Finite Group Databasebeta

← #10735627

Subgroups — #10735627

Order 768.

2162 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4988C211yesmaximal, characteristic, complemented
2C2×#4671C211yesmaximal, characteristic
3C2×#4665C211yesmaximal, characteristic, complemented
4C2×#4665C211yesmaximal, characteristic, complemented
5C2×#4674C211yesmaximal, characteristic, complemented
6C2×#4670C211yesmaximal, characteristic, complemented
7C3×#1442C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#15450—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C4⋊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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
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
52#4988—24no—
53#4674—24no—
54#4671—24no—
55#4670—24no—
56#4665—24no—
57#4665—24no—
58C2×#397—31no—
59C2×#392—31no—
60C2×#390—31no—
61C2×#388—31no—
62C2×#386—31no—
63C2×#386—31no—
64#1442D311yescharacteristic, complemented
65#1440—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69#1438—31no—
70#1438—31no—
71#1434—31no—
72C22⋊#95—31no—
73C24×D3C2311yescharacteristic
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
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—41no—
101C22×D12—41no—
102C22×D12—41no—
103C22×D12—41no—
104C22×D12—41no—
105C22×D12—41no—
106C22×D12—41no—
107C22×D12—41no—
108C22×D12D414yes—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
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—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4—41no—
149C2×(C2×D3)⋊C4—41no—
150C2×(C2×D3)⋊C4—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×C4⋊Dic3—22no—
162C2×C4⋊Dic3—22no—
163C2×C4⋊Dic3—41no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—22no—
166C2×C4×Dic3—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—22no—
170C3×#95—41no—
171C3×#95—41no—
172C3×#95D414yescomplemented
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95—41no—
180C3⋊#95D414yescomplemented
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C24×C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4C2×D311yescharacteristic
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C42—31no—
202#397—64no—
203#392—64no—
204#390—64no—
205#388—64no—
206#386—64no—
207#386—64no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C24×C3C2411yescharacteristic
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×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3C2×D412yes—
264C23×D3C2×D412yes—
265C23×D3#4112yes—
266C23×D3#4112yes—
267C23×D3#4112yes—
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×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4#4112yes—
316C22×C3×C4#4112yes—
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×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3#4112yes—
352C2×D12—28no—
353C2×D12—28no—
354C2×D12—28no—
355C2×D12—44no—
356C2×D12—44no—
357C2×D12—44no—
358C2×D12—44no—
359C2×D12—44no—
360C2×D12—44no—
361C2×D12—44no—
362C2×D12—44no—
363C2×D12—44no—
364C2×D12—44no—
365C2×D12—44no—
366C2×D12—44no—
367C2×D12—44no—
368C2×D12—44no—
369C2×D12—44no—
370C2×D12—44no—
371C2×D12—44no—
372C2×D12—44no—
373C2×C4×D3—44no—
374C2×C4×D3—44no—
375C2×C4×D3—44no—
376C2×C4×D3—44no—
377C2×C4×D3—44no—
378C2×C4×D3—44no—
379C2×C4×D3—44no—
380C3×C4⋊C4—44no—
381(C2×D3)⋊C4—28no—
382(C2×D3)⋊C4—44no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4—44no—
385(C2×D3)⋊C4—44no—
386(C2×D3)⋊C4—44no—
387(C2×D3)⋊C4—44no—
388(C2×D3)⋊C4—44no—
389(C2×D3)⋊C4—44no—
390(C2×D3)⋊C4—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394(C2×D3)⋊C4—44no—
395C4⋊Dic3—44no—
396C4×Dic3—44no—
397C25—31no—
398C25—31no—
399C25—31no—
400C22×D4—34no—
401C22×D4—62no—
402C22×D4—62no—
403C22×D4—62no—
404C22×D4—62no—
405C22×D4—62no—
406C22×D4—62no—
407C22×D4—62no—
408C22×D4—62no—
409C22×D4—62no—
410C22×D4—62no—
411C22×D4—62no—
412C22×D4—62no—
413C22×D4—121no—
414C22×D4—121no—
415C22×D4—121no—
416C22×D4—121no—
417C22×D4—121no—
418C22×D4—121no—
419C22×D4—121no—
420C22×D4—121no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—62no—
427C23×C4—62no—
428C23×C4—62no—
429C23×C4—121no—
430C23×C4—121no—
431C23×C4—121no—
432C23×C4—121no—
433C23×C4C22×D311yescharacteristic
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C2×C4⋊C4—22no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—121no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—121no—
473C2×C22⋊C4—121no—
474C2×C22⋊C4—121no—
475C2×C22⋊C4—121no—
476C2×C22⋊C4—121no—
477C2×C22⋊C4—121no—
478C2×C22⋊C4—121no—
479C2×C22⋊C4—121no—
480C2×C22⋊C4—121no—
481C2×C22⋊C4—121no—
482C2×C22⋊C4—121no—
483C2×C22⋊C4—121no—
484C2×C22⋊C4—121no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4—121no—
488C2×C42—62no—
489C2×C42—62no—
490C2×C42—62no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—34no—
495#95—41no—
496#95—41no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95—121no—
502#95—121no—
503#95—121no—
504#95D1214yescomplemented
505C23×C3C22×D411yescharacteristic
506C23×C3C22×D411yescharacteristic
507C23×C3C22×D411yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3C2×#4111yescharacteristic
512C23×C3C2×#4111yescharacteristic
513C23×C3C2×#4111yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C23×C3H(5,𝔽2)11yescharacteristic
516C23×C3H(5,𝔽2)11yescharacteristic
517C23×C3H(5,𝔽2)11yescharacteristic
518C23×C3H(5,𝔽2)11yescharacteristic
519C23×C3H(5,𝔽2)11yescharacteristic
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—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3#12314yes—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4#12114yes—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685C2×Dic3—41no—
686C2×Dic3—41no—
687C2×Dic3—41no—
688C2×Dic3—41no—
689C2×Dic3—41no—
690C2×Dic3—41no—
691C2×Dic3—41no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709D12—416no—
710D12—416no—
711D12—416no—
712C4×D3—416no—
713C24—32no—
714C24—32no—
715C24—32no—
716C24—32no—
717C24—32no—
718C24—61no—
719C24—61no—
720C24—61no—
721C24—61no—
722C24—61no—
723C24—61no—
724C24—61no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24—61no—
733C24—61no—
734C24—61no—
735C24—61no—
736C24—61no—
737C24—61no—
738C24—61no—
739C24—61no—
740C24—61no—
741C24—61no—
742C24—61no—
743C24—61no—
744C24—61no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24C23×D311yescharacteristic
759C2×D4—68no—
760C2×D4—68no—
761C2×D4—68no—
762C2×D4—124no—
763C2×D4—124no—
764C2×D4—124no—
765C2×D4—124no—
766C2×D4—124no—
767C2×D4—124no—
768C2×D4—124no—
769C2×D4—124no—
770C2×D4—124no—
771C2×D4—124no—
772C2×D4—124no—
773C2×D4—124no—
774C2×D4—124no—
775C2×D4—124no—
776C2×D4—124no—
777C2×D4—124no—
778C2×D4—124no—
779C2×D4—124no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—32no—
823C22×C4—32no—
824C22×C4—32no—
825C22×C4—61no—
826C22×C4—61no—
827C22×C4—61no—
828C22×C4—61no—
829C22×C4—61no—
830C22×C4—61no—
831C22×C4—61no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—124no—
858C22×C4—124no—
859C22×C4—124no—
860C22×C4—124no—
861C22×C4—124no—
862C22×C4—124no—
863C22×C4—124no—
864C22×C4C2×D1212yes—
865C22×C4C2×D1212yes—
866C22×C4C2×D1212yes—
867C22×C4D3×D412yes—
868C22×C4D3×D412yes—
869C22×C4#23912yes—
870C22×C4#23912yes—
871C4⋊C4—44no—
872C4⋊C4—124no—
873C22⋊C4—68no—
874C22⋊C4—124no—
875C22⋊C4—124no—
876C22⋊C4—124no—
877C22⋊C4—124no—
878C22⋊C4—124no—
879C22⋊C4—124no—
880C22⋊C4—124no—
881C22⋊C4—124no—
882C22⋊C4—124no—
883C22⋊C4—124no—
884C22⋊C4—124no—
885C22⋊C4—124no—
886C22⋊C4—124no—
887C42—124no—
888C22×C3C2×#12111yescharacteristic
889C22×C3C2×#12311yescharacteristic
890C22×C3#52511yescharacteristic
891C22×C3#52511yescharacteristic
892C22×C3#52911yescharacteristic
893C22×C3#53211yescharacteristic
894C22×C3#53411yescharacteristic
895C22×C3#53511yescharacteristic
896C22×C3#53511yescharacteristic
897C22×C3#53811yescharacteristic
898C22×C3#53811yescharacteristic
899C22×C3#53811yescharacteristic
900C22×C3#53811yescharacteristic
901C22×C3#54011yescharacteristic
902C22×C3#54011yescharacteristic
903C22×C3D4211yescharacteristic
904C22×C3D4211yescharacteristic
905C22×C3#54611yescharacteristic
906C22×C3#54611yescharacteristic
907C22×C3#54611yescharacteristic
908C22×C3#54611yescharacteristic
909C22×C3#54611yescharacteristic
910C22×C3#54611yescharacteristic
911C22×C3#55011yescharacteristic
912C22×C3#55011yescharacteristic
913C22×C3#55111yescharacteristic
914C22×C3#55111yescharacteristic
915C22×C3#55111yescharacteristic
916C22×C3#55111yescharacteristic
917C22×C3#55311yescharacteristic
918C22×C3#55311yescharacteristic
919C22×C3#55311yescharacteristic
920C22×C3#55311yescharacteristic
921C22×C3#56011yescharacteristic
922C22×C3H(3,𝔽4)11yescharacteristic
923C2×D3—24no—
924C2×D3—24no—
925C2×D3—24no—
926C2×D3—42no—
927C2×D3—42no—
928C2×D3—42no—
929C2×D3—42no—
930C2×D3—42no—
931C2×D3—42no—
932C2×D3—42no—
933C2×D3—42no—
934C2×D3—42no—
935C2×D3—42no—
936C2×D3—42no—
937C2×D3—42no—
938C2×D3—42no—
939C2×D3—42no—
940C2×D3—42no—
941C2×D3—42no—
942C2×D3—42no—
943C2×D3—42no—
944C2×D3—42no—
945C2×D3—42no—
946C2×D3—42no—
947C2×D3—42no—
948C2×D3—42no—
949C2×D3—42no—
950C2×D3—42no—
951C2×D3—42no—
952C2×D3—81no—
953C2×D3—81no—
954C2×D3—81no—
955C2×D3—81no—
956C2×D3—81no—
957C2×D3—81no—
958C2×D3—81no—
959C2×D3—81no—
960C2×D3—81no—
961C2×D3—81no—
962C2×D3—81no—
963C2×D3—81no—
964C2×D3—81no—
965C2×D3—81no—
966C2×D3—81no—
967C2×D3—81no—
968C3×C4—24no—
969C3×C4—42no—
970C3×C4—42no—
971C3×C4—42no—
972C3×C4—42no—
973C3×C4—81no—
974C3×C4—81no—
975Dic3—42no—
976Dic3—42no—
977Dic3—42no—
978Dic3—81no—
979Dic3—81no—
980C23—34no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—62no—
998C23—62no—
999C23—62no—
1000C23—62no—
1001C23—62no—
1002C23—62no—
1003C23—62no—
1004C23—62no—
1005C23—62no—
1006C23—62no—
1007C23—62no—
1008C23—62no—
1009C23—62no—
1010C23—62no—
1011C23—62no—
1012C23—62no—
1013C23—121no—
1014C23—121no—
1015C23—121no—
1016C23—121no—
1017C23—121no—
1018C23—121no—
1019C23—121no—
1020C23—121no—
1021C23—121no—
1022C23—121no—
1023C23—121no—
1024C23—121no—
1025C23—121no—
1026C23—121no—
1027C23—121no—
1028C23—121no—
1029C23—121no—
1030C23—121no—
1031C23—121no—
1032C23—121no—
1033C23—121no—
1034C23—121no—
1035C23—121no—
1036C23—121no—
1037C23—121no—
1038C23—121no—
1039C23—121no—
1040C23—121no—
1041C23—121no—
1042C23—121no—
1043C23—121no—
1044C23—121no—
1045C23—121no—
1046C23—121no—
1047C23—121no—
1048C23—121no—
1049C23—121no—
1050C23—121no—
1051C23—121no—
1052C23—121no—
1053C23—121no—
1054C23—121no—
1055C23—121no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—121no—
1060C23—121no—
1061C23—121no—
1062C23—121no—
1063C23—121no—
1064C23—121no—
1065C23—121no—
1066C23—121no—
1067C23—121no—
1068C23—121no—
1069C23—121no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23C22×D1211yescharacteristic
1086C23C2×D3×D411yescharacteristic
1087C23C2×D3×D411yescharacteristic
1088C23#100411yescharacteristic
1089C23#100411yescharacteristic
1090C23C2×#23911yescharacteristic
1091C23C2×#23911yescharacteristic
1092C23D3×#4111yescharacteristic
1093C23D3×#4111yescharacteristic
1094C23D3×#4111yescharacteristic
1095C23D3×#4111yescharacteristic
1096C23#100911yescharacteristic
1097C23#100911yescharacteristic
1098C23#100911yescharacteristic
1099C23#100911yescharacteristic
1100D4—1216no—
1101D4—1216no—
1102D4—1216no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—62no—
1152C2×C4—62no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—62no—
1157C2×C4—62no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—1216no—
1161C2×C4—121no—
1162C2×C4—121no—
1163C2×C4—121no—
1164C2×C4—121no—
1165C2×C4—121no—
1166C2×C4—121no—
1167C2×C4—121no—
1168C2×C4—121no—
1169C2×C4—121no—
1170C2×C4—121no—
1171C2×C4—121no—
1172C2×C4—121no—
1173C2×C4—121no—
1174C2×C4—121no—
1175C2×C4—121no—
1176C2×C4—121no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4—121no—
1180C2×C4—121no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4#89514yes—
1188C2×C3#241211yescharacteristic
1189C2×C3#241811yescharacteristic
1190C2×C3#242811yescharacteristic
1191C2×C3#244411yescharacteristic
1192C2×C3#245611yescharacteristic
1193C2×C3#247111yescharacteristic
1194C2×C3#253511yescharacteristic
1195C2×C3#255411yescharacteristic
1196C2×C3#260311yescharacteristic
1197C2×C3#267011yescharacteristic
1198C2×C3#267311yescharacteristic
1199C2×C3#268411yescharacteristic
1200C2×C3#271411yescharacteristic
1201C2×C3#274911yescharacteristic
1202C2×C3#275311yescharacteristic
1203D3—44no—
1204D3—82no—
1205D3—82no—
1206C22—64no—
1207C22—64no—
1208C22—64no—
1209C22—122no—
1210C22—122no—
1211C22—122no—
1212C22—122no—
1213C22—122no—
1214C22—122no—
1215C22—122no—
1216C22—122no—
1217C22—122no—
1218C22—122no—
1219C22—122no—
1220C22—122no—
1221C22—122no—
1222C22—122no—
1223C22—122no—
1224C22—122no—
1225C22—122no—
1226C22—122no—
1227C22—122no—
1228C22—122no—
1229C22—122no—
1230C22—122no—
1231C22—122no—
1232C22—122no—
1233C22—122no—
1234C22—122no—
1235C22—241no—
1236C22—241no—
1237C22—241no—
1238C22—241no—
1239C22—241no—
1240C22—241no—
1241C22—241no—
1242C22—241no—
1243C22—241no—
1244C22—241no—
1245C22—241no—
1246C22—241no—
1247C22—241no—
1248C22—241no—
1249C22—241no—
1250C22—241no—
1251C22C2×#89511yescharacteristic
1252C22#552411yescharacteristic
1253C22#552511yescharacteristic
1254C22D4×D1211yescharacteristic
1255C22#555411yescharacteristic
1256C22#555411yescharacteristic
1257C22#557711yescharacteristic
1258C22#558911yescharacteristic
1259C22#559911yescharacteristic
1260C22#560711yescharacteristic
1261C22#560911yescharacteristic
1262C22#563011yescharacteristic
1263C22#563711yescharacteristic
1264C22#563711yescharacteristic
1265C22#563711yescharacteristic
1266C22#564411yescharacteristic
1267C22D3×#12311yescharacteristic
1268C22#565411yescharacteristic
1269C22#565611yescharacteristic
1270C22#566311yescharacteristic
1271C22#566611yescharacteristic
1272C22#567611yescharacteristic
1273C22#567611yescharacteristic
1274C22#567811yescharacteristic
1275C22#568311yescharacteristic
1276C22#569111yescharacteristic
1277C22#569511yescharacteristic
1278C22#569511yescharacteristic
1279C22#569511yescharacteristic
1280C22#569711yescharacteristic
1281C22#570411yescharacteristic
1282C22#570411yescharacteristic
1283C22#570511yescharacteristic
1284C22#570911yescharacteristic
1285C22#572511yescharacteristic
1286C4—24no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—81no—
1292C4—81no—
1293C4—122no—
1294C4—122no—
1295C4—122no—
1296C4—241no—
1297C4—241no—
1298C3#1545011yescharacteristic, complemented, Sylow
1299C2—124no—
1300C2—242no—
1301C2—242no—
1302C2#7423911yescharacteristic
1303C2#7440611yescharacteristic
1304C2#7516011yescharacteristic
1305C2#7533211yescharacteristic
1306C2#7550311yescharacteristic
1307C2#7591311yescharacteristic
1308C2#7622011yescharacteristic
1309C2#7687611yescharacteristic
1310C2#7713411yescharacteristic
1311C2#7766911yescharacteristic
1312C2#7778911yescharacteristic
1313C2#7781211yescharacteristic
1314C2#7825211yescharacteristic
1315C2#7834311yescharacteristic
1316C2#7839011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1442C2
prime radicalC2×#4671C2
hypercenter#1442D3
hypocenterC3#15450
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#4988C2semidirect
3. C2×#4665C2semidirect
4. C2×#4665C2semidirect
5. C2×#4674C2semidirect
6. C2×#4670C2semidirect
7. C3×#1442C2semidirect
8. #71570C2semidirect
9. #69429C2semidirect
10. #69427C2semidirect
11. #69426C2semidirect
12. #69426C2semidirect
13. #69426C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69402C2semidirect
64. #1442D3semidirect
172. C3×#95D4semidirect
180. C3⋊#95D4semidirect
504. #95D12semidirect
1298. C3#15450semidirect

Maximal subgroups

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

subgroupindex
C2×#49882
C2×#46712
C2×#46652
C2×#46742
C2×#46702
C3×#14422
#715702
#694292
#694272
#694262
(C2×D3)⋊#952
#694022
#154503