Finite Group Databasebeta

← #10727614

Subgroups — #10727614

Order 768.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic, complemented
3C2×#4960C211yesmaximal, characteristic
4C2×#4675C211yesmaximal, characteristic, complemented
5C2×#4665C211yesmaximal, characteristic, complemented
6C2×#4669C211yesmaximal, characteristic, complemented
7C3×C22⋊#95C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69421C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#14795—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C2×C4×#67—24no—
27C2×C4×#67—24no—
28C2×C4×#67—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45#5213—24no—
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4960—24no—
57#4675—24no—
58#4669—24no—
59#4665—24no—
60C22×C4×D4—31no—
61C2×#397—31no—
62C2×#392—31no—
63C2×#388—31no—
64C2×#386—31no—
65C2×#386—31no—
66#1445—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438—31no—
71#1438—31no—
72#1434—31no—
73C22⋊#95—31no—
74C22⋊#95D311yescharacteristic, complemented
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—41no—
84C23×C3×C4—41no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67D414yes—
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×D12—22no—
112C22×D12—22no—
113C22×D12—22no—
114C22×D12—22no—
115C22×D12—22no—
116C22×D12—41no—
117C22×D12—41no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—41no—
124C22×C4×D3—41no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—41no—
129C2×C3×C22⋊C4—41no—
130C2×C3×C22⋊C4—41no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—41no—
137C4×#67—232no—
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—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
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×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4D414yescomplemented
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—41no—
169C2×Dic3⋊C4—41no—
170C2×Dic3⋊C4D414yescomplemented
171C2×C4×Dic3—22no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3D414yescomplemented
174C3×#95—22no—
175C3×#95—22no—
176C3×#95—22no—
177C3×#95—41no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—41no—
188C23×D4—31no—
189C23×D4—31no—
190C23×D4—31no—
191C24×C4—31no—
192C24×C4C2×D311yescharacteristic
193C2×C4×D4—64no—
194C2×C4×D4—64no—
195C2×C4×D4—64no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#397—64no—
213#392—64no—
214#388—64no—
215#386—64no—
216#386—64no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95C2×D311yescharacteristic
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3C2×D412yes—
244C24×C3#4112yes—
245C24×C3#4112yes—
246C24×C3C2411yescharacteristic
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×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3C2×D412yes—
274C23×D3C2×D412yes—
275C23×D3#4112yes—
276C23×D3#4112yes—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—28no—
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×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4—44no—
318C22×C3×C4—44no—
319C22×C3×C4—44no—
320C22×C3×C4—44no—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4#4112yes—
325C22×C3×C4#4112yes—
326C2×#67—28no—
327C2×#67—28no—
328C2×#67—28no—
329C2×#67—28no—
330C2×#67—28no—
331C2×#67—28no—
332C2×#67—28no—
333C2×#67—28no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
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×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3#4112yes—
382C2×D12—28no—
383C2×D12—44no—
384C2×D12—44no—
385C2×D12—44no—
386C2×D12—44no—
387C2×D12—44no—
388C2×D12—44no—
389C2×C4×D3—28no—
390C2×C4×D3—44no—
391C2×C4×D3—44no—
392C2×C4×D3—44no—
393C2×C4×D3—44no—
394C2×C4×D3—44no—
395C2×C4×D3—44no—
396C3×C22⋊C4—44no—
397C3×C22⋊C4—44no—
398#217—28no—
399#217—44no—
400(C2×D3)⋊C4—28no—
401(C2×D3)⋊C4—28no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405(C2×D3)⋊C4—44no—
406(C2×D3)⋊C4—44no—
407(C2×D3)⋊C4—44no—
408(C2×D3)⋊C4—44no—
409Dic3⋊C4—28no—
410Dic3⋊C4—44no—
411C4×Dic3—28no—
412C25—31no—
413C25—31no—
414C25C22×D311yescharacteristic
415C22×D4—34no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—62no—
432C22×D4—121no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4—121no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447C23×C4—41no—
448C23×C4—41no—
449C23×C4—62no—
450C23×C4—62no—
451C23×C4—62no—
452C23×C4—62no—
453C23×C4—62no—
454C23×C4—121no—
455C23×C4—121no—
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461C23×C4C22×D311yescharacteristic
462C4×D4—632no—
463C2×C4⋊C4—34no—
464C2×C4⋊C4—62no—
465C2×C4⋊C4—62no—
466C2×C4⋊C4—62no—
467C2×C4⋊C4—121no—
468C2×C4⋊C4—121no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—34no—
473C2×C22⋊C4—41no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—41no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4—121no—
503C2×C22⋊C4—121no—
504C2×C22⋊C4—121no—
505C2×C22⋊C4—121no—
506C2×C22⋊C4—121no—
507C2×C22⋊C4—121no—
508C2×C42—34no—
509C2×C42—62no—
510C2×C42—62no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—41no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—62no—
520#95—62no—
521#95—62no—
522#95—62no—
523#95—62no—
524#95—121no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3#12314yes—
560C23×C3C22×D411yescharacteristic
561C23×C3C22×D411yescharacteristic
562C23×C3C22×D411yescharacteristic
563C23×C3C22×D411yescharacteristic
564C23×C3C2×#4111yescharacteristic
565C23×C3C2×#4111yescharacteristic
566C23×C3C2×#4111yescharacteristic
567C23×C3C2×#4111yescharacteristic
568C23×C3C2×#4111yescharacteristic
569C23×C3C2×#4111yescharacteristic
570C23×C3C2×#4111yescharacteristic
571C23×C3H(5,𝔽2)11yescharacteristic
572C23×C3H(5,𝔽2)11yescharacteristic
573C23×C3H(5,𝔽2)11yescharacteristic
574C23×C3H(5,𝔽2)11yescharacteristic
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
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—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3#12314yes—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—416no—
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—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4#12114yes—
688#67—232no—
689#67—416no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3#12014yes—
732D12—416no—
733C4×D3—416no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—32no—
747C24—32no—
748C24—32no—
749C24—32no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24—61no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24#23512yes—
777C24D3×D412yes—
778C24#23912yes—
779C24C23×D311yescharacteristic
780C2×D4—68no—
781C2×D4—68no—
782C2×D4—68no—
783C2×D4—68no—
784C2×D4—68no—
785C2×D4—68no—
786C2×D4—68no—
787C2×D4—68no—
788C2×D4—68no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
797C2×D4—124no—
798C2×D4—124no—
799C2×D4—124no—
800C2×D4—124no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—28no—
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—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—32no—
843C22×C4—32no—
844C22×C4—32no—
845C22×C4—32no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—68no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—124no—
889C22×C4—124no—
890C22×C4—124no—
891C22×C4—124no—
892C22×C4—124no—
893C22×C4—124no—
894C22×C4#23512yes—
895C22×C4#23512yes—
896C22×C4D3×D412yes—
897C22×C4D3×D412yes—
898C22×C4D3×D412yes—
899C4⋊C4—68no—
900C4⋊C4—124no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—68no—
904C22⋊C4—68no—
905C22⋊C4—68no—
906C22⋊C4—124no—
907C22⋊C4—124no—
908C22⋊C4—124no—
909C22⋊C4—124no—
910C22⋊C4—124no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C42—68no—
915C22×C3—24no—
916C22×C3—24no—
917C22×C3—24no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3C2×#12011yescharacteristic
931C22×C3C2×#12111yescharacteristic
932C22×C3C2×#12311yescharacteristic
933C22×C3C2×#12311yescharacteristic
934C22×C3#52511yescharacteristic
935C22×C3#52511yescharacteristic
936C22×C3#52511yescharacteristic
937C22×C3#52511yescharacteristic
938C22×C3#52511yescharacteristic
939C22×C3#52511yescharacteristic
940C22×C3#52911yescharacteristic
941C22×C3#52911yescharacteristic
942C22×C3#53211yescharacteristic
943C22×C3#53511yescharacteristic
944C22×C3#53511yescharacteristic
945C22×C3#53811yescharacteristic
946C22×C3#53811yescharacteristic
947C22×C3#53811yescharacteristic
948C22×C3#53811yescharacteristic
949C22×C3D4211yescharacteristic
950C22×C3D4211yescharacteristic
951C22×C3#54611yescharacteristic
952C22×C3#54611yescharacteristic
953C22×C3#54611yescharacteristic
954C22×C3#54611yescharacteristic
955C22×C3#54611yescharacteristic
956C22×C3#54611yescharacteristic
957C22×C3#55011yescharacteristic
958C22×C3#55011yescharacteristic
959C22×C3#55111yescharacteristic
960C22×C3#55111yescharacteristic
961C22×C3#55311yescharacteristic
962C22×C3#55311yescharacteristic
963C22×C3#55311yescharacteristic
964C22×C3#55311yescharacteristic
965C2×D3—24no—
966C2×D3—24no—
967C2×D3—24no—
968C2×D3—42no—
969C2×D3—42no—
970C2×D3—42no—
971C2×D3—42no—
972C2×D3—42no—
973C2×D3—42no—
974C2×D3—42no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C2×D3—81no—
992C2×D3—81no—
993C2×D3—81no—
994C2×D3—81no—
995C3×C4—24no—
996C3×C4—42no—
997C3×C4—42no—
998C3×C4—81no—
999C3×C4—81no—
1000C3×C4—81no—
1001Dic3—24no—
1002Dic3—42no—
1003Dic3—42no—
1004Dic3—42no—
1005Dic3—42no—
1006Dic3—81no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—34no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—62no—
1048C23—62no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
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—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23#89414yes—
1112C23C2×#23511yescharacteristic
1113C23C2×#23511yescharacteristic
1114C23C2×#23511yescharacteristic
1115C23C2×D3×D411yescharacteristic
1116C23C2×D3×D411yescharacteristic
1117C23C2×D3×D411yescharacteristic
1118C23C2×D3×D411yescharacteristic
1119C23#100411yescharacteristic
1120C23#100411yescharacteristic
1121C23#100411yescharacteristic
1122C23C2×#23911yescharacteristic
1123C23D3×#4111yescharacteristic
1124C23D3×#4111yescharacteristic
1125C23D3×#4111yescharacteristic
1126C23#100911yescharacteristic
1127D4—632no—
1128D4—1216no—
1129D4—1216no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—34no—
1143C2×C4—416no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—62no—
1191C2×C4—1216no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4#88414yes—
1216C2×C3—44no—
1217C2×C3#239211yescharacteristic
1218C2×C3#240811yescharacteristic
1219C2×C3#241811yescharacteristic
1220C2×C3#241811yescharacteristic
1221C2×C3#243111yescharacteristic
1222C2×C3#244411yescharacteristic
1223C2×C3#244411yescharacteristic
1224C2×C3#245611yescharacteristic
1225C2×C3#245611yescharacteristic
1226C2×C3#246711yescharacteristic
1227C2×C3#246711yescharacteristic
1228C2×C3#253511yescharacteristic
1229C2×C3#260311yescharacteristic
1230C2×C3#263111yescharacteristic
1231C2×C3#284911yescharacteristic
1232D3—44no—
1233D3—82no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—64no—
1250C22—64no—
1251C22—64no—
1252C22—122no—
1253C22—122no—
1254C22—122no—
1255C22—122no—
1256C22—122no—
1257C22—122no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—241no—
1272C22—241no—
1273C22—241no—
1274C22—241no—
1275C22—241no—
1276C22—241no—
1277C22—241no—
1278C22—241no—
1279C22#547911yescharacteristic
1280C22C2×#88411yescharacteristic
1281C22#549011yescharacteristic
1282C22#549011yescharacteristic
1283C22#549011yescharacteristic
1284C22#549411yescharacteristic
1285C22C2×#89411yescharacteristic
1286C22#551411yescharacteristic
1287C22#551411yescharacteristic
1288C22#552811yescharacteristic
1289C22#553011yescharacteristic
1290C22#554711yescharacteristic
1291C22#554711yescharacteristic
1292C22#554711yescharacteristic
1293C22#554711yescharacteristic
1294C22#554811yescharacteristic
1295C22#555311yescharacteristic
1296C22#555611yescharacteristic
1297C22#556011yescharacteristic
1298C22D3×#12011yescharacteristic
1299C22#559011yescharacteristic
1300C22#559011yescharacteristic
1301C22#559211yescharacteristic
1302C22#559911yescharacteristic
1303C22#560711yescharacteristic
1304C22#561211yescharacteristic
1305C22#561311yescharacteristic
1306C22#562711yescharacteristic
1307C22#562711yescharacteristic
1308C22#563011yescharacteristic
1309C22#563711yescharacteristic
1310C22D3×#12311yescharacteristic
1311C22#565411yescharacteristic
1312C22#565711yescharacteristic
1313C22#566111yescharacteristic
1314C4—24no—
1315C4—42no—
1316C4—42no—
1317C4—64no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—122no—
1322C4—122no—
1323C4—122no—
1324C4—122no—
1325C4—241no—
1326C3#1479511yescharacteristic, complemented, Sylow
1327C2—44no—
1328C2—124no—
1329C2—242no—
1330C2#7337711yescharacteristic
1331C2#7349911yescharacteristic
1332C2#7358111yescharacteristic
1333C2#7382411yescharacteristic
1334C2#7390611yescharacteristic
1335C2#7393311yescharacteristic
1336C2#7412811yescharacteristic
1337C2#7442711yescharacteristic
1338C2#7449911yescharacteristic
1339C2#7460311yescharacteristic
1340C2#7465611yescharacteristic
1341C2#7470011yescharacteristic
1342C2#7478311yescharacteristic
1343C2#7489211yescharacteristic
1344C2#7489911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC2×#4960C2
hypercenterC22⋊#95D3
hypocenterC3#14795
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×C4×#67C2semidirect
2. C2×#5213C2semidirect
4. C2×#4675C2semidirect
5. C2×#4665C2semidirect
6. C2×#4669C2semidirect
7. C3×C22⋊#95C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71547C2semidirect
11. #69428C2semidirect
12. #69426C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69421C2semidirect
15. #69403C2semidirect
74. C22⋊#95D3semidirect
164. C2×(C2×D3)⋊C4D4semidirect
170. C2×Dic3⋊C4D4semidirect
173. C2×C4×Dic3D4semidirect
1326. C3#14795semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#672
C2×#52132
C2×#49602
C2×#46752
C2×#46652
C2×#46692
C3×C22⋊#952
#715502
#715472
#694282
#694262
(C2×D3)⋊#952
#694212
#694032
#147953