidirect
15. Dic3⋊#95C2semidirect
70. #1434D3semidirect
1125. C3#14838semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D3)⋊C42
C2×#46652
C2×#46642
C2×#46722
C3×#14342
#715372
#694292
#694282
#694262
#694172
#694142
#694082
Dic3⋊#952
#148383