Finite Group Databasebeta

← #10735633

Subgroups — #10735633

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×#5213C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic, complemented
3C2×#4960C211yesmaximal, characteristic
4C2×#4957C211yesmaximal, characteristic, complemented
5C2×#4675C211yesmaximal, characteristic, complemented
6C2×#4669C211yesmaximal, characteristic, complemented
7C3×C22⋊#95C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#15450—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42#5213—24no—
43#5213—24no—
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
53C2×C3⋊#95C2211yescharacteristic
54#4960—24no—
55#4957—24no—
56#4675—24no—
57#4669—24no—
58C2×#397—31no—
59C2×#392—31no—
60C2×#390—31no—
61C2×#388—31no—
62C2×#386—31no—
63C2×#386—31no—
64#1442—31no—
65#1440—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69#1438—31no—
70#1438—31no—
71#1434—31no—
72C22⋊#95D311yescharacteristic, complemented
73C25×C3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—41no—
80C23×C3×C4—41no—
81C23×C3×C4—41no—
82C23×C3×C4—41no—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—41no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67—41no—
102C22×#67D414yes—
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C22×D12—22no—
110C22×D12—22no—
111C22×D12—22no—
112C22×D12—41no—
113C22×D12—41no—
114C22×D12—41no—
115C22×D12—41no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—41no—
127C2×#217—41no—
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—22no—
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×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—41no—
162C2×Dic3⋊C4—41no—
163C2×Dic3⋊C4—41no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—22no—
166C2×C4×Dic3—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—41no—
170C3×#95—41no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95D414yescomplemented
180C3⋊#95D414yescomplemented
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C24×C4C2×D311yescharacteristic
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
200C22×C22⋊C4C2×D311yescharacteristic
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×#95—31no—
217C2×#95—31no—
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3C2×D412yes—
235C24×C3#4112yes—
236C24×C3#4112yes—
237C24×C3C2411yescharacteristic
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×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3C2×D412yes—
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—44no—
307C22×C3×C4—44no—
308C22×C3×C4—44no—
309C22×C3×C4—44no—
310C22×C3×C4—44no—
311C22×C3×C4—44no—
312C22×C3×C4—44no—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4#4112yes—
316C22×C3×C4#4112yes—
317C2×#67—28no—
318C2×#67—28no—
319C2×#67—28no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
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×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×Dic3C2×D412yes—
368C22×Dic3C2×D412yes—
369C22×Dic3C2×D412yes—
370C22×Dic3C2×D412yes—
371C22×Dic3C2×D412yes—
372C22×Dic3#4112yes—
373C2×D12—44no—
374C2×D12—44no—
375C2×D12—44no—
376C2×D12—44no—
377C2×D12—44no—
378C2×D12—44no—
379C2×D12—44no—
380C3×C22⋊C4—44no—
381C3×C22⋊C4—44no—
382#217—44no—
383#217—44no—
384(C2×D3)⋊C4—28no—
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—
394Dic3⋊C4—44no—
395Dic3⋊C4—44no—
396C4×Dic3—44no—
397C25—31no—
398C25—31no—
399C25C22×D311yescharacteristic
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—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—121no—
444C2×C4⋊C4—121no—
445C2×C4⋊C4—121no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—41no—
451C2×C22⋊C4—41no—
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—62no—
473C2×C22⋊C4—62no—
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—34no—
494#95—34no—
495#95—41no—
496#95—41no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95—62no—
502#95—121no—
503#95—121no—
504#95—121no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3#12314yes—
540C23×C3C22×D411yescharacteristic
541C23×C3C22×D411yescharacteristic
542C23×C3C22×D411yescharacteristic
543C23×C3C2×#4111yescharacteristic
544C23×C3C2×#4111yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3C2×#4111yescharacteristic
548C23×C3C2×#4111yescharacteristic
549C23×C3H(5,𝔽2)11yescharacteristic
550C23×C3H(5,𝔽2)11yescharacteristic
551C23×C3H(5,𝔽2)11yescharacteristic
552C23×C3H(5,𝔽2)11yescharacteristic
553C23×C3H(5,𝔽2)11yescharacteristic
554C23×C3H(5,𝔽2)11yescharacteristic
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
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—41no—
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—416no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
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—
668#67—416no—
669#67—416no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
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—22no—
684C2×Dic3—22no—
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—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3#12114yes—
712D12—416no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—32no—
726C24—32no—
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#23512yes—
756C24D3×D412yes—
757C24#23912yes—
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—32no—
819C22×C4—32no—
820C22×C4—32no—
821C22×C4—32no—
822C22×C4—32no—
823C22×C4—32no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
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—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#23512yes—
868C22×C4#23512yes—
869C22×C4D3×D412yes—
870C22×C4D3×D412yes—
871C4⋊C4—124no—
872C4⋊C4—124no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—68no—
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×C3—24no—
889C22×C3—24no—
890C22×C3—24no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—42no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3—42no—
902C22×C3—42no—
903C22×C3C2×#12111yescharacteristic
904C22×C3C2×#12311yescharacteristic
905C22×C3#52511yescharacteristic
906C22×C3#52511yescharacteristic
907C22×C3#52911yescharacteristic
908C22×C3#53211yescharacteristic
909C22×C3#53411yescharacteristic
910C22×C3#53511yescharacteristic
911C22×C3#53511yescharacteristic
912C22×C3#53811yescharacteristic
913C22×C3#53811yescharacteristic
914C22×C3#53811yescharacteristic
915C22×C3#53811yescharacteristic
916C22×C3#54011yescharacteristic
917C22×C3#54011yescharacteristic
918C22×C3D4211yescharacteristic
919C22×C3D4211yescharacteristic
920C22×C3#54611yescharacteristic
921C22×C3#54611yescharacteristic
922C22×C3#54611yescharacteristic
923C22×C3#54611yescharacteristic
924C22×C3#54611yescharacteristic
925C22×C3#54611yescharacteristic
926C22×C3#55011yescharacteristic
927C22×C3#55011yescharacteristic
928C22×C3#55111yescharacteristic
929C22×C3#55111yescharacteristic
930C22×C3#55111yescharacteristic
931C22×C3#55111yescharacteristic
932C22×C3#55311yescharacteristic
933C22×C3#55311yescharacteristic
934C22×C3#55311yescharacteristic
935C22×C3#55311yescharacteristic
936C22×C3#56011yescharacteristic
937C22×C3H(3,𝔽4)11yescharacteristic
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—42no—
969C3×C4—42no—
970C3×C4—42no—
971C3×C4—42no—
972C3×C4—81no—
973C3×C4—81no—
974Dic3—24no—
975Dic3—42no—
976Dic3—42no—
977Dic3—42no—
978Dic3—81no—
979Dic3—81no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—62no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—62no—
1019C23—62no—
1020C23—62no—
1021C23—62no—
1022C23—62no—
1023C23—62no—
1024C23—62no—
1025C23—62no—
1026C23—62no—
1027C23—62no—
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#89414yes—
1085C23C2×#23511yescharacteristic
1086C23C2×#23511yescharacteristic
1087C23C2×#23511yescharacteristic
1088C23C2×D3×D411yescharacteristic
1089C23C2×D3×D411yescharacteristic
1090C23C2×D3×D411yescharacteristic
1091C23#100411yescharacteristic
1092C23#100411yescharacteristic
1093C23#100411yescharacteristic
1094C23#100411yescharacteristic
1095C23C2×#23911yescharacteristic
1096C23D3×#4111yescharacteristic
1097C23D3×#4111yescharacteristic
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—34no—
1116C2×C4—416no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
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—62no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
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—62no—
1161C2×C4—62no—
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—121no—
1188C2×C3—44no—
1189C2×C3#241211yescharacteristic
1190C2×C3#241811yescharacteristic
1191C2×C3#242811yescharacteristic
1192C2×C3#244411yescharacteristic
1193C2×C3#245611yescharacteristic
1194C2×C3#247111yescharacteristic
1195C2×C3#253511yescharacteristic
1196C2×C3#255411yescharacteristic
1197C2×C3#260311yescharacteristic
1198C2×C3#267011yescharacteristic
1199C2×C3#267311yescharacteristic
1200C2×C3#268411yescharacteristic
1201C2×C3#271411yescharacteristic
1202C2×C3#274911yescharacteristic
1203C2×C3#275311yescharacteristic
1204D3—82no—
1205D3—82no—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
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—
1251C22#547911yescharacteristic
1252C22#549011yescharacteristic
1253C22#549011yescharacteristic
1254C22#549011yescharacteristic
1255C22#549011yescharacteristic
1256C22#549411yescharacteristic
1257C22C2×#89411yescharacteristic
1258C22#551411yescharacteristic
1259C22#551411yescharacteristic
1260C22#552711yescharacteristic
1261C22#552711yescharacteristic
1262C22#554011yescharacteristic
1263C22#554711yescharacteristic
1264C22#554811yescharacteristic
1265C22#555311yescharacteristic
1266C22#555311yescharacteristic
1267C22#555611yescharacteristic
1268C22#556011yescharacteristic
1269C22#556211yescharacteristic
1270C22#559011yescharacteristic
1271C22#559211yescharacteristic
1272C22#559211yescharacteristic
1273C22#559411yescharacteristic
1274C22D3×#12111yescharacteristic
1275C22#560511yescharacteristic
1276C22#560911yescharacteristic
1277C22#561011yescharacteristic
1278C22#562711yescharacteristic
1279C22#563011yescharacteristic
1280C22#563711yescharacteristic
1281C22#564411yescharacteristic
1282C22#565711yescharacteristic
1283C22#566111yescharacteristic
1284C22#566311yescharacteristic
1285C22#566611yescharacteristic
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—64no—
1291C4—81no—
1292C4—81no—
1293C4—122no—
1294C4—122no—
1295C4—122no—
1296C4—241no—
1297C4—241no—
1298C3#1545011yescharacteristic, complemented, Sylow
1299C2—44no—
1300C2—242no—
1301C2—242no—
1302C2#7337711yescharacteristic
1303C2#7350011yescharacteristic
1304C2#7353511yescharacteristic
1305C2#7383711yescharacteristic
1306C2#7401811yescharacteristic
1307C2#7402111yescharacteristic
1308C2#7414111yescharacteristic
1309C2#7442711yescharacteristic
1310C2#7449911yescharacteristic
1311C2#7453011yescharacteristic
1312C2#7454911yescharacteristic
1313C2#7469811yescharacteristic
1314C2#7475111yescharacteristic
1315C2#7491511yescharacteristic
1316C2#7491911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC2×#4960C2
hypercenterC22⋊#95D3
hypocenterC3#15450
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#5213C2semidirect
2. C2×#5213C2semidirect
4. C2×#4957C2semidirect
5. C2×#4675C2semidirect
6. C2×#4669C2semidirect
7. C3×C22⋊#95C2semidirect
8. #71550C2semidirect
9. #71547C2semidirect
10. #69429C2semidirect
11. #69428C2semidirect
12. #69426C2semidirect
13. #69426C2semidirect
14. #69414C2semidirect
15. #69403C2semidirect
72. C22⋊#95D3semidirect
179. C3⋊#95D4semidirect
180. C3⋊#95D4semidirect
1298. C3#15450semidirect

Maximal subgroups

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

subgroupindex
C2×#52132
C2×#49602
C2×#49572
C2×#46752
C2×#46692
C3×C22⋊#952
#715502
#715472
#694292
#694282
#694262
#694142
#694032
#154503